Download Evolutionary Processes: An Entropic Principle

Emergence of
Organization and
Markets
Lloyd Demetrius
June 2014
Claim
The Origin and Evolution of Organizational
Structures
Can be analytically explained in terms of a theory
of autocatalytic networks.
Classes of Networks
(1)
(2)
(3)
Social Networks: cooperation between
individuals in a community
Economic Networks: transformation and
production of economic commodities
Linguistic Networks: production and generation
of symbols
2
Autocatalytic Networks
Chemical Reaction Networks
A + C
D
D + B
E
E
2C
Product C catalyses ist own synthesis from precursors
A and B
Biochemical Examples
1) Glycolysis:
2) Oxidative
Phosphorylation
2 ATP
36 ATP
3
4
5
Problem
To what extent is the conceptual
framework of autocatalytic networks
an appropriate model for the analytic
study of the origin and evolution of
socio-economic networks?
6
Origin and Evolution in Three Classes
of Networks
(1) Metabolic Networks: Energy production
(2) Social Networks: Evolution of cooperation
(3) Demographic Networks: Evolution of life
history
7
Metabolic Networks
Origin and Evolution of Energy Production in Cells
Glycolytic Networks
Oxidative Phosphorylation
Cancer cells: Predominantly Glycolysis
Normal cells: Predominantly Ocidative Phosphorylation
Problem
The Evolutionary Basis for Glycolysis and Ocidative Phosphorylation
8
Social Networks
Origin and Evolution of Cooperation
1
2
Random Interaction
3
Origin
1
2
Structured Interaction
3
Evolution
1
1
2
2
3
3
Stratified Network
Egalitarian Network
9
Non-Autocatalytic Networks
Aggregates of Interacting Molecules
Solid
Liquid
Gas
Problem
Explain the stability of these states
10
Thermodynamic Entropy
Measure of Complexity in Material Aggregates
S  k log W
W = number of ways that the molecules of a system can be arranged to achieve
the same total energy
Solid: low entropy
Gas: high entropy
Second Law of Thermodynamics:
Thermodynamic entropy increases
11
Demographic Networks
Origin and Evolution of Iteroparity
1
2
3
d
md
md
m3
m2
1
b1
2
b2
3
b3
Annual Plants
bd-1
d
1
b1
2
b2
3
b3
bd-1
d
Perennial Plants
Problem: The evolutionary rationale for the diversity in life
history
12
Organismic Evolution
(1)
(2)
(3)
Variation: individuals within a species vary in
terms of their physiology and behavior
Heredity: there exists a positive correlation
between the behavioral and physiological traits
of parents and their offspring
Selection: individuals differ in their capacity to
appropriate resources from the external
environment and to convert their resources into
offspring
13
Prerequisites for an Analytical Model of
Network Evolution
(1)
(2)
(3)
(4)
A mathematical description of network
complexity
A formal description of the
network-environment interaction
An analytic description of natural
selection
A description of the rules of inheritance
14
Demographic Networks
Network Complexity
S  k log W  Evolutionary Entropy
W = number of distinct pathways of energy flow in the network
md
md
m3
m2
1
b1
2
b2
3
b3
Annual Plants
W=1, S=0
bd-1
d
1
b1
2
b2
3
b3
bd-1
d
Perennial Plants
W>1, S>0
Network-Environment
Resource abundance, resource composition
Laws of Inheritance
Mendelian
15
Evolution of Demographic Networks
Evolutionary Changes in Network Complexity
Variation: Changes in the topology and interaction
intensity of the network – changes in life history
Selection: Competition between variant and
ancestral network for the resources
X = ancestral type
X* = variant type
16
Principles of Demographic Evolution
The outcome of selection is predicted by
evolutionary entropy and is contingent on the
external resource constraints:
(I) Resources constant in abundance and
diverse in composition
Evolutionary entropy increases (selection for
iteroparity)
(II) Resources variable in abundance,
singular in composition
Evolutionary entropy decreases (selection for
semelparity)
17
From Demographic Networks to Social
Networks
Properties
Demographic
Networks
Social
Networks
Unit
Life Cycle
Cooperative and
Selfish Transactions
Target of Selection
Phenotypic Traits
Behavioral Traits
Laws of Inheritance
Mendelian
Cultural
Environmental
Constraints
Energy: Foodstuffs
Energy: Foodstuffs,
Information
Measure of Fitness Degree of Iteroparity Degree of
Network Complexity
Cooperation
18
Evolutionary Entropy
Measure of Network Complexity
S  k log W
W = number of distinct pathways of energy flow within a network
1
2
3
Few pathways = low entropy
1
2
3
Several distinct pathways
= high entropy
Network
Low Entropy
High Entropy
Demographic
Annual Plants
Perennial Plant
Metabolic
Glycolysis
Oxidative Phosphorylation
Social
Selfishness
Cooperative
Political
Stratified
Egalitarian
19
Applications of the Entropic
Principles of Network Evolution
Resource
constraints
Metabolic
networks
constant
abundance diverse
composition
variable
abundance singular
composition
oxidative
cooperation economic
phosphorylation
equality
glycolysis
Social
networks
selfishness
Economic
networks
economic
inequality
20