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Evolutionary Biology in Silico:
Explorations of Adaptation in Artificial Populations
by
Owen Grant Woodberry
Thesis
Submitted by Owen Grant Woodberry
for fulfillment of the Requirements for the Degree of
Doctor of Philosophy (0190)
Supervisors: Dr. Kevin B. Korb & Dr. Ann E. Nicholson
Clayton School of Information Technology
Monash University
August, 2014
Notice 1
Under the Copyright Act 1968, this thesis must be used only under the normal conditions of
scholarly fair dealing. In particular no results or conclusions should be extracted from it, nor
should it be copied or closely paraphrased in whole or in part without the written consent of the
author. Proper written acknowledgement should be made for any assistance obtained from this
thesis.
c Copyright
by
Owen Grant Woodberry
2014
For Noah,
who, through intense joy and sadness, for better or worse, changed my life.
iii
Contents
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
ix
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
x
List of Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
xii
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
xiii
Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
xvi
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
1.1
The Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
1.2
The Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4
1.3
Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6
1.3.1
Summary of the thesis’ contributions to ALife: . . . . . . . . . . . .
6
1.3.2
Summary of the thesis’ contributions to evolutionary biology: . . . .
7
1.3.3
Publications arising from this thesis: . . . . . . . . . . . . . . . . . .
8
Overview of Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9
1.4
2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1
2.2
11
Evolution by Natural Selection . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.1.1
Conditions of Evolution . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.1.2
Survival of the fittest . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
Artificial Life . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.2.1
Evolutionary ALife . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2.2
Agent Based Models (ABMs) . . . . . . . . . . . . . . . . . . . . . . 19
2.2.3
Epistemology of Computer Simulation . . . . . . . . . . . . . . . . . 21
iv
3 Levels of Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
23
3.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.2
Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.3
3.4
3.5
3.2.1
Inclusive Fitness Theory . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.2.2
Group Selection
3.2.3
Species Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.2.4
Mitteldorf’s Aging Simulation . . . . . . . . . . . . . . . . . . . . . . 32
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.3.1
Mitteldorf Simulation Replica . . . . . . . . . . . . . . . . . . . . . . 34
3.3.2
Disabling Kin Selection via an Adoption Queue . . . . . . . . . . . . 34
Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.4.1
Simulations Replicating Mitteldorf’s Results . . . . . . . . . . . . . . 36
3.4.2
Disabling Kin Selection . . . . . . . . . . . . . . . . . . . . . . . . . 38
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4 Evolution of Aging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
43
4.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.2
Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.3
4.2.1
Early Adaptive Theories . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.2.2
Non-Adaptive Theories . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.2.3
Aging for the Sake of Diversity . . . . . . . . . . . . . . . . . . . . . 50
Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.3.1
4.4
4.5
Simulation Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
4.4.1
Mutation Accumulation . . . . . . . . . . . . . . . . . . . . . . . . . 58
4.4.2
Disposable Soma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
4.4.3
Diversity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.4.4
Mixed Aging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
5 Testing the Punctuated Equilibrium Hypothesis . . . . . . . . . . . . .
79
5.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
5.2
Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
v
5.3
5.4
5.5
5.2.1
Species & Speciation . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
5.2.2
Punctuated Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . 82
5.2.3
Evolutionary Activity Statistics . . . . . . . . . . . . . . . . . . . . . 84
Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
5.3.1
Simulation Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
5.3.2
Adapting the Evolutionary Activity Statistics . . . . . . . . . . . . . 88
5.3.3
Neutral Shadow Simulation Design . . . . . . . . . . . . . . . . . . . 91
Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
5.4.1
Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
5.4.2
Species Tree . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
5.4.3
Component Activity Distributions . . . . . . . . . . . . . . . . . . . 97
5.4.4
Evolution Activity Threshold . . . . . . . . . . . . . . . . . . . . . . 99
5.4.5
New Evolutionary Activity . . . . . . . . . . . . . . . . . . . . . . . 100
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
6 Conclusions and Future Work . . . . . . . . . . . . . . . . . . . . . . . . . 105
6.1
6.2
Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
6.1.1
Using Artificial Life Simulations to Study Evolutionary Biology . . . 105
6.1.2
Units of Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
6.1.3
Evolution of Adaptive Aging and Sexual Reproduction . . . . . . . . 107
6.1.4
Punctuated Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . 108
Further Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
6.2.1
Applying ALife techniques to Evolutionary Biology . . . . . . . . . . 109
6.2.2
Species Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
6.2.3
Evolutionary Ethics . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
Appendix A ODDs — Evolution of Aging . . . . . . . . . . . . . . . . . . . 113
A.1 Mutation Accumulation Simulation Design
. . . . . . . . . . . . . . . . . . 113
A.1.1 Purpose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
A.1.2 Entities, State Variables and Scales . . . . . . . . . . . . . . . . . . . 114
A.1.3 Process overview and scheduling . . . . . . . . . . . . . . . . . . . . 115
A.1.4 Design concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
A.1.5 Initialization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
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A.1.6 Input . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
A.1.7 Submodels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
A.2 Disposable Soma Simulation Design . . . . . . . . . . . . . . . . . . . . . . 117
A.2.1 Purpose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
A.2.2 Entities, State Variables and Scales . . . . . . . . . . . . . . . . . . . 117
A.2.3 Process overview and scheduling . . . . . . . . . . . . . . . . . . . . 119
A.2.4 Design concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
A.2.5 Initialization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
A.2.6 Input . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
A.2.7 Submodels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
A.3 Diversity Simulation Design . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
A.3.1 Purpose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
A.3.2 Entities, State Variables and Scales . . . . . . . . . . . . . . . . . . . 123
A.3.3 Process overview and scheduling . . . . . . . . . . . . . . . . . . . . 124
A.3.4 Design concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
A.3.5 Initialization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
A.3.6 Input . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
A.3.7 Submodels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
A.4 Mixed Aging Simulation Design . . . . . . . . . . . . . . . . . . . . . . . . . 131
A.4.1 Purpose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
A.4.2 Entities, State Variables and Scales . . . . . . . . . . . . . . . . . . . 131
A.4.3 Process overview and scheduling . . . . . . . . . . . . . . . . . . . . 131
Appendix B ODDs — Testing the Punctuated Equilibrium Hypothesis . 133
B.1 Foreground Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
B.1.1 Purpose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
B.1.2 Entities, State Variables and Scales . . . . . . . . . . . . . . . . . . . 133
B.1.3 Process overview and scheduling . . . . . . . . . . . . . . . . . . . . 135
B.1.4 Design concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
B.1.5 Initialization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
B.1.6 Input . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
B.1.7 Submodels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
vii
B.2 Shadow Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
B.2.1 Purpose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
B.2.2 Entities, State Variables and Scales . . . . . . . . . . . . . . . . . . . 142
B.2.3 Process overview and scheduling . . . . . . . . . . . . . . . . . . . . 143
B.2.4 Design concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
B.2.5 Initialization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
B.2.6 Input . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
B.2.7 Submodels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
Vita . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
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List of Tables
4.1
Aging Simulation Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.2
Aging Chromosome Components . . . . . . . . . . . . . . . . . . . . . . . . 55
4.3
Aging Comparative Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
5.1
Punctuated Equilibrium Simulation Parameters . . . . . . . . . . . . . . . . 86
5.2
Movement Rate Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
5.3
Mate Compatibility Threshold Calibration . . . . . . . . . . . . . . . . . . . 94
5.4
Signature Mutation Rate Calibration . . . . . . . . . . . . . . . . . . . . . . 94
5.5
New Activity versus Speciation Events . . . . . . . . . . . . . . . . . . . . . 103
A.1 Mutation Accumulation Simulation Entities and State Variables
. . . . . . 114
A.2 Mutation Accumulation Simulation Processes . . . . . . . . . . . . . . . . . 115
A.3 Mutation Accumulation Simulation Initialization of State Variables . . . . . 116
A.4 Disposable Soma Simulation Entities and State Variables . . . . . . . . . . 118
A.5 Disposable Soma Simulation Processes . . . . . . . . . . . . . . . . . . . . . 119
A.6 Disposable Soma Simulation Initialization of State Variables . . . . . . . . . 121
A.7 Diversity Simulation Entities and State Variables . . . . . . . . . . . . . . . 124
A.8 Diversity Simulation Processes . . . . . . . . . . . . . . . . . . . . . . . . . 126
A.9 Diversity Simulation Initialization of State Variables . . . . . . . . . . . . . 127
B.1 Foreground Simulation Entities and State Variables . . . . . . . . . . . . . . 134
B.2 Foreground Simulation Scales . . . . . . . . . . . . . . . . . . . . . . . . . . 135
B.3 Foreground Simulation Processes . . . . . . . . . . . . . . . . . . . . . . . . 137
B.4 Foreground Simulation Initialization of State Variables . . . . . . . . . . . . 138
B.5 Shadow Simulation Entities and State Variables . . . . . . . . . . . . . . . . 143
B.6 Shadow Simulation Processes . . . . . . . . . . . . . . . . . . . . . . . . . . 144
ix
List of Figures
3.1
Old Group Selection Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.2
New Group Selection Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.3
Chaotic Population Dynamics Without Aging . . . . . . . . . . . . . . . . . 37
3.4
Chaotic Population Dynamics With Aging and Kin Selection . . . . . . . . 37
3.5
Chaotic Population Dynamics Without Kin Selection . . . . . . . . . . . . . 38
4.1
Reproductive Value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.2
Mutation Accumulation Mutation Rate Calibration . . . . . . . . . . . . . . 59
4.3
Mutation Accumulation Accident Rate Calibration . . . . . . . . . . . . . . 60
4.4
Disposable Soma Maintenance Calibration . . . . . . . . . . . . . . . . . . . 62
4.5
Agent Survivorship . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.6
Evolving Maintenance Modifier . . . . . . . . . . . . . . . . . . . . . . . . . 64
4.7
Group Age Diversity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
4.8
Group Diversity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
4.9
Group Life History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
4.10 Evolution of Genetic Expiry Age . . . . . . . . . . . . . . . . . . . . . . . . 70
4.11 Evolution of Sexual Reproduction . . . . . . . . . . . . . . . . . . . . . . . . 71
4.12 Comparative Study of Evolution of Genetic Expiry Age . . . . . . . . . . . 73
4.13 Detailed Comparative Study of Evolution of Genetic Expiry Age . . . . . . 74
4.14 Comparative Study of Evolution of Death Mutation and Maintenance Modifier 76
4.15 Detailed Comparative Study of Evolution of Maintenance Modifier . . . . . 77
5.1
Phyletic Gradualism / Punctuated Equilibrium Contrast . . . . . . . . . . . 82
5.2
Species Tree . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
5.3
Species Tree Close Up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
x
5.4
Foreground Component Activity Distributions . . . . . . . . . . . . . . . . . 98
5.5
Neutral Component Activity Distributions . . . . . . . . . . . . . . . . . . . 99
5.6
Grouped Component Activity Distributions . . . . . . . . . . . . . . . . . . 100
5.7
Component Activity Distributions Crossover Point . . . . . . . . . . . . . . 101
5.8
Species New Activity History . . . . . . . . . . . . . . . . . . . . . . . . . . 101
5.9
Species Size versus New Activity . . . . . . . . . . . . . . . . . . . . . . . . 102
A.1 Example Signature Crossover, Mutation and Infection . . . . . . . . . . . . 130
B.1 Example Signature Comparison, Crossover and Mutation . . . . . . . . . . 140
xi
List of Algorithms
2.1
Simple Genetic Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
A.1 Mutation Accumulation Main Simulation Loop . . . . . . . . . . . . . . . . . 115
A.2 Mutation Accumulation Reproduction Algorithm . . . . . . . . . . . . . . . . 116
A.3 Disposable Soma Main Simulation Loop . . . . . . . . . . . . . . . . . . . . . 119
A.4 Disposable Soma Reproduction Algorithm
. . . . . . . . . . . . . . . . . . . 122
A.5 Diversity Main Simulation Loop . . . . . . . . . . . . . . . . . . . . . . . . . 125
A.6 Diversity Migration Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . 128
A.7 Diversity Reproduction Algorithm . . . . . . . . . . . . . . . . . . . . . . . . 128
A.8 Combined Aging Main Simulation Loop . . . . . . . . . . . . . . . . . . . . . 132
B.1 Punctuated Equilibrium Main Simulation Loop . . . . . . . . . . . . . . . . . 136
B.2 Punctuated Equilibrium World Cycle . . . . . . . . . . . . . . . . . . . . . . 136
B.3 Punctuated Equilibrium Agent Reproduction . . . . . . . . . . . . . . . . . . 140
B.4 Punctuated Equilibrium Kill Species . . . . . . . . . . . . . . . . . . . . . . . 141
xii
Evolutionary Biology in Silico:
Explorations of Adaptation in Artificial Populations
Owen Grant Woodberry
Monash University, 2014
Supervisors: Dr. Kevin B. Korb & Dr. Ann E. Nicholson
Abstract
The complexity, detail and diversity of life has intrigued and excited both scientist and
layperson alike. How such intricate design, as that commonly found in biological life, could
have come about is the subject of millennia of thought. Charles Darwin’s (1859) theory
of evolution (co-discovered by Alfred Wallace) proposes a simple mechanism of change
across generations, and provides a testable explanation of such design. Although united
on the validity of evolution, scientists remain divided on many open questions, including
the adaptive nature of traits that benefit the group at the cost of individual fitness — that
is, biological altruism.
Interpreting the progress of evolutionary history from the fossil record is fraught
with challenges. The large gaps between fossilization events hide the transitions between
species, and much of the details of the organisms themselves are lost in the process. While
we can conduct experiments on living organisms in the laboratory, the temporal and spatial scales involved in evolution in nature do not lend themselves to easily controllable and
repeatable experiments. The recent field of artificial life (ALife) (Langton, 1989) provides
new exciting potentials for experimental exploration of evolution. Within the software
medium we can create simulations of populations of artificial organisms, which are subject
to evolutionary forces, existing in an artificial environment, competing with each other for
the opportunity to survive and reproduce. By incorporating such simulation techniques
into the studies of evolutionary biology we greatly enhance our experimental repertoire.
In this thesis I show that ALife provides new experimental techniques to explore open
questions in evolutionary biology. In particular, I consider questions on the adaptive
nature of groups and biological altruism. Firstly, I examine the relationship between the
xiii
two popular explanations of altruism, group and kin selection, demonstrating a common
dependence on inclusive fitness (Hamilton, 1964). Next, I investigate an extreme form
of biological altruism, genetically programmed aging. Commonly thought to be nonadaptive (Medawar, 1952; Williams, 1957; Kirkwood and Holliday, 1979), I develop my
own hypothesis of adaptive aging for the sake of group diversity, confirming it in simulated
worlds of hosts and parasites. Lastly, I test, and find support for, Eldredge and Gould’s
(1972) claim that punctuated equilibrium, a pervasive phenomena in the fossil record,
provides the foundations for a species/group selection mechanism.
xiv
Evolutionary Biology in Silico:
Explorations of Adaptation in Artificial Populations
Declaration
I declare that this thesis is my own work and has not been submitted in any form for
another degree or diploma at any university or other institute of tertiary education. Information derived from the published and unpublished work of others has been acknowledged
in the text and a list of references is given.
Owen Grant Woodberry
August 20, 2014
xv
Acknowledgments
This work represents the conclusion of a journey not only in my intellectual development,
as an academic, but also much personal growth. I am humbled to have such a prestigious
achievement to my name, and am greatly indebted to the support and encouragement of
the many people who have made such an accomplishment possible. It is not practical to
attempt to thank, by name, all the colleagues, family, friends and well wishers that have
made this such a memorable experience, but I trust you will know who you are.
Foremost, I must express my deep gratitude to my supervisors, Kevin Korb and Ann
Nicholson, for their guidance, inspiring discussions, support and encouragement, throughout good times and bad. I feel strongly that over the years our relationship has evolved
beyond that of academic tutorage to enduring friendship. I very much look forward to
continuing to work with you both in an environment that is both intellectually ambitious
and personally fulfilling. It is very valuable to me have colleagues who aspire to the same
standards of ethics through personal interactions and quality in work that I hold dear.
Of the many fellow postgraduates who’ve, at one time or another, shared with me in
this lofty undertaking, I’d like to particularly acknowledge Steven Mascaro and Dhananjay
(DJ) Thiruvady — who have been with me throughout the entirety of my candidature.
Again, I feel that, over the years, the shared experiences and challenges have forged the
foundations of a strong friendship. Steven, your input on my thesis has been invaluable
and I’ve come to think of you as a secondary supervisor. I’ve no doubt that our continued
collaboration, in both the fields of ALife and Bayesian networks, will be very fulfilling
and productive. DJ, the overlap of our work was not as great, however, your involvement
in my academic development has been profound. Having initially formed our friendship
during our honours year together, I look forward to many more years of the same, as we
continue to develop in our careers.
No acknowledgement section would be complete without a recognition of family. I’ve
no hesitation in saying that I wouldn’t be the person I am today without your selfless
support and belief in my abilities. I am forever indebted to you. Mum and Dad, I’d
particularly like to acknowledge your prioritizing of quality education, the obtainment of
wide and varied experience through travel, and working to achieve family closeness by
making time for everything from regular camping trips to sit down meals every Sunday.
These values are profoundly ingrained in my self identity and it’s by these values that I
see the good in myself, despite my flaws, and in the others that I’ve had the privilege to
meet, and be affected by, in my life journey into adulthood.
Of the many friends that have supported me and provided company over the years, I
owe special gratitude to Jodi Kok. My partner through the beginnings and the greater part
of the thesis duration, and a close friend in the final days of writing up. Of all the things
xvi
you gave me it’s especially pertinent to acknowledge you for helping me in finding and
gaining confidence in my written expression. You are very dear to me, and I’m delighted
that we’ve been able to remain such close friends.
Owen Grant Woodberry
Monash University
August 2014
xvii
xviii
Chapter 1
Introduction
1.1
The Problem
The complexity, detail and diversity of life has intrigued and excited both scientists and
laypersons. How such intricate design, such as that commonly found in biological life,
could have come about is the subject of millennia of thought. Darwin’s (1859) theory
of evolution proposes a simple mechanism of change across generations, and provides a
testable explanation of such design. It is a challenging thought that such a simple process
could explain phenomena that seem to presuppose a creator with specific intentions. But
the theory of evolution has become firmly established as fact in science, and there is no real
doubt that any system including the ingredients of inheritance, selection and variance will
inevitably invoke an evolutionary process. What remains in question is whether evolution
can explain the complexity that we observe in real world organisms and how exactly it
could have come about. William Paley (1802) was confounded that the discovery of a
watch lying on the ground could imply anything other than a designer with the intention
of creation. It takes an open mind to appreciate the raw grinding power of mindless
evolution to create something as complex as the human eye — or a watch. Yet scientists
have united to provide such explanations, strengthening the theory of evolution. The story
of evolution relies on presenting a gradation of changes leading to the finished product we
observe, along with an explanation of the possible fitness benefits (or fitness neutrality)
of every intermediate form.
Scientists remain divided on the evolution of traits that appear selfless or altruistic.
How is it that a characteristic that reduces the fitness of its bearer, for the benefit of
1
2
CHAPTER 1. INTRODUCTION
others, could possibly become more prominent in the population? How can one go about
explaining anti-predator sentinel behaviour in groups of birds and mammals, or the complex collective hive mentality of some insects, let alone the advanced moral systems present
in human societies? The whole idea of such traits being adaptive is counterintuitive to
popular evolutionary thinking, which emphasizes the import of selective competition. For
such reasons, altruistic behaviour is often explained as an artifact of other traits that
can be explained in terms of individual self interest,1 rather than something that has its
own evolutionary benefit — that there is no truly altruistic behaviour, only disguised self
interest. Such thinking is deep seated in evolutionary thought, and can be dated back to
Darwin and his advocacy of Spencer’s (1864) slogan “survival of the fittest”. The phrase
became the centerpiece of the Social Darwinism political movement (Hofstadter, 1955)
which advocated social polices based on promoting competition between individuals. This
has led many to think in terms of individual fitness, which, undoubtably, is a major driving
force in evolution, but doesn’t tell the entire story.
Hamilton (1963) showed that what is optimized by evolution is not simply individual
fitness, but inclusive fitness. Inclusive fitness works at the gene level, accounting not
only for the effects of an allele on the individual holding it (the self serving, individual
selection, component), but also on other members of the population (providing an altruistic
component). This is important as those other members may also hold the allele, especially
if they tend to be related by common descent. The consequence of inclusive fitness is that
it is not simply enough that a trait increases its own fitness, if this is done at the expense
of others holding the gene. Conversely, it also demonstrates that a trait that is detrimental
to its holder could still evolve, if its benefits to other carriers of the gene are enough to
offset those costs. Although inclusive fitness goes a long way to explaining the evolution of
altruistic traits, it still has to contend with the direct impact of an individual’s actions upon
its own fitness. As it is, inclusive fitness is accepted as an explanation of weaker forms of
altruism, such as sharing food with offspring, which would only temporally inconvenience
the actor, but it is doubted whether it could explain stronger forms of altruism, such as
actions that result in the possible, or definite, death of the actor (Wilson, 1980; Mitteldorf,
2004b). For inclusive fitness to explain such phenomena it is not enough to simply point
out that parents, offspring and siblings will tend to be located close to one another, as
1
For example, cooperation in the iterated prisoner’s dilemma thought experiment (see Axelrod, 1984).
1.1. THE PROBLEM
3
will naturally happen in viscous populations. In the case of some traits, the relatedness
required between the actor and the receivers of the benefits needs to be so great that some
barriers to mixing, forming sub-population groups, may be needed. In such groups highly
related individuals collectively reproduce and die together creating for-the-benefit-of-thegroup selection forces that can counteract the inevitable individual selection within the
group.
We often think of groups as defined by geographical physical barriers, such as oceans or
mountain ranges, dividing and isolating sub-populations. Groups may also be formed due
to reproductive isolation, as occurs during speciation events when sub-populations become
so distinct that any crossbreeds are not viable. Such a view of species as a unit of selection would depend heavily on how species are formed and go extinct. There are two main
modes of speciation, anagenesis and cladogenesis. Anagenetic speciation occurs when a
species slowly evolves into new species. Cladogenetic speciation differs in that the offspring
species branches from the parent species and becomes distinct, whilst the parent species
remains, more or less, the same. The Punctuated Equilibrium hypothesis (Eldredge and
Gould, 1972) proposes that most evolutionary change occurs during punctuated cladogenetic speciation events, with the large part of evolutionary history transpiring in stasis
or equilibria. In other words, the makeup of offspring species is formed, abruptly, from a
parent species and stays static until it becomes extinct. Furthermore, it is proposed that
a large part of species makeup is not determined by adaptation, but rather genetic drift
(i.e., randomly sampling from the parent species). This view of species creates a strong
analogy with individuals and individual selection. Species become fixed units, which are
born via descent with modification and compete against each other via a species selection
mechanism.
Clearly there are many open questions about biological phenomena, and there is much
to gain in experimental exploration. The fossil record is limited in illustrating the processes of evolution. It provides snapshots of a variety of species present in and during select
locations and times of the world’s geological history. However, it lacks detail in the progression of evolution between these snapshots, and in the details of organisms themselves,
which are lost during the fossilization process. On the other hand, we are also limited in
experiments we can do in the laboratory with fruit flies and the like (Rose, 1984; Spitze,
1991; Leroi et al., 1994). While much important work has been done in the laboratory,
4
CHAPTER 1. INTRODUCTION
the temporal and spatial scales involved in evolution in nature do not lend themselves to
easily controllable and repeatable experiments.
1.2
The Approach
Artificial life (ALife) (Langton, 1989) provides new and exciting potential for experimental
exploration of evolution. Within the software medium we can create simulations of agents
that reproduce, inheriting traits with occasional mutations, and are subject to different
selective forces. In this thesis I show that the use of such ALife experimental techniques allows us to explore open questions in evolutionary biology. These simulation techniques use
a bottom-up approach to overcome the complexity of such biological systems — which do
not easily lend themselves to breaking into subcomponents — by allowing such phenomena
to emerge from simple interaction rules between simulated agents and environment.
Each of the main central chapters of this thesis describes the design, implementation
and experiments of an agent based virtual world, created to replicate the conditions required for the real world phenomena of interest. Three topics from evolutionary biology
are investigated: the mechanisms of selection that could favour the evolution of altruism;
the evolution of adaptive aging; and the validity (and consequences) of the punctuated
equilibrium hypothesis as a mechanism for species selection.
The units of selection chapter contributes to research exploring the mechanisms of
selection that potentially favour the evolution of altruistic traits. In particular, I review
and contribute to the debate on kin and group selection, and the relationship between
them. Often thought distinct, the Price formulation (Price, 1970; Hamilton, 1975) of
inclusive fitness shows that both kin and group selection can be expressed in the same
terms and are mathematically equivalent (Queller, 1992). I replicate an agent based group
selection model, created by Mitteldorf (2004b) to illustrate his hypothesis on the evolution
of aging to dampen fluctuating population dynamics. I extend the model, devising a
method of disabling kin selection by removing kin associations, whilst keeping the group
structures intact. Conducting experiments on the model, I demonstrate its reliance on the
kin selection mechanism by showing the failure of group selection when kin selection is
disabled. This reinforces the relationship between the two processes outlined by the Price
equation.
1.2. THE APPROACH
5
The evolution of aging chapter reviews the history of thinking on aging as a species
characteristic, describing ALife simulations to test the popular hypotheses of aging alongside my own hypothesis. The more popular hypotheses of aging rely on non-adpative
explanations, based on Fisher’s (1930) observations on the declining selection pressure of
late life acting genes (which are less likely to be expressed). Possible non-adaptive explanations of a trait are that it is selectively neutral, and occurs by chance, or it is a
by-product of some other adaptive trait, and selected for an overall increase in fitness, in
spite of the non-adaptive aspect’s negative effect on fitness. The non-adaptive hypotheses
investigated in this chapter are: mutation accumulation (Medawar, 1952), antagonistic
pleiotropy (Williams, 1957) and disposable soma (Kirkwood and Holliday, 1979). My hypothesis gives an adaptive account of aging for the sake of diversity. Closely related to the
“Red Queen” hypothesis (van Valen, 1973) of sexual reproduction for the sake of diversity,
my hypothesis holds that the diversity created by population turnover due to shorter individual life-spans benefits populations in co-evolutionary “arms races” (e.g., predator/prey
or host/parasite). The experiments conducted with the simulations demonstrate the validity of all the hypotheses, in particular they establish that the group selection mechanisms
are enough to support the evolution of both aging and sexual reproduction, for their own
(adaptive) sakes.
Lastly, I apply the ALife simulation techniques to explore the Punctuated Equilibrium
hypothesis (Eldredge and Gould, 1972). I develop a simulation of agents with evolving
mate signatures, which determine compatibility between mating agents, and inversely,
reproductive isolation of sub-populations (i.e., species). Adapting Bedau and Packard’s
(1991) evolutionary activity statistics, developed to test for open ended evolution, I measure the rates of evolutionary change during and between speciation events to confirm the
Punctuated Equilibrium hypothesis in my simulation. Punctuated Equilibrium is particularly relevant to the evolution of altruism as it provides the foundation for species selection
— another flavour of group selection. Species become analogous with individuals: offspring
species, modifications of the parent species, are produced during punctuation events; and,
during equilibrium, they retain a stable form and compete with one another. The simulation experiments support the Punctuated Equilibrium hypothesis, confirming that a large
amount of evolutionary activity during the punctuated speciation events is non-adaptive.
6
CHAPTER 1. INTRODUCTION
The fixation of such traits provides the group variation material for a species selection
mechanism to work on during the stasis phase.
1.3
Contributions
The primary intent of this thesis is to demonstrate the utility of the ALife simulation
techniques for the exploration of open questions in evolutionary biology. Thus, the contributions are two pronged. On one hand, this work develops and implements a number
of the agent based simulations and experiments, creating a substantial contribution to
the growing pool of ALife simulations developed for this purpose. In addition, the thesis
reviews and contributes to a few of the prominent open debates in evolutionary biology,
namely: units of selection, evolution of aging and punctuated equilibrium.
1.3.1
Summary of the thesis’ contributions to ALife:
1. Demonstrates the utility of ALife simulation techniques to evolutionary biology research (originally published in Woodberry et al., 2005, 2007, 2008, 2009; Mascaro
et al., 2010).
2. Develops agent based simulations of a variety of biological phenomena (originally
published in Woodberry et al., 2005, 2007, 2008, 2009; Mascaro et al., 2010):
(a) Group and kin selection
(b) Adaptive aging and sexual reproduction via group selection
(c) Non-adaptive aging:
• Mutation Accumulation (Medawar, 1952)
• Antagonistic Pleiotropy (Williams, 1957)
• Disposable Soma (Kirkwood and Holliday, 1979)
(d) Host/parasite interaction
(e) Species groupings and speciation
(f) Punctuated Equilibria
1.3. CONTRIBUTIONS
1.3.2
7
Summary of the thesis’ contributions to evolutionary biology:
1. Reviews and contributes to the units of selection debate (originally published in
Woodberry et al., 2005, 2008; Mascaro et al., 2010).
(a) Corrects Mitteldorf’s (2004b) discussion on importance of the kin selection
mechanism in his group selection model.
(b) Develops a method of isolating and removing the kin selection mechanism from
agent based simulations with topology.
(c) Reinforces the group selection mechanism concept for the evolution of altruism
by demonstrating it in a simulation.
(d) Reinforces the relationship between kin and group selection described by the
Price (1970) formulation of inclusive fitness, by demonstrating the dependence
on kin associations within groups.
2. Reviews and contributes to the evolution of aging debate (originally published in
Woodberry et al., 2007, 2008; Mascaro et al., 2010).
(a) Develops an adaptive hypothesis of aging for the sake of population diversity.
(b) Demonstrates the feasibility of the evolution of aging and sexual reproduction
for the sake of diversity in a host/parasite group selection simulation.
(c) Demonstrates the feasibility of the popular non-adaptive hypotheses of aging.
• Mutation Accumulation (Medawar, 1952)
• Antagonistic Pleiotropy (Williams, 1957)
• Disposable Soma (Kirkwood and Holliday, 1979)
3. Reviews and contributes to the punctuated equilibrium debate (originally published
in Woodberry et al., 2008, 2009; Mascaro et al., 2010).
(a) Presents a measure of evolutionary activity to test for Punctuated Equilibrium,
and demonstrates that it is occurring in a species simulation.
(b) Shows that an adaptive account cannot fully explain the evolutionary activity
during speciation events and that genetic drift and population bottlenecks plays
a central role.
8
CHAPTER 1. INTRODUCTION
1.3.3
Publications arising from this thesis:
Woodberry, O.G., Korb, K.B., Nicholson, A.E., (2005), The Evolution of Aging,
Proceedings of the Australian Conference on Artificial Life, Recent Advances in Artificial Life: Advances in Natural Computation, 05 December 2005 to 08 December
2005, World Scientific Publishing Co. Pty. Ltd, Singapore, pp. 319-333.
Contributions: all experimental work and lead in analysis of results and write up.
Woodberry, O.G., Korb, K.B., Nicholson, A.E., (2007), A Simulation Study of
the Evolution of Aging, Evolutionary Ecology Research, vol 9, issue 7, Evolutionary
Ecology Ltd, Tucson AZ US, pp. 1077-1096
Contributions: all experimental work and lead in analysis of results and write up.
Woodberry, O.G., Korb, K.B., Nicholson, A.E., (2008), Species Selection of
Aging for the Sake of Diversity, Proceedings of the Eleventh International Conference
on the Simulation and Synthesis of Living Systems, 5 August 2008 to 8 August 2008,
The MIT Press, London England UK, pp. 710-716.
Contributions: all experimental work and lead in analysis of results and write up.
Woodberry, O.G., Korb, K.B., Nicholson, A.E., (2009), Testing Punctuated
Equilibrium Theory using Evolutionary Activity Statistics, Proceedings of the 4th
Australian Conference on Artificial Life: Borrowing from Biology (ACAL 2009), 1
December 2009 to 4 December 2009, Springer-Verlag, Berlin Germany, pp. 86–95.
Contributions: all experimental work and lead in analysis of results and write up.
Mascaro, S., Korb, K.B., Nicholson, A.E., Woodberry, O.G., (2010), Evolving
Ethics: The New Science of Good and Evil, Imprint Academic, Exeter UK.
Contributions: all experimental work of the sections of Levels of Selection, Evolution of Aging and Evolution of Suicide in Chapter 3; lead on analysis of results and
write up of the sections of Levels of Selection, Evolution of Aging in Chapter 3; and
proof reading the remainder of the manuscript.
1.4. OVERVIEW OF THESIS
1.4
9
Overview of Thesis
In Chapter 2, I review some general background for the thesis, namely a general introduction to the theory of evolution and an outline of the ALife research field. More specific
background is provided in the particular chapters.
Chapters 3, 4 and 5 comprise the main body chapters of the thesis. In these chapters I investigate the units of selection, evolution of aging and punctuated equilibrium
debates, respectively. Detailed discussion of my approach with each of these chapters can
be found above, in Section 1.2. In all cases I review the debate, providing a specialized
background literature review, and develop simulations and experiments to provide my own
contribution.
Finally, in Chapter 6, I conclude the thesis and discuss possible future directions for
research.
Appendices A & B contain simulation descriptions for the evolution of aging (Chapter
4) and Punctuated Equilibrium (Chapter 5) chapters respectively. These simulation descriptions follow the ODD (Overview, Design concepts, Details) protocol (Grimm et al.,
2006, 2010) and are detailed enough to allow any reader with a programming background
to replicate the simulation experiments.
10
CHAPTER 1. INTRODUCTION
Chapter 2
Background
In this chapter, I review the background topics that are common to the central chapters of
the thesis, namely background on evolution by natural selection and artificial life (ALife).
Background for the specific areas of units of selection, evolution of aging and punctuated
equilibrium are provided in the relevant chapters, alongside my simulation design descriptions, experiments and discussion. Firstly, in Section 2.1, I give an overview of the theory
of evolution by natural selection, introducing the concepts of fitness and selection, which
are foundation themes throughout this thesis. In Section 2.2, I give background on artificial life, focusing on evolutionary ALife and agent based models (ABMs), which underlie
my experimental techniques, before providing a brief account on the current status of the
epistemology of computer simulation.
2.1
Evolution by Natural Selection
Darwin’s (1859) theory of evolution by natural selection describes how heritable characteristics become more or less prevalent over successive generations, based on their impact on
survival and reproduction. It aims to explain observations on the adaptation and diversity
of organisms in the natural world. Evolutionary theory is considered as an established
fact in science by biologists (National Academy of Sciences and Institute of Medicine,
2008), and underlies much of our understanding about life at all levels of organisation:
from molecular and cellular biology to organism behaviour and further up to population,
species and ecosystem.
11
12
CHAPTER 2. BACKGROUND
2.1.1
Conditions of Evolution
There are three necessary conditions for adaptive evolution to occur (Huxley, 1942; Dobzhansky, 1951; Mayr, 1976).
Heritability:
That traits are passed, with reasonable fidelity, between parent and child
generations. Heritable characteristics or traits are predominantly controlled by genes.1
Genes correspond to regions of chromosomal DNA, and particular instantiations of genes
are called alleles (e.g., eye colour is controlled by a gene, and blue eye colour is an allele
of the eye colour gene). The set of an organism’s alleles makes up its genotype, which is
copied during germ cell line division and inherited by offspring. Interactions between the
genotype and environment, during an organism’s development, determine its observable
characteristics or traits, known as the phenotype. As the expression of inherited DNA
making up the genotypes, it is the phenotypic traits that selection (the next ingredient of
evolution) directly acts upon.
Selection:
That there are differential tendencies for phenotypes to reproduce them-
selves. For natural selection, Darwin observed that there is a greater production of offspring than can be supported by the environment, resulting in selective survival and
reproduction.2 Consequently, traits that positively affect the survival and reproduction
of offspring demonstrating them will become more frequent in the population. Natural
selection is the cause of adaptation to the natural environment, but it’s not the only possible cause of evolution. An obvious non-natural cause of evolution (one which heavily
influenced Darwin’s thinking) is the human (‘artificial’) selection in the process of animal
husbandry. Some type of selection, be it natural or artificial, is required for adaptive
evolution. However, not all evolution is adaptive. Evolution can also be caused by genetic
drift, caused by random sampling of populations, or produced as a side effect of adaptation
in other traits, such as pleiotropic genes (where a gene has multiple effects).
1
Epigenetic inheritance (i.e., inheritance not involved in the DNA sequence) is currently receiving a
lot of research attention (Jablonka and Szathmáry, 1995).
2
Drawing upon Thomas Malthus’ (1798) observations on the geometric growth of populations and
linear growth of resources.
2.1. EVOLUTION BY NATURAL SELECTION
Variation:
13
The last condition is that there are genetic variations in the population. As
selection has the effect of reducing variation, removing the less fit alleles and driving populations toward genetic homogeneity, it is necessary, for long term evolution, that variations
are introduced (typically, during reproduction) providing new material for selection (or
random chance) to act upon. The world is also a constantly evolving place, with species
often pitted against each other in an “arms race”. A species with no variation will quickly
go extinct as predators and parasites evolve to exploit its homogeneity (as will be shown
in Chapter 4). In natural populations of organisms, this variation is introduced in the
form of new genes created via mutations or recombination of genotypes during sexual reproduction crossover. Mutations are essentially copying errors and are usually detrimental
to the organism’s fitness. Only occasionally are mutations beneficial to fitness. For this
reason genotype replication is predominantly focused on copying fidelity, and variation is
maintained by genotype recombination, during sexual reproduction, acting on the existing
gene pool.
2.1.2
Survival of the fittest
The phrase “Survival of the fittest”, introduced by Spencer (1864), was intended to summarize Darwin’s theory of evolution by natural selection. However, the phrase has a
history of misuse (most notably by the Social Darwinism movement (Hofstadter, 1955),
which advocated social polices based on promoting competition between individuals) and
is a source of some of the most common misunderstandings about evolution. Although
the term is used with considerable caution by modern biologists, two prominent misunderstandings remain widespread.
Firstly, the phrase overemphasizes the import of survival of individual organisms. Survival is just a means to an end, and that end is the reproduction of heritable traits. This is
particularly pertinent when we consider the evolution of a trait like aging (i.e., the deterioration and eventual death of an organism by internal causes), an explanation of which, by
definition, cannot lie in differential survival of individuals. Survival is very important for
the newly born organism, as it tries to find its feet, but its importance decreases rapidly
after the organism has had opportunity to reproduce itself, and ensured that its genes
are preserved for the next generation. In Chapter 4, I explore Fisher’s (1930) proposal of
14
CHAPTER 2. BACKGROUND
reproductive value (expected future reproduction) as a function of age — that is, reproductive value of a trait is greatest at birth and decreases thereafter. This age function of
selective value can be used to explain the selection of late life acting traits, such as aging,
in a tradeoff for other benefits.
The second flaw with Spencer’s slogan is that there is ambiguity in the term ‘fitness’.
Fitness in natural selection refers to relative reproductive rate, however, in most other
contexts it is used to simply refer to ‘physical’ fitness, e.g., strength, speed and size. This
has led to a particular emphasis on individual fitness selection, and, for many, to the denial
of the evolution of altruism (i.e., selflessness), which, by definition, reduces an individual’s
relative fitness. In Chapter 3, I investigate the mechanisms of kin (Maynard Smith, 1964)
and group selection (Wynne-Edwards, 1962), which favour the evolution of altruism. The
heart of these mechanisms is Hamilton’s (1964) inclusive fitness theory. Inclusive fitness
differs from individual fitness in that it shifts the focus downwards from the individual
to the gene, whether held by the individual or, as a replica, by a relative. Furthermore,
in Chapter 5, I investigate the concept of Punctuated Equilibrium (Eldredge and Gould,
1972) — that evolution proceeds in geologically rapid punctuated bursts during speciation
events with relative stasis or equilibrium between. Such a view of evolutionary history
opens the door to the idea of species competing against each other as units of selection.
2.2
Artificial Life
The term artificial life (ALife) is a recent term, coined by Langton (1989) to unite work
performed across a wide range of disciplines — predominantly, computer science and
biology. The term literally means human created life, as opposed to life as it occurs in real
natural world biology. While there was certainly awareness of the potential for computer
simulation in the 1950s, 60s and 70s (e.g., Selfridge, 1959; Conrad and Pattee, 1970) this
did not translate into any sustained research programs until the 1980s. As a recent field,
drawing from multiple background disciplines, its full scope is yet to be settled. However,
it certainly embraces the study of human made systems and processes that were designed
to replicate and imitate natural life systems and processes — which is how it is applied in
this thesis.
2.2. ARTIFICIAL LIFE
15
The study of life is done at various levels of organization (including molecular, cellular,
organism and population) and ALife models have been created in various environmental
mediums (including wetware, hardware and software). Wetware ALife is focused on creating artificial molecular and celluar life within laboratories using biochemicals (e.g., Rasmussen et al., 2007). Hardware ALife is predominantly focused on developing embodied
artificial intelligence within mechanical robots, for example, in evolutionary robotics (e.g.,
Nolfi and Floreano, 2000). Software ALife generates life at all levels of organization within
the information/logical realm of computer programs, notably with Von Neumann’s (1951)
and Conway’s (Berlekamp et al., 1982) cellular automata. Most ALife research — this
work included — is performed in the software medium.
The application of ALife techniques is diverse. Just like its parent discipline of artificial
intelligence, ALife has divided into two major research paths (Taylor and Jefferson, 1993).
Often, ALife is applied to engineering solutions for complex search/optimization problems
and systems, drawing, however loosely, from natural systems and processes — for example,
early genetic algorithm applications (Holland, 1975) and ant colony approaches to optimization problems (Dorigo, 1992). However, a large part of the field is dedicated to the
accurate modeling of life itself, and, ultimately, to better understanding of the laws that
govern the natural biological phenomena being replicated. ALife is a powerful research
tool for studying these phenomena. Biology is restricted to the study of life as it naturally
occurs (life-as-it-is), albeit in controlled experiments, such as the laboratory. By adding
synthetic life (life-as-it-could-be) to our toolbox, which is easily controllable and repeatable, we greatly increase our resources for experimental observation (Langton, 1989). This
is how ALife is applied in this thesis. In particular, ALife techniques allow the study of
evolutionary phenomena that would be impossible, or at least difficult, to replicate in the
laboratory, especially due to the temporal and spatial scales evolution operates on.
2.2.1
Evolutionary ALife
Evolutionary approaches to ALife incorporate the three ingredients of evolution: heritability, selection and variation (see above for detailed discussion), into the artificial medium
utilized. When these three components are included in any process, evolution will inevitably emerge (as discussed in Section 2.1.1). Evolutionary ALife within the software
16
CHAPTER 2. BACKGROUND
medium draws heavily from the field of evolutionary computation — a subfield of artificial
intelligence — which I introduce next, before discussing the simulation of natural systems.
Evolutionary Computation
Evolutionary computation encompasses work from four distinct areas: evolutionary programming (Fogel et al., 1966), evolution strategies (Rechenberg, 1973), genetic algorithms
(Holland, 1975) and, later, genetic programming (Koza, 1992). These four areas developed independently, until they were united under the banner of evolutionary computation
during the early nineties (Back et al., 1997). Originally developed as search/optimization
heuristics, evolutionary computation techniques (or rather, mutated versions of them)
underlie most of evolutionary ALife, including the simulation of natural systems.3 Evolutionary computation algorithms work on a population of chromosomes, each of which
are candidate solutions to a problem. The main difference between the evolutionary computation techniques is in the chromosomal data structures used to represent candidate
solutions. Evolutionary programming uses finite state automata, represented by statetransistion tables; evolution strategies uses vectors of real numbers; genetic algorithms
use bit string chromosome representations; and genetic programming uses computer programs, defined by a set of instructions. In my simulations, I draw from a combination of
these data types: evolving real values, as per evolution strategies, for representing continuous value attributes, such as expiry age (see Chapter 4), and genetic algorithm bit
strings for signatures determining interactions between parasitic diseases and their hosts
(see Chapter 4) and to determine sexual compatibility between reproducing agents of
sub/species groupings (see Chapter 5). For all of these algorithms, by iteratively applying
evolutionary operators (selection, mutation, recombination, etc.), subsequent population
generations are created that optimize some fitness — for the evolutionary computation
algorithms, this is an explicit fitness, i.e., the value of the solution encoded at solving the
given problem.
Algorithm 2.1 gives a simple form of the evolutionary computation algorithm. The
population is initialized with an amount of randomly generated chromosomes, and each
step/generation the entire population is replaced (i.e., the population size is stable). Each
generation, the fitness of all chromosomes are evaluated, using an explicit fitness function,
3
Here I discuss the original usage as conceived by their creators.
2.2. ARTIFICIAL LIFE
17
Algorithm 2.1: Simple genetic algorithm
1
2
3
4
5
6
Randomly generate initial population of chromosomes;
repeat
Evaluate fitness for each chromosome;
Breed new population, applying selection and genetic operators;
Remove old population;
until termination condition (e.g., step limit reached, target fitness achieved . . . );
and used to select which agents are to reproduce. The fitness is predominantly determined
by how well the chromosome performs on the given problem — it may incorporate additional aspects, potentially stochastic (again drawing from natural evolution), commonly
to promote diversity in the population so that the search avoids getting caught in local
maxima. There are many possible selection methods, e.g., retaining the top performing
chromosomes and replacing the others, or selecting reproducers with a probability proportional to fitness, or splitting the population into subgroups and using a tournament
selection algorithm, etc. Reproduction can be sexual or asexual, determined by sampling
a fixed crossover probability. In sexual reproduction, parent chromosomes are combined
via crossover — often single-point, two-point or uniform crossover with bit strings and finite automata — to create offspring chromosomes; for asexual reproduction, chromosomes
are cloned. Single-point crossover involves randomly selecting a crossover point, at the
same position on both parent chromosomes, and forming a new chromosome consisting of
the genes before the crossover point from one parent and the genes after from the other
parent. Two-point crossover differs in two crossover points being selected and a new chromosome formed by the genes drawn from alternating parent chromosomes, switching at the
crossover points. For uniform crossover, each chromosome gene is copied independently
from a randomly selected parent chromosome, usually with a 50% probability. After a
chromosome is generated, copying errors are introduced via mutation. For bit strings and
finite automata, this usually involves flipping bits (or states, with finite automata) with a
small fixed probability, or inversion of sections of the bit strings. Real values, in evolution
strategies, are mutated by sampling a normal distribution — the variance of the mutator distribution is itself also often the subject of evolution by a meta-mutator — again,
another, naturally inspired, method of avoiding convergence on local maxima.
18
CHAPTER 2. BACKGROUND
Simulating Natural Systems
Evolutionary computation takes inspiration from natural evolution, however it differs in
some important aspects. Evolutionary computation techniques were developed for searching abstract problem spaces and therefore the reproduction and selection operations are
tailored to produce better, efficient, search algorithms in those problem spaces. In particular, to ensure that evolution converges on an optimal solution to the problem at hand,
fitness in the algorithms is explicit, measured by how well chromosome representations
perform on a given problem. In natural evolution, fitness is endogenous, determined by
the complex interactions between an agent phenotype and its environment, which will
usually include other agents in the population, to varying degrees. The agents of early
evolutionary computation do not interact with each other, except during recombination of
genotypes during sexual reproduction. Another important difference is the use of explicit
generations. In Algorithm 2.1, each step sees the entire population replaced, whereas in
natural systems it is common to find, at any point, agents at all stages of their life cycle
interacting with each other — this intergenerational interaction is important for many
traits, for example, those determining parental behaviour toward offspring.
This is not to say that simulations must have the properties of endogenous fitness
and overlapping generations to be of interest in studying natural systems. It is often just
a matter of interpretation. One of the early ALife simulations of natural phenomena,
demonstrating the Baldwin effect (Hinton and Nowlan, 1987), is a simple extension of
Holland’s genetic algorithms. The Baldwin effect argues that there is a benefit to learning in evolutionary adaptation (Baldwin, 1896). That is, phenotypes that have a bit of
plasticity will be rewarded for being close enough to the solution, allowing chromosomes
to converge on narrow spikes in a fitness landscape. The chromosomes in the simulation
are strings of genes which represent the connections in a neural network. Genes have
three alleles, they are either connected, unconnected or open (wildcard). Open alleles
eventually take on a connected or unconnected state, after trialling during the learning
phase. Generations in Hinton and Nowlan’s simulation are divided into two phases, an
evolutionary phase and a learning phase. The evolutionary phase is a simple variant of
Holland’s genetic algorithms, with fitness of chromosomes determined during the learning
phase. The learning phase is another iterative process. A target chromosome is specified
2.2. ARTIFICIAL LIFE
19
and the fitness of a chromosome is determined by how quickly it finds the target whilst iterating through random instantiations of the wildcard locus. Using their ALife simulation,
Hinton and Nowlan were able demonstrate the possibility of the Baldwin effect and make
a substantial contribution to our understanding of the importance of phenotype plasticity
in natural evolution.
On the other hand, some natural system simulations are far removed from, not only
evolutionary computation, but also real world biology; for example, the Tierra simulation
(Ray, 1991). In Tierra, agent chromosomes are computer programs (i.e., sets of machine
instructions), which compete for CPU resources. Allocated equal amounts of processor
time, agents that find innovative ways of replicating themselves within memory become
more prominent in the population. Ray’s objective with Tierra is to replicate natural
evolution, however his ecosystem bears little resemblance to any real world ecosystem.
Instead he concerns himself with evolving agents that are adapted to the medium within
which they exist (in this case, the computer architecture). Tierra was able to evolve diverse
ecological communities, with many different types of agents that were recognizable in real
world ecologies, for example, parasites, hosts and immune host, and symbionts.
2.2.2
Agent Based Models (ABMs)
Agent based modelling4 (Epstein and Axtell, 1996) is a bottom-up approach to studying
group/population behaviour. The technique involves simulating systems as a collection of
autonomous individual agents, sharing an environment and interacting with each other.
The main power of the ABM methodology lies in the study of complex systems. Complex systems are difficulty to study, as many complex phenomena cannot be broken into
subcomponents that can be studied independently. Such complex phenomena are called
emergent. Emergent phenomena cannot be reduced to components because they are the
result of the interaction between the components. That is to say, emergent system properties are decoupled from the individual properties (Bonabeau, 2002). For example, consider
a population of individuals that are restricted to moving in the four compass directions
(N,W, S, E). Such a restriction wouldn’t hold for a population of those agents, which
could conceivably move in the diagonal directions. In this case the population property
of diagonal movement is emergent from the individual rules (Epstein and Axtell, 1996).
4
Agent based modelling is also known as individual based modelling in ecology science (Grimm and
Railsback, 2005).
20
CHAPTER 2. BACKGROUND
ABMs are also a natural way of describing a system, as opposed to the top down method
of dynamic equations. By taking a bottom up approach, implementing, and experimenting with, a simple set of rules to simulate the actions and interactions between multiple
autonomous agents and their environment, complexity may naturally emerge.
There is no universal definition of agent based models (Macal and North, 2006). Agents
can be any type of independent entity, and may have behaviour ranging from simple
reactive trigger rules to complex adaptive artificial intelligence. Often agents will occupy
a world with a grid topology — sometimes wrapped so that the edges meet to form
spherical or toroidal worlds — however this is not prescribed. Some example applications
of ABM methodology are: cooperation in the iterated prisoners dilemma (Axelrod, 1997);
stock market dynamics (LeBaron, 2002); traffic flow management (Smith et al., 1995);
business organization (Prietula et al., 1998); ecology (Smajgla et al., 2011; Waddington
et al., 2014; Kulakowska et al., 2014), evolutionary dynamics (Medernach et al., 2013),
electronic art (Dorin, 2004; Kowaliw et al., 2012) and natural populations (Epstein and
Axtell, 1996).
The agents of an ABM are typically described by a set of state variables, some fixed
at conception, such as gender, and some variable, such as health or age, changing as a
consequence of interactions with other agents and the environment. In evolutionary ABMs
(such as the ones implemented in this thesis), agents typically have chromosomes, which
are mutated during reproduction, but otherwise stay fixed for the agent’s life span. Chromosomes are used to determine the agent phenotype — the characteristics and behaviour
that distinguishes it from other agents. They can contain any number of data structure
types — often data structures inherited from the evolutionary computation legacy, i.e.,
finite automata, bit-strings and real values (see above), but also more complex structures
are possible, such as decision trees (Mascaro, 2008) or Bayesian networks, allowing agents
with complicated decision making functions to evolve. My simulations are ABMs, using
the real value and bit string data types found in the earlier evolutionary computation techniques. Agents exist in an environment that will usually have an interaction topology and
environmental variables, such as food. In addition to the entities of ABMs, processes/rules
are specified determining the behaviour of agents and the update functions of agent and
environment variables. Behavioural rules may be globally fixed for agents, or be subject
to learning/evolution.
2.2. ARTIFICIAL LIFE
21
In order to improve consistency, understandability and completeness in documenting
agent/individual based models, Grimm et al. (2006, 2010) developed the Overview, Design
Concepts and Details (ODD) protocol. The central idea of the protocol is to present
model descriptions in a manner that is easily, and quickly, understood and compared with
other model descriptions, yet provides enough details to guide the reader in accurately
reproducing the model. Throughout this thesis I use the ODD protocol to describe the
simulations I developed.
2.2.3
Epistemology of Computer Simulation
Clearly there is much to be gained from experimental observation in the study of evolutionary characteristics and processes. However, we are limited in the techniques available
to us. The fossil record provides snapshots of a variety of species present in and during select locations and times of the world’s geological history. However, it lacks detail
in the progression of evolution between these snapshots, and in the details of organisms
themselves, which are lost during the fossilization process. The study of Drosophila in laboratories offers the opportunity to perform intervention experiments (Rose, 1984; Spitze,
1991; Leroi et al., 1994). Whilst much important work has been done in the laboratory,
the complexity, temporal and spatial scales involved in evolution in nature do not lend
themselves to easily controllable and repeatable experiments. The utility of simulations
for studying intractable systems is well established in other scientific disciplines, such as
physics, economics, weather prediction, astronomy, etc... In many of these disciplines, the
use of simulation experimental techniques are well accepted, whereas in other applications
(particularly regarding contentious science) it is doubted that we can learn anything new
from simulations.
The majority of discussion (Oreskes et al., 1994; Axelrod, 1997; Di Paolo et al., 2000)
on the epistemological value of simulation holds that simulations cannot be used to acquire
any empirical knowledge and instead they are treated as elaborate thought experiments:
elaborate in the sense that they can include a far greater amount of detail than something
we could hold in our heads, or calculate on a piece of paper; and thought experiments
in the sense (it is argued) that it has no physical relationship with the process that is
being modelled. Be that as it may, thought experiments are very useful as they allow us
to explore the deductive consequences of a model, potentially surprising us and triggering
22
CHAPTER 2. BACKGROUND
re-evaluation of our theory. Thought experiments/simulations can also increase a theory’s
plausibility by showing how it can actually work.
A prominent feature of empirical investigation is that it involves instances of the physical system being investigated, as opposed to theory or pure logic. The obvious challenge
to the epistemological parity of traditional experimentation and simulations is that simulations (performed on a computer) don’t interact with the real world target system —
that there is a gap between simulations and reality, which doesn’t exist between real-world
experiments and real-world targets (Morgan, 2002). Mascaro et al. (2010) argue that simulations can be used for both theoretical and empirical exploration, subject to validation
and verification. Validation techniques are used to determine whether a simulation conforms to the target process (i.e., testing for a homomorphism) and verification techniques
are used to determine if the simulation correctly implements the theory (e.g., proving the
simulation is free of bugs). They argue that a fully validated simulation qualifies as an instance of the physical system. For the most part, complete validation and verification is an
ideal rarely achieved (even in non-simulation research); it is a matter of degree. This is not
a problem, simulations, like any other real world experiment, can still be probabilistically
informative.
Chapter 3
Levels of Selection
In this chapter I review and contribute to the debate surrounding group selection and its
relationship to kin selection (inclusive fitness). Originally thought of as distinct opposing
theories, a ‘new’ generation of group selection models has emerged via a reformulation
of inclusive fitness, into level of selection. This has led people to draw a distinction
between ‘old’ and ‘new’ group selection models — with the ‘old’ group selection models
generally thought infeasible. Mitteldorf (2004b) developed an ‘old’ group selection model
demonstrating the evolution of aging, arguing that aging is an “ . . . ‘extreme’ altruism
in the sense that the cost to the individual is high and direct, while the benefit to the
population is far too diffuse to be accounted for by kin selection.” I argue that ‘old’ group
selection is simply a special case of ‘new’ group selection and can be expressed in a kin
selection framework as well. I conduct experiments on Mitteldorf’s group selection model
removing kin associations (hence, disabling kin selection) via the use of an adoption queue.
The results of my investigations demonstrate that the ‘old’ group selection model is indeed
dependent on the kin selection mechanism.
23
24
CHAPTER 3. LEVELS OF SELECTION
3.1
Introduction
The theories of both group and kin selection were developed in an effort to explain the
evolution of altruism. Originally thought of as opposing theories, inclusive fitness theory
(the theory that underlies kin selection) has since been redefined, by its creator, using
components describing within and between group selection pressures, demonstrating its
mathematical equivalence with group fitness. Regardless, a distinction is often drawn,
splitting group selection models into ‘old’ and ’new’ - where ‘new’ group selection is defined
in terms of inclusive fitness and ‘old’ group selection is defined in terms of group fitness,
requiring the existence of isolated multi-generational group populations. Whereas ‘new’
group selection is commonly accepted, particularly in the form of multi-level selection
(Wilson, 1980), ‘old’ group selection still retains the legacy of ill-repute that plagued early
group selection arguments, and is generally thought unfeasible (Maynard Smith, 1976;
Grafen, 1984; West et al., 2007).
Mitteldorf (2004b) claims that aging is an “. . . ‘extreme’ altruism in the sense that the
cost to the individual is high and direct, while the benefit to the population is far too
diffuse to be accounted for by kin selection”.1 The argument is that the evolution of an
aging trait requires an ‘old’ group selection mechanism and cannot be explained in terms of
kin selection — i.e., ‘old’ group selection and kin selection are distinct. To test Mitteldorf’s
claim, I replicate his ‘old’ group selection simulation and experiments demonstrating the
evolution of aging and conduct further experiments disabling kin selection via the use of
an adoption queue to test the reliance of the simulation on a kin selection mechanism.
The result is the failure of the simulation, demonstrating that the ‘old’ group selection
mechanism used is, in fact, reliant on kin selection.
In Section 3.2, I review the debate surrounding group selection and inclusive fitness
theory, and introduce the principles behind Mitteldorf’s aging simulation — a detailed
review of aging is left to Chapter 4, where I investigate various hypotheses about aging.
In Section 3.3, I give a detailed description of the simulation and outline my method of
removing kin associations (and, therefore, kin selection) via the use of an adoption queue.
In Section 3.4, I discuss my experiments, firstly replicating Mitteldorf’s results, and then
demonstrating the model’s dependence on kin selection by activating the adoption queue.
1
Mitteldorf’s work was republished (Mitteldorf, 2006) without this claim, however this occurred after
my published response (Woodberry et al., 2005)
3.2. BACKGROUND
25
This chapter draws from work originally published in Woodberry et al. (2005) and
Mascaro et al. (2010), with modified simulations and experiments.
3.2
Background
The evolution of an aging trait would appear to be in direct conflict with the individual
selection concept of natural selection. Individual selection refers to selection of the organism with the greatest individual fitness, measured as ability to survive and reproduce, or
simply the individual’s expected number of descendants. It is easy to see that an organism exhibiting a trait, such as aging, which by definition reduces its own survivability, will
leave less descendants than a competing organism without the trait. The benefits of an
aging trait, if there are any, could only be received by organisms other than the organism
exhibiting the trait. For this reason such a trait is called selfless or altruistic. In order
to give an explanation of such an altruistic adaptation, one must call upon a mechanism
of selection which incorporates such altruistic benefits, or otherwise deny that it is an
adaptation.
There have been two notable attempts at explaining such a mechanism, these are:
group selection, introduced by Darwin (1880), though often attributed to Wynne-Edwards
(1962), and inclusive fitness theory (also known as kin selection), proposed by Hamilton
(1964). Inclusive fitness theory differs from individual fitness in a further augmentation by
the benefits, and harms, caused to the fitness of neighbours, weighted by their relatedness.
This gene selection mechanism is often labelled kin selection, as neighbours will often
be related to the individual holding the gene, inheriting the same genes, and hence an
altruistic gene will increase its own inclusive fitness by benefiting copies of itself in kin. It
is discussed, in detail, in Section 3.2.1.
There is disagreement on what the term group selection refers to. Historically, group
selection was defined in terms of group fitness (as analogous with individual fitness), entailing the existence of multigenerational, reproductively isolated sub-populations, which
reproduce (via emigration) and die (via extinction). However, inclusive fitness theory,
often cited as an alternative to group selection in explaining altruistic adaptations, has
since been redefined by Hamilton & Price into hierarchical levels of selective forces (Price,
26
CHAPTER 3. LEVELS OF SELECTION
1970; Hamilton, 1975) — separating selection into individual (intragroup) and group (intergroup) component forces. This reformulation is the basis of Wilson’s (1980) multilevel
selection theory, and is often referred to as ‘new’ group selection. The primary distinction
between ‘new’ and ‘old’ group selection is that ‘new’ group selection is defined in terms
of inclusive fitness, whereas ‘old’ group selection is defined in terms of group fitness. The
early, ‘old’, group selection models are generally thought to only work under extremely
restrictive conditions (Maynard Smith, 1976; Grafen, 1984; West et al., 2007), whereas the
‘new’ group selection models are generally accepted as uncontroversial, simply a different
way of conceptualizing inclusive fitness, and thus hold the same validity (Hamilton, 1975;
Grafen, 1984; West et al., 2007). Both ‘old’ and ‘new’ group selection are discussed, in
detail, in Section 3.2.2.
Mitteldorf (2004b) created an ‘old’ group selection simulation for which he ascribes
the benefit of an aging trait to demographic homeostasis. This is, group populations of
individuals with longer lives will exhibit chaotic population dynamics and will be more
likely to become extinct. Individual selection will result in the selection of organisms which
live longer and longer lives, eventually causing chaotic population dynamics, leading to
the group’s extinction. Mitteldorf claims this “tragedy of the commons” can never be
addressed by individual selection and that the differential extinction of groups outweighs
individual selection to enforce growth restraint through birth restraint and aging. Detailed
discussion of Mitteldorf’s simulation can be found in Section 3.2.4.
In this section, I first provide background on inclusive fitness theory, in Section 3.2.1,
which is instrumental in providing mathematical justification for both the kin and group
selection mechanism. I also outline kin selection, which is often used to refer to any
selection maximizing inclusive fitness. Next, in Section 3.2.2. I provide background on
group selection, both ‘old’ and ‘new’, with a side reference to the species selection mechanism (which is discussed later in Chapter 5). Finally, I give a description of Mitteldorf’s
simulation in Section 3.2.4.
3.2.1
Inclusive Fitness Theory
Inclusive fitness differs from individual fitness in that it shifts the focus downwards from
the individual to the gene, whether held by the individual or, as a replica, by a relative.
The inclusive fitness of an allele is just the organism’s individual fitness augmented by the
3.2. BACKGROUND
27
harms and benefits caused to the fitness of others, weighted by their relatedness, i.e., the
probability of their carrying the same allele (Hamilton, 1964).
Hamilton’s inclusive fitness rule states that the criterion for the positive selection of
an allele is:
X
(bi − ci )ri > 0
(3.1)
i
where the subscript i denotes the ith member of the species, ri is the relatedness coefficient
between the actor and individual i, bi is the benefit to the fitness of the individual i, and
ci is the cost to the fitness of the individual i. The relatedness r is proportional to the
chance that a copy of the same allele at a given locus will be held by both the actor and
recipient. For example, siblings have an equal chance of inheriting the alleles of either
parent at a particular locus and hence have a relatedness of 12 . Considering the simplified
case of an allele which only bestows benefit on a single sibling s at some cost to its carrier
a, applying (3.1) we can see that for an allele to be selected bs ×
1
2
− ca > 0. That is, the
benefit to the receiving sibling must be greater than twice the cost to the carrier. The
consequences of the theory are summed up by Hamilton (1964) in two points:
1. For an allele to be selected for it is not sufficient that it should increase the fitness
of its bearer above the average if this is done at the expense of related individuals.
Being selfish does not imply being fit.
2. Conversely, an allele may be selected for while disadvantageous to its bearers, if it
sufficiently benefits relatives. Being altruistic does not imply being unfit.
Kin Selection
There are a number of mechanisms which can cause the r term in Hamilton’s rule to be
non-zero. Common ancestry of neighbours is the most obvious and common mechanism,
leading to the identification of inclusive fitness with the term “kin selection”. However,
other mechanisms are possible, such as preferential assortment — where holders of a gene
share a preference for a common habitat — or intervention by some designer.
Kin selection is sometimes incorrectly used in a broader sense, to refer to any selection
maximizing inclusive fitness — regardless of relatedness occurring due to common ancestry
(West et al., 2007). I will not be using it in this way.
28
3.2.2
CHAPTER 3. LEVELS OF SELECTION
Group Selection
The group selection concept has an enduringly bad reputation for many. Introduced by
Darwin (1880), although often attributed to Wynne-Edwards (1962), it was widely used
by evolutionary biologists, without due regard for its theoretical backing, until the highly
successful critique of Williams (1966), which raised doubts that a workable model of group
selection could be devised. While perfectly sensible models for it have been developed
in the meantime, it still carries the taint from Williams’ attack. Current thinking often
distinguishes between two generations of group selection models (Grafen, 1984; West et al.,
2007). The first generation (old group selection) is characterized by Wynne-Edwards
(1962) argument for reproductive restraint. The second generation (new group selection)
relies on a reformulation of inclusive fitness by Price (1970), and is the basis of Wilson’s
(1980) multilevel selection theory. Both are discussed in the following sections.
Old Group Selection
Old group selection models treat groups as analogous with individuals. Groups have a life
span — they are created, via pioneering from existing groups, and die, via extinction. It
is the differing viability of the groups, together with their fecundity, i.e., their tendency to
establish new groups, that drives group selection. Selfish individuals within groups may
be more fit within the group, however the group as a whole pays a price in the degradation
of its average fitness; i.e., the group survives a shorter time than more altruistic groups
and so establishes fewer colonies. Selfish individual fitness flourishes, but only within the
group and its few offspring; even though altruistic behavior may be less fit within the
group, it can be more fit across the population if groups favoring it are themselves more
fit relative to other groups.



Figure 3.1: States and transitions of the early group selection models (adapted from
Maynard Smith, 1976).
3.2. BACKGROUND
29
This kind of group selection model was reviewed by Maynard Smith (1976) using
a simplified version of Gilpin’s (1975) predator-prey model (see Figure 3.1). Maynard
Smith’s model contains some number of discrete patches, each capable of supporting a
single group. There are three different states each patch can take at a given time: empty
(E), containing no group population; selfish (S), holding a group that contains at least
some selfish individuals; or altruistic (A), holding a group that contains only altruistic
individuals. A sharp distinction is drawn between selfish and altruistic groups, ignoring
the transient groups based on the strong (worse case scenario) assumption that altruists
will be quickly replaced by selfish free riders who share the altruist’s benefit without
paying any cost. Transitions occur between states due to extinction (S or A → E),
migration or re-population (E → S or A), or the introduction of selfish genes by mutation
or invasion from other selfish groups (A → S).2 In these models the main question is
how the cooperation of the altruistic individuals will affect the factors of extinction and
migration. In particular, how cooperation reduces extinctions of altruistic groups.
Maynard Smith (1976) observes that the fate of these models, when viewed in this
manner, is dependent on the single parameter M , which is “the expected number of
successful ‘selfish’ emigrants from an S patch during the lifetime of the patch.” A successful
selfish emigrant is one that establishes itself and leaves descendants in a neighboring E or
A patch. If the average number of emigrants from S patches is greater than one (M > 1)
then the S patches will increase in frequency. Otherwise, if M < 1, the S patches will
become extinct faster than they can found new groups and will therefore be selected out
of the system.
Although the model demonstrates a mechanism of group selection that is clearly a
logical possibility, it has been loudly doubted whether the stringent conditions required
for this kind of evolution of altruism could be realized in nature (Maynard Smith, 1976;
Grafen, 1984; West et al., 2007). However, Maynard Smith’s analysis is based on the
worse case scenario assumption that selection against altruistic genes is as strong as it
could be within groups (Wilson, 1987), i.e., mixed groups immediately succumb to selfish
gene selection. This assumption is obviously wrong — transient populations, with at
least some altruists (i.e., the S groups in Maynard-Smith’s model), are capable of seeding
2
The transition S → A by mutation can be ignored, since it requires simultaneous mutations throughout the group.
30
CHAPTER 3. LEVELS OF SELECTION
partially, or even purely, altruistic populations — especially if the founding population is
small.
New Group Selection
Inclusive fitness theory was considered an incompatible alternative to group selection for
explaining the evolution of altruistic behavior until Price (1970) and Hamilton (1975) reformulated it into different levels of selection, namely within- and between-group selection,
with two distinct terms which sum to explain total change in the frequency of an allele.
The Price equation is formulated by Hamilton (1975) thus:
w∆q = Covariance(ws , qs ) + Expectation(ws ∆qs )
(3.2)
where the subscript s denotes the sth subpopulation, q the frequency of the gene (qs the
frequency of the gene in the sth subpopulation and ∆q the change in gene frequency
from generation to generation) and w the mean fitness (ws the mean fitness of the sth
subpopulation). The covariance term represents how fitness varies with gene frequency
and, if positive, will drive the positive selection of the gene across groups, that is, change
the relative sizes of the groups. The expectation term represents the change of the gene
frequency between generations due to selection pressure within groups.
In these models, for an altruistic allele to be positively selected, the magnitude of
between-group selection (the covariance term) must be greater than within-group selection
(the expectation term). That is, groups with a higher frequency of altruists can perform
better by increasing the group’s fitness and hence increasing the size and proportion of
altruistic groups in the population. If this increase outweighs the decrease in frequency of
altruists within each group, altruism will increase in global frequency. The more varied the
frequency of altruists across the groups, and the more benefit bestowed by the altruists on
the group, the greater this between-group selection pressure will be. Figure 3.2 illustrates
this effect in a population divided, for a period, into two groups with a varied frequency
of altruists, represented by slices of pies. Within-group selection causes the altruistic “pie
slice” to shrink in both groups. However, between-group selection causes a global increase
in the altruistic “pie size” resulting in an increase in the overall frequency of altruist genes.
3.2. BACKGROUND
31
S
A
A
S
S
A
S
A
A
S
S
A
Figure 3.2: Within- and between-group selection (adapted from Sober and Wilson, 1998).
The relationship between the Price equation and group selection is considered by some
to be simply one of mathematical convenience (e.g., Maynard Smith, 1976). Wilson (1980),
on the other hand, uses the equation as the basis of his multilevel selection theory, which
asserts the compatibility of multiple levels of selection that are simultaneously active.
Queller (1992) uses the Price equation to argue that any group selection model can be
recast in terms of inclusive fitness. van Veelen et al. (2012) claim that, under certain
conditions, this equivalency doesn’t hold — however they still allow that the intuition of
the Price equation could be correct.
On the controversy over the relative importance of group selection versus kin selection
for the evolution of altruism, Hamilton (1975) remarked:
Because of the way that it was first explained, the approach using inclusive
fitness has often been identified with ‘kin selection’ and presented as an alternative to ‘group selection’ as a way of establishing altruistic social behavior by
natural selection. . . Kinship should be considered just one way of getting positive regression of genotype in the recipient, and that it is positive regression
that is vitally necessary for altruism.
32
CHAPTER 3. LEVELS OF SELECTION
The key idea is that inclusive fitness is more general than kin selection and might arise
by mechanisms other than kin selection. What is needed for group selection of altruistic
behavior is, first, a variable distribution of altruism between groups and, second, a positive association between group fitness and the altruistic genes, as required by the Price
Equation. Such an association can arise by kin selection or by other means, but, however
it arises, it will result in differential group fitness leading to a spread of altruism.
3.2.3
Species Selection
Eldredge and Gould (1972) introduced the idea that evolution proceeds through long
periods of genetic stasis, punctuated by short periods of rapid change, or punctuated
equilibrium. Under punctuated equilibrium, once a species becomes static and defined,
it takes on a kind of individuality. It has a lifespan; it has the opportunity to reproduce
through further speciation; and, in the end, it will die. This supports a strong analogy
with individual reproduction and, therefore also, with individual fitness (Gould, 2002).
But the similarity is more than analogical with group selection, for this just is a kind of
group selection. Species become units of selection, competing with other species within
the biosphere for the opportunity to create new species and to avoid early extinction; this
creates a species selection mechanism within the ‘old’ group selection model described in
section 3.2.2. Punctuated Equilibrium theory is investigated in Chapter 5.
3.2.4
Mitteldorf ’s Aging Simulation
Mitteldorf’s simulation (2004b) is based on the old group selection models of WynneEdwards (1962) and Gilpin (1975), in which group extinction is the driving force (see
Section 3.2.2). Mitteldorf’s simulation experiments demonstrate the evolution of population regulation through aging and birth restraint.
Mitteldorf’s model is composed of a grid of cells, each capable of holding a single group
of individuals, which migrate to neighbouring cells at a very low rate. Mitteldorf employs
a logistic equation to model death by overcrowding in his population,
x
dx
= rx(1 − )
dt
K
(3.3)
3.3. METHODS
where
dx
dt
33
is the population growth rate; x is the population size; r is the maximal growth
rate and K is the steady state population level. When the population size is less than the
steady state level (x < K) the population exhibits exponential growth, whereas, when x >
K the population exhibits exponential decline. Populations governed by this equation are
normally well-behaved, approaching K asymptotically either from above or below. When a
small delay is introduced into these equations — modelling an environment recovery period
— x instead of approaching K asymptotically will overshoot and oscillate to K. If this
delay is further increased, the behaviour of the group undergoes a transition into dynamic
chaos, resulting in fluctuations that cause the extinction of the group. The solution of
population regulation, either by restraining birth rate or increasing aging rate, is permitted
to evolve in Mitteldorf’s simulations. If the individuals fail to regulate population growth,
the group will experience chaotic fluctuations, causing it to become extinct.
In Mitteldorf’s paper, he describes three simulation runs: the first run is a calibration
run, determining, in the absence of aging, the maximum sustainable birth rates; the second
run permitted aging rates to evolve whilst the birth rate was kept constant; and in the
third run both aging and birth rates where permitted to evolve independently. In this
chapter I review only experiments concerning the evolution of an aging rate, holding birth
rates fixed. Mitteldorf’s simulation works because, below a certain threshold rate of aging,
groups become extinct faster than they can export their members, as can be seen from
Maynard Smith’s analysis, M < 1, (see Section 3.2.2). This threshold rate of aging is
determined from the migration rate — at higher migration rates the threshold rate will
be lower, as groups require a shorter “lifetime” to export their members.
3.3
Methods
The experiments of this chapter are performed on a replica of Mitteldorf’s chaotic population dynamics simulation. The simulation is discussed, briefly, in Section 3.3.1 (a detailed
simulation description can be found in Mitteldorf, 2004b). My kin selection experiments
with the simulation required the addition of kin-selection on/off switch, which is discussed
in Section 3.3.2.
34
CHAPTER 3. LEVELS OF SELECTION
3.3.1
Mitteldorf Simulation Replica
The Mitteldorf simulation replica uses a 9x9 grid of cells, containing groups of agents,
with a steady state population level (K) of 100. Each cycle every agent has a chance of
reproducing asexually with a probability of 0.045 (r); and migrating to a neighbouring
cell with a probability of 0.003. The agents also have a chance of dying either by cell
crowding or old age. The chance of a death by crowding is proportional to the population
sharing the site after a time delay of 50 cycles is applied (see Equation 3.3). Otherwise the agent will die of aging once it exceeds its genetically determined natural age of
death. There is no background (accident) cause of death in the simulation. Each agent
has: a position; an age, which is incremented each time step; and an age of natural
death, which is determined at birth from a chromosome holding an evolving expiry age
gene. The expiry age gene is inherited and mutated according to a normal distribution:
N (expiry age gene, expiry age gene×0.01). Mechanisms to switch aging and kin selection
on and off are also included: aging is switched “off” by halting all deaths caused by aging;
and kin selection is switched “off” by implementing an adoption queue, discussed next.
3.3.2
Disabling Kin Selection via an Adoption Queue
To test the reliance of Mitteldorf’s model on kin selection, I need a method of removing kin
associations. Toggling kin selection “on” and “off” allows us to see directly the effect of
inclusive fitness and contrast it with other fitness effects. Kin selection normally operates
via the correlation between agent proximity and kin relatedness. As Maynard Smith
(1976) noted, “kin selection can operate whenever relatives live close to one another, and
hence can influence one another’s chances of survival and reproduction”3 — which, in
fact, is the normal state of nature. As long as agents do not have very high rates of
motion, which would tend to spread them over the world uniformly, two agents who are
near each other are more likely to be closely related than two agents at distance. So,
actions which are selectively beneficial to neighbors will also be selectively beneficial to
relatives. This suggests that to remove kin selection it is enough to ensure that there is no
correlation between the locations of the parent and child. The simplest way of doing this
would be to remove the spatial component of simulation, resulting in all agents sharing one
3
An alternative proposed mechanism for kin selection is when agents are capable of recognizing their
kin and acting accordingly. However, the agents in my simulations have no such perceptual and cognitive
ability.
3.3. METHODS
35
location, and therefore being equidistant. Alternatively, I could spawn children a random
locations in the world, which would have a similar effect. Unfortunately, either such direct
approach to eliminating kin selection would also radically alter the population dynamics
of the simulation. For example, in the case of a Mitteldorf’s Gilpin-type group selection
model (Figure 3.1) randomly spawning children to empty patches would negate the effects
of migration founding new groups. To address this problem I use the mechanism of a
compulsory adoption queue.
Adoption Queue
The purpose of the adoption queue was to disable kin association, whilst maintaining
the group structure and sizes of the world. It had the effect of mixing the individual
constituents of the groups, whilst maintaining the group dynamics of pioneering and extinction. This is different to simply increasing the migration rate to the point of allowing
agents to move to any point in the world, which would totally obliterate any group structure. There are three aspects of the group which are important to the group selection
effect: group reproduction and death (i.e., pioneering and extinction), and inter-group
relatedness, accounting for the kin selection effect. With the adoption queue enabled,
agents are only born into existing groups, new groups may only be pioneered by agents
migrating from existing groups and groups may still be driven extinct via chaotic population fluctuations. Thus the simulation remains a group selection model in all aspects,
except that the members of the groups are not related by common descent and thus will
not be subject to kin selection forces.
Implementation:
The adoption queue was implemented as a list of agents, which are
in stasis, awaiting placement in the world — i.e., they are not updated and have no value
attached to their position field. The length of the list, beyond one agent, was found to be
inconsequential, so an adoption queue of length one was used.
Initialisation:
The adoption queue was initialised, during world initialisation, with a
single agent, generated as any other agent but with an unassigned location.
36
CHAPTER 3. LEVELS OF SELECTION
Adoption process:
As new agents were born into the world, they were swapped with
the agent in adoption queue and the adopted agent was placed in the same group as its
adopted parent.
3.4
Experiments
In order to demonstrate Mitteldorf’s simulation’s reliance on kin selection, I replicated his
simulation experiments (see Section 3.2.4), first without aging and then evolving a genetic
expiry age. Next, I repeated the simulation runs, implementing an adoption queue (see
Section 3.3.2) in order to identify the impact of kin associations and kin selection. In my
simulations I concern myself exclusively with the evolution of aging rate and hold birth
rate constant.
3.4.1
Simulations Replicating Mitteldorf ’s Results
In order to test my simulation I replicated Mitteldorf’s simulation experiments (see Section 3.2.4): firstly simulating the group chaotic population dynamics without aging genes,
and the expected result of eventual global extinction; and secondly with aging genes, and
the expected evolution of a steady aging rate and population.
Without Aging
Figure 3.3 was generated by averaging the results of 20 simulation runs, each lasting until
all groups had become extinct. In these runs the simulation described in Section 3.3.1
was used, with all deaths by aging switched “off”. This meant that all agent deaths were
only attributable to group crowding, and the agents had no means to regulate population
growth. Figure 3.3 shows that the entire population, in agreement with Mitteldorf findings,
eventually dies out, as the individual groups drove themselves into extinction.
With Aging
Figures 3.4(a) - 3.4(c) were generated by averaging the results of 20 simulation runs, each
lasting 2000 epochs (×10 cycles). In these runs the simulation described in Section 3.3.1
was used, with aging switched “on”. Figure 3.4(a) shows that the global population
evolves to a steady state of approximately 3500 agents, with, on average, approximately
3.4. EXPERIMENTS
37
9000
8000
Global Population
7000
6000
5000
4000
3000
2000
1000
0
0
200
400
600
800
1000
Epochs (10 cycles)
Figure 3.3: Without aging the global population is quickly driven extinct through chaotic
population dynamics within the individual groups.
9000
0.2
8000
Deaths From Aging
Global Population
7000
6000
5000
4000
3000
2000
0.15
0.1
0.05
1000
0
0
0
500
1000
1500
2000
0
500
Epochs (10 cycles)
1000
1500
2000
Epochs (10 cycles)
(a) With aging and kin selection the global pop- (b) With kin selection the type of deaths evolves
ulation evolves to a steady state of approxi- to a steady state with approximately 15% of
mately 3500 agents.
deaths attributable to aging.
120
Expiry Age Gene
100
80
60
40
20
0
0
500
1000
1500
2000
Epochs (10 cycles)
(c) With kin selection genetic expiry age evolves
to a steady state of approximately 45 cycles.
Figure 3.4: Simulation results with aging and kin selection enabled. Genetic expiry age
evolved to a steady state.
38
CHAPTER 3. LEVELS OF SELECTION
9000
0.2
8000
Deaths From Aging
Global Population
7000
6000
5000
4000
3000
2000
0.15
0.1
0.05
1000
0
0
0
200
400
600
800
1000
1200
1400
0
200
400
Epochs (10 cycles)
600
800
1000
1200
1400
Epochs (10 cycles)
(a) Without kin selection the global population
is quickly driven extinct through chaotic population dynamics within groups after the aging
gene has been selected out of the system.
(b) Without kin selection the aging gene is selected against, resulting in the decrease of aging
death as cause of agent death. The plot fluctuates near the end of the run, because there are
fewer agents and, thus, agent deaths to average
over.
120
Expiry Age Gene
100
80
60
40
20
0
0
200
400
600
800
1000
1200
1400
Epochs (10 cycles)
(c) Without kin selection the genetic expiry age
is quickly lengthened, until the population is
driven extinct.
Figure 3.5: Simulation results with kin selection disabled. The expiry age gene is quickly
selected against, resulting in global extinction.
1
2
of patches are empty at any point in time. Figure 3.4(b) shows the percentage of the
population that died from aging, each cycle, indicating that approximately 15% of deaths
are attributable to aging. Figure 3.4(c) shows the evolving rate of aging, the population
evolves a genetic expiry age of approximately 45 cycles (which, due to calibration techniques, is very close to the initial parameter selection). These results are in accord with
Mitteldorf’s findings.
3.4.2
Disabling Kin Selection
To test the importance of kin selection on the working of the model, I performed simulation runs using the simulation described in Section 3.3.1 with kin selection turned “off”,
generating the Figures 3.5(a) - 3.5(c) by averaging the results of 20 simulation runs. As
can be seen from Figure 3.5(c) the genetic expiry age is quickly selected against, resulting
in the decrease of aging deaths (hence, increase in crowding deaths) seen in Figure 3.5(b).
3.5. CONCLUSIONS
39
Figure 3.5(a) shows the population eventually dying out, as in the runs without aging,
unable to sustain itself with the high growth rates and consequent chaotic population
fluctuations.
When kin selection is “on”, we would expect the members of the same group to be
more genetically related with each other than to members of different groups. Conversely,
when kin selection is “off”, we would expect that members of the same group will be just
as closely related to each other as to members of different groups. In order to test this I
measured the genetic relatedness between agents as the difference between their genetic
expiry age values and a t-test was performed to compare the means of the two groups.
When kin selection was “on”, the means of genetic relatedness of members of the same
group and members of different groups were found to differ significantly with p < .001.
When kin selection was “off”, while there was a difference in the mean genetic relatedness
of members of the same group and members of different groups, the difference was not
statistically significant with p = 0.42.
3.5
Conclusions
It is commonly recognized that there exists a large amount of semantic confusion surrounding the group/kin selection and inclusive fitness concepts (Maynard Smith, 1976;
Grafen, 1984; West et al., 2007). Due to the close publications of Wynne-Edwards’ (1962)
book on group selection and Hamilton’s (1964) paper on inclusive fitness theory, there has
been a tendency to see the two theories as in opposition with each other. Even though
Hamilton (1975) has since redefined inclusive fitness into different levels of selection, there
still exists a desire to draw a distinction between the two. Maynard Smith (1976) suggests
such a distinction:
The term group selection should be confined to cases in which the group (deme
or species) is the unit of selection. This requires that groups be able to “reproduce,” by splitting or by sending out propagules, and that groups should
go extinct. Kin selection requires only that relatives should live close to one
another. The division of the population into groups, either permanently or
for part of the life cycle, may favor the operation of kin selection but is not a
necessary feature.
40
CHAPTER 3. LEVELS OF SELECTION
The suggestion here is that we reserve the term “group selection” for situations where
groups are analogous to individuals: lasting multiple generations and reproducing and
dying through migration and extinction. This group definition is central to the ‘old’ group
selection model. Meanwhile, the between-group component of the Price reformulation of
inclusive fitness continues to be referred to as group selection, for example, in Wilson’s
(1980) popular multi-level selection theory, creating a need for a ‘new’ group selection
distinction, and undermining Maynard Smith usage of the term ‘group’. Hamilton (1975),
when pressed, suggests an alternative distinction, that the term group selection “. . . be
restricted to situations definitely not involving kin”, which would, in multigenerational
groups (where offspring are necessarily born into the same group as their parents), void
the term of any practical application. Hamilton is against the idea of drawing a distinction,
arguing:
. . . it seems on the whole preferable to retain a more flexible use of terms; to
use group selection where groups are clearly in evidence and to qualify with
mention of kin . . . , relatedness or low migration . . . , or else assortation, as
appropriate.
All this is to say, if we distinguish between ‘old’ and ‘new’ group selection, the distinction is only one way — ‘old’ group selection is just a special case of ‘new’ group
selection, where Maynard Smith’s multigenerational, reproductively isolated, groups are
in operation.
Mitteldorf’s (2004b) explanation of adaptive aging requires an ‘old’ group selection
mechanism, in the sense that the chaotic population fluctuations triggered by lack of population growth restraint, must result in the death of group sub-populations to weed out the
selfish long lived individuals. However, Mitteldorf goes further to claim that his mechanism cannot “. . . be accounted for by kin selection”, implying that it cannot be formulated
in terms of ‘new’ group selection. Nevertheless, as the results of Section 3.4.2 show, Mitteldorf’s model is dependent on the kin associations within its groups and therefore is a
kin selection model.
We can see that Mitteldorf’s groups are in fact highly related, as new groups are
founded by small groups: indeed, in Mitteldorf’s asexually reproducing, sparse and low
migrating rate model, most groups will be founded by a single individual and have little or
3.5. CONCLUSIONS
41
no contact with other groups throughout its lifetime. This results in groups of individuals
which are practically clones of each other.
42
CHAPTER 3. LEVELS OF SELECTION
Chapter 4
Evolution of Aging
In this chapter, using an individual based simulation, I investigate various theories to
explain differential aging rates across species. I outline my own adaptive hypothesis of
aging for the sake of diversity, and compare it with other popular hypotheses. I hold
that, although aging may reduce individual fitness, it may adaptively arise because aging increases population turnover and enhances genetic diversity within subpopulations. I
outline simulation environments testing the popular non-adaptive theories, mutation accumulation, antagonistic pleiotropy and disposable soma, alongside a group selection model
of subpopulations of hosts and diseases to test my adaptive theory of aging. The results
of my investigations demonstrate the validity of all the hypotheses, in particular showing
conditions which are favourable to the adaptive evolution of aging for the sake of diversity.
43
44
CHAPTER 4. EVOLUTION OF AGING
4.1
Introduction
In this chapter I develop simulations and experiments to test various hypotheses, both nonadaptive and adaptive, about the evolution of aging in species. I outline my own adaptive
theory of aging for the sake of diversity — that populations with shorter individual life
spans will turnover faster, introducing variation through recombination and mutation
faster. Diversity will be beneficial in co-evolution scenarios, where predator/parasites will
have less opportunity to exploit genetic homogeneity in the prey/host population. My
hypothesis is closely related to the Red Queen hypothesis (van Valen, 1973), which holds
that sexual reproduction is selected for the sake of diversity.
Historically, aging was thought of as an adaptive characteristic, which better fit with
observations of the variety of longevity across species. However, the reliance of such
theories on a hypothetical group selection mechanism created a second wave of theories
explaining aging as a non-adaptive characteristic, i.e., as a by-product of some other
adaptive characteristic or as a chance product. Recently there has accumulated compelling
experimental evidence that aging is an adaptation (Mitteldorf, 2004a; Bredesen, 2004;
Skulachev, 1997), leading to a renewal of adaptive theories of aging.
To test the various theories about aging, I develop simulations of individual agents
with genetic components that cause agent death, testing each mechanism on its own and
combining all the components to conduct a comparative investigation. Whilst testing my
aging for the sake of diversity hypothesis, I also test the Red Queen diversity hypothesis.
The results demonstrate the feasibility of all the theories in these kinds of simulation
environments. They also support the hypothesis of an adaptive benefit of aging for the
sake of diversity in co-evolutionary scenarios, demonstrating a group selection pressure on
all the aging mechanisms modeled.
In Section 4.2, I review the debate surrounding the evolution of aging and describe
the popular theories about aging suggested during the discourse. I also present my own
adaptive hypothesis of aging for the sake of diversity and the related Red Queen hypothesis
on the evolution of sexual reproduction. In Section 4.3, I describe the simulations used in
the chapter. In Section 4.4, I present and discuss my experiments, including calibration
of the standalone simulations (investigating each hypothesis of aging) and the results of
combining the aging mechanisms in a single mixed simulation.
4.2. BACKGROUND
45
This chapter draws from work originally published in Woodberry et al. (2007) and
Mascaro et al. (2010), adding work on the evolution of sexual reproduction and modified
simulations and experiments.
4.2
Background
Williams (1957) defines aging as the general deterioration of an organism, and its eventual
death, by internal causes. The different rates at which different species age is a perplexing
phenomenon. The challenge lies in the question of why an organism, which produced itself
via a morphogenetic process, does not perform the relatively simple tasks of maintenance
and ongoing repair (Williams, 1957). Since Darwin proposed the theory of evolution by
natural selection, observations of aging in organisms have confounded biologists. The
wide variety in longevity observed across species — ranging from a few hours for some
phytoplankton cells (Agustı́ et al., 1998) to a few days for some insects to thousands
of years for the bristlecone pine tree — indicates that aging is a species characteristic.
Furthermore, these different rates have themselves not varied greatly during recorded
history, so far as we can tell. The genetic control of aging is beginning to come into view,
with multiple genes already identified as participating in aging rates (e.g., Belenky et al.,
2007). All of this seems to suggest that aging rates have evolved because of their adaptive
value.
Evolution by natural selection holds that many of the traits we observe in organisms are
the result of adaptation to the environment of their ancestors. That is, selection between
alternative alleles is based on reproductive success, or fitness. This is often, erroneously,
interpreted simply as individual selection — the reproductive success of the individual
organism bearing the gene. Clearly, following this interpretation, a self-destructive trait,
such as aging, can only have a negative effect on fitness. Organisms which age faster will
have fewer expected offspring than others. The benefits of aging, if any, are not benefits
directly received by the individual. The obvious fitness costs of fast aging on individuals
would cause strong direct selection pressure against it, suggesting that aging may be a
side effect of some more essential characteristic, i.e., that it is non-adaptive.
Evolutionary explanations of aging were initially studied theoretically. Weismann
(1889) was one of the first biologists to propose an evolutionary explanation for aging,
46
CHAPTER 4. EVOLUTION OF AGING
postulating that aging was an adaptive trait. The theory, and criticisms of it, are discussed in Section 4.2.1. A major criticism of Weismann’s theory was its heavy reliance on
a hypothetical group selection. This led others to put forth non-adaptive theories of aging
— those that proposed aging was a by-product of another adaptive trait or a chance product. These alternative theories include Medawar’s (1952) mutation accumulation theory,
Williams’ (1957) antagonistic pleiotropy theory and Kirkwood and Holliday’s (1979) disposable soma theory. These non-adaptive theories are described together in Section 4.2.2.
Although literature on the topic treats the adaptive/non-adaptive question as settled in
favour of non-adaptive aging (Hughes and Reynolds, 2005), there has recently accumulated compelling experimental evidence that aging is an adaptation (Mitteldorf, 2004a;
Bredesen, 2004; Skulachev, 1997). This has led to a resurgence of research into possible
adaptive benefits of aging, including my own theory, presented in Section 4.2.3.
4.2.1
Early Adaptive Theories
Weismann (1889) was one of the first biologists to publish an evolutionary explanation of
aging, holding that aging is an adaptation, i.e., selected for its own sake. In recognition
of the obvious direct cost of aging to the individual, Weismann argued that aging death
is beneficial to the species/group as it removes the worn out individuals which “. . . are
not only valueless to the species, but they are even harmful, for they take the place
of those which are sound” (Weismann, 1889). Weismann believed that over time an
individual would be unable to avoid accumulating slight injuries, causing it to become
defective and crippled, affecting its value to the species. Note that some recent authors
have misrepresented Weismann, holding that he claimed the benefit of aging was the
adaptability of the species/group to a changing environment (Goldsmith, 2004; Mitteldorf,
2006).
Williams (1957) criticizes a fallacy in Weissmann’s argument, in that it identifies the
process of wearing out of organisms with the process of mechanical wear of human artifacts.
He points out a fundamental dissimilarity between the processes. Whereas human artifacts
are static, consisting of the same material throughout its lifespan (unless someone replaces
a worn out component), organisms are open systems, continuously exchanging material
with their environments, and are quite capable of self repair (indeed, even replacement).
Williams argues that Weismann’s proposed benefit of aging hinges on the assumption
4.2. BACKGROUND
47
that the older members of the species will have deteriorated, regardless of senescence.
He contends that Weismann’s argument is circular, that is, it assumes what it claims to
explain, which is the deterioration and declining vigour with age.1
Williams also criticizes adaptive theories of aging in general. He pointed out that such
theories are inexplicable in terms of individual selection, and must rely on selection at
the group/species level — adding that individual selection theories are preferable, unless
motivated otherwise by evidence. He also claimed that a death mechanism (that is, a gene
that has the purpose to terminate life at a particular age) would be expressed extremely
rarely in natural populations — that aging is better defined as an increasing deterioration
with age (rather than a suicide trigger). The accumulation of evidence that aging is an
adaption (Mitteldorf, 2004a; Bredesen, 2004; Skulachev, 1997), including the existence
of complex death mechanisms in semelparous species2 and “aging” genes, with no other
apparent purpose, motivates a group selection explanation of aging. Also, the simulation
experiments conducted in this chapter demonstrate that (at least, for the group benefit I
hypothesize) it is irrelevant whether the aging expression is a death mechanism (suicide
gene) or a general deterioration of vigour (or increasing probability of death with age) —
in both cases, the group selection benefit drives the evolution of shorter lifespans.
Overall, Weismann’s hypothesis was heavily criticized, particularly for being unable
to translate its proposed fitness benefits of aging into individual organism fitness (i.e., its
reliance on group selection). Consequently, the more popular theories have held that aging
has an inherent negative effect on fitness and therefore must be non-adaptive.
4.2.2
Non-Adaptive Theories
There are three non-adaptive theories of aging reviewed here: mutation accumulation
(Medawar, 1952); antagonistic pleiotropy (Williams, 1957); and disposable soma (Kirkwood and Holliday, 1979). These theories are closely related in that all are based on the
declining force of natural selection over age.
Hamilton (1966), in a correction to Fisher’s (1930) reproductive value concept, argued
that the force of natural selection is a function of survivorship (the probability that an
individual will reach an age), l(x) in Figure 4.1(a), and reproductive rate, b(x) in Figure
1
This mistake is also made more recently in (Travis, 2004; Dytham and Travis, 2006) who tie their
aging mechanism to fecundity declining with age.
2
Such as salmon and octopuses, where rapid deterioration, resulting in death, is triggered by the end
of a reproductive cycle.
CHAPTER 4. EVOLUTION OF AGING
Survivorship, l(x)
Rate of Reproduction, b(x)
48
age, x
age, x
Force of Selection, s(x)
Reproduction Probability, p(x)
(a) Probability that an individual will be alive, given (b) Average rate of reproduction, jumping to a cona constant rate of death (by external causes).
stant rate after sexual maturity.
age, x
age, x
(c) Probability of reproduction — the probability of (d) The remaining expected reproduction, or force
survivorship times the rate of reproduction.
of selection — the area remaining under the reproduction probability curve.
Figure 4.1: (a) and (b) plot the trends of mortality, l(x), and reproduction, b(x), in a
population without aging. (c) plots the reproductive probability of an individual, given it
reached an age: p(x) = l(x) × b(x). (d) plots the force
R ∞ of selection acting at an age, which
is the remaining reproductive probability: s(x) = x p(z)dz.
4.1(b). Even without aging, mortality from other, external, causes (such as predators,
disease or injury) will result in survivorship deceasing with age, and the rate of reproduction, starting at zero before sexual maturity, will quickly rise to (and stay at, presuming
no internal deterioration) its peak thereafter. By multiplying survivorship with reproductive rate, l(x) × b(x), we get the probability of reproduction of an individual at an age,
p(x) in Figure 4.1(c), accounting for the chance that it may not survive to that age. The
probability of reproduction will be zero before sexual maturity, after which it will rise to
a maximum and then decrease with survivorship. The expected future reproduction, s(x)
in Figure 4.1(d), is what we’re really interested in, as this will be proportional to natural selection pressure — which acts through reproduction. Expected future reproduction
R∞
is the remaining fraction of total reproduction probability at age x: x p(z)dz. It will
be greatest at birth, and will decrease asymptotically, approaching zero, after maturity.
4.2. BACKGROUND
49
Consequently, we expect the force of selection acting on organisms to be greatest before
sexual maturity, and decline to zero thereafter, with minimal pressure at later ages.
Mutation Accumulation
Mutation accumulation, proposed by Peter Medawar (1952), holds that aging is a chance
product, the result of mutational load. The argument relies on declining selection pressure
with age (outlined above). Medawar argued that, because there is very little or no selection
pressure at later ages (see Figure 4.1(d)), deleterious alleles affecting the organism later in
life will arise by mutation faster than they can be selectively removed from the population.
Williams (1957) criticized the mutation accumulation hypothesis, pointing out that
aging not only results in the eventual death of an organism, but also a general deterioration
— which can be observed soon after maturity. An actual aging death will be extremely rare
in natural populations, and thus have little or no selective pressure, however the effects
of aging deterioration are not rare — even the slightest deterioration will be subject
to selection. For example, the deterioration of a predator’s speed and strength, won’t
necessarily result in death, however it will certainly affect how effective it is at capturing
food, and hence reproducing. Williams argued that the declining force of selection is not
enough, by itself, to explain this type of deterioration, suggesting that pleiotropic genes
must be involved.
Antagonistic Pleiotropy
Extending the mutation accumulation concept, Williams (1957) proposed the hypothesis
of antagonistic pleiotropy. Antagonistic Pleiotropy holds that aging is a side effect of an
amalgam of pleiotropic genes, which have opposite effects on fitness at different stages of
the bearer’s life-cycle. Such genes, which display benefits earlier in life, could be selected
for regardless of self-destructive costs associated with the gene later in life, which will
have, relatively, minimal selection pressure acting on it.
Neither the mutation accumulation or antagonistic pleiotropy hypotheses commit to
particular genes being responsible for aging. However both presume that genes may have
early or late life expression — that is, organisms have some inbuilt “clock” which would
trigger such timely expression. Kirkwood and Holliday (1979) point out that there is
a danger of circularity in this presumption. The obvious way an organism could track
50
CHAPTER 4. EVOLUTION OF AGING
time, after maturity, is via aging. Like the argument against Weismann’s hypothesis
above, an organism that doesn’t already age, and maintains and repairs itself, would be
physiologically the same throughout its lifespan. It will not deteriorate or necessarily have
any characteristic which will identify its age. In such a situation, it is meaningless for
genes to have early or late life expression, and calling upon such a trigger would make
the argument circular, unless something other than aging is used to indicate the passing
of time. This poses a problem for the mutation accumulation and antagonistic pleiotropy
hypotheses — creating a dependence on an explanation for another clock mechanism
(which neither Medawar or Williams address) — unless the costs of such genes are a
result of accumulation of an expression that has surpassed its benefit, as proposed by the
next theory of aging.
Disposable Soma
The disposable soma3 hypothesis, proposed by Kirkwood and Holliday (1979), is a special
case of antagonistic pleiotropy. It holds that aging is due to accumulation of errors in
the copy accuracy of the somatic cell line — which, via error feedback, leads to a lethal
“error catastrophe”. Soma cell line errors could be controlled via maintenance and repair,
however, this requires energy. When there is a limited amount of energy (as will certainly
be the case in competitive real world scenarios), and given declining selection pressure
with age, it may be more beneficial to adopt a strategy that uses energy elsewhere, such
as the maintenance and repair of the germ cell line, which is essential for the continuation
of the organism’s genes.
4.2.3
Aging for the Sake of Diversity
Mitteldorf (2004a), Bredesen (2004) and Skulachev (1997) argue that, although nonadaptive theories of aging had good support forty years ago, there has since accumulated
experimental evidence that is inconsistent with them. For example, pleiotropic theories,
which require a direct causal link between fertility and aging, are undermined by experiments that increase longevity without any apparent cost to fertility (Leroi et al., 1994).
Also, caloric restriction experiments demonstrate that animals increase life span, without
any fitness cost, in times of dietary stress (Weindruch and Walford, 1986), which raises the
3
The term “disposable soma” is based on a analogy to the manufacture of disposable goods, which
have a short expected life and are therefore made as cheaply as possible (Kirkwood and Holliday, 1979).
4.3. METHODS
51
question of why aging is not forestalled in times of plenty. This has lead to a resurgence
of research into possible adaptive benefits of aging, including Mitteldorf’s demographic
theory (2006) (which was investigated in Chapter 3), my own theory (discussed below)
and others (Travis, 2004; Dytham and Travis, 2006; Yang, 2013).
My hypothesis, like that of Weismann, postulates an adaptive explanation of aging,
that it is selected for its own fitness benefit. I suggest that aging creates a group fitness
benefit of diversity that can outweigh the individual fitness costs. Groups with shorter
individual life spans will turn over faster, introducing variation through recombination
and mutation faster, and consequently have greater diversity. This will confer benefits to
the groups with faster aging in situations where new adaptations are needed, such as in
periods of rapid climate change or co-evolutionary competitions. In co-evolution scenarios,
e.g., predator-prey and host-parasite interactions, groups with greater diversity will be less
easily exploited, creating a stronger and healthier subpopulation.
This hypothesis is related to the Red Queen hypothesis (van Valen, 1973), explaining
the evolution of sexual reproduction. On the face of it, asexual reproduction should lead
to greater fitness than sexual reproduction. Sexual reproduction is far more complex
to negotiate: in addition to requiring more complex reproductive equipment (such as,
the production of gametes), it requires organisms to locate a suitable mate and carry
out a more complex mating act. However, as van Valen emphasized, species engaged in
co-evolutionary races with predators and parasites require continued infusions of new and
diverse genetic material for selection to operate upon, just to keep up in the co-evolutionary
race (“It takes all the running you can do, to keep in the same place”, said the Red Queen,
in the novel Through the Looking-Glass (Carroll, 1871)). Van Valen’s hypothesis suggests
that the diversity benefit of sexual reproduction, in allowing the recombination of two
parents’ genes in addition to copying error mutations, outweighs even the substantial
obstacles to carrying it out successfully.
4.3
Methods
This section outlines the simulation methods used to investigate the theories of aging.
Four simulations (three to test the individual hypotheses mechanisms, and one combining
them all) were implemented, each following a common design. For the sake of brevity, in
52
CHAPTER 4. EVOLUTION OF AGING
this section, I describe all the simulations together (noting the distinctions as they arise),
and provide, in Appendix A, a detailed coverage (following the ODD protocol, Grimm
et al., 2006, 2010) for each of the simulations independently.
4.3.1
Simulation Design
In order to test the various hypotheses of aging, I developed agent based simulations for
each of the hypotheses: Mutation Accumulation, Disposable Soma,4 Diversity via Aging
and Sex and the hypotheses combined. All the simulations have a common design, as
required for the combined hypotheses simulation, with each of the individual hypothesis
simulations involving disabling the simulation components not relevant to the hypothesis.
Table 4.1 summarizes the parameters of the simulation.
Table 4.1: Default Aging Simulation Parameters.
Parameter
Default Value
Environment
world size
11 × 11 cells
max group size
100 agents
migration neighbourhood
3 × 3 cells
migration party size
2 agents
Time
statistical epoch
100 cycles
Agent
accident rate
p = 0.1
Agent Chromosome: Mutation Accumulation
death gene string length
100 bits
death gene string mutator
p = 0.001
Agent Chromosome: Disposable Soma
residual error rate
0.0005
base maintenance
0.98
maintenance modifier mutator
N(maintenance modifier, 0.01)
Agent Chromosome: Diversity
vulnerability/infection signature length 100 bits
vulnerability signature mutator
p = 0.01
infection wildcard prob
p = 0.94
gene
expiry gene mutator
N(expiry gene, expiry
)
100
expiry gene expression
N(expiry gene, expiry3 gene )
sexual reproduction rate mutator
N(sexual reproduction rate, 0.005)
4
As the disposable soma hypothesis is a sub case of antagonistic pleiotropy, I don’t bother with separate
simulations.
4.3. METHODS
53
Environment
The simulation environments consist of an 11 × 11 grid of cells, each holding an agent
population capped in size at 100 agents. This cap was enforced by disallowing birth
events. Constraining reproduction, as opposed to, say, randomly killing agents, due to
overcrowding, was selected as it provided a more realistic model of the world — the high
resource intensive activities of reproduction and offspring maturation would be the first
to be constrained in times of overcrowding (presuming no aging is implicit in the world).
Agents interact, via mating, within their cells and occasionally migrate small pioneering
parties (of 2 agents) between the cells in the 3 × 3 neighbourhood. Agents were only able
to migrate to empty cells; thus, migration is only effective in group selection scenarios,
where cell groups are also driven to extinction. Disallowing group invasion enhances the
group selection effect — reducing the altruistic to selfish group conversion rate discussed
in Section 3.2.2. I could have permitted agents to migrate to occupied cells, with low
probability, however, such simulations were less stable, occasionally resulting in global
extinction. All the environmental parameter values were selected via an informal process
of experimenting with various values and selecting ones that gave the desired effect whilst
maintaining simplicity. The world grid and group size parameters selection was driven by
a tradeoff between stability of the results and computation time. Whereas, the migration
neighbourhood and party size parameters where minimised, motivated by the underlying
theory.
Time
Time in the simulations is represented by discrete time steps (cycles). During each cycle,
all cells and agents are asynchronously updated in a random order. The simulations are
run for a fixed period, with a statistical epoch period of 100 cycles.
The choice of 100
cycles was large enough to capture a representative statistic whilst frequent enough to
show evolutionary change.
Agents
Agents occupy the cells of the worlds, and occasionally migrate between cells (see above).
Each has an age and chromosome. The agent chromosome, and its various components,
are discussed in the following sections.
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CHAPTER 4. EVOLUTION OF AGING
Every cycle agents attempt to reproduce, usually sexually without gender,5 if there is
enough room for the offspring in the cell and, in the disposable soma simulations, if they are
fertile. When reproducing sexually, a mate is randomly selected from the cell population,
and its genetic material used for creating of the offspring’s chromosome. Agents may
reproduce the cycle after they are born, i.e., they have a maturation period of one cycle.6
After reproduction, agents are tested for death conditions. There are five death triggers
across the simulations: three genetically triggered mechanisms (one for each hypothesis);
and two external mechanisms. For the two non-adaptive hypotheses, the death genetics is
essential: in the mutation accumulation simulations, agents die if there is an active death
gene for their age; and, in the disposable soma simulations, agents die if there is a soma
line failure. In the diversity simulations, agents evolve a genetic expiry age. As there are
no side effects to this gene, agents will always evolve longer life spans, unless there is some
selective benefit to aging. The two external causes of death are an accident rate, with
fixed probability, of 0.1, every cycle (which was only enabled for the simulations testing
the non-adaptive hypothesis, where it was required), and disease infection (which was only
enabled for the simulations testing the diversity hypothesis). The value for the accident
rate was picked after informal investigation of potential values, with 0.1 being large enough
to show significant deaths and small enough to not dominate. In the combined simulation
experiments, all death triggers may be active.
For the diversity simulations, there are also disease agents. Disease agents only live
for a single cycle. A disease agent (with random genetics) is spawned each cycle for each
cell, and will instantaneously7 spread through the host agent8 population resulting in the
immediate death of infected hosts (potentially, the entire cell group population).
Agent Chromosome
Discussion of the agent chromosome is broken into components (see Table 4.2). Depending
on the simulation, certain groups of components are active. Three different aging mechanisms were developed and implemented for each of the aging hypotheses, to capture the
5
Variations of the diversity simulations permit the agents to evolve a sexual/asexual reproduction
propensity.
6
This was motived by keeping the simulation parameter space as simple as possible.
7
The disease epidemic takes place in a single time step. If I modelled time continuously, or made the
time steps finer, I could model the spread of diseases differently, however, for the sake of computation and
analytical simplicity, I don’t.
8
Throughout the text, I use agent, host agent and host interchangeably, depending on the context.
4.3. METHODS
55
Table 4.2: Chromosome components particular to each hypothesis simulation.
Hypothesis
Mutation Accumulation
Disposable Soma
Diversity
Chromosome/Agent Component
Death Gene String
Germ Line Error Rate
Soma Line Error Rate
Maintenance Modifier
Fertility Flag
Genetic Expiry Age
Agent Expiry Age
Sexual Reproduction Rate
Host Vulnerability
Disease Infection
essence of each in the simplest manner possible. Death gene strings are only active in simulations testing the mutation accumulation hypothesis. Germ and soma line error rates,
maintenance and the fertility flag are only active in simulations testing the disposable
soma hypothesis. Genetic expiry age (and its expression in the agent expiry age), sexual
reproduction rate and host vulnerability/disease infection components are only active in
simulations testing the diversity hypothesis.
Death Gene String: Used to model the accumulation of death mutations, death gene
strings are age indexed vectors of death genes. Each index indicates the presence of a death
gene for a given age, and, when triggered by the agent reaching that age, it causes the
agent to immediately die. During reproduction death gene strings are uniformly crossed
over, with a chance of mutation activating (or deactivating) the genes at each locus.
This mutation rate value was determined via calibration experiments, reported in Section
4.4.1. This mechanism was selected for the Mutation Accumulation hypothesis, over a
single death gene (as used for the diversity hypothesis mechanism, see below) because it
allowed death genes to appear at any age simultaneously and thus accumulate. In the
interests of simplicity, death gene strings are limited to 100 positions (an age the agents
very infrequently reached), with the last position always active.
Germ and Soma Line Maintenance: Used to model the germ/soma maintenance
tradeoff, there are four components used in this grouping: germ and soma line error rates;
a maintenance modifier; and a flag which determines if an agent is still fertile. Errors
in the germ line may render the agent infertile, that is, the germ line is corrupted and
56
CHAPTER 4. EVOLUTION OF AGING
once infertile, the agent stays infertile; and errors in the soma line result in an increased
probability of death. Checks, for infertility and death, are determined by sampling a
uniform distribution each cycle. Both error rates are inherited from a random parent’s
germ line, which better models the real world mechanism, as opposed to resetting error
rate with new offspring. That is, mechanisms for ensuring gene copy fidelity are part of an
organism’s genetics and are themselves subject to meta evolution. Soma copy mechanisms
are discarded with the soma cells and initialised with the germ error rate template. Both
the error rates are updated each cycle, via a function of residual error rate and base
maintenance level constants and the agent’s evolvable maintenance modifier:
cn+1 = R + αcn
(4.1)
where cn is the error frequency in the nth generation, R is the residual error frequency
and α is the proportionality constant between generation errors. The α value for the
germ and soma error accumulation is determined from a base maintenance value and the
maintenance modifier, which can direct maintenance energy from one line to the other:
αgerm = base maintenance + modif ier; and αsoma = base maintenance − modif ier. The
maintenance modifier modifies a base maintenance value, and thus represents the offset
each agent places on maintenance of the germ/soma line error rates. A positive value
means an increased maintenance of the soma line and deceased maintenance of the germ
line. A negative value means the opposite. If α ≥ 1, then the error frequency will increase
— exponentially if α > 1. When α < 1 the error frequency will reach a steady state of
R
1−α .
The residual error rate and base maintenance were determined via calibration experiments,
reported in Section 4.4.2. The maintenance modifier is inherited during reproduction from
a random parent, with a chance of mutation via a normal distribution. The maintenance
modifier mutator parameter value was determined by informal investigation of potential
values, finding a value which showed stable evolutionary change.
Genetic Expiry Age: Used to model a decisive expiry death. There are two components used in this grouping: a genetic expiry age gene and the actual agent expiry age.
The expiry age gene is inherited from a random parent, with a chance of mutation via
a normal distribution. The agent’s actual expiry age, i.e., the expression of the expiry
age gene, is determined, at conception, by sampling another normal distribution, with the
4.3. METHODS
57
genetic expiry age as mean. Both the expiry age gene mutator and expression parameter values were selected after informal investigation of parameter values, finding values
which showed stable evolutionary change. When an agent’s age exceeds its expiry age it
immediately dies. As the gene has no side effects, it will always evolve longer life spans,
unless there is some selective benefit to aging. For the diversity experiments testing the
evolution of the sexual reproduction alone, the genetic expiry age is fixed.
Sexual Reproduction Rate:
Used to model sexual/asexual propensity. The sexual
reproduction rate gene is checked each reproduction attempt to determine if the agent
reproduces sexually or asexually. If reproduction is sexual, a mate is selected from the
agent’s group, and genetic material is combined, via crossover, and chance of mutation.
If reproduction is asexual, the agent’s genetic material is cloned with chance of mutation.
Checks against the sexual reproduction rate gene are performed by sampling a uniform
distribution. The sexual reproduction rate gene is inherited from a random parent, with a
chance of mutation via a normal distribution. This mutator parameter value was selected
after informal investigation of parameter values, finding a value which showed stable evolutionary change. Because successful asexual reproduction guarantees the replication of
the gene, whereas sexual reproduction only has a 50% chance, the gene will always evolve
toward asexual reproduction, unless there is some selective benefit to sexual reproduction. For the diversity experiments testing the evolution of the aging alone, the sexual
reproduction rate is fixed.
Host Vulnerability and Disease Infection:
Used to model disease virulence during
epidemics. The host agents have a vulnerability bit signature, of length 100, and disease agents have a matching infection bit signature (potentially, with wild-card values).
The signature length of 100 was selected after informal investigation of parameter values,
finding a value which was long enough to capture the specificity in the interactions between the agents, whilst minimising computation time in comparing them. Vulnerability
signatures are fixed throughout the host agent’s lifespan, and used to determine disease
infection success. They are created, during reproduction, via uniform crossover of the
parent signatures, with a chance of mutation flipping each bit. Only the epidemic aspect
of disease interaction is modelled — that is, diseases are presumed to be always present
in background amounts, but not modelled for simplicity’s sake. Occasionally diseases go
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CHAPTER 4. EVOLUTION OF AGING
epidemic, wiping out all matching hosts, testing the diversity of the population.9 Infection signatures are formed randomly during disease spawning, and have wild-card values
(generated with a probability representing the disease’s virulence). Both the vulnerability
signature mutator and infection signature wildcard probability were determined by calibration experiments, reported in Section 4.4.3. Infection success is determined by testing
if all, non wild-card, infection locus match the corresponding vulnerability locus.
4.4
Experiments
In this section I present the results of the experiments with the simulations. In Sections
4.4.1, 4.4.2 and 4.4.3, I report the results of calibration and experiments of each of the
standalone simulations (respectively: mutation accumulation, disposable soma and diversity). With the non-adaptive hypotheses experiments (i.e., mutation accumulation and
disposable soma) I measured the emergence of aging deaths, experimenting with a variety
of external (i.e., accidental) death rates. With the diversity hypothesis experiments, I examined the life history of groups, identifying the relationship between aging/sex and group
diversity, and thus the ability of the host populations with fixed/evolving aging and sexual
reproduction rates to resist exploitation by a disease population with a variety of disease
virulences. In Section 4.4.4, I report the results of combining the standalone simulations
into a single simulation, to determine the consequences of activating various combinations
of the mutation accumulation, antagonistic pleiotropy and diversity components. Unless
otherwise reported, all results were statistically significant, with p < 0.001.
4.4.1
Mutation Accumulation
This section contains experiments with the standalone mutation accumulation simulation.
First, I report on calibration experiments of the simulation mutation rate, before reporting
on the evolution of aging for a variety of external, accidental, death rates. As there are
multiple genes evolving in these simulations, one for each age index up to 100, I usually
just report on the occurrence of the first chronological appearance of a death gene (which,
since death genes are decisive, will be that agent’s expiry age).
9
This means, strictly speaking, the simulation is not a co-evolution simulation. However the dynamics
of host/parasite epidemics are retained.
4.4. EXPERIMENTS
59
Mutation Rate Calibration
0.2
Mutation Rate: 0.0001
Mutation Rate: 0.0010
Mutation Rate: 0.0020
100
Mutation Death Frequency
Age of First Death Mutation
120
80
60
40
20
Mutation Rate: 0.0001
Mutation Rate: 0.0010
Mutation Rate: 0.0020
0.15
0.1
0.05
0
0
0
20
40
60
80
100
120
140
160
180
200
0
20
40
Epochs (100 cycles)
80
100
120
140
160
180
200
Epochs (100 cycles)
(a) Average age of first death mutation.
1
(b) Proportion of deaths attributable to death
mutation.
Mutation Rate: 0.0001
Mutation Rate: 0.0010
Mutation Rate: 0.0020
0.8
Survivourship
60
0.6
0.4
0.2
0
0
10
20
30
40
50
60
Agent Age
(c) Agent survivorship.
Figure 4.2: The effect of varying the mutation rate parameter across values [0.0001, 0.0010,
0.0020] on the (a) average age of first chronological death mutation, (b) proportion of
deaths attributable to death mutation, and (c) survivorship curves. In all simulations the
accident rate was fixed at 0.1 per cycle. As expected, higher mutation rates resulted in
an accumulation of earlier deaths genes and death by mutation.
Figure 4.2 shows the results of trying different mutation rates, with the accident rate
fixed at a probability of 0.1 per cycle. Each parameter set had one simulation run,10
over 200 epochs (20,000 cycles). All mutation strings were initially empty, except for the
fixed death mutation at 100 cycles. Over time the death mutations stabilized, with higher
mutation rates resulting in death mutations appearing at earlier ages, as can be seen in
Figure 4.2(a), which plots the average age of first chronological death mutation over the
simulation run. As the non-mutation deaths (i.e., accidental deaths) were fixed across
the simulations, earlier death mutation ages resulted in a greater proportion of deaths
attributable to those death mutations, as can be seen in Figure 4.2(b). A slight difference
can be seen in the survivorship curves of Figure 4.2(c), as the agents in runs with greater
mutation rates experienced an increased rate of death in later ages. Survivorship curves
10
As there is no migration between cells, this is equivalent to 121 individual runs.
60
CHAPTER 4. EVOLUTION OF AGING
were approximated by a frequency distribution across age of all agents at the conclusion
of the run.
Varying Accident Rate
Age of First Death Mutation
120
Accident Rate: 0.05
Accident Rate: 0.10
Accident Rate: 0.20
100
80
60
40
20
0
0
20
40
60
80
100
120
140
160
180
200
Epochs (100 cycles)
Figure 4.3: The effect of varying the accident rate parameter across values [0.05, 0.10, 0.20]
on the age of first death mutation. Labels are sorted by final position. In all simulations
the mutation rate was fixed at 0.001. As expected, higher accident rates resulted in an
accumulation of earlier deaths genes.
Figure 4.3 shows the results of varying the accident rate, with mutation rate fixed at a
probability of 0.001. Each parameter set had one simulation run, over 200 epochs (20,000
cycles). The mutation accumulation hypothesis predicts that higher accident rates will
result in earlier ages of death mutations, as selective pressure at later ages is reduced. The
plots in Figure 4.3, of the average age of first death mutation for a variety of accident
rates, show that this is indeed the case.
4.4.2
Disposable Soma
This section presents experiments with the standalone disposable soma simulation. First I
calibrated the base maintenance and residual error rate parameters and found the resulting
germ and soma error rates across agent age for a variety of maintenance modifier values. I
4.4. EXPERIMENTS
61
then experimented with evolution of the maintenance modifier, and resulting soma failure
deaths, for a variety of external, accidental, death rates.
Base Maintenance and Residual Error Rate Calibration
To calibrate the parameters of the simulation, I explored the effects of varied base maintenance [0.98, 0.99] and residual error rate [0.0002, 0.0005] parameter constants and fixed
maintenance modifiers on the germ and soma error rates across agent age. The maintenance modifier values for each parameter set were dependent on the base maintenance
value, such that the soma error rate11 (1) became steady, (2) increased linearly, and (3)
increased exponentially — thus, [0.00, -0.01, -0.02] for base maintenance of 0.99 and [0.00,
-0.02, -0.04] for base maintenance of 0.98. Accidental deaths were disabled, each parameter set was run with a single simulation12 for 1,000 cycles (long enough to stabilize),
and the final germ and soma error rates plotted against agent age (see Figure 4.4). The
plots behave as expected from Equation 4.1. Greater residual error rates (R) and base
maintenance values resulted in greater germ error rates, and, as initial soma error rates
are copied from the germ error rate, greater initial soma error rates. For the soma error
rates, greater residual error rates (R) and base maintenance values resulted in faster error
accumulation (best seen in the linear error accumulation experiments).
Figure 4.5 plots the survivorship curves for the base maintenance 0.98, residual error
rate 0.0005 runs. There are two interesting things to note from the plots in Figure 4.5.
Firstly, as expected, maintenance modifiers with greater negative magnitude resulted in
greater maintenance directed to the germ line, at the cost of the soma line, and consequently, such agents had shorter life spans. Secondly, because soma error rates were copied
from the parent’s germ line, the runs with lower germ line maintenance resulted in higher
initial soma line error rates, reflected in the initial slope of the survivorship curves.
Evolving Maintenance Modifier
Next, the maintenance modifier was permitted to evolve. Preliminary investigation led to
the selection of fixed values for the base maintenance and residual error rate at 0.98 and
0.0005 respectively. Each parameter set was run with a single simulation13 for 200 epochs
11
Non-steady germ error rates were unstable as the entire population would quickly become infertile.
As there is no migration between cells, this is equivalent to 121 individual runs.
13
As there is no migration between cells, this is equivalent to 121 individual runs.
12
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CHAPTER 4. EVOLUTION OF AGING
Maintenance Mod: +0.00
Maintenance Mod: -0.01
Maintenance Mod: -0.02
0.14
Maintenance Mod: +0.00
Maintenance Mod: -0.01
Maintenance Mod: -0.02
0.14
0.12
Soma Error Rate
Germ Error Rate
0.12
0.1
0.08
0.06
0.04
0.02
0.1
0.08
0.06
0.04
0.02
0
0
0
20
40
60
80
100
120
140
0
20
40
60
Age
80
100
120
140
Age
(a) Germ Error Rate: Base Maintenance: 0.99, (b) Soma Error Rate: Base Maintenance: 0.99,
R: 0.0002
R: 0.0002
Maintenance Mod: +0.00
Maintenance Mod: -0.01
Maintenance Mod: -0.02
0.14
Maintenance Mod: +0.00
Maintenance Mod: -0.01
Maintenance Mod: -0.02
0.14
0.12
Soma Error Rate
Germ Error Rate
0.12
0.1
0.08
0.06
0.04
0.02
0.1
0.08
0.06
0.04
0.02
0
0
0
20
40
60
80
100
120
140
0
20
40
60
Age
80
100
120
140
Age
(c) Germ Error Rate: Base Maintenance: 0.99, (d) Soma Error Rate: Base Maintenance: 0.99,
R: 0.0005
R: 0.0005
Maintenance Mod: +0.00
Maintenance Mod: -0.02
Maintenance Mod: -0.04
0.14
Maintenance Mod: +0.00
Maintenance Mod: -0.02
Maintenance Mod: -0.04
0.14
0.12
Soma Error Rate
Germ Error Rate
0.12
0.1
0.08
0.06
0.04
0.02
0.1
0.08
0.06
0.04
0.02
0
0
0
20
40
60
80
100
120
140
0
20
40
60
Age
80
100
120
140
Age
(e) Germ Error Rate: Base Maintenance: 0.98, (f) Soma Error Rate: Base Maintenance: 0.98,
R: 0.0002
R: 0.0002
Maintenance Mod: +0.00
Maintenance Mod: -0.02
Maintenance Mod: -0.04
0.14
Maintenance Mod: +0.00
Maintenance Mod: -0.02
Maintenance Mod: -0.04
0.14
0.12
Soma Error Rate
Germ Error Rate
0.12
0.1
0.08
0.06
0.04
0.02
0.1
0.08
0.06
0.04
0.02
0
0
0
20
40
60
80
Age
100
120
140
0
20
40
60
80
100
120
140
Age
(g) Germ Error Rate: Base Maintenance: 0.98, (h) Soma Error Rate: Base Maintenance: 0.98,
R: 0.0005
R: 0.0005
Figure 4.4: Results of calibration of base maintenance [0.98, 0.99] and residual error
rate (R) [0.0002, 0.0005] for a variety of fixed maintenance modifier values. Maintenance
modifier values were selected to cause the soma error rate to become stable (red points),
increase linearly (green points), and increase exponentially (blue points). In all cases the
lower maintenance modifier results in lower germ error rate and greater slope, over time,
in the soma error rate.
4.4. EXPERIMENTS
63
1
Maintenance Mod: +0.00
Maintenance Mod: -0.02
Maintenance Mod: -0.04
Survivorship
0.8
0.6
0.4
0.2
0
0
50
100
150
200
Agent Age
Figure 4.5: The agent survivorship for the parameter set: base maintenance 0.98 and
residual error rate 0.0005 (see Figures 4.4(g) & 4.4(h)).
(20,000 cycles). Figure 4.6(a) plots the evolution of the average maintenance modifier for
a variety of accident rates and Figure 4.6(b) plots the proportion of deaths attributable
to soma error deaths. The disposable soma hypothesis predicts that higher accident rates
will result in greater diversion of maintenance to the germ line, as selective pressure at
later ages is reduced and soma errors are less likely to be realized. The experimental
results in Figure 4.6 confirm this prediction. Note that, even when there are no accident
deaths, the maintenance modifier still evolved in slight favour of germ line maintenance as
an optimal strategy. Even though the accident rate was disabled, there was still a small
chance of death each cycle from soma death, which could never be totally eliminated, and
hence a decreasing agent survivorship with age. This places enough selection pressure on
the early ages to drive the maintenance modifier slightly in favour of reducing the germ
error rate.
4.4.3
Diversity
This section contains experiments with the standalone diversity simulation. Calibration
of the simulation proceeded in a number of steps. First, I examined the within group
dynamics, disabling the disease component of the simulation, and fixing aging and sex to
64
CHAPTER 4. EVOLUTION OF AGING
0.01
Accident Rate: 0.0
Accident Rate: 0.1
Accident Rate: 0.2
Maintenance Modifier
0
-0.01
-0.02
-0.03
-0.04
-0.05
-0.06
0
20
40
60
80
100
120
140
160
180
200
180
200
Epochs (100 cycles)
(a) Evolution of maintenance modifier over time.
Soma Death Frequency
0.25
Accident Rate: 0.1
Accident Rate: 0.2
0.2
0.15
0.1
0.05
0
0
20
40
60
80
100
120
140
160
Epochs (100 cycles)
(b) Proportion of deaths attributable to soma error death. When accident rate is 0.0 (i.e., disabled) all
deaths were caused by soma error, thus it is omitted.
Figure 4.6: The effect of varying the accident rate parameter across values [0.0, 0.1, 0.2]
on (a) average maintenance modifier, and (b) proportion of deaths attributable to soma
error. Greater accident rates resulted in lower maintenance modifier values (i.e., greater
maintenance diversion to germ line, at the expense of soma line maintenance).
measure the resulting group diversity. Next, the disease component was enabled and the
4.4. EXPERIMENTS
65
life history of groups was examined. Finally, aging and sex were permitted to evolve in
simulations with a variety of disease virulences.
Group Diversity
In the first set of calibration experiments, the disease component was disabled, and the
effects of fixed genetic expiry age, sexual reproduction rate and vulnerability signature
mutation on the group diversity were explored (see Figures 4.7 & 4.8). Figure 4.7 shows
how the mean group diversity changes with the group age, for a variety of genetic expiry
age and sexual reproduction rate values. Figure 4.8 shows the resultant mean and standard deviation of group diversities, after they settled, with varying genetic expiry age,
sexual reproduction rate and vulnerability signature mutation rates.14 I used a measure
of group diversity obtained by splitting the host members vulnerability signatures into 4
bit sub-sequence components, counting the number of unique components, and dividing
by the total number of possible components (i.e., 24 ∗
100
4
= 400). Detailed discussion of
this diversity measure can be found in Chapter 5. There was one simulation run15 per parameter set over 2,000 cycles (long enough for the simulations to stabilize). The first half
of the run was used for initialization. During the second half of the run, each statistical
epoch (10 cycles), group diversity was measured for all groups and the average reported.
Figures 4.7 & 4.8 show that groups with lower genetic expiry ages (greater population
turnover), greater sexual reproduction rates (more sexual reproduction) and greater vulnerability signature mutation rates had, on average, a higher group diversity and achieved
it faster. This result was expected as groups with a greater turnover rate will have less
variance in number of offspring per agent and sexual reproduction enabled vulnerability
signature recombination increasing the production of new components.
14
15
All results were significant, with p < 0.001.
As there is no migration between cells, this is equivalent to 121 individual runs.
66
CHAPTER 4. EVOLUTION OF AGING
1
GEA: 5
GEA: 20
GEA: 50
Group Diversity
0.8
0.6
0.4
0.2
0
0
200
400
600
800
1000
Group Age
(a) Change in group diversity over group age resulting from various fixed genetic expiry age (GEA).
1
SRR: 0.0
SRR: 0.5
SRR: 1.0
Group Diversity
0.8
0.6
0.4
0.2
0
0
200
400
600
800
1000
Group Age
(b) Change in group diversity over group age resulting from various fixed sexual reproduction rate (SRR).
Figure 4.7: Changes in the mean group diversity over group age resulting from (a) varied
(non-evolving) genetic expiry ages (with sexual reproduction rate fixed at 1) and (b) varied
(non-evolving) sexual reproductive rates (with genetic expiry age fixed at 20 cycle). For
all plots, group diversity increases over time and plateaus — with lower GEA and higher
SRR resulting in faster diversification and greater diversity plateau.
4.4. EXPERIMENTS
67
1
GEA: 5
GEA: 20
GEA: 50
Group Diversity
0.8
0.6
0.4
0.2
0
0.015
0.01
0.005
Vulnerability Signature Mutator
(a) Group diversity resulting from various fixed genetic expiry age (GEA) and vulnerability signature
mutator values.
1
SRR: 1.0
SRR: 0.5
SRR: 0.0
Group Diversity
0.8
0.6
0.4
0.2
0
0.015
0.01
0.005
Vulnerability Signature Mutator
(b) Group diversity resulting from various fixed sexual reproduction rate (SRR) and vulnerability signature
mutator values.
Figure 4.8: The group diversity (mean and standard deviation) resulting from varied
vulnerability signature mutation rates and (a) varied (non-evolving) genetic expiry ages
(with sexual reproduction rate fixed at 1) and (b) varied (non-evolving) sexual reproductive
rates (with genetic expiry age fixed at 20 cycle). For all vulnerability signature mutation
rates, the group diversity decreases with later genetic expiry ages (longer life span) and
lower sexual reproduction rates (more asexual reproduction).
68
CHAPTER 4. EVOLUTION OF AGING
Group Life History
In this section I conduct experiments treating groups as analogous with individuals —
groups are born, via migration from existing groups, and die, via extinction caused by
disease epidemics, thus groups have a life history like individuals. The disease component
was enabled and simulation experiments were conducted with a variety of fixed disease
virulences (controlled by the infection wild-card probability parameter), genetic expiry
ages and sexual reproduction rates, to measure the average group life history. Group age
was measured as the number of cycles since it was pioneered. One simulation was run
per parameter set, for 200 epochs (20,000 cycles). The first half of the run was used for
initialization, and statistics were collected during the second half.
1200
1000
800
600
GEA 5
GEA 20
GEA 50
0.8
Survivorship
Mean Group Age
1
GEA: 5
GEA: 20
GEA: 50
1400
0.6
0.4
400
0.2
200
0
0
0.93
0.94
0.95
0
500
Disease Virulence
1000
1500
2000
Patch Age
(a) Mean group age resulting from fixed genetic (b) Patch survivorship for a variety of genetic
expiry ages (GEA) and disease virulences.
expiry ages (GEA) — disease virulence fixed at
0.94 (the middle bars in Figure 4.9(a)).
1200
1000
800
600
SRR 1.0
SRR 0.5
SRR 0.0
0.8
Survivorship
Mean Group Age
1
SRR: 1.0
SRR 0.5
SRR 0.0
1400
0.6
0.4
400
0.2
200
0
0
0.93
0.94
Disease Virulence
0.95
0
500
1000
1500
2000
Patch Age
(c) Mean group age resulting from fixed sex- (d) Patch survivorship for a variety of sexual
ual reproduction rates (SRR) and disease vir- reproduction rates (SRR) — disease virulence
ulences.
fixed at 0.94 (the middle bars in Figure 4.9(c)).
Figure 4.9: The mean group age resulting from varied fixed genetic expiry ages (GEA),
sexual reproduction rates (SRR) and disease virulence (infection wild-card probability).
Figures 4.9(a) & 4.9(c) plot the mean group age for varied genetic expiry age (with sexual
reproduction rate fixed at 1) and sexual reproduction rate (with genetic expiry age fixed
at 20 cycles) respectively. Figures 4.9(b) & 4.9(d) plot patch survivorship for the varied
genetic expiry ages and sexual reproduction rates respectively, with disease virulence fixed
at 0.94. Greater genetic expiry ages, lower sexual reproduction rates and greater disease
virulences resulted in a greater rate of group turnover.
4.4. EXPERIMENTS
69
Figure 4.9 shows the group life history results of varied genetic expiry age (GEA) [5,
20, 50], sexual reproduction rate (SRR) [0, 0.5, 1] and disease virulence [0.93, 0.94, 0.95].
Figures 4.9(a) & 4.9(c) plot the mean group age for varied genetic expiry age (with sexual
reproduction rate fixed at 1) and varied sexual reproduction rate (with genetic expiry
age fixed at 20 cycles), respectively. Figures 4.9(b) & 4.9(d) plot patch survivorship for
the runs with disease virulence fixed at 0.94. Obviously, greater disease virulences caused
greater group extinction rates. It can also be seen from the plots that groups with lower
expiry ages and greater sexual reproduction rates (resulting in greater diversity) did, on
average, last (survive) longer, and thus had greater opportunity to pioneer (reproduce)
new groups.
Evolution of Aging and Sex
Finally, I conducted experiments permitting the genetic expiry age gene and sexual reproductive rate to evolve, for a variety of disease virulences (infection wild-card probabilities).
10 simulations were run per parameter set, for 200 epochs (20,000 cycles) and the results
were averaged.
First, the genetic expiry age was permitted to evolve, with the sexual reproduction
rate fixed at 1 (all sexual reproduction). Figure 4.10(a) shows the evolution of genetic
expiry age over time, and Figure 4.10(b) shows the proportion of deaths attributable to
genetic expiry. As expected, greater disease virulences resulted in the evolution of lower
genetic expiry ages — the increased turnover rate of groups increased the group selection
pressure on aging for the sake of diversity, counter balancing the individual selection
pressure against it.
Next, the sexual reproductive rate was permitted to evolve, with the genetic expiry
age fixed at 20 cycles. Figure 4.11 shows the evolution of sexual reproduction rate over
time. Again, as expected, greater disease virulences resulted in the evolution of greater
sexual reproduction rates, as group selection pressure for diversity was increased.
70
CHAPTER 4. EVOLUTION OF AGING
60
Disease Virulence 0.93
Disease Virulence 0.94
Disease Virulence 0.95
Genetic Expiry Age
50
40
30
20
10
0
0
20
40
60
80
100
120
140
160
180
200
180
200
Epochs (100 cycles)
(a) Evolution of genetic expiry age over time.
Expiry Death Frequency
1
Disease Virulence 0.93
Disease Virulence 0.94
Disease Virulence 0.95
0.8
0.6
0.4
0.2
0
0
20
40
60
80
100
120
140
160
Epochs (100 cycles)
(b) Proportion of deaths attributable to genetic expiry death.
Figure 4.10: The effects of varying disease virulence (infection wild-card probability) on
the (a) evolution of genetic expiry age and (b) proportion of deaths attributable to genetic
expiry over time. Greater disease virulences resulted in the evolution of lower expiry ages.
4.4. EXPERIMENTS
1
Disease Virulence 0.93
Disease Virulence 0.94
Disease Virulence 0.95
0.8
Sex Rate
71
0.6
0.4
0.2
0
0
20
40
60
80
100
120
140
160
180
200
Epochs (100 cycles)
Figure 4.11: The effects of varying disease virulence (infection wild-card probability) on
the average sexual reproduction rate over time. Greater disease virulences resulted in the
evolution of higher sexual reproduction rates.
72
CHAPTER 4. EVOLUTION OF AGING
4.4.4
Mixed Aging
In this section I combine and investigate all the hypotheses of aging in a single simulation.
There are three different aging mechanisms I investigate:
• mutation accumulation (MA);
• disposable soma (DS); and
• diversity (DIV).
Each mechanism is coupled with a set of simulation components which could be
switched “on” or “off” for any given simulation (see Table 4.2). The DIV mechanism
requires the existence of a disease population, which will exploit genetic relatedness. The
DS and MA mechanisms require different chromosome components to be enabled, namely,
germ/soma line error rates or death gene string respectively. In all simulations, the genetic
expiry age gene was active. It was expected that if any given component set was disabled
then the associated mechanism would not be active, either because the genetics were not
present, with the non-adaptive mechanisms, or the benefit was absent, with the adaptive
mechanisms. In order to do a complete comparative study of these mechanisms, various simulations were conducted with all the different combinations of these components
enabled (see Table 4.3). Each experiment configuration had 20 runs, over 1,000 epochs
(100,000 cycles), and the results were averaged.
Table 4.3: Simulation Experiment Settings
Experiment
NULL
Diversity (DIV)
Disposable
Soma (DS)
Mutation
Accumulation (MA)
DIV & DS
DIV & MA
DS & MA
DIV & DS & MA
Diseases
7
3
7
Germ/Soma
Error Rates
7
7
3
Death Gene
String
7
7
7
7
7
3
3
3
7
3
3
7
3
3
7
3
3
3
Figure 4.12(a) plots the evolution of the genetic expiry age for each of the experiments
in Table 4.3. Figure 4.12(b) plots the corresponding proportion of deaths attributable to
4.4. EXPERIMENTS
NULL
DS
MA
MA/DS
DIV
DIV/DS
DIV/MA
DIV/MA/DS
140
120
Genetic Expiry Age
73
100
80
60
40
20
0
0
200
400
600
800
1000
Epochs (100 cycles)
(a) Evolution of genetic expiry age over time.
Expiry Death Frequency
0.2
DIV
DIV/DS
DIV/MA/DS
DIV/MA
MA/DS
MA
DS
NULL
0.15
0.1
0.05
0
0
200
400
600
800
1000
Epochs (100 cycles)
(b) Proportion of deaths attributable to genetic expiry death.
Figure 4.12: Plots over experiments outlined in Table 4.3. Labels are sorted by final
position. (a) plots the evolution of the genetic expiry age gene which is present in all
simulations. All the runs show an increase in the genetic expiry age over time, with the
increase less pronounced in the DIV simulations, with the disease component enabled,
where aging has an adaptive benefit. (b) plots the proportion of deaths caused by the
genetic expiry age gene. When diseases were disabled, death frequency, due to the genetic
expiry age, drops below 2%.
74
CHAPTER 4. EVOLUTION OF AGING
70
70
DIV
DIV/DS
DIV
DIV/MA
60
Genetic Expiry Age
Genetic Expiry Age
60
50
40
30
50
40
30
20
20
0
100
200
300
400
500
600
700
800
900 1000
0
100
200
300
Epochs (100 cycles)
(a) DIV and DIV/DS experiment runs.
70
70
DIV
DIV/MA/DS
600
700
800
900 1000
DIV/DS
DIV/MA
60
Genetic Expiry Age
Genetic Expiry Age
500
(b) DIV and DIV/MA experiment runs.
60
50
40
30
50
40
30
20
20
0
200
400
600
800
1000
0
100
200
Epochs (100 cycles)
300
400
500
600
700
800
900 1000
Epochs (100 cycles)
(c) DIV and DIV/MA/DS experiment runs.
(d) DIV/DS and DIV/MA experiment runs.
70
70
DIV/DS
DIV/MA/DS
DIV/MA
DIV/MA/DS
60
Genetic Expiry Age
60
Genetic Expiry Age
400
Epochs (100 cycles)
50
40
30
50
40
30
20
20
0
200
400
600
800
1000
Epochs (100 cycles)
(e) DIV/DS and DIV/MA/DS experiment runs.
0
200
400
600
800
1000
Epochs (100 cycles)
(f) DIV/MA and DIV/MA/DS experiment runs.
Figure 4.13: Comparative analysis of the 95% confidence intervals of the evolved genetic
expiry age in the mixed aging runs with the DIV component enabled (see Figure 4.12(a)).
In all cases, this is an overlap of the confidence intervals, indicating there is little difference
between the resultant aging rates.
the expiry gene. It was expected that the genetic expiry gene would only have selective
value in the simulations with the disease population enabled (DIV). As can be seen in
Figure 4.12(a), this was the case. In the remaining simulations, with diseases disabled
(No DIV), longer life spans are selected for16 — as individual selection reigns supreme,
and there is no possible adaptive benefit to aging. Figure 4.12(b) shows that in these runs,
16
Up until the point where selective pressure is negligible (i.e., no agents are triggering the gene) at
which point passive drift will drive the aging gene to greater values — with a fixed lower bound and no
upper bound, the mean genetic expiry age would be expected to increase over time even in the absence of
selection (McShea, 1996).
4.5. CONCLUSIONS
75
the deaths caused by genetic expiry age dropped to background noise, below 2%. Figure
4.13 shows a comparative analysis of the 95% confidence intervals of evolved genetic expiry
age between the DIV, DIV/DS, DIV/MA, DIV/MA/DS experiment runs, i.e., where the
gene is selected for. As can be seen from these plots, there is little difference between the
resultant aging rates, the selection of which is predominantly driven by adaptive benefit
to aging.
Figures 4.14(a) & 4.14(b) are included to show the evolution of the non-adaptive
mechanisms. Figure 4.14(a) plots the evolution of the first mutation accumulation death
gene and Figure 4.14(b) plots the evolution of the disposable soma maintenance modifier
gene. Both the MA and DS hypotheses rely on a decreasing probability of reproduction
with age, thus I expected a synergy effect when the multiple aging mechanisms were
enabled (i.e. DIV or MA or DS). From the figures, this appears to be the case. For
example, the age of first death mutation and the maintenance modifier gene, in Figures
4.14(a) and 4.14(b) respectively, are selected towards greater aging, i.e., lower age of
first death mutation and maintenance modifier values, when additional components were
enabled. When the disease component (DIV) was enabled, I expected to see additional
effects on the MA & DS components, as per my hypothesis, when the DIV component is
enabled, shorter life span has an adaptive benefit. This effect can be seen in both Figures
4.14(a) and 4.14(b). It is also noteworthy that there was very little difference between the
DIV & MA & DS and DIV & MA runs in Figure 4.14(a) and the DIV & MA & DS and
DIV & DS runs in Figure 4.14(b), where the DIV component diminished the synergy effect
between the DS and MA component genes. Figure 4.15 shows a comparative analysis of the
95% confidence intervals of evolved maintenance modifier between the MS/DS, DIV/DS,
DIV/MA/DS experiment runs. As can be seen from these plots, there is little difference
between the resultant maintenance modifiers in the two experiments with DIV enabled
(DIV/DS and DIV/MA/DS).
4.5
Conclusions
Using my simulations, I have demonstrated the logical possibility of all the aging hypotheses explored. The host/parasite simulations, implementing my diversity hypothesis,
demonstrate conditions that are favourable to adaptive aging and sexual reproduction.
76
CHAPTER 4. EVOLUTION OF AGING
Age of First Death Mutation
30
25
20
15
10
MA
MA/DS
DIV/MA
DIV/MA/DS
5
0
0
200
400
600
800
1000
Epochs (100 cycles)
(a) Average age of first death mutation.
Maintenance Modifier
0
DS
MA/DS
DIV/MA/DS
DIV/DS
-0.05
-0.1
-0.15
-0.2
0
200
400
600
800
1000
Epochs (100 cycles)
(b) Evolution of maintenance modifier over time.
Figure 4.14: (a) The age index of the first appearance of a death mutation in the death
gene string. (b) The disposable soma maintenance modifier gene value.
They also demonstrate that the actual aging genetics — be it a suicide gene, expressed
extremely rarely, or the general deterioration of the organism after maturity — doesn’t
matter; the adaptive benefit of aging drives organisms to moderate life span. The results show that groups with shorter life spans (and sexual reproduction) do indeed have a
4.5. CONCLUSIONS
77
0
MA/DS
DIV/MA/DS
Maintenance Modifier
Maintenance Modifier
0
-0.05
-0.1
-0.15
-0.2
MA/DS
DIV/DS
-0.05
-0.1
-0.15
-0.2
0
200
400
600
800
1000
0
100
200
Epochs (100 cycles)
400
500
600
700
800
900 1000
Epochs (100 cycles)
(a) MA/DS and DIV/MA/DS experiment runs.
(b) MA/DS and DIV/DS experiment runs.
0
Maintenance Modifier
300
DIV/MA/DS
DIV/DS
-0.05
-0.1
-0.15
-0.2
0
200
400
600
800
1000
Epochs (100 cycles)
(c) DIV/MA/DS and DIV/DS experiment runs.
Figure 4.15: Comparative analysis of the 95% confidence intervals of the evolved maintenance modifier in the mixed aging runs (see Figure 4.14(a)).
greater diversity, and that this diversity has a fundamental effect in the interactions between host agents and the disease agents which parasitise them. Host population groups
with greater diversity are less likely to experience a disease epidemic, resulting in groups
with longer life spans. The group selection mechanism meant that groups with greater
survival rates were more likely to produce successful migrant parties to found new groups.
In this environment, the evolution of aging genes and sexual reproduction occurred readily.
78
CHAPTER 4. EVOLUTION OF AGING
Chapter 5
Testing the Punctuated
Equilibrium Hypothesis
In this chapter I investigate the punctuated equilibrium hypothesis of Eldredge and Gould
(1972) in an individual based species simulation. I use evolutionary activity statistics,
based on the work of Bedau and Packard (1991), to measure the rates of evolutionary
change during speciation events and the importance of adaption versus genetic drift on
speciation. The results of my investigation support the punctuated equilibrium hypothesis
and show that genetic drift in bottleneck populations is an important contributing factor
in the evolution of species.
79
80
CHAPTER 5. TESTING THE PUNCTUATED EQUILIBRIUM HYPOTHESIS
5.1
Introduction
In this chapter I develop simulations, statistics and experiments, which allow me to test
the punctuated equilibrium hypothesis (Eldredge and Gould, 1972; Gould and Eldredge,
1993; Gould, 2007). The punctuated equilibrium hypothesis states that the progress of
evolution occurs in alternating periods of rapid change (punctuation) and relative stasis
(equilibrium). The theory has implications for how we understand evolution, especially
the concepts of evolutionary selective units and the importance of adaptation in explaining species characteristics. To test the hypothesis, I develop a simulation of individual
agents forming species, based on mate compatibility, and adapt the evolutionary activity
statistics of Bedau and Packard (1991) and Bedau et al. (1998), originally conceived to
test for open ended evolution. I develop a measure of new evolutionary activity and a set
of adaptively neutral shadow simulations. Using these statistics and shadow simulations,
I test the changes in the rates of evolution during speciation events in the simulation and
the importance of adaptation in the resulting species identity. The results support the
punctuated equilibrium hypothesis, demonstrating that higher levels of new evolutionary
activity are indeed correlated with speciation events and, more specifically, population bottlenecks. A population bottleneck occurs when a reproductively isolated sub-population
significantly shrinks in size over a short period. I also find evidence that new evolutionary
activity is caused largely by genetic drift and doesn’t necessarily have to be adaptive.
In Section 5.2, I provide background on the concept of species, punctuated equilibrium and the original evolutionary activity statistics on which the methods are based. In
Section 5.3, I describe the simulations used in the chapter and discuss how I adapted the
evolutionary activity statistics for my purposes. In Section 5.4, I discuss my experiments,
including simulation calibration, and give the results of the application of the evolutionary
activity statistics.
This chapter draws from work originally published in Woodberry et al. (2009), with
modified simulations and experiments.
5.2. BACKGROUND
5.2
81
Background
This section provides background on the punctuated equilibrium hypothesis, including discussion of the concepts of species and speciation. It also reviews the evolutionary activity
statistics developed by Bedau et al. (1998), which I later adapt for my own purposes.
5.2.1
Species & Speciation
The concept of “species” remains central to biology, evolutionary and otherwise, and to
a host of related fields. However, the concept, like the concept of life, resists efforts
to capture it in a precise definition (Hey, 2006). There seems to be an ineradicable
vagueness to it, exhibited in application to, for example, asexual species, ring species
and hybrids. The most generally accepted definition of species, which I follow here, is as
a “reproductively isolated sub-population” (Mayr, 1963) — that is, a group of actually
or potentially interbreeding individuals that are reproductively isolated from other such
groups.
Speciation typically occurs when a species splits into reproductively isolated subgroups, thus forming multiple descendent species. Species may form via the mechanisms
of cladogenesis and anagenesis. Cladogenesis refers to the formation of a species, which
is distinctly different from the original, via a branching event, usually involving a small
sub-population of the parent species. Anagenesis refers to a more gradual process, where
the entire species transforms, replacing the ancestor species. There are four modes of
speciation, based on degree of geographic isolation: allopatric speciation occurs when a
species is split into two geographically isolated populations; peripatric speciation, a subtype of allopatric speciation, occurs when one sub-population is much smaller than the
other; parapatric speciation differs from allopatric speciation in that the population is geographically spread, so that parts of the population will not come into contact with each
other (such as a ring species), but there is no physical barrier; and sympatric speciation
occurs when geography is not a factor. Cladogenesis is usually associated with peripatric
speciation, as the population bottleneck caters for a founder effect.1 Geographic isolation
is important as it is the primary cause of restricted gene flow. Gene flow will tend to
make populations similar to each other and will act against speciation. However, when
1
The founder effect occurs when a loss of genetic variation in the bottleneck population results in a
distinctly different population (Mayr, 1942).
82
CHAPTER 5. TESTING THE PUNCTUATED EQUILIBRIUM HYPOTHESIS
gene flow is restricted between populations, the influences of natural selection (i.e., adaptation) and genetic drift will cause the populations to diverge, potentially to the extent
of reproductive isolation. The relative importance of adaptation and genetic drift in the
divergence driving speciation is a point of debate, which we address.
5.2.2
Punctuated Equilibrium
The punctuated equilibrium hypothesis (Eldredge and Gould, 1972) proposes that sexually
reproducing species experience little evolutionary change (stasis or equilibria) over most of
their history and that the greater part of evolutionary change occurs in punctuations, during relatively rare cladogenetic speciation events. Eldredge and Gould label the extreme
contrasting position “phyletic gradualism” (see Figure 5.1), the view that evolution can
only occur gradually and, indeed, can only occur at a constant, continuous rate, asserting:
The history of life is more adequately represented by a picture of “punctuated
equilibria” than by the notion of phyletic gradualism. The history of evolution
is not one of stately unfolding, but a story of homeostatic equilibria, disturbed
only “rarely” (i.e., rather often in the fullness of time) by rapid and episodic
events of speciation. (Eldredge and Gould, 1972, p. 84)
Figure 5.1: Caricature schematic of phyletic gradualism, contrasted with punctuated equilibrium.
5.2. BACKGROUND
83
While acknowledging that the fossil record cannot definitively settle the question of
whether most evolutionary change occurs in punctuation events,2 they assert that Punctuated Equilibrium theory better matches the paleontological record. Whereas the fossil
record is limited in its ability to support or undermine Punctuated Equilibrium, my artificial life simulations can provide clear tests of whether or not Punctuated Equilibrium is
actually occurring within different simulations.
On a wider front, Punctuated Equilibrium theory has been applied to the hierarchical
theory of evolution (i.e., species selection) and the debate on the importance of adaptation
for explaining evolutionary phenomena (Stanley, 1975; Gould, 1980). Species selection is
an extension of the group selection concept — the idea that species can be units of selection.
Gould claims that punctuation events are associated with population bottlenecks and
genetic drift rather than natural selection pressure. In effect, he is saying that rapid shifts
in genetics and speciation events are not specifically adaptive, rather, they are random.
He proposes a pluralism in which adaptation plays only a part. He positions himself
against “Ultra Darwinists” who insist that all evolutionary phenomena are the result of
adaptation by natural selection. However, what he feels about the relative importance of
adaptation is unclear. On one hand he states, in clear terms, that he does “not deny either
the existence and central importance of adaptation, or the production of adaptation by
natural selection”(Gould, 1997). On the other hand he often argues that the consequences
of Punctuated Equilibrium theory herald the death of the modern synthesis, stating, for
example, “. . . if Mayr’s characterization of the synthetic theory is accurate, then that
theory, as a general proposition, is effectively dead, despite its persistence as textbook
orthodoxy” (Gould, 1980).3 Views such as this have led many to consider Gould an antiadaptationist.
My simulations, and use of Bedau’s evolutionary activity statistics, demonstrate evidence for a “pluralist” argument — in that both adaptive and non-adaptive forces work
to shape the species.
2
For example, Dawkins (1986) argues that apparent gaps in the fossil record can be explained by
migratory events without the need to call upon evolutionary punctuations.
3
The Mayr characterization referred to is: “The proponents of the synthetic theory maintain that
all evolution is due to the accumulation of small genetic changes, guided by natural selection, and that
trans-specific evolution is nothing but an extrapolation and magnification of the events that take place
within populations and species.” (Mayr, 1963).
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CHAPTER 5. TESTING THE PUNCTUATED EQUILIBRIUM HYPOTHESIS
5.2.3
Evolutionary Activity Statistics
In work on open-ended evolution and long-term evolutionary dynamics, Bedau and Packard
(1991) introduce statistics for quantifying evolutionary activity (cf. also Bedau et al., 1998;
Channon, 2006). Evolutionary activity is defined by them as “the rate at which useful genetic innovations are absorbed into the population”. They specifically refer to established
genetic innovations as adaptive, however for my purposes I make no such presumption,
allowing for genetic innovations also to be fixed by chance. An evolving system is represented by a set of “components” which changes over time. Exactly what components
consist of is left open by the authors; they may be alleles or genetically dependent phenotypic traits. These components may be introduced into the system via mutation and may
persist, either by chance or because they’re adaptive.
Given a discrete design space of possible components, we can index them and associate
a counter with each one.4 Component activity is recorded by:
∆i (t) =



1
if component i is in use at t


0
otherwise
(5.1)
Note the qualification “is in use at t”; this is meant to exclude the counting of, for example,
recessive alleles which are not actually in use.5 Now, ai (t) will measure the history of the
ith component’s activity level up to time t:
ai (t) =
X
∆i (k)
(5.2)
k≤t
I now define some of Bedau’s activity statistics based on these activity counters.
System Diversity:
The system diversity, D(t), is the total number of components
present in the system at time t:
D(t) = #{i : ai (t) > 0}
4
(5.3)
Throughout this section I use the notation as presented by Bedau et al. (1998).
In the example provided by Bedau et al. (1998), component activity is updated by the mere presence
of the component, however they say “various activity incrementation functions can be used depending on
the nature of the components and the purposes at hand” (Bedau et al., 1998, pp. 229).
5
5.3. METHODS
85
Component Activity Distribution:
The component activity distribution, C(t, a),
measures the frequency of components with exactly activity level a at t:
C(t, a) =
X
δ(a − ai (t))
(5.4)
i
where δ(a − ai (t)) is the Dirac delta function, equal to one if a = ai (t) and zero otherwise.
New Evolutionary Activity:
Rates of change in new evolutionary activity are what I
am primarily interested in here. New evolutionary activity, Anew (t), measures the average
activity of new components up to time t:
Anew (t) =
1
D(t)
X
ai (t)
(5.5)
i,a0 ≤ai (t)≥a1
where [a0 , a1 ] is selected so as to exclude components which have too little activity (i.e.,
which have not established themselves in the genome) and also to exclude components
which have too much activity (i.e., which are fixed in the population and not new). I shall
discuss exactly how I adapt Bedau’s statistics for my purposes in Section 5.3.2.
5.3
Methods
This section outlines the simulation methods used. First I developed a simulation demonstrating speciation (Section 5.3.1), for testing the punctuated equilibrium effect. Next I
adapted the evolutionary activity statistics, introduced in Section 5.2.3, to monitor the
rates of evolutionary change in the simulation during, and between, speciation events (Section 5.3.2). For the purpose of distinguishing between adaptive and non-adaptive change,
I developed and trialled three neutral shadow simulation worlds (Section 5.3.3). These
simulations are briefly described here, with detailed coverage (following the ODD protocol,
Grimm et al., 2006, 2010) in Appendix B.
5.3.1
Simulation Design
In order to test the implications of the punctuated equilibrium hypothesis, I developed an
agent based simulation of the formation of species. Species identity is determined by mate
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CHAPTER 5. TESTING THE PUNCTUATED EQUILIBRIUM HYPOTHESIS
compatibility signatures and a mate compatibility threshold, which represents, on an individual level, the mate compatibility of agents and, on a population level, the reproductive
isolation of sub-groups. Table 5.1 summarizes the parameters of the simulation.
Table 5.1: Default Foreground Simulation Parameters.
Parameter
Default Value
Environment
world size
30 × 30 cells
agent interaction neighbourhood 3 × 3 cells
new food
2 units
Time
speciation epoch
20 cycles
statistical epoch
5 speciation epochs
Agent
initial health
10 units
mate health
20 units
expiry age
20 cycles
move rate
p = 0.0
Agent Chromosome
mate signature mutator
p = 0.002
mate compatibility threshold
95 bits (i.e., 95%)
Agent Species
species extinction rate
p = 0.01
Environment
The simulation environment consists of a grid of cells, each holding an agent population
and food. Agents are able to interact (move,6 eat and reproduce) within their 3 × 3 cell
neighbourhood. Each cycle, new food is generated for all cells and is used to sustain the
agent population. The amount of new food has the effect of limiting the population size
to an average per cell (one agent per food unit). The usage of food to limit population
size, as opposed to placing a hard limit per cell (such as that used in the aging simulations
of Chapter 4), meant that population density needn’t be evenly distributed and populations, such as species groups, could cluster. All the environmental parameter values were
selected via an informal process of experimenting with various values and selecting ones
that gave the desired effect whilst maintaining simplicity. The world grid and new food
6
Calibration experiments were conducted with agent movement, however, the final simulation disabled
movement (i.e., set probability of movement at 0.0, see Table 5.1) making agents like plants.
5.3. METHODS
87
parameters selection was driven by a tradeoff between stability of the results and computation time. The agent interaction neighbourhood parameter was minimised, motivated
by the underlying theory.
Time
Time in the simulation is represented by discrete time steps (cycles). During each cycle, all
cells and agents are activated for updating in a random order. The simulation is run for a
fixed period with two epoch time units. Speciation epochs are the periods between species
identifications (discussed below). Statistical epochs are the periods during which statistics
are collected. The speciation epoch length of 20 was selected as it was the shortest period
of a guaranteed entire population turnover (agent expiry age was fixed at 20 cycles, see
below). The statistical epoch length of 4 speciation epochs (i.e., 100 cycles) was selected
to be large enough to capture a representative statistic whilst frequent enough to show
evolutionary change.
Agents
Agents occupy the cells of the world and move between cells at a fixed rate. The movement rate parameter was selected via calibration experiments, reported in Section 5.4.1,
and fixed at 0 (i.e., no movement). Each has an age, health, chromosome and species
membership. Age is incremented every cycle and the agent dies once its age exceeds an
expiry age. A fixed expiry age of 20 cycles was selected after informal investigation of
various values, finding a value that gave agents ample opportunity to reproduce, whilst
small enough to ensure quick population turnover. Agents are born with an initial health,
formed via parental investments. Health is increased by eating from the cell food and
decreased by a metabolic overhead and parental investments. When the agent’s health
exceeds a mating health threshold it attempts to reproduce (if it can find a compatible
mate, discussed below). The selection of the metabolism, initial and mate health parameter values was done via informal investigation — metabolism was fixed at one health
unit and the initial and mate health values were selected in relation to this: initial health
parameter selection driven, predominantly, by minimising crowding death rate: and mate
health by average period to maturity. The agent dies if its health ever falls below zero.
The agent chromosome and species membership are discussed below.
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CHAPTER 5. TESTING THE PUNCTUATED EQUILIBRIUM HYPOTHESIS
Agent Chromosome
Agent chromosomes have two components, a mate bit signature and junk bit signature
(both of length 100). Mate signatures are used to determine reproductive compatibility, by comparing the Hamming distance between two agents with a mate compatibility
threshold (by default 95%). Junk signatures are non-functional genetic material, included
for measuring non-adaptive genetic activity. Both signatures are inherited via uniform
crossover of the parents signatures, with a probability of mutation flipping each bit. Both
the signature mutator and mate compatibility threshold parameter values were determined
via calibration experiments, reported in Section 5.4.1.
Agent Species
Species are groups of reproductively isolated agents, determined by mate compatibility.
The species membership changes as agents are born and die and is reassessed (via regrouping of mate signatures) over speciation epoch periods. To ensure a continuous turnover
of species, there is a small chance, each cycle, that an entire species will be made extinct,
over and above the simultaneous death of individuals. The species kill rate was fixed
at a probability of 0.01 per cycle, selected after informal investigation, finding a value
which optimised species turnover whilst providing enough time for species to form and,
potentially, reproduce.
5.3.2
Adapting the Evolutionary Activity Statistics
In order to measure the rates of evolutionary change in the simulation, I adapted the
evolutionary activity statistics introduced in Section 5.2.3.
Evolutionary Components
The first problem was to identify the components I should be counting. Since we are
interested in rates of genetic change in diverging species and sub-species, it was natural to
focus on the mating signatures.7,8 Since those signatures had no functional substructure
7
It should be noted that there are no recessive alleles. I could consider only the components responsible
for a successful mate action, but that would be meaningless in the neutral shadow run.
8
Note, the species membership labels (discussed above) would not serve as evolutionary components.
The aim of the research is to measure the rate of genetic change. The mate signatures are the evolving
components, so they, or sub-components of them, are the natural choice for measuring genetic change.
The species labels would not serve this purpose.
5.3. METHODS
89
(they only mattered for computing Hamming distances), any fixed substrings could be
used to identify components. However, taking either too long or too short a substring of
those signatures would cause problems. Substrings that were too long would lead to very
few components showing enough activity to be counted as fixed; Substrings that were too
short would lead to components that were present too often. After considering substring
lengths easily divided into 100 (i.e., 1, 2, 4, 5), I found that bit strings of length four,
with sixteen distinct combinations (for a total of 400 possible components, i.e.,
100
4
× 24 ),
exhibited enough distinction between fixed and occasional mutational activity to give
meaningful results.
For example, consider the example mate signature of 20 bits:
(1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0)
This signature would be broken into 5 components, each comprising a list of (position,
4 bit subsequence):
(1, 1, 0, 1, 0) (2, 0, 0, 1, 1) (3, 1, 1, 0, 0) (4, 0, 1, 0, 0) (5, 0, 0, 1, 0)
Activity Counters and Increment Function
Activity counters are kept for each species and for the world. Each activity counter
is a list of activity window elements, representing the activity during the most recent
activity window cycles. I use an activity window as the simulation has bounded diversity
and, in particular, a fairly small space of possible components (consequently, the maximum
diversity of 400 components would be quickly reached and become a constant divisor in
Equation 5.5) I found that an activity window length of 100 worked well to balance the
tradeoff between identifying activity as it occurs (shortness) and storing past activity
(longness).
The activity counters are incremented whenever two agents successfully mate. This
event was selected as it is the only time when the components are used. The two parent’s
mate signatures are broken into evolutionary components, as defined above. For each
component, the component activity counter is found and the first element of the counter
list, representing activity at that cycle, is incremented.
Each cycle, the activity counters are updated by moving the window, i.e., adding an
element to the beginning of each counter list and removing the last element. Whenever a
speciation event occurs the activity counters are copied to the descendant species.
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CHAPTER 5. TESTING THE PUNCTUATED EQUILIBRIUM HYPOTHESIS
To compensate for the differences in species size, when determining the activity level of
a component, all activities in the activity window are counted and the per capita activity
value is reported:
ai(per
cap) (t)
ai (t)
=P
i ai (t)
(5.6)
that is, the activity of the component i at time t (ai (t)), divided by the sum of all activity,
across the species.
Component Activity Distribution
Two different component activity distributions are reported: one for the entire population
and the other for the species, when relevant. The species activity distribution is calculated by determining component activities for each species, independently, and merging
the results into a single average distribution. Every statistical epoch the activity distributions are updated, incrementing the relevant value for every component with a particular
activity, thus they accumulate over time. When reporting, the activity distributions are
normalized so that they can sit, meaningfully, on the same plot.
Evolutionary Activity Threshold
Because I implement the activity counters with a moving window, I needed to modify
the methods of counting new evolutionary activity. Mid-range activities represent both
components that are becoming more and less prevalent in the system. By using a range
of activities, as suggested by Equation 5.5 I would be counting both these types of components. Instead I pick an activity level threshold, athreshold , beyond which I count components as fixed.9 We are interested in how this fixed component set changes over time.
As components are added to the set, i.e., they pass over the activity threshold, I flag them
as new evolutionary activity and ignore components which pass the other way.
To find a value for athreshold I use Bedau et al’s method (Bedau and Packard, 1991;
Bedau et al., 1998) of using a “neutral shadow” simulation. That is, I keep a shadow
population corresponding to the normal population, where selective pressure on genetic
change is eliminated (discussed in detail below). Births, deaths and speciations in the
9
As suggested by Russell Standish in feedback on earlier versions of the work
5.3. METHODS
91
foreground simulation trigger equivalent events in the shadow simulation, but using randomly selected agents. The shadow simulation is used to identify background mutation
activity. By plotting the component activity distributions for the foreground and shadow
simulations I selected, as the activity threshold, the point where the two distributions
cross. At this point the activity count is equally likely to be caused by selective fixation
and background mutational noise.
We trialled three variant shadow worlds, which are discussed next.
5.3.3
Neutral Shadow Simulation Design
To identify an activity threshold, I compliment the foreground simulation with a neutral
shadow world. The shadow worlds have no spatial aspect and birth, death and speciation
events involve randomly selected agents. All events in the shadow world are triggered by
corresponding events in the foreground simulation run. Using randomly selected agents
for these events ensures that the presence and frequency of evolutionary components can
not be attributed to their adaptive significance. By filtering out adaptive activity, the
simulation can be used to determine what activity is caused by genetic drift. The three
variant shadow worlds are defined here:
Shadow World 1: This is the simplest interpretation of the adaptively-neutral shadow
concept. Any mate or death events in the foreground simulation triggers an equivalent event in the shadow, using randomly selected agents from the entire population.
There is no spatial or species aspects to the simulation.
Shadow World 2: This shadow simulation adds species. All shadow agents have a
species membership and mating requires agents to be members of the same species
(compatibility of mate signatures is not a factor). Each foreground species has an
equivalent shadow species and events in the foreground simulation species triggers
events within the corresponding shadow species.
Shadow World 3: This shadow simulation is built upon shadow world 2, adding an
adoption queue (discussed below), thereby removing any kin associations from the
shadow species.
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CHAPTER 5. TESTING THE PUNCTUATED EQUILIBRIUM HYPOTHESIS
Shadow Agents
Shadow agents are much like the agents of the foreground world, expect they only have a
chromosome and, in shadows worlds 2 & 3, species membership. The shadow agents have
no location, age or health. The shadow agent chromosome only has a single component,
a junk bit signature. This signature is inherited and mutated in the same way as the
foreground agent mate signature.
Shadow Agent Species
Shadow species are much like the foreground species, except they are not based on mate
compatibility. Instead the member agents are randomly selected from the ancestor species
as it is created. In the shadow worlds with species (i.e., shadow worlds 2 & 3) a speciation
event in the foreground world triggers an equivalent speciation event in the shadow world.
The species shadowing the species in the foreground is randomly split into sub-groups
corresponding, in size, to the splits in the foreground species and these sub-groups are
used to form new shadow species.
Adoption Queue
An adoption queue (of length one) is utilized to remove any possible kin associations
between species members in shadow world 3. As new shadow agents are created they are
placed at the end of the queue and, in their stead, an agent is selected from the front
of the queue. As there is no spatial aspect to the shadow simulation worlds, this only
affects the species membership and means that species will be as diverse as the entire
world population. Detailed discussion of the adoption queue method of removing kin
associations can be found in Chapter 3.
5.4
Experiments
In this section I present the results of the experiments with the simulations. First, in
Section 5.4.1, I investigate the calibration of the foreground simulation world. Next, in
Section 5.4.2, I present and discuss preliminary results with the foreground simulation,
before conducting experiments with the evolutionary activity statistics. Investigations
with the evolutionary statistics are covered over three sections: Section 5.4.3 covers the
5.4. EXPERIMENTS
93
component activity distributions of the foreground and shadow worlds; this leads to the
selection of an activity threshold for fixed activity, in Section 5.4.4; and lastly we give the
new activity results in Section 5.4.5.
5.4.1
Calibration
Before applying the activity statistics and shadow simulations I experimented with the
foreground simulation parameters to verify that species groups were indeed forming. I
report on the calibration of the movement rate, mate compatibility threshold and signature mutation rate parameters, which I identified as having the greatest effect on speciation
rate and species size. The parameters of new food, grid size, expiry age, mate health threshold,
initial health and mate signature length were chosen after informal investigations identified
reasonable values. All results in this section were generated from a single simulation run,
per parameter set, for 10,000 cycles, long enough for the statistics to stabilise.
Movement Rate Movement rate affects the mixing of species and competition between
them. At higher movement rates we expect species to be larger in size as more mixing
will occur and smaller offspring species will be outcompeted by larger species. The results
given in Table 5.2 confirm that as movement rates increase, species tend to larger sizes and
are less numerous. The default parameter value was selected at zero, making the agents
like plants — which don’t move after initial birth dispersal.
Table 5.2: Effect of movement rate parameter on the number of species units and median
species size (all other parameters kept as default).
Movement Rate
0.000
0.025
0.050
0.075
0.100
#Species
µ = 16.88, σ = 3.10
µ = 15.73, σ = 2.69
µ = 13.05, σ = 2.18
µ = 9.69, σ = 2.10
µ = 2.35, σ = 2.47
Species Size
µ = 49.62, σ = 46.83
µ = 52.60, σ = 47.49
µ = 62.88, σ = 53.45
µ = 84.44, σ = 70.29
µ = 366.54, σ = 375.03
Mate Compatibility Threshold The mate compatibility threshold affects the diversity a species can obtain before speciation will occur. At higher mate compatibility thresholds we expect species to be smaller in size, as speciation events will occur faster. The
results given in Table 5.3 confirm that as the mate compatibility thresholds increase,
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CHAPTER 5. TESTING THE PUNCTUATED EQUILIBRIUM HYPOTHESIS
species tend to smaller sizes and are more numerous. The default parameter value was
selected at 95 bits.
Table 5.3: Effect of the mate compatibility threshold parameter on the number of species
units and median species size (all other parameters kept as default).
Mate Compatibility
Threshold
70 bits
80 bits
90 bits
95 bits
97 bits
#Species
µ = 2.90, σ = 1.59
µ = 6.10, σ = 1.03
µ = 11.88, σ = 1.99
µ = 16.88, σ = 3.10
µ = 23.43, σ = 2.85
Species Size
µ = 305.47,
µ = 143.49,
µ = 72.23,
µ = 49.62,
µ = 34.83,
σ
σ
σ
σ
σ
=
=
=
=
=
294.88
120.21
56.02
46.83
30.10
Signature Mutation Rate The signature mutation rate affects the rate at which
species diversify and thus speciate. At higher signature mutation rates we expect species
to be smaller in size, as species diversify faster, and thus speciate faster. The results given
in Table 5.4 confirm that as the signature mutation rates increase, species tend to smaller
sizes and are more numerous. The default parameter value was selected at 0.002.
Table 5.4: Effect of the signature mutation rate parameter on the number of species units
and median species size (all other parameters kept as default).
Signature Mutation Rate
0.0005
0.0010
0.0015
0.0020
0.0030
5.4.2
#Species
µ = 3.35, σ = 1.84
µ = 10.51, σ = 1.99
µ = 15.24, σ = 2.63
µ = 16.88, σ = 3.10
µ = 25.94, σ = 3.33
Species Size
µ = 264.59, σ = 263.41
µ = 81.52, σ = 61.59
µ = 55.49, σ = 46.76
µ = 49.62, σ = 46.83
µ = 31.61, σ = 25.41
Species Tree
Figure 5.2 shows a representation of the species tree, generated using the Graphviz tool
(Ellson et al., 2003), for a portion of the simulation run. The vertical axis represents time,
with ancestors above descendants. The horizontal axis represents an abstraction of the
design space.10 Each of the nodes represents a species at a particular speciation epoch —
with area of the node proportional to the size of the species. The nodes are connected by
10
We’d need 100 dimensions — one dimension for each element of the mate signature bit string — to
represent it properly!
5.4. EXPERIMENTS
95
Figure 5.2: A species tree. The vertical axis represents time, progressing downward, and
the vertical axis is an abstraction of design space. Each of the nodes represents a species
at a speciation epoch, with area proportional to the species size. Edges between species
represents ancestry, with red (non-bolded) edges indicating greater genetic transitions (i.e.,
speciation). The circled speciation events are represented in greater detail in Figure 5.3.
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CHAPTER 5. TESTING THE PUNCTUATED EQUILIBRIUM HYPOTHESIS
edges representing ancestry. In order to create a more meaningful representation of the
mate signature space, I developed a similarity measure between descendants and ancestors.
A frequency distribution over each locus in the species member’s mate signatures was
created (giving a vector of 100 probabilities) and the average Bhattacharyya distance was
computed for each locus in the mate signatures. This resulted in a similarity measure
between [0:1], with 1 being an identical species. A threshold value of 0.99 was adopted,
a value great enough to ensure that no split would result in more than one descendent
with similarity greater than the threshold. Edges to descendants with similarity greater
than the threshold were colored black (red, if below the threshold), bolded and weighted
(making the edge straighter).11 Note that edges below the threshold often do have a small
amount of dissimilarity, which, if compared over greater epoch periods would accumulate.
Figure 5.3: Close up of speciation events — a cladogenetic speciation event closely followed
by a anagenetic speciation event.
Of particular interest are the points where lineages split. Splits occasionally result
in descendants which are all dissimilar to the parent species, however, more often, one
descendant will be similar to the parent species, indicating a continuation of a species
with “offspring” species being created. Figure 5.3 shows, in greater detail, the speciation
11
However, due to the automated graphing algorithm, this effect was not stable
5.4. EXPERIMENTS
97
events circled in Figure 5.2, where the morphology axis represents the similarity measure.
The lineage first splits via a cladogenetic speciation event, where the leftmost lineage is a
new distinct offspring species, and shortly after splits via another speciation event, where
all descendent species are dissimilar to the ancestor. It’s during such cladogenetic splits
that we expect a punctuated equilibrium effect. Next we applied the evolutionary activity
statistics, described in Section 5.3.2, to measure this effect.
5.4.3
Component Activity Distributions
To determine the new activity threshold value, athreshold (see Section 5.3.2), I found the
component activity distributions (CADs) for each of the worlds. I considered distributions
of both the entire world population and averaged across species, for the foreground and
corresponding shadow worlds. In each of these plots, the x axis represents activity levels
and the y axis represents relative frequency of the components with an activity level. The
plots have one or two peaks: one at low activity levels and, depending on the simulation,
one at high activity levels. Components with low activity are, usually, mutations which
have little adaptive value that are quickly removed by natural selection. Components with
high activity are fixed in the species. Components with activity levels between these peaks
are transitional, i.e., they may be lucky mutations becoming more prevalent, to the point
of fixation, or in the process of being phased out.
Figure 5.4 shows the CADs for the entire world population (red) and average species
(green) in the foreground simulation world. Figure 5.4(a) shows the overall distributions
and Figures 5.4(b), 5.4(c) & 5.4(d) show the same plots, with the axis ranges selected to
focus on low activity, high species activity and high world activity respectively. A peak
in high activity can be clearly seen in the average species CAD plot from Figure 5.4(c).
This indicates that there is some amount of fixed components in each species over the
epoch period. The world CAD plot has no clear peak at high activity levels. This is due
to the fact that, although there are fixed components within the species, across the entire
population species rarely share the same fixed components (otherwise, they would have
failed to speciate).
Next I considered the CADs for neutral signatures in the shadow worlds and junk
signatures in the foreground world. Figure 5.5 shows the CADs for the 5.5(a) foreground
junk signatures, 5.5(b) shadow world 1 (no species units), 5.5(c) shadow world 2 (with
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CHAPTER 5. TESTING THE PUNCTUATED EQUILIBRIUM HYPOTHESIS
0.9
Frequency of Activity Counts
Frequency of Activity Counts
0.9
World
Species
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
World
Species
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
0
0.002
0.004
Activity
(a) Activity distributions for the foreground simulation
0.03
0.008
0.01
0.005
World
Species
0.025
(b) Focus on low activities levels
Frequency of Activity Counts
Frequency of Activity Counts
0.006
Activity
0.02
0.015
0.01
0.005
0
World
Species
0.004
0.003
0.002
0.001
0
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
0
0.005
Activity
(c) Focus on species high activities levels
0.01
0.015
0.02
0.025
0.03
0.035
0.04
Activity
(d) Focus on world high activities levels
Figure 5.4: Component activity distributions of the normal simulation run — entire world
population activity in red and average species activity in green. Figure 5.4(a) shows
the overall distributions and Figures 5.4(b), 5.4(c) & 5.4(d) show the same plots, with
the axis ranges selected to focus on low activity, high species activity and high world
activity respectively. A peak can be seen at high activity levels for the species activity
distribution, indicating an amount of components fixed throughout the epoch. The world
activity distribution has only one peak, at low activity levels.
species units) and 5.5(d) shadow world 3 (with species units and adoption queue). The
world population CADs for the neutral components show no clear high activity peak —
which was expected after the foreground results. It is interesting to see the high activity
peaks in the average species activities of the junk signatures and shadow world 2 (with
species units). Both these plots indicate fixed components in the species which cannot
readily be attributed to adaptation. Instead, these components become fixed, randomly,
during population bottle neck events. Shadow world 3 (with species units and adoption
queue) shows no such peak, as mixing, caused by the use of the adoption queue, eliminates
all possibility of selection pressure.
Figure 5.6 shows these CADs grouped by the number of peaks. Of particular interest
is the relative heights of the peaks in high activity of the plots.12 The gaps between
12
Differences between the peaks were significant, with p < 0.001.
5.4. EXPERIMENTS
99
0.03
World
Species
0.025
Frequency of Activity Counts
Frequency of Activity Counts
0.03
0.02
0.015
0.01
0.005
0
World
0.025
0.02
0.015
0.01
0.005
0
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
0
0.005
0.01
0.015
Activity
0.02
0.025
0.03
0.035
0.04
Activity
(a) Activity distributions for the junk signature in (b) Activity distributions for shadow world 1 (no
the foreground simulation
species units). Only entire world activities plotted.
0.03
World
Species
0.025
Frequency of Activity Counts
Frequency of Activity Counts
0.03
0.02
0.015
0.01
0.005
0
World
Species
0.025
0.02
0.015
0.01
0.005
0
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
Activity
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
Activity
(c) Activity distributions for shadow world 2 (with (d) Activity distributions for shadow world 3 (with
species units)
species units and adoption queue)
Figure 5.5: Component Activity distributions for the neutral junk signature in the foreground world and mate signatures in the shadow worlds. Peaks can be seen at high activity
levels for foreground junk signatures, and shadow 2 (with species units) mate signatures,
indicating an amount of fixed component activity in these simulations.
the foreground mate signature CAD and the foreground junk and shadow world 2 CAD
appear to illustrate the effect of adaptation. That is to say, the adaptive nature of the
mate signatures causes an increase in the frequency of fixed components. The differences
between the junk and shadow world 2 CADs can be explained by the level of association
each has to the adaptive mate signature. The junk signatures are coupled with the adaptive
mate signatures in the agent chromosome and thus are influenced — albeit, as a byproduct, piggybacking on the mate signatures — more than the shadow world signatures.
5.4.4
Evolution Activity Threshold
Given the component activity distributions, I next select an activity level, athreshold , as
the threshold for recording activity. I follow Bedau et al’s methods (Bedau and Packard,
1991; Bedau et al., 1998) by using the point where the foreground CAD and neutral shadow
CAD intersect. Figure 5.7 shows the foreground mate signature species CAD plotted with
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CHAPTER 5. TESTING THE PUNCTUATED EQUILIBRIUM HYPOTHESIS
Frequency of Activity Counts
0.03
Foreground Species
Foreground Species Junk
Shadow2 Species
0.025
0.02
0.015
0.01
0.005
0
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
Activity
Figure 5.6: The component activity distributions grouped according to number of peaks
in activity frequency, for comparison purposes. The Figure shows the relative height of
the peaks for foreground species mate signatures and junk signatures and shadow world
2 (with species units). Both the foreground CADs show a, relatively, higher peak in the
high activity levels, with foreground mate signatures slightly higher than the foreground
junk signatures.
the shadow world 3 (with species units and adoption queue) species CAD. The crossover
point varies only slightly between runs (≈ ± 0.005) and is approximately 0.02.
5.4.5
New Evolutionary Activity
New evolutionary activity is measured by determining changes to the fixed component
set, i.e., components with an activity level greater than athreshold . Any addition to the
fixed component set over time is counted as new evolutionary activity. Here I report the
results using 0.02 as the athreshold . Figure 5.8 plots the history of a randomly selected lineage13 , tracking the size of the species (in red), along with speciation events (represented
by green points) and new activity (in blue) in the mate signature (Figure 5.8(a)), junk
signature (Figure 5.8(b)) and associated shadow species in shadow world 2 (Figure 5.8(c)).
Speciation events occur frequently, as a species will produce many — mostly unsuccessful
— offspring species. Of interest is when the selected lineage itself goes through a population bottle neck — creating the conditions for a punctuation event. The punctuated
13
Similar results were observed in the other linages, as shown in Figure 5.9.
5.4. EXPERIMENTS
101
Frequency of Activity Counts
0.03
Foreground Species
Shadow3 Species
0.025
0.02
0.015
0.01
0.005
0
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
Activity
Figure 5.7: The foreground mate signature species CAD plotted with the shadow world
3 (with species units and adoption queue) species CAD. The crossover point of the two
CADs is approximately 0.02.
Size
Speciation
Activity
6
5
100
4
3
50
150
2
300
4
3
50
2
1
0
400
350
0
200
250
300
Speciation Epoch
350
0
400
Speciation Epoch
(a) Foreground mate signature
(b) Foreground junk signature
200
Size
Speciation
Activity
150
Species Size
6
8
7
6
5
100
4
3
50
New Activity
250
7
5
100
1
0
200
8
New Activity
200
7
Species Size
150
Species Size
8
Size
Speciation
Activity
New Activity
200
2
1
0
200
250
300
350
0
400
Speciation Epoch
(c) Shadow 2 mate signature
Figure 5.8: The history of a randomly selected lineage, showing changes in size (in red),
speciation events (green points) and new activity (in blue) in the (a) mate signatures, (b)
junk signatures and (c) shadow 2 (with species units) signatures.
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CHAPTER 5. TESTING THE PUNCTUATED EQUILIBRIUM HYPOTHESIS
equilibrium hypothesis predicts that it is during these events that most new evolutionary
activity will occur. Due to the moving activity window, we expect this new activity to be
revealed in the proceeding steps. This correlation can be detected in lineage history plots
10
12
8
10
6
8
New Activity
New Activity
— especially for the mate signature activity.
4
2
0
6
4
2
-2
0
0
50
100
150
200
250
300
350
400
0
50
100
Species Size
150
200
250
300
350
400
Species Size
(a) Foreground mate signature
(b) Foreground junk signature
14
12
New Activity
10
8
6
4
2
0
-2
0
50
100
150
200
250
300
350
400
Species Size
(c) Shadow 2 mate signature
Figure 5.9: Plots of the species size versus new activity in the (a) foreground mate signature, (b) junk signature and (c) shadow 2 (with species units) signature. A negative
correlation between species size and new activity was found in all cases.
To test for a correlation between species size and new activity (5 steps, or speciation
epochs, later) the plots in Figure 5.9 were created across all species linages. The punctuated equilibrium hypothesis predicts that new evolutionary activity will accompany small
species sizes and indeed this is the correlation (with significances p < 10−21 ) found in all
plots.
An alternative explanation for the observed pattern would be that, with a larger
species, there will be a wider variety of components in existence, hence less chance of
new ones appearing. However, new evolutionary activity is defined as changes to the fixed
component set, and although larger species have a wider variety of components in existence (i.e., with > 0 activity), they’ll tend to have a smaller set of fixed components as
they are capable of maintaining greater diversity. Either way, the impact of this difference
5.5. CONCLUSIONS
103
in the fixed component set size isn’t significant — most species will have between 24-25
fixed components — and wouldn’t have much effect on the results, but is enough to rule
out the alternative explanation.
Table 5.5: Comparison of the mean new activity in lineages with and without speciation
events. New activity is greater during speciation for all cases.
Component
Mate Signature
Junk Signature
Shadow 2 signature
Speciation New
Activity (Mean)
0.58
0.79
0.63
No Speciation New
Activity (Mean)
0.23
0.35
0.58
Difference of Means
Sig. Test
p = 0.0
p = 0.0
p = 0.022
To test for a correlation between new activity during speciation events versus nonspeciation events, the new activity was categorized into the two groups and the mean new
activity was found (see Table 5.5). The punctuated equilibrium hypothesis predicts that
new evolutionary activity will tend to accompany speciation events (i.e., offshoot species),
which is what was found.
5.5
Conclusions
Using my evolutionary activity statistics, I have demonstrated an association between
speciations and evolutionary activity in a species simulation. It’s clear that something
like the punctuation events posited by Eldredge and Gould (1972) are occurring, with
periods of rapid change and speciation alternating with periods of relative stasis. To an
extent this result might be expected, as the activity statistics were based on the mating
traits and new species will need new mating signatures. However, anagenetic gradualism
is certainly conceivable and it could result in species-level divergence accompanied by only
modest levels of evolutionary activity. Further, it was not obvious that there should be
similar effects in the junk and shadow signatures and relatively little change in activities
when no speciation occurs.
The association between punctuations and speciation in the neutral signatures demonstrate that an adaptive account cannot fully explain the resulting species — that is, something akin to Gould’s pluralism is justified. The species identity (i.e., fixed component
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CHAPTER 5. TESTING THE PUNCTUATED EQUILIBRIUM HYPOTHESIS
set) is formed, substantially, through a random process during speciation. Although adaptation has an important role, especially during stasis periods, in my simulations, at least,
it is clear that it doesn’t play an exclusive role during speciation events.
Chapter 6
Conclusions and Future Work
This thesis presents an experimental approach to using simulated artificial worlds to study
open questions in evolutionary biology. To demonstrate the value of this approach, it
has explored — and in the process, contributed to — research in evolutionary biology
on phenomena of: group and kin selection; the evolution of biologically altruistic traits,
and especially, the evolution of aging; and punctuated equilibrium. In this chapter, I
summarize the contributions of the thesis to the fields of ALife and evolutionary biology.
I also outline potential directions for further research.
6.1
6.1.1
Contributions
Using Artificial Life Simulations to Study Evolutionary Biology
A main contribution of this thesis is its substantial additions to the growing pool of
ALife simulation models of biological phenomena and techniques. Simulation worlds and
experiments were developed and applied throughout the thesis to explore particular open
questions on group selection, the evolution of aging and punctuated equilibrium. However,
the techniques developed have potential to be applied in other related models.
Each of the experimental chapters saw the implementation of group and kin selection
mechanisms. Group selection was modeled in a variety of ways, from the explicit groupings
in Chapters 3 & 4 — where group interactions and migration were explicitly controlled
by simulation parameters — to the species groupings in Chapter 5 — emergent from
individual mate signatures, used to determine sexual reproductive compatibility, or, more
importantly, incompatibility. In Chapter 3, I demonstrated the reliance of group selection
105
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CHAPTER 6. CONCLUSIONS AND FUTURE WORK
on kin selection by devising a method of removing kin associations via the use of an
adoption queue, a technique that can be used to isolate and study the impact of kin
selection on any type of evolutionary phenomenon.
A major theme throughout the thesis was the evolution of biological altruism, which
I investigated in an extreme form of programmed death by aging. In the comparative
study of Chapter 4, of my own hypothesis of aging with popular non-adaptive hypotheses
— mutation accumulation (Medawar, 1952), antagonistic pleiotropy (Williams, 1957) and
disposable soma (Kirkwood and Holliday, 1979) — I developed a variety of potential
models of aging mechanisms. For my aging-for-the-sake-of-diversity hypothesis, I created
a simulation of parasites and hosts, which could be used to study other epidemiological
phenomena.
In chapter 5, I created and implemented a species simulation, based on mate compatibility signatures, demonstrating punctuated speciation. I adapted existing statistics
(Bedau and Packard, 1991; Bedau et al., 1998) to measure the rate of evolutionary change,
and showed how they can be used to analyze the effects of adaptive and non-adaptive evolutionary activity on species identity. The Appendices A & B contain detailed descriptions
of the simulations developed throughout this thesis, following the ODD protocol (Grimm
et al., 2006, 2010), to assist the reader in understanding and replicating the simulations
and experiments.
6.1.2
Units of Selection
Throughout this thesis I’ve modelled mechanisms of selection that potentially favour the
evolution of biologically altruistic traits — this is, traits that benefit the fitness of others
(such as kin, the group or species) at the expense of individual-fitness. In Chapter 3,
in particular, I focused and reviewed the debate surrounding group selection. Historically used without due regard to theoretical backing, groups selection still retains a bad
reputation, even though the author of its greatest rival theory, the generally accepted kin
selection, has shown a mathematical unification of the two theories (Price, 1970; Hamilton,
1975). This has led to a distinction often being drawn in the literature between ‘old’ and
‘new’ group selection models (Grafen, 1984; West et al., 2007). The ‘new’ group selection
model encompasses Price and Hamilton’s reworking of inclusive fitness and kin selection,
6.1. CONTRIBUTIONS
107
whereas ‘old’ group selection is reserved for situations that rely on isolated multigenerational groups — which, much like individual organisms, are born and eventually die via
extinction. Whilst ‘new’ group selection is supported by the validity of inclusive fitness
theory, ‘old’ group selection models are denounced as unfeasible (Maynard Smith, 1976;
Grafen, 1984; West et al., 2007).
In Chapter 3, I tested the criticisms of group selection. Firstly, to challenge the
distinction made between new and old group selection, I developed an adoption queue
method of isolating, and removing, the kin selection component of an old group selection
model. The failure of the group selection model under these conditions demonstrated a
common dependence between the two. The method removed kin associations, however,
the dependence is more general than that. Both old and new group selection mechanisms
have Hamilton’s (1964) inclusive fitness at their hearts. What is needed for positive
selection of altruistic traits is, first, a variable distribution of altruism between groups
and, second, a positive association between group fitness and the altruistic genes. Such an
association can arise by kin associations or by other means, but, however it arises, it will
result in differential group fitness leading to a spread of altruism. Additionally, it has been
loudly doubted whether a group selection mechanism could overcome the direct influence
of individual selection, which will be acting against altruistic traits. However, my artificial
worlds, particularly those modelling the evolution of adaptive aging, demonstrate, at very
least, the feasibility of a group selection mechanism.
6.1.3
Evolution of Adaptive Aging and Sexual Reproduction
Two of the greatest challenges to adaptationist thinking are the widespread biological
phenomena of aging and sexual reproduction. These processes are core characteristics of
most species, yet they defy explanation in terms of individual fitness. Sexual reproduction
carries a two-fold cost, as sexually reproducing individuals need to reproduce twice as
much to have the same total number of descendants, even while the conditions required
for reproduction are harder to satisfy (Maynard Smith, 1978). Likewise, an aging trait
cannot have its benefits in individual fitness — it’s clear that an individual who dies of
aging (or simply deteriorates over time) could only have less expected offspring than one
who doesn’t. In Chapter 4, I explore both the aging and sexual reproduction phenomena,
focusing on the evolution of aging. Originally thought of as adaptive (Weismann, 1889),
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CHAPTER 6. CONCLUSIONS AND FUTURE WORK
but never properly modeled, the popular theories of aging, instead, rely on non-adpative
processes, attempting to explain it as a by-product of individual selection. Such a nonadaptive explanation was seen as preferable due to the lack of theoretical backing for group
selection (Williams, 1957) at the time. However, as shown in Chapter 3, groups selection
has now achieved a strong theoretical backing, via inclusive fitness theory. Additionally,
there has recently accumulated compelling experimental evidence that aging is an adaptation (Mitteldorf, 2004a; Bredesen, 2004; Skulachev, 1997) motivating a reexamination
of the problem
A popular explanation of sexual reproduction, known as the Red Queen hypothesis
(van Valen, 1973), holds that the diversity created via sexual recombination assists in coevolution “arms races” — for example, between hosts and parasites or predators and prey.
Building upon the group selection mechanisms explored in Chapter 3, and drawing from
the Red Queen hypothesis, I developed my own hypothesis of adaptive aging for the sake
of diversity — arguing that populations with shorter individual life spans will turnover
faster, introducing variation through recombination and mutation faster. In Chapter 4, I
developed a simulation of my adaptive hypothesis of aging and compared it with some of
the more popular non-adaptive hypotheses — mutation accumulation (Medawar, 1952),
antagonistic pleiotropy (Williams, 1957) and disposable soma (Kirkwood and Holliday,
1979). The results of these investigations demonstrated conditions that are favourable to
adaptive aging and sexual reproduction, as well as the feasibility of all the hypotheses.
6.1.4
Punctuated Equilibrium
With their punctuated equilibrium hypothesis, Eldredge and Gould (1972) not only criticize the emphasis of evolutionary thinking on the gradual nature of evolution, they also
provide the foundations of a species selection mechanism. The punctuated equilibrium
hypothesis states that the progress of evolution occurs in alternating periods of rapid
change (punctuation) and relative stasis (equilibrium). Gould (2002) points out that a
consequence of the theory is that, due to genetic drift during peripatric speciation events,
some part of what evolves is non-adaptive. This has broad implications on adaptationist
thinking, and Gould argues for a pluralism in which adaptation plays only a part — positioning himself against “Ultra Darwinists” who insist that all evolutionary phenomena
are the result of adaptation by natural selection. It also has implications for the group
6.2. FURTHER WORK
109
selection debate, as once species become defined and static, they form another group for
selection to act upon. The non-adaptive material evolved during speciation events, can
then be subject to species (group) selection forces, if it makes a species collectively perform better than other species occupying the same niche, such as parent or sibling species.
Exploring the evolution of altruism via such a species selection mechanism in an ALife
simulation is left for further work (see below).
In Chapter 5, I focused on testing Eldredge and Gould’s claims in my species simulation. Firstly, I wanted a test of evolutionary change during and between speciation
events in the simulation. Secondly, I wanted to determine how much of that change was
due to adaptation versus random chance (i.e., genetic drift). I developed a set of statistics to measure evolutionary activity, based on existing statistics to measure open ended
evolution (Bedau and Packard, 1991; Bedau et al., 1998). I used the statistics to confirm
the punctuated equilibrium phenomenon in my simulation, demonstrating an association
between speciation events and evolutionary activity. Furthermore, by investigating adaptively neutral shadows of the simulated worlds, I was able to identify the contribution of
adaptation to the evolved species identity. The results showed that, although adaptation
has an important role, it is clear that it doesn’t play an exclusive role during the speciation
events.
6.2
6.2.1
Further Work
Applying ALife techniques to Evolutionary Biology
In the short period since its formation in 1989, there have been many applications of ALife
in the study of evolutionary biology. Clearly, ALife is a promising experimental technique.
Whereas biology is restricted to the study of life as it naturally occurs (life-as-it-is), by
adding synthetic life (life-as-it-could-be) to our toolbox, which is easily controllable and
repeatable, we greatly increase our resources for experimental observation (Langton, 1989).
However, ALife is a new science and has limitations. To count as true representations of
the world, simulations must be verified and validated. Much work has been done on
developing an epistemology of computer simulation (e.g., Mascaro et al., 2010), however,
a fully fledged account is yet to be given. Ideally, we’d like to see a two-way interaction
between ALife and other disciplines. For example, ALife work done to demonstrate the
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CHAPTER 6. CONCLUSIONS AND FUTURE WORK
feasibility of adaptive aging traits could be used to guide genome research on where to
look for such genes — for example, whether it’s a pleiotropic gene, or a gene with the sole
purpose of causing deterioration with age, will affect how it will appear in the genome.
Such inter-discipline communication requires clarity and consistency in describing models,
so that they may be understood and critiqued by other scientists. For describing the
simulations developed throughout this thesis (see Appendices A & B), I’ve followed the
ODD (Overview, Design and Details) protocol, outlined by Grimm et al. (2006, 2010). The
ODD is a fledgling protocol, which has already had one major update and much success
in acceptance within the simulation community. As a communication tool, the protocol is
also valuable in making explicit the design decisions of the model and standardizing such
design. This is an important consideration in agent based modeling. For example, when
designing my simulations, it was apparent that there is an important tradeoff between
complexity and completeness. Clearly, in order to validate our simulations, it is beneficial
to make them as similar as possible to the real world being modelled (Grimm et al., 2005).
However, more complex models are harder to analyze — and when we model emergent
properties (which, by some definitions, are necessarily surprising) it may not be clear what
lower level components they are emergent from. Indeed, my experience with replicating
the published results on an earlier version of the adaptive aging simulation (Woodberry
et al., 2005), fixed in Chapter 4, and a simulation demonstrating the evolution of suicide
(Mascaro et al., 2001), fixed in (Mascaro et al., 2010), illuminated tests that demonstrated
the simulations were not behaving as the authors had reported (however, in both cases,
the underlying arguments were sound). The ODD goes a long way in improving both the
documentation and design of simulation models. However, as a fledging protocol of such
high aspirations, there is much work to be done on developing it.
6.2.2
Species Selection
In Chapter 5, I developed a species simulation exhibiting the properties of punctuated
equilibrium. A logical next step would be to see if the simulation is capable of evolving
altruistic traits via a species selection mechanism. I tested for the impact of adaptation
during speciation events, and it was clear that a founder effect caused a substantial part
of the species gene pool to be determined by the random process of genetic drift. This
is important as it provides for the establishment of altruistic groups, i.e., groups with an
6.2. FURTHER WORK
111
increased frequency of altruists, which will remain fixed as such for the duration of the
species lifespan. Once we have a variable distribution of altruism between groups, then we
could expect the positive selection of altruism via between group selection — as per the
Price equation (Price, 1970; Hamilton, 1975). It seems clear that the species simulation, as
it is, provides the foundation for a species selection model. However, preliminary attempts
(Woodberry et al., 2008), incorporating the evolution of aging mechanisms of Chapter 4
(i.e., co-evolving diseases and genetic expiry age) failed to present reliable results. In
this case the complexity of the combined simulations created difficulties in analysis and
misleading results. A better approach would be to attempt the evolution of a less extreme
altruism (such as a simple health donation behaviour) or develop a simpler species/group
selection simulation.
6.2.3
Evolutionary Ethics
In this thesis I have concerned myself with the evolution of biological altruism. Biological
altruism differs from the everyday concept of altruism, in that there is no requirement of
psychological choice. The dissertation of Mascaro (2008), and the following book (Mascaro
et al., 2010), investigates evolutionary ethics using ALife simulation techniques, opening
a plethora of potential research possibilities. By incorporating research from the fields of
evolutionary psychology (Cosmides and Tooby, 1987; Dupré, 1987) and utilitarian ethics
with the concept of inclusive fitness, and its expression via kin and group selection, there is
great potential to understand and study the ethical psychology and societal codes present
in rational decision making. This is not limited to the evolution of altruistic behaviour,
however, it clearly plays an important role in human morality and ethics — a large part
of which concerns selfless cooperative and social behaviour. This results in phenomena
ranging from the psychological feeling of well being (utility) experienced from performing
selfless acts, to the societal codes we adopt and enforce to ensure justice and equality. For
example, consider the golden rule “do unto others as you would have them do to you”,
which can be found, in some form, in most ethical traditions. What stops the selfish
free-rider from ignoring the rule, or feigning adherence, whilst receiving the benefits from
other more complicit peers, or rather, what determines when we should choose to break
the rule or adhere to it? Could the propensity to altruistic behaviour be hard-coded into
our psychology, in the same way that learning language appears to be? A strong case can
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CHAPTER 6. CONCLUSIONS AND FUTURE WORK
be made in case of direct kin — stories abound about parents and siblings making selfless
sacrifices for one another. It is clear that groups of individuals become highly related
units over multiple generations, hence it follows that altruistic genes could increase their
inclusive fitness by acting for the benefit of the group, when that group is in competition
with other groups.
Appendix A
ODDs — Evolution of Aging
In Chapter 4, four simulation worlds were used to test various adaptive and non-adative
hypotheses of aging. There was standalone simulations for the mutation accumulation,
disposable soma, my own diversity hypotheses, and a simulation combining all the aging
hypotheses. In this appendix I provide simulation design descriptions following the ODD
(Overview, Design concepts, Details) protocol (Grimm et al., 2006, 2010). The standalone
mutation accumulation simulation is described in Section A.1; the disposable soma simulation is described in Section A.2; the diversity simulation is described in Section A.3; and
the mixed aging simulation is described in Section A.4. The simulations were implemented
using the NetLogo modeling environment (Wilensky, 1999).
A.1
A.1.1
Mutation Accumulation Simulation Design
Purpose
To test the mutation accumulation hypothesis of aging, I developed a simulation of agents
each with an age indexed vector (string) of death genes. Mutations toggled the state
of each gene locus (between active/inactive states), resulting in the accumulation of late
age death genes. This mechanism was selected, over a single death gene (as used for the
diversity hypothesis mechanism, see below) because it allowed death genes to appear at
any age simultaneously and thus accumulate.
113
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APPENDIX A. ODDS — EVOLUTION OF AGING
A.1.2
Entities, State Variables and Scales
The simulation world holds an 11 × 11 grid of discrete cells. Each cell contains an agent
population, which mates within the cell. There is no interaction between the cells.1 The
two entities in the world are listed here:
Cells are locations within the world. In addition to holding a reference to the world to
which it belongs, each has an agent population, which changes over time.
Agents are the focus of the simulation. Each agent has a location, age and chromosome.
The chromosome consists of a string of death genes, which is inherited and mutated
during reproduction. Location and chromosomes are fixed at birth, and age changes
over time.
Table A.1 lists the state variables, along with a brief description, for each of the entities.
The state variable particular to this simulation is the death gene string. Death gene strings
are age indexed vectors of death genes. Each index indicates the presence of a death gene
for a given age, and, when triggered, causes the agent to immediately die. In the interests
of simplicity, death gene strings are limited to 100 positions, with the last position always
active.2
Table A.1: Mutation Accumulation Simulation Entities and State Variables
Entity
World
Cell
Agent
Chromosome
State Variable (Type)
Grid (2D Array)
Agents (List)
Location (Cell)
Age (Integer)
Chromosome (Chromosome)
Death Gene String (Vector)
Description
Grid of cells.
Occupant agent population.
Cell the agent occupies.
Age of the agent.
Chromosome of the agent.
String of death genes, of length 100.
Time in the simulation is represented by discrete time steps (cycles). The simulation is
run for a fixed period (default: 20,000 cycles) with a statistical epoch time unit (default:
100 cycles) during which statistics are collected.
A.1. MUTATION ACCUMULATION SIMULATION DESIGN
115
Algorithm A.1: Main Simulation Loop Algorithm
1
2
3
4
5
6
7
8
9
10
11
12
for epoch ← 0 to run length do
// Statistical epoch
for cycle ← 0 to statistical epoch length do
forall the Shuffle(agents) do
age ← age + 1;
attempt reproduction;
if death conditions then
remove agent;
end
end
end
report statistics;
end
A.1.3
// Update agents
Process overview and scheduling
Algorithm A.1 gives pseudocode for the main simulation loop. Each cycle, all agents are
updated in a random shuffle order. During each update, agents: attempt to reproduce, if
there is room; and die, if an accident occurs or death gene is triggered. Table A.2 shows
the simulation processes, categorized by entity.
Table A.2: Mutation Accumulation Simulation Processes
Entity
Agent
Process
Description
Reproduction
Agent attempts to reproduce.
Death of agent.
Death
Death gene string
Chromosome inheritance
and
mutation
A.1.4
Inheritance and mutation of
the death gene string.
State
Variables
affected
Cell agents. Create
new agent entity.
Cell agents. Remove
agent entity.
Death gene string.
Design concepts
Adaptation:
The accumulation of death mutations is non-adaptive. Instead, death
genes accumulate by mutation faster than selective pressures act to remove them.
Interaction:
1
Agents interact via mating.
Grouping of agents on cells was a common design decision across all the simulation worlds in this
chapter. This standalone simulation doesn’t require a spatial element, and it may be omitted.
2
Hence, agent have a maximum age of 100 cycles.
116
APPENDIX A. ODDS — EVOLUTION OF AGING
Stochasticity:
Stochasticity is used in a number of the processes: agent update order,
reproduction (i.e., mate selection and crossover/mutation of chromosomes) and accidental
deaths.
Observation:
Data is collected and reported on: the mean first death gene occurrence;
relative frequency of death types; and survivorship of agents.
A.1.5
Initialization
Table A.3: Mutation Accumulation Simulation Initialization of State Variables
Entity
Cell
Agents
State Variable
Agents
Age
Death Gene String
Initialization
Initialized with two agents.
Initialized at 0 cycles.
Initialized with string of inactive (except the
last) death genes of length 100.
To initialize the simulation two agents are spawned on each cell. All agents are initialized with a death gene string, with all indexes (except the 100th) inactive.
A.1.6
Input
The model does not use input data to represent time-varying processes.
A.1.7
Submodels
Algorithm A.2: Mutation Accumulation Reproduction Algorithm
1
2
3
4
5
6
7
8
9
// Check if room for offspring
if group size < max group size then
// Pick a mate
mate ← OneOf(group agents with age > 0);
// Create chromosome
// If mate available, then reproduce sexually
if mate != nobody then
chromosome ← Mutate(Crossover(Chromo(agent), Chromo(mate)));
else
// Else asexually
chromosome ← Mutate(Chromo(agent));
end
// Create offspring from chromosome
offspring ← NewAgent(chromosome);
end
A.2. DISPOSABLE SOMA SIMULATION DESIGN
Reproduction:
117
Algorithm A.2 shows the pseudocode for the reproduction process.
Each cycle, all agents attempt to reproduce sexually without gender. Agents only reproduce if there is room for the offspring — i.e., group size < max group size (default:
100 agents). If there is room for the offspring, a mate, with age > 0, is randomly selected
from the group population, and both are mated to produce an offspring in their cell. In
the rare event that no mate is available, the agent reproduces asexually. The offspring is
created with: a chromosome, consisting of a death gene string formed via crossover and
mutation of the parents death gene strings (see below); and an age of 0.
Death:
Each cycle agents are checked for death conditions. An agent dies: if it has an
active death gene for its age; or with fixed accident probability (default: uniform[0, 1] <
0.1).
Death gene string crossover and mutation: The offspring death gene string is determined by uniform crossover of the parent’s death gene strings, with a mutator (default:
0.001) probability of mutation activating or deactivating a death gene for an age index.
The death gene string has a length of 100, the last of which is always active.3
A.2
A.2.1
Disposable Soma Simulation Design
Purpose
To test the Disposable Soma hypothesis of aging, I developed a simulation of agents with
germ and soma line error rates, and an evolvable maintenance switch, which could keep
either error rate in check. Maintenance energy was limited, so increased maintenance of
one line would be at the expense of the other.
A.2.2
Entities, State Variables and Scales
The simulation world holds an 11 × 11 grid of discrete cells. Each cell contains an agent
population, which mates within the cell. There is no interaction between the cells.4 The
two entities in the world are listed here:
3
Consequently, agents have a maximum age of 100.
Grouping of agents on cells was a common design decision across all the simulation worlds in this
chapter. This standalone simulation doesn’t require a spatial element, and it may be omitted.
4
118
APPENDIX A. ODDS — EVOLUTION OF AGING
Cells are locations within the world. In addition to holding a reference to the world to
which it belongs, each has an agent population, which changes over time.
Agents are the focus of the simulation. Each agent has a location, age, germ and soma line
error rates and chromosome. The chromosome consists of a maintenance modifier,
which is inherited and mutated during reproduction. Location and chromosomes are
fixed at birth, and all other attributes change over time.
Table A.4: Disposable Soma Simulation Entities and State Variables
Entity
World
Cell
Agent
Chromosome
State Variable (Type)
Grid (2D Array)
Agents (List)
Location (Cell)
Age (Integer)
Germ Line Error Rate (Float)
Soma Line Error Rate (Float)
Fertile? (Boolean)
Chromosome (Chromosome)
Maintenance Modifier (Float)
Description
Grid of cells.
Occupant agent population.
Cell the agent occupies.
Age of the agent.
Error rate of the germ line.
Error rate of the soma line.
Agent able to reproduce.
Chromosome of the agent.
Modifier determining relative maintenance of the germ and soma error rates.
Table A.4 lists the state variables, along with a brief description, for each of the entities.
The state variables particular to this simulation are the germ/soma line error rates and
maintenance modifier and fertility flag. All agents are born fertile (i.e., fertile? set to
true) and errors in the germ line may render the agent infertile, setting the fertile? flag
as false. Errors in the soma line may result in the immediate death of the agent each
cycle. Error rates are updated each cycle, potentially accumulating exponentially. The
maintenance modifier modifies a base maintenance value, and thus represents the offset
each agent places on maintenance of the germ/soma line error rates. A positive value
means an increased maintenance of the soma line and deceased maintenance of the germ
line. A negative value means the opposite. The agent age state variable has no effect on
the simulation run,5 and is only kept for reporting purposes.
Time in the simulation is represented by discrete time steps (cycles). The simulation is
run for a fixed period (default: 20,000 cycles) with a statistical epoch time unit (default:
100 cycles) during which statistics are collected.
5
As discussed in Section 4.2.2, the disposable soma hypothesis doesn’t rely on a “clock” mechanism.
A.2. DISPOSABLE SOMA SIMULATION DESIGN
A.2.3
119
Process overview and scheduling
Algorithm A.3: Main Simulation Loop Algorithm
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
for epoch ← 0 to run length do
// Statistical epoch
for cycle ← 0 to statistical epoch length do
forall the Shuffle(agents) do
age ← age + 1;
update germ error rate;
update soma error rate;
check germ line failure;
attempt reproduction;
if death conditions then
remove agent;
end
end
end
report statistics;
end
// Update agents
Algorithm A.1 gives pseudocode for the main simulation loop. Each cycle, all agents
are updated in a random shuffle order. During each agent update the agent’s germ and
soma line error rates are updated, and the germ line is checked to determine if the agent
becomes infertile. Agents then: attempt to reproduce, if there is room and it is still fertile;
and die, if an accident or soma line error occurs. Table A.5 shows the simulation processes,
categorized by entity.
Table A.5: Disposable Soma Simulation Processes
Entity
Agent
Chromosome
Process
Description
Update of germ/
soma line error
rates.
Germ line failure
Reproduction
Accumulation of germ/soma
line error rates.
Death
Check for germ line failure.
Agent attempts to reproduce.
Death of agent.
Maintenance modifier mutation
Inheritance and mutation of
the maintenance modifier.
State Variables
affected
Germ/Soma line
error rates.
Agent fertile?
Cell agents. Create
new agent entity.
Cell agents. Remove agent entity.
Maintenance modifier.
120
A.2.4
APPENDIX A. ODDS — EVOLUTION OF AGING
Design concepts
Basic Principles: The method of error frequency accumulation is based on the mathematical model of Orgel (1970):
cn+1 = R + αcn
(A.1)
where cn is the error frequency in the nth generation, R is the residual error frequency
and α is the proportionality constant between generation errors. If α ≥ 1, then the error
frequency will increase — exponentially if α > 1. When α < 1 the error frequency will
reach a steady state of
R
1−α .
The α value for the germ and soma error accumulation is
determined from a base maintenance value and a modifier, which can direct maintenance
energy from one line to the other: αgerm = base maintenance + modifier; and αsoma =
base maintenance - modifier. The base maintenance value is fixed for a simulation run,
and the maintenance modifier evolves.
Adaptation:
The agent maintenance modifier is adaptive, however, the resulting soma
deaths are not (instead, they are a by-product). The maintenance modifier can divert
maintenance to the germ line, decreasing the probability of infertility, at the cost of soma
death probability, or vice versa.
Interaction:
Stochasticity:
Agents interact via mating.
Stochasticity is used in a number of the processes: agent update order,
reproduction (germ line error check, mate selection and crossover/mutation of chromosome) and death (accident deaths and soma line error check).
Observation:
Data is collected and reported on: the mean maintenance modifier value;
relative frequency of death types; and survivorship of agents.
A.2.5
Initialization
To initialize the simulation two agents are spawned on each cell. All agents are initialized
with error rates of 0 and a maintenance modifier of 0.
A.2. DISPOSABLE SOMA SIMULATION DESIGN
121
Table A.6: Disposable Soma Simulation Initialization of State Variables
Entity
Cell
Agents
A.2.6
State Variable
Agents
Age
Germ Error Rate
Soma Error Rate
Fertile?
Maintenance Modifier
Initialization
Initialized with two agents.
Initialized at 0 cycles.
Initialized at 0.
Initialized at 0.
Initialized as True.
Initialized at 0.
Input
The model does not use input data to represent time-varying processes.
A.2.7
Submodels
Update germ/soma error rate: Error rates in the germ/soma lines are updated each
cycle according to Equation A.1, where R is, by default, 0.005 and α is calculated as
maintenance base + maintenance modifier for the germ line, and maintenance base maintenance modifier for the soma line (default maintenance base: 0.98).
Germ line failure:
Every cycle, agents are checked for a germ line failure (uniform[0, 1] <
germ error rate). If a failure occurs, the agent becomes infertile (i.e., the Fertile? flag is
set to false).
Reproduction:
Algorithm A.4 shows the pseudocode for the reproduction process.
Each cycle, all agents attempt to reproduce sexually without gender. Agents only reproduce if they are fertile (i.e., they haven’t experienced a germ line failure) and there is
room for the offspring — i.e., group size < max group size (default: 100 agents). If there
is room for the offspring, a mate, also fertile with age > 0, is randomly selected from the
group population, and both are mated to produce an offspring in their cell. In the rare
event that no mate is available, the agent reproduces asexually. The offspring is created
with: a chromosome, inherited from a randomly selected parent, consisting of a mutated
maintenance modifer (see below); an age of 0; a true fertility flag; and germ and soma line
error rates copied from a randomly selected parent’s germ line.
122
APPENDIX A. ODDS — EVOLUTION OF AGING
Algorithm A.4: Disposable Soma Reproduction Algorithm
1
2
3
4
5
6
7
8
9
10
11
12
13
// Check if room for offspring and fertile
if Fertile? and group size < max group size then
// Pick a fertile mate
mate ← OneOf(group agents with age > 0 and Fertile?);
// Create chromosome
// If mate available, then reproduce sexually
if mate != nobody then
chromosome ← Mutate(Crossover(Chromo(agent), Chromo(mate)));
// Copy germ error rate to offspring’s germ and soma error
rates
germ error rate ← germ error rate of RandomChoice(agent, mate);
soma error rate ← germ error rate;
else
// Else, asexually
chromosome ← Mutate(Chromo(agent));
// Copy germ error rate to offspring’s germ and soma error
rates
germ error rate ← germ error rate of agent;
soma error rate ← germ error rate;
end
// Create offspring
offspring ← NewAgent(chromosome, germ error rate, soma error rate);
end
Death:
Each cycle, agents are checked for death conditions. An agent dies: if it has a
soma error (uniform[0, 1] < soma error rate); or with fixed accident probability (default:
uniform[0, 1] < 0.1).
Maintenance modifier mutation:
During reproduction, the maintenance modifier of
a random parent is inherited and mutated via a normal distribution, N(maintenance modifier,
0.01). It is permitted to evolve either a positive or negative value.
A.3
A.3.1
Diversity Simulation Design
Purpose
To test my diversity hypothesis of aging, and explore the red queen hypothesis of sex, I
developed a group selection simulation of host agents, with vulnerability signatures, and
disease agents, with infection signatures. Host agents evolved an expiry age and sexual
reproduction rate, which could promote diversity within groups, allowing them to resist
group extinction by the disease epidemics.
A.3. DIVERSITY SIMULATION DESIGN
A.3.2
123
Entities, State Variables and Scales
The simulation world holds an 11 × 11 grid of discrete cells, wrapped so that the edges
meet, to form a torus shape. Each cell contains a host agent population, which mates
within the cell, with occasional migration between the cells in the 3 × 3 neighbourhood.
Every cycle, a disease agent is created for each cell population and all host agents are
checked for infection. The three entities in the world are listed here:
Cells are locations within the world. In addition to holding a reference to the world to
which it belongs, each has a host agent population, which changes over time. Cells
also keep track of the age of the population (i.e., the period of time since it was
pioneered).
Host Agents are the focus of the simulation. Each host agent has a location, age, expiry
age and chromosome. The chromosome consists of a genetic expiry age gene, sexual
reproduction rate and vulnerability signature, all of which are inherited and mutated
during reproduction. Chromosomes and expiry ages are fixed at birth, all other
attributes change over time.
Disease Agents consist solely of a chromosome, containing an infection signature fixed
at birth.
Table A.7 lists the state variables, along with a brief description, for each of the entities.
The state variables particular to this simulation are cell age and agent expiry age, expiry
age gene, sexual reproduction rate, vulnerability and infection. The cell age state variable
has no effect on the simulation run, and is only kept for reporting purposes. The agent
expiry age is determined by sampling a normal distribution with the expiry age gene as
mean. When an agent’s age exceeds its expiry age it immediately dies. Sexual reproduction
rate is a probability that is sampled during each reproduction attempt and determines if
the agent reproduces sexually, selecting a mate (regardless of sexual propensity) from
its group, or asexually. Host vulnerability and disease infection are bit signatures used
to determine the success of infection attempts, via a function of the hamming distance
between them.
124
APPENDIX A. ODDS — EVOLUTION OF AGING
Table A.7: Diversity Simulation Entities and State Variables
Entity
World
State Variable (Type)
Grid (2D Array)
Host Agents (List)
Age (integer)
Cell
Host Agent
Host Chromosome
Location (Cell)
Age (Integer)
Expiry Age (Integer)
Chromosome (Chromosome)
Expiry Age Gene (Float)
Sexual Reproduction Rate
(Float)
Vulnerability (Vector)
Disease Agent
Infection (Vector)
Description
Grid of cells.
Occupant host agent population.
Number of cycles since group was
pioneered.
Cell the agent occupies.
Age of the agent.
Expiry age of the agent.
Agent’s chromosome.
Gene used to determine the expiry
age of the agent.
Gene used to determine agents
propensity for sexual, versus asexual, reproduction.
100 bit string, used to determine
infection success.
100 bit string, used to determine
infection success.
Time in the simulation is represented by discrete time steps (cycles). The simulation is
run for a fixed period (default: 20,000 cycles) with a statistical epoch time unit (default:
100 cycles) during which statistics are collected.
A.3.3
Process overview and scheduling
Algorithm A.5 gives pseudocode for the main simulation loop. Each cycle, first all cells
are updated in a random shuffle order and then all hosts are updated in a random shuffle
order. During each cell update a disease agent is created and the entire cell host population
is tested for infection. Any hosts (potentially the entire cell population) infected by the
disease immediately die. Next, the 3 × 3 cell neighbourhood is checked for empty cells
(that have been driven extinct) and if any is found, a migration is attempted. During each
host update the host: attempts to reproduce, if there is room; and dies, if its age exceeds
its expiry age. Table A.8 shows the simulation processes, categorized by entity.
A.3.4
Design concepts
Basic Principles:
The methods of disease infection and host vulnerability are adapted
from Epstein and Axtell’s (1996) immunity simulation. In their simulation, hosts have
an immunity bit signature, which is inherited and modified over the agent’s lifespan —
A.3. DIVERSITY SIMULATION DESIGN
125
Algorithm A.5: Main Simulation Loop Algorithm
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
for epoch ← 0 to run length do
// Statistical epoch
for cycle ← 0 to statistical epoch length do
forall the Shuffle(cells) do
// Update cells
age ← age +1;
// Disease Epidemic
disease ← spawn disease;
forall the hosts do
// Check all hosts for infection
if Infect?(host, disease) then
die;
end
end
if Empty?(neighbouring cells) then
// Check for empty cells
migrate;
end
end
forall the Shuffle(hosts) do
// Update hosts
age ← age + 1;
attempt reproduction;
if death conditions then
remove agent;
end
end
end
report statistics;
end
developing immunity to the disease infection signatures, which are sub-signatures of the
immunity signatures. My simulation differs in both the host and disease signatures. Vulnerability signatures are fixed throughout the host agent’s lifespan, and used to determine
infection success (vulnerability), rather than failure (immunity). Disease infection signatures are the same length as the vulnerability signatures and have wild-card values
(generated with a probability representing the diseases virulence), which match any vulnerability locus value.
Emergence:
There are two emergent properties of interest: group diversity and extinc-
tion. Diversity emerges from the processes of crossover, mutation and population turnover.
Group extinction emerges from the interaction between group diversity and the disease
virulence.
126
APPENDIX A. ODDS — EVOLUTION OF AGING
Table A.8: Diversity Simulation Processes
Entity
Cell
Process
Description
Epidemic
Create disease and check
infection of hosts
Migrant party relocates to
neighbouring cell.
Host attempts to reproduce.
Migration
Reproduction
Host
Host Chromosome
Disease
Adaptation:
Death
Death of host.
Expiry Gene Mutation
Expiry Gene Expression
Sexual Reproduction
Rate Mutation
Inheritance and mutation
of expiry gene.
Generate expiry age from
expiry age gene.
Inheritance and mutation
of sexual reproduction rate
gene
Determine sexual reproduction preference.
Crossover and mutation of
vulnerability signatures.
Sexual Reproduction
Check
Vulnerability
Crossover and Mutation
Spawn
Infection?
State Variables
affected
Remove host entity.
Host location and
cell host agents.
Cell host agents.
Create new host entity.
Cell host agents.
Remove host entity.
Expiry age gene.
Expiry age.
Sexual
reproduction rate.
Vulnerability signature.
Create disease entity.
Determine success of disease infection on host vulnerability.
The host expiry age and sexual reproduction rate are adaptive. Expiry
age has two counteracting selective pressures. Hosts with later expiry ages have greater
opportunity to reproduce. However, groups of hosts with a higher turnover, i.e., hosts
with earlier expiry ages, have greater diversity and thus are less likely to be driven extinct
during disease epidemics. Likewise, sexual reproduction rate also has two counteracting
selective pressures. Hosts that reproduce sexually are less likely to pass on their genes,
i.e., there is a 50% chance that the offspring will inherit from the parent, whereas asexual
reproduction is certain. However, like expiry age, groups of sexually reproducing hosts
will have greater diversity, via crossover of vulnerability signatures.
Interaction:
Agents interact via mating.
A.3. DIVERSITY SIMULATION DESIGN
Stochasticity:
127
Stochasticity is used in a number of the processes: cell/agent update or-
der, migration, reproduction (sexual preference check, mate selection, crossover/mutation
of chromosome and expression of expiry gene) and disease creation.
Observation:
Data is collected and reported on the: genetic expiry gene value; sexual
reproduction rate; group diversity; relative frequency of death types; and survivorship of
hosts and groups.
A.3.5
Initialization
Table A.9: Diversity Simulation Initialization of State Variables
Entity
Cell
Hosts
State Variable
Agents
Expiry gene
Sexual reproduction rate
Vulnerability
Age
Initialization
Initialized with two host agents.
Initialized at 20 cycles.
Initialized at 0.5 or 1.
Initialized with random 100 bit vector.
Initialized at 0 cycles.
To initialize the simulation two hosts agents are spawned on each cell. All host agents
are initialized with an expiry age gene (default: 20 cycles), a sexual reproduction rate
(default: 0.5 or 1, depending on the experiment) and a random vulnerability signature,
100 bits in length.
A.3.6
Input
The model does not use input data to represent time-varying processes.
A.3.7
Submodels
Epidemic:
Each cycle, all cell groups are tested for an disease epidemic. A disease agent,
with random genetics, is spawned for each cell and is tested against all the host agents
in that cell for infection. Disease creation and infection is discussed below. Any host
agent infected by the disease immediately dies and the entire group is driven extinct if all
hosts are infected — the cell may be recolonized later via a migration from a neighbouring
group.
128
APPENDIX A. ODDS — EVOLUTION OF AGING
Algorithm A.6: Diversity Migration Algorithm
1
2
3
4
5
6
7
8
9
10
if group size > migrant party size then
// If enough agents to migrate
// Get empty neighbouring cells
empty cells ← neighbour cells with no agents;
if any? empty cells then
// Check if there are empty cells
// Randomly pick one
destination ← OneOf(empty cells);
// Move agents to destination
for 0 to migrant party size do
Move(OneOf(group agents), destination);
end
// Reset destination cell age
age of destination ← 0;
end
end
Migration:
Algorithm A.6 shows the pseudocode for the migration process. Every cycle
all cell host agent populations attempt to export a small, randomly selected, party of
migrant party size (default: 2 host agents) to a neighbouring empty cell. First the empty
cells in the 3 × 3 neighbourhood are identified, and, if any exist, one is randomly selected
as the destination cell. After the migration group has relocated, the destination cell age
is reset at 0. The migration attempt is aborted if there are no empty cells nearby, or the
host agents available is ≤ migrant party size.
Algorithm A.7: Diversity Reproduction Algorithm
1
2
3
4
5
6
7
8
9
10
if group size < max group size then
// If room for offspring
// Get mate and check for sexual reproduction
mate ← OneOf(neighbour hosts with age > 0);
// If there is a mate available and sexual reproduction
if mate != nobody and unif orm[0, 1] < sexual reproduction rate then
chromosome ← Mutate(Crossover(Chromo(agent), Chromo(mate)));
else
// Otherwise, reproduce asexually
chromosome ← Mutate(Chromo(agent));
end
// Determine expiry age from expiry gene
expiry age ← GetExpiry(chromosome);
// Create offspring from chromosome and expiry age
offspring ← NewHostAgent(chromosome, expiry age);
end
Reproduction:
Algorithm A.7 shows the pseudocode for the reproduction process. Ev-
ery cycle all host agents attempt to reproduce. Hosts only reproduce if there is room for
the offspring (default max group size: 100 host agents). If there is room for the offspring,
A.3. DIVERSITY SIMULATION DESIGN
129
the host agent determines if it will reproduce sexually or asexually (see below). If reproduction is sexual, a mate, with age > 0, is randomly selected from the group population
and the two agents are mated. The mate’s sexual reproduction rate is not checked; the
reproducing agent simply borrows genetic material from the mate.6 Occasionally no mate
can be be found (e.g., if the group is near extinction), in which case the host agent defaults
to asexual reproduction. The offspring host agent is created with: a chromosome of an
expiry gene, sexual reproduction rate and vulnerability signature, formed via crossover (if
sexual) and mutation of the parent’s chromosomes (see below); an age of 0; and an expiry
age — a function of the expiry gene (see below).
Death:
Every cycle host agents are checked for death conditions. A host agent dies if:
it is infected by a disease agent; or its age exceeds its expiry age.7 Death results in the
immediate removal of the agent from the world.
Expiry Gene Mutation: During reproduction, the expiry gene of the parent (randomly selected, if the product of a sexual reproduction) is inherited and mutated via
a normal distribution with variance proportional to its magnitude, i.e., N(expiry gene,
expiry gene
expiry gene mutator )
(default expiry gene mutator: 100). As this gene has no side effects, it
is expected that fast aging will always be selected against, unless the scenario provides
aging its own selective value.
Expiry Gene Expression:
The expiry gene is used at conception to determine an
expiry age for the agent by sampling a normal distribution with variance proportional to
its magnitude, i.e., N (expiry gene,
expiry gene
expiry gene expression )
(default expiry gene expression:
3).
Sexual Reproduction Rate Mutation:
During reproduction, the sexual reproduc-
tion rate of the parent (randomly selected, if the product of a sexual reproduction) is
6
This means that sexual reproduction is always successful, as long as there is another agent available.
The cost of sexual reproduction is in the decreased probability of inheritance. Preliminary experiments
were conducted with sexual reproduction requiring consenting partners, i.e., both agents passing a sexual
reproduction check, and thus affecting the probability of success. However, this made the initial establishment of sexual reproduction challenging.
7
The accidental death mechanism was not required for the hypothesis, unlike the other two hypotheses,
which rely on declining selection pressure over age (see section 4.2.2).
130
APPENDIX A. ODDS — EVOLUTION OF AGING
inherited and mutated via a normal distribution, i.e., N(sexual reproduction rate, sexual reproduction rate mutator) (default sexual reproduction rate mutator: 0.005).
Sexual Reproduction Check: During each reproduction attempt the agent determines
if it will reproduce sexually, or asexually, by checking its sexual reproduction rate gene,
reproducing sexually if uniform[0, 1] < sexual reproduction rate.
Figure A.1: Example signature crossover, mutation and infection.
Vulnerability Crossover and Mutation:
The offspring vulnerability signature is de-
termined by uniform crossover of the parent’s vulnerability signatures, if the product
of sexual reproduction, with a signature mutator (default: 0.01) probability of mutation
flipping each bit value. An example vulnerability signature crossover and mutation is
illustrated in Figure A.1.
Spawn Disease:
Every cycle a disease agent is spawned for every cell. Disease agents
consist, solely, of an infection signature, used to match the host vulnerability signatures.
Infection signatures are generated randomly with an infection wildcard prob (default: 0.94)
chance of each locus taking a wildcard value. An example infection signature is illustrated
in Figure A.1
Infection?:
After a disease agent is created for a group, all host agents are checked for
infection. Infection is successful if all the non wildcard loci of disease infection signature
A.4. MIXED AGING SIMULATION DESIGN
131
match the host vulnerability signature. An example successful infection attempt in illustrated in Figure A.1. If the infection is successful, the infected host agent immediately
dies.
A.4
A.4.1
Mixed Aging Simulation Design
Purpose
To do a comparative study of different aging hypotheses, I developed a simulation combining them, with flags to enable or disable various combinations of components — thereby,
activating or deactivating the hypotheses. The three hypotheses were mutation accumulation (MA), disposable soma (DS) and diversity (DIV). In all runs, the accident rate was
enabled, as was the genetic expiry age component and agent expiry age. The MA and DS
hypotheses required particular genetics — namely the death gene string and germ/soma
line error rates, respectively — and so to disable these hypotheses, it was sufficient to disable the component effects on death. To disable the DIV hypothesis, I needed to remove
the adaptive benefit of aging, which was done by disabling the disease population.
A.4.2
Entities, State Variables and Scales
The simulation world and scales are the same as the diversity simulation (see above),
with the exception that the host agents have all state variables particular to the mutation
accumulation and disposable soma components: i.e., death gene string, germ and soma
error rates and maintenance modifier. These state variables are described in the previous sections. The sexual reproduction rate state variable is not used in the combined
simulation.
A.4.3
Process overview and scheduling
Algorithm A.8 gives pseudocode for the main simulation loop. This is the result of merging
the main simulation loops of previous sections and including flags to disable particular
components. Cell update, incorporating disease epidemics and migration, was only enabled
in the DIV runs. Germ and soma line error updating was only enabled in the DS runs.
Deaths and fertility checks, via the cell line error rates and death gene string, were only
enabled when the relevant component was active.
132
APPENDIX A. ODDS — EVOLUTION OF AGING
Algorithm A.8: Main Simulation Loop Algorithm
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
for epoch ← 0 to run length do
// Statistical epoch
for cycle ← 0 to statistical epoch length do
// If diversity hypothesis enables, update cells
if DIV enabled then
forall the Shuffle(cells) do
// Update cells
// Disease Epidemic
disease ← spawn disease;
forall the hosts do
// Check all hosts for infection
if Infect?(host, disease) then die;
end
attempt migration;
end
end
forall the Shuffle(hosts) do
// Update hosts
age ← age + 1;
// If disposable soma enabled, update error rates and do
fertility check
if DS enabled then
update germ error rate;
update soma error rate;
check germ line failure;
end
attempt reproduction;
if death conditions then
remove agent;
end
end
end
report statistics;
end
Appendix B
ODDs — Testing the Punctuated
Equilibrium Hypothesis
In Chapter 5, four simulation worlds were used to test the punctuated equilibrium hypothesis, and its implications on the importance of adaptation. There was a foreground
simulation world and three neutral shadow simulation worlds. In this appendix I provide
simulation design descriptions following the ODD (Overview, Design concepts, Details)
protocol (Grimm et al., 2006, 2010). The foreground simulation is described in Section
B.1 and the shadow simulations are described, together, in Section B.2. The simulations
were implemented in the Lisp programming language.
B.1
B.1.1
Foreground Simulation
Purpose
In order to test the implications of the punctuated equilibrium hypothesis, I developed an
agent based simulation simulating the formation of species and their creation via speciation
events.
B.1.2
Entities, State Variables and Scales
The simulation world holds a grid of discrete cells, wrapped so that the edges meet, to
form a torus shape. Each cell contains an unlimited agent population, which is able to
interact with the other cell and agent entities within its agent interaction neighbourhood.
133
134APPENDIX B. ODDS — TESTING THE PUNCTUATED EQUILIBRIUM HYPOTHESIS
The spatial scales of the world are listed in Table B.2. There are four entities in the world,
each listed below:
Cells are locations within the world. In addition to holding a reference to the world to
which it belongs, each has an agent population (unlimited in size) and a food store,
from which the agent population feeds. Both cell attributes change over time.
Agents are the organisms that interact with the world. Each agent has a location, age,
health, chromosome and species membership. The agent’s chromosome is fixed at
birth, and all other attributes change over time.
Chromosomes has two components: a mate signature, which is used to determine mate
compatibility and, ultimately, species membership; and a selectively neutral junk
signature. Chromosomes are inherited and mutated during reproduction and fixed
throughout an agent’s lifespan.
Species are groups of reproductively isolated agents, determined by mate compatibility.
Species units are monitored over time, for statistical purposes. The species membership changes as agents are born and die, and is reassessed (via regrouping of mate
signatures) over epoch periods.
Table B.1: Simulation Entities and State Variables
Entity
World
Cell
Chromosome
State Variable (Type)
Grid (2D Cell Array)
Agents (Agent List)
Food (Float)
Location (Cell)
Age (Integer)
Health (Float)
Chromosome (Chromosome)
Species (Species)
Mate signature (Bit Vector)
Species
Junk signature (Bit Vector)
Agents (Agent List)
Agent
Description
Grid of cells.
Occupant agent population.
Food energy.
Cell the agent occupies.
Age of the agent.
Health of the agent.
Chromosome of the agent.
Species of the agent.
100 bit string, used to determine
mate compatibility.
100 bit string.
Agent members of the species.
Table B.1 lists the state variables, along with a brief description, for each of the entities. Most of the state variables (location, age, health and food) are common across the
B.1. FOREGROUND SIMULATION
135
simulations. Mate signatures are bit vectors used to determine reproductive compatibility — and hence species membership — by comparing Hamming Distance with a mate
compatibility threshold. The agent junk signatures are non-functional genetic material,
included for measuring non-adaptive genetic activity.
Table B.2: Simulation Scales
Aspect
Spatial
Temporal
Scale
World size
Agent interaction neighbourhood
Speciation epoch
Statistical epoch
Simulation run
Value
30 × 30 cells.
3 × 3 cells.
20 cycles.
5 speciation epochs.
100 statistical epochs.
Time in the simulation is represented by discrete time steps (cycles). The temporal
scales of the world are listed in Table B.2. During each cycle, all cells and agents are
activated for updating in a random order. The simulation is run for a fixed period with
two epoch time units:
Speciation epoch is the number of cycles (by default, 20 cycles) between speciation
event checks. Note that, speciations could occur at any point in time, but for
computational reasons, a check is only run occasionally.
Statistical epoch is the number of “speciation epochs” (by default, 5 speciation epochs)
between statistic reporting events.
Pre-run length is the number of “speciation epochs” (by default, 100 speciation epochs)
run before statistics are collected. The pre-run is included to ensure that the species
units in the simulation have the opportunity to stabilize. The pre-run length was
selected as the average cycles it took for a simulation, initialized with a single mega
species, to diversify and stabilize in the number of species.
Run length is the number of “statistical epochs” (by default, 100 statistical epochs) the
simulation is run collecting statistics.
B.1.3
Process overview and scheduling
Algorithm B.1 gives pseudocode for the main simulation loop. In addition to a pre-run
loop, to initialize the simulation, there are three nested loops, each representing the time
136APPENDIX B. ODDS — TESTING THE PUNCTUATED EQUILIBRIUM HYPOTHESIS
Algorithm B.1: Main Simulation Loop Algorithm
1
2
3
4
5
6
7
8
9
// Pre-run simulation to initialize species
for cycle ← 0 to pre run length do world cycle;
reset statistics;
// Run simulation proper
for epoch1 ← 0 to run length do
// Statistical epoch
for epoch2 ← 0 to statistical epoch length do
// Speciation epoch
forall the species do speciate species; // Check for speciation events
for cycle ← 0 to speciation epoch length do world cycle;
end
report statistics;
end
Algorithm B.2: World Cycle Algorithm
1
2
3
4
5
6
7
8
9
10
11
12
13
14
// With small probability, kill off a species
if uniform[0, 1] < species kill rate then kill species;
// Shuffle and update all agent and cell entities
entities ← shuffle(cells ∪ agents);
forall the entities do
if entity is a cell then
generate food;
else
// entity is an agent
age ← age + 1;
health ← health - 1;
move;
eat;
reproduce;
if age > expiry age || health < 0 then die;
end
end
scales in Table B.2. At the base of the loops is the world cycle process, given in Algorithm
B.2. Each world cycle, all agent and cell entities are synchronously updated in a random
order.1 Population and statistics are initialized after the pre-run and two variations are
reported each speciation and statistical epoch. Table B.3 shows the simulation processes,
categorized by entity.
1
The decision to update agents and cells synchronously, as opposed to asynchronously updating cells
and agents separately, was an effort to model a continuous process with discrete time steps — and informal
investigations showed no effect on the results.
B.1. FOREGROUND SIMULATION
137
Table B.3: Simulation Processes
Entity
Process
Description
Cell
Generate Food
Movement
Generate cell food.
Agent attempts movement.
Agent
Eating
Agent eats from cell.
Reproduction
Agent selects mate partner
and reproduces sexually.
Death of agent.
Death
Compatible?
Species
Chromosome
Speciation
Determine mate compatibility.
Test for speciation event.
Species Kill
Kill random species.
Crossover
Crossover of two chromosome’s components.
Mutate chromosome components.
Mutation
B.1.4
State
Variables
affected
Cell food.
Agent location and
cell agents.
Cell food and agent
health.
Agent health. Create agent entity.
Cell and species
agents.
Remove
agent entity.
Agent species. Create species entity.
Remove species entity.
Create chromosome
entity.
Chromosome mate
and junk signatures.
Design concepts
Basic Principles: The simulations employ the most generally accepted definition of
species, identifying them as reproductively isolated sub-populations (Mayr, 1963) — that
is, a group of actually or potentially interbreeding populations that are reproductively
isolated from other such groups. Species are implemented via the use of mate compatibility
signatures. The Hamming distance, with a threshold, between signatures is calculated to
determine mate compatibility, and, conversely, reproductive isolation — membership of a
species requires that there exists a living mate compatibility connection between agents.
A limitation of the species definition we use is that species can be quite fractured — the
process of speciation could be well underway by the time we identify a separate species.
Emergence:
There are two emergent properties of interest: species and rates of evo-
lutionary change. Species, and their formation, emerge from the processes of movement
and crossover, mutation and comparison of mate signatures. Movement affects the mixing
138APPENDIX B. ODDS — TESTING THE PUNCTUATED EQUILIBRIUM HYPOTHESIS
of species, competition between species and the occurrence of spatial isolation of subpopulations (catering for peri/parapatric speciation). The crossover and mutation processes affect the diversification rate of species. The rates of evolutionary change, emerge
from the processes of crossover and mutation of mate signatures and speciation events.
Adaptation:
The agent mate signatures are, at least partially, adaptive. The fitness of
an agent’s mate signature is determined implicitly — agents with mate signatures similar
to those of agents around them are more likely to reproduce.
Interaction:
Agents interact in two ways: indirectly via food sources, and directly via
mating.
Stochasticity:
Stochasticity is used in a number of the processes: cell/agent update
order, cell food generation; agent movement and mating; chromosome crossover and mutation; and species kill.
Observation:
Data is collected and reported on species, including number, size, ancestry
and evolutionary activity (discussed in detail in Section 5.3.2).
B.1.5
Initialization
Table B.4: Initialization of State Variables
Entity
Cell
Agent
Chromosome
Species
State Variable
Agents
Food store
Age
Health
Species
Mate signature
Junk signature
Agents
Initialization
1
9 probability of being the center of
a species.
Initialized at 0 units.
Initialized at 0.
Initialized at 10 units.
Initialized with random bit vector.
Initialized with random bit vector.
-
To initialize the simulation, species, each containing 9 agents, are spawned across the
board — with each cell having a
1
9
probability of being the center of a species (i.e., when a
cell is selected, 9 agents, with the same mate signature, are spawned evenly across the 3×3
neighbourhood). Each species is formed by creating an agent with randomly generated
B.1. FOREGROUND SIMULATION
139
mate and junk signatures and cloning it to ensure that mating can occur. Table B.4
outlines the initialization values for the state variables. Before any statistics are collected,
the simulation is run in a pre-run mode, so that species can diversify and stabilize. After
the pre-run, all statistics are initialized.
B.1.6
Input
The model does not use input data to represent time-varying processes.
B.1.7
Submodels
Generate Food: Each cycle, food is generated for every cell at a constant rate, new food
(default: 2 units). The new food is added to any existing food.
Agent Movement: Each cycle, agents have a chance, move rate (default: 0.0), of moving to a neighbouring cell. A destination cell is randomly selected from the agent interaction neighbourhood and the agent is relocated to it.
Agent Eating: Each cycle, agents attempt to eat. A food cell is randomly selected from
the agent interaction neighbourhood and all food on that cell is transfered to the agent’s
health.
Agent Reproduction: Agents attempt to reproduce, sexually without gender, whenever their health exceeds a threshold, mate health (default: 20 units). A consequence of
this is that agents are, potentially, mate ready in the cycle after birth (if enough food
is available). A potential mating partner is randomly selected from the agents occupying the agent interaction neighbourhood. The mate is then tested to determine if: its
health exceeded the mate health threshold; and it is mate compatible (discussed below).
If successful, an offspring is created:
• with health, initial health (default: 10 units), created via equal health donations
from its parents;
• in a cell, randomly selected from the union of the agent interaction neighbourhoods
of both parents;
140APPENDIX B. ODDS — TESTING THE PUNCTUATED EQUILIBRIUM HYPOTHESIS
• with a chromosome, created via crossover and mutation of the parent chromosomes
(discussed below); and
• the species membership of the parents.
Algorithm B.3 shows the pseudocode for the process.
Algorithm B.3: Agent Reproduction Algorithm
1
2
3
4
5
6
7
8
9
10
11
if Health(agent) > mate health then
// select mate partner
mate ← OneOf(neighbour agents);
if Health(mate) > mate health & MateCompatible(agent, mate) then
// parental investments
Health(agent) ← Health(agent) - initial2health ;
Health(mate) ← Health(mate) - initial2health ;
// select birth cell
birth cell ← OneOf(NeigbourCells(agent) ∪ NeighbourCells(mate));
// create chromosome
chromosome ← Mutate(Crossover(Chromosome(agent),
Chromosome(mate)));
// assign species membership
species ← Species(agent, mate);
offspring ← NewAgent(initial health, birth cell, chromosome, species);
end
end
Agent Death: Death is triggered by either an age exceeding expiry age (default: 20
cycles) or a sub-zero health, and causes the agent to be removed from the world.
Figure B.1: Example signature comparison, crossover and mutation.
Mate Compatibility:
Mate compatibility is determined by two conditions: species
membership; and the Hamming distance between the mate signatures of the two agents
(see Figure B.1). Given the agents share membership in the same species, the mate
B.1. FOREGROUND SIMULATION
141
attempt is successful if the Hamming distance between their mate signatures is less than
a threshold, 100−mate compatibility threshold (default: 100 − 95 = 5 bits).
Chromosome Crossover:
The crossover processes of both the mate and junk signa-
tures is the same. Crossover of signatures is performed by creating new signatures and
randomly selecting each resulting loci from the two parents respective signatures (See
Figure B.1).
Chromosome Mutation:
The mutation processes of both the mate and junk signatures
is the same. Mutation of signatures is performed by mutating (i.e., flipping the bit) each
loci with a probability, mate signature mutator (default: 0.002) (See Figure B.1).
Species Kill: To ensure space for new species, there is a small probability, species kill rate
(default: 0.01 — much lower than the speciation rate), per cycle that a randomly selected
species will be killed off. The selection of species is performed by selecting a random
agent from the population and killing all members of its species. Algorithm B.4 shows the
pseudocode for the process.
Algorithm B.4: Kill Species Algorithm
1
2
3
4
5
6
7
if uniform[0, 1] < species kill rate then
// randomly select an agent
agent ← OneOf(agents);
// get members of its species
species ← Species(agent);
forall the agent ∈ Agents(species) do
Kill(agent);
end
end
Speciation:
Speciation is only tested within existing species populations, and, once
split, species are no longer permitted to inter-mate.2 This was primarily done to simplify
the simulation computation — as testing for speciation has O(n2 ) complexity — and for
the sake of species history statistics collection. To speciate, agents within a species are
clustered into groups based solely on mate compatibility (spatial aspects are ignored).
2
Quick investigations showed this had a negligible effect, due to the infrequency of such occurrences
(affecting, approximately, 1 in 9000 mate attempts ).
142APPENDIX B. ODDS — TESTING THE PUNCTUATED EQUILIBRIUM HYPOTHESIS
B.2
Shadow Simulations
B.2.1
Purpose
To identify an activity threshold and test the importance of adaptation, I complimented
the foreground simulation with a neutral shadow world. The shadow worlds have no
spatial aspect and birth, death and speciation events involve randomly selected agents.
All events in the shadow world are triggered by corresponding events in the foreground
simulation run. Three variant shadow worlds were trialled:
Shadow World 1 is the simplest interpretation of the adaptively-neutral shadow concept. The shadow agents consist, solely, of a chromosome. Any mate or death events
in the foreground simulation trigger an equivalent event in the shadow, using randomly selected agents from the entire population. There is no spatial or species
aspects to the simulation.
Shadow World 2 added species. All shadow agents have a species membership and
mating requires agents to be members of the same species (compatibility of mate
signatures is not a factor). Each foreground species has an equivalent shadow species,
and events in the foreground simulation species trigger events within the corresponding shadow species.
Shadow World 3 is built upon shadow world 2, adding an adoption queue (discussed
below), thereby removing any kin associations from the shadow species.
B.2.2
Entities, State Variables and Scales
The shadow worlds are much like the foreground world, except they have no spatial aspect
(i.e., grid of cells) and all genetic components are selectively neutral. For these worlds we
define three entities:
Shadow Agents are much like the agents of the foreground world, expect they only have
a chromosome and, in shadows worlds 2 & 3, species membership. The shadow
agents have no location, age or health. The shadow agent chromosome is fixed at
birth, and species membership changes over time.
B.2. SHADOW SIMULATIONS
143
Shadow Chromosomes are the same as the foreground world except they only have a
single junk signature, corresponding to the mate signature in the foreground world,
which is selectively neutral.
Shadow Species are much like the foreground species, except they are not based on
mate compatibility, instead they are randomly selected as they were formed, and,
additionally, hold a reference to their corresponding foreground species.
Table B.5: Shadow Simulation Entities and State Variables
Entity
Shadow World
Shadow Agent
Shadow Chromosome
Shadow Species
State Variable (Type)
Agents (Agent List)
Chromosome (Chromosome)
Species (Species)
Junk signature (Bit Vector)
Agents (Agent List)
Description
Occupant agents.
Chromosome of the shadow agent.
Species of the shadow agent.
Selectively neutral 100 bit string.
Agent members of the species.
Table B.5 lists the state variables, along with a brief description, for each of the entities.
The shadow worlds use the same timescales as the foreground simulation.
B.2.3
Process overview and scheduling
All processes in the shadow world are triggered by corresponding events in the foreground
simulation world. Table B.3 shows these simulation processes, categorized by entity.
B.2.4
Design concepts
Adaptation:
The purpose of the shadow world simulation is to replicate the dynamics
of the foreground simulation world without any adaptive elements.
Interaction:
Stochasticity:
Agents interact with each other via mating.
Stochasticity is used in the: selection of agents for mate and death
processes; chromosome crossover and mutation process; and species splitting during speciation.
Observation:
Data is collected and reported on the evolutionary activity of species.
144APPENDIX B. ODDS — TESTING THE PUNCTUATED EQUILIBRIUM HYPOTHESIS
Table B.6: Shadow Simulation Processes
Entity
Shadow Agent
Process
Description
Shadow mate
Mate and birth event,
using randomly selected
agents,
triggered by
equivalent
event
in
foreground world.
Death event, using a Remove shadow
randomly selected agent, agent entity.
triggered by equivalent
event
in
foreground
world.
Same as the foreground process
Same as the foreground process
Speciation event, us- Shadow
agent
ing randomly selected species. Create
agents,
triggered by species entity.
equivalent
event
in
foreground world.
Shadow death
Shadow Chromosome
Shadow Species
Crossover
Mutate
Shadow speciation
State
Variables affected
Create shadow
agent entity.
Adoption Queue: An adoption queue (of length one) is utilized to remove kin associations between species members in shadow world 3. As new shadow agents are created
they are placed at the end of the queue and, in their stead, an agent is selected from the
front of the queue. The new adopted offspring then is assigned the species membership
of its adopted parents. As there is no spatial aspect to the shadow simulation worlds,
this only affects the species membership, and meant that species are as diverse as the
entire world population. Detailed discussion of the adoption queue method of removing
kin associations can be found in Chapter 3.
B.2.5
Initialization
After the foreground world is created, it is copied to the shadow worlds — i.e., shadow
agents are created with copied chromosomes and, where relevant, species memberships
are retained. When used, the adoption queue is initialized with a single randomly generated chromosome. We experimented with re-syncing the shadow worlds occasionally (see
discussion in Channon, 2006) but found this had minimal impact on the results.
B.2. SHADOW SIMULATIONS
B.2.6
145
Input
Birth, death and speciation events in the foreground simulation run are input into the
shadow simulation, triggering equivalent processes.
B.2.7
Submodels
Shadow Mate:
In all shadow worlds, a mate event in the foreground world triggers an
equivalent mate event in the shadow world. The selection of shadow agents to mate differs
in each of the shadow worlds:
Shadow world 1 (without species): agent selection is performed by randomly selecting two agents from the entire shadow world population and mating them.
Shadow world 2 & 3 (with species): agent selection is performed by, first identifying
the species shadowing the species in the foreground where the mate event occurred,
and then randomly selecting two agents from that shadow species.
Note that in the shadow worlds compatibility of mate signatures is not considered. The
creation of the offspring shadow agent chromosome and species membership differs in each
of the shadow worlds:
Shadow world 1 & 2 (without adoption queue): the offspring is created with a chromosome formed via crossover and mutation of the parent chromosomes. In shadow
world 2 (with species) the offspring is also initialized with the species membership
of the parents.
Shadow world 3 (with adoption queue): offspring creation differs in that an adoption queue is utilized. The newly formed chromosome (as per above) is placed on
the end of the adoption queue and, in its stead, the chromosome from the front
is given to the new offspring. The newly adopted offspring is assigned the species
membership of its adopted parents.
Shadow Death:
In all shadow worlds, a death event in the foreground world triggers
an equivalent death event in the shadow world. The selection of the shadow agent differs
in each of the shadow worlds:
146APPENDIX B. ODDS — TESTING THE PUNCTUATED EQUILIBRIUM HYPOTHESIS
Shadow world 1 (without species): agent selection is performed by randomly selecting an agent from the entire shadow world population.
Shadow world 2 & 3 (with species): agent selection is performed by, first identifying
the species shadowing the species in the foreground where the death event occurred,
and then randomly selecting an agent from that shadow species.
In all cases, the death results in the removal of the agent from the shadow world.
Shadow Speciation: In the shadow worlds with species (i.e., shadow worlds 2 & 3)
a speciation event in the foreground world triggers an equivalent speciation event in the
shadow world. First the species shadowing the species in the foreground where the speciation event occurred is identified. This species is then randomly split into sub-groups
corresponding to the splits in the foreground species, and these sub-groups are used to
form new shadow species.
Vita
Publications arising from this thesis include:
Woodberry, O.G., Korb, K.B., Nicholson, A.E., (2005), The Evolution of Aging,
Proceedings of the Australian Conference on Artificial Life, Recent Advances in Artificial Life: Advances in Natural Computation, 05 December 2005 to 08 December
2005, World Scientific Publishing Co. Pte. Ltd, Singapore, pp. 319-333.
Woodberry, O.G., Korb, K.B., Nicholson, A.E., (2007), A Simulation Study of
the Evolution of Aging, Evolutionary Ecology Research, vol 9, issue 7, Evolutionary
Ecology Ltd, Tucson AZ US, pp. 1077-1096
Woodberry, O.G., Korb, K.B., Nicholson, A.E., (2008), Species Selection of
Aging for the Sake of Diversity, Proceedings of the Eleventh International Conference
on the Simulation and Synthesis of Living Systems, 5 August 2008 to 8 August 2008,
The MIT Press, London England UK, pp. 710-716.
Woodberry, O.G., Korb, K.B., Nicholson, A.E., (2009), Testing Punctuated
Equilibrium Theory using Evolutionary Activity Statistics, Proceedings of the 4th
Australian Conference on Artificial Life: Borrowing from Biology (ACAL 2009), 1
December 2009 to 4 December 2009, Springer-Verlag, Berlin Germany, pp. 86-95.
Mascaro, S., Korb, K.B., Nicholson, A.E., Woodberry, O.G., (2010), Evolving
Ethics: The New Science of Good and Evil, Imprint Academic, Exeter UK.
Permanent Address: Clayton School of Information Technology
Monash University
Australia
This thesis was typeset with LATEX 2ε 3 by the author.
3 A
LT
EX 2ε is an extension of LATEX. LATEX is a collection of macros for TEX. TEX is a trademark of
the American Mathematical Society. The macros used in formatting this thesis were written by Glenn
Maughan and modified by Dean Thompson and David Squire of Monash University.
147
148
VITA
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