Download Chapter 1 - New England Complex Systems Institute

Is Ecosystem Homeostasis
an Adaptation?
Josh Mitteldorf
Temple University, Dept of Statistics
Ambler, PA 19002
[email protected]
John Pepper
University of Arizona, Dept of Ecology and Evolutionary Biology
Tucson, AZ 85721
[email protected]
Four broad phenomena of the biosphere have persisted in inspiring controversy
because they seem to require higher levels of selection, which standard population
genetic theory dismisses as negligibly weak. These are:
 The ubiquity of sexual reproductive, despite a twofold disadvantage (by
some counts) in r.
 The persistence of high levels of genetic diversity in wild populations mocks
the theoretical fiat that all such diversity much be selectively neutral.
 Senescence is maintained as a near universal characteristic of the eukaryotic
genome, despite its negative contribution to individual fitness.
 Evidence of reproductive restraint and “prudent predation” is widely
accepted by field ecologists, but dismissed as nonsense by evolutionary
theorists.
We propose that evolutionary dynamics of ecosystems may provide a key to
understanding these dilemmas. In an ecological context, no species can afford to
maximize its reproductive potential without threatening the ecosystem on which it
depends. The fact that r is not subject to optimization voids a basic premise of the
standard paradigm, and makes room for many more subtle evolutionary effects – like
the four described above. We present a simple model ecosystem to illustrate these
ideas. The model tracks individuals of two animal species plus a non-evolving plant
food in a toy ecosystem, co-evolving on a viscous grid. In preliminary model results,
we find that predatory restraint evolves easily, that prey may become dependent on
their predators to help maintain stable population dynamics, and that senescence may
evolve as part of a co-evolutionary mechanism for maintaining population
homeostasis. A key to understanding the model's behavior is the local
interdependence of species, which supports the efficient punishment of any
population that expands at the expense of the ecosystem.
Is Ecological
Stability an Adaptation?
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1. Introduction
Two chapters in the history of evolutionary theory helped to shape attitudes toward
the mechanisms of evolution that are still prevalent today. In the early 20 th Century,
the first attempts to create quantitative models of Darwinian evolution were based on
the rate at which an individual gene could penetrate a population. And in the 1960’s
and 70’s, a cultural shift in favor of quantitative, mechanistic explanations swept into
evolutionary theory the premise that the dominant level of natural selection is the
individual.
The legacy of this second chapter is that the imperative for quantitative, mechanistic
thinking has been eclipsed, while a pervasive belief has emerged that arguments from
group selection are unscientific.
Paradoxically, proponents have sometimes
demonstrated the mechanisms of group selection with great precision, while some
competing explanations of the same phenomena are more easily accepted simply
because they claim to invoke individual selection, despite though detailed
mechanisms remain vague.
Modelers and theorists of the complex systems community are in a unique position to
be able to broaden the biologists’ conceptions of what is possible in evolution. We
have constructed a science of just those processes and effects that were dismissed as
unscientific in and after the cultural shift.
2. Population Genetics: the Standard paradigm of Evolutionary Theory
The foundation for population genetic theory was laid early in the 20 th century, with a
great deal of the credit accruing to R.A. Fisher (1930). The most basic paradigm is to
model a trait as a single gene, and to trace the progress of that gene’s frequency in the
gene pool of a large population. The gene is assumed to contribute to fitness in a way
that is independent of the action of other genes, and independent of the environment,
physical, biological, and social, in which the bearer of the gene is embedded. Under
these circumstances, the change in frequency x of a gene from one generation to the
next is just the covariance of that gene with fitness f, defined as the proportion of
offspring an individual contributes to the population’s next generation.
x = cov(x,f)
(1
Every population geneticist realizes in principle that this is an approximation,
neglecting:




Gene-gene interactions (epistasis)
Group interactions (cooperation or altruism)
Inter-species interactions (ecological population dynamics)
Advantages that don't show up in a single generation? (e.g. rate of evolution
effects.)
Nevertheless, it is conventional to take Eqn (1) as an approximation, and treat effects
like the above as small perturbations.
Is Ecological Stability an Adaptation?
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2.1. Vulnerability of the standard paradigm
The obvious question to ask is whether it is legitimate to treat these complexities as
perturbations, or whether their effect (individually or collectively) is sufficiently
strong as to render the original approximation inoperable as a starting point. This is
an empirical question, and it deserves to be addressed by experiment; but historically,
experimentalists have not posed the question. One reason is the substantial technical
problems that confront any attempt to design controlled experiments in a natural
ecology. But a second reason is essentially cultural: biological scientists are often
expert in the art of experimental design, but uncomfortable with theory. It has not
taken much browbeating to keep the experimentalists in line, accepting the Laws of
Nature as they have been bequeathed by biological theorists, designing and
interpreting their experiments in a context where these Laws are not called into
question.
2.2. Problems with the standard paradigm
Indeed, there are many well-delimited problems in evolution that are treatable by the
standard paradigm. No experiment in evolution is easy, and experiments that track
the fate of a single gene are quite challenging enough in themselves. Such
experiments have been taken as validation of the standard paradigm.
Meanwhile, there are a number of broad observations about nature that are difficult to
embrace in a model based on evolution of single genes in independent organisms.
These have become the subject of a specialized literature, frequently characterized by
misguided attempt to stretch single-gene theory in attempting to encompass them.
They have not generally been accepted as a reason to abandon the standard paradigm.
The prime examples are:
1.
2.
3.
The ubiquity of sex
By the most appropriate accounting, the cost of giving birth to males and
females rather than self-fertilizing hermaphrodites is a factor of 2 in fitness.
2 is an enormous number in a context where natural selection has finally
honed traits that offer an advantage of only 10 -5 or 10-4. Yet higher animals
have evolved to reproduce exclusively via sex. It is inconceivable that a
satisfactory explanation for the ubiquity of sex can be invented within the
context of the standard paradigm.
The persistence of diversity
This was a problem recognized early by Darwin, and rediscovered by anyone
who has ever created an individual-based evolutionary model. Under the
assumptions of the standard paradigm, even a tiny advantage in fitness
causes a gene to spread rapidly to fixation. Yet diversity, both within
species and among species, is one of the most striking broad observations
about the biosphere.
The ubiquity of Aging
Traditionally, aging has been explained not as an adaptation, but as a sideeffect of selection, because it is impossible for aging to evolve as an
Is Ecological
Stability an Adaptation?
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4.
5.
6.
adaptation within the standard paradigm. Yet there is overwhelming
evidence that aging is a developmental stage, and that a program of selfdestruction is designed into the soma expressly to limit life span (Mitteldorf
2004). This implies that aging has evolved as an adaptation; yet its effect on
fitness of the individual is wholly negative. Adaptive aging could not have
evolved according to the standard paradigm.
Adaptations that enhance evolvability
Chromosomes are structured so as to keep together genes that work together.
Rates of mutation change in response to environmental stress. Critical parts
of the genome are much less likely to mutate than other parts. These are all
adaptations that have no immediate effect on fitness as conventionally
defined; yet they seem to be very general and highly evolved features of the
eukaryotic genome. How could they have evolved under the standard
paradigm?
Reproductive restraint
Field biologists routinely report that predators hold back their numbers and
the intensity of predation in order to avoid driving their prey into extinction;
theorists of the standard paradigm say that they know better, on purely
theoretical grounds.
Stability of ecosystems
This subject is far less clear than the five above (Cropp & Gabric 2002). Has
nature had an easy time finding parameters that make ecosystems stable? Or
have whole species adjusted their life histories so as to be compatible with
each other in homeostatic food webs? This is the topic we propose to
investigate, and offer a beginning herein.
3. The Modeler’s Perspective
The above six phenomena offer challenges – I would say insurmountable challenges –
to the standard paradigm of gene-by-gene, individual-based selection. When we
approach these problems with evolutionary models, the results for the first four
corroborate the experience of those who work with the standard paradigm:
1.
2.
3.
4.
Sex: Individual-based evolutionary models reach the same conclusion as
does the analytic theory: If we allow a gene for hermaphrodism, it will take
off like wildfire in a dimorphic sexual population.
Diversity: Every student of evolutionary modeling discovers early on that
genetic diversity collapses quickly, and we frequently add extra-biological
gimmicks to maintain diversity in our models.
Aging: A population that suffers aging evolves more nimbly in the face of
environmental changes, because the effective population cycle time is
shorter. However, this effect is overwhelmed by the selective cost to the
individual of early death and forgone progeny.
In straightforward
individual-based models, a gene for aging fails to penetrate a population.
Evolvability: Only in a large, long-running model, including population
viscosity or a subdivided population, can evolvability emerge. If any
Is Ecological Stability an Adaptation?
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individual cost is ascribed to the adaptation, it will die out long before its
long-term benefits become apparent.
5. Predatory restraint
However, for #5, predatory restraint, the situation is entirely different. The
emergence of predatory restraint is a robust prediction of individual-based
evolutionary models that allow for predators and prey arrayed on any
reasonable geographic structure (Gilpin 1975; Pepper & Smuts 2002; Pels et
al 2002). It is standard in such models to assume that reproductive output
increases directly with predatory success; nevertheless, the group benefit of
restraint is seen to overwhelm handily the individual cost.
Why do evolutionary models for predatory restraint succeed, while models
for sex, diversity, aging, and evolvability fail? The difference is not in the
ratio of individual cost to group benefit, which is the focus of Hamilton’s
Rule (or the Price Equation). Rather, the difference is one of time scale.
Group adaptations #1-#4 offer benefits that accrue only on evolutionary time
scales, hundreds or thousands of generations in which a population must be
protected from invasion and mixing with neighboring populations. In
contrast, the failure of predatory restraint can cause food shortages in a
single generation. Population dynamics operates on a time scale far faster
than evolutionary dynamics.
Population geneticists have traditionally missed this distinction. Many have
assumed that group selection is always weaker than individual selection, and
have persisted in the theoretical prediction that predatory restraint cannot
evolve.
6. Stability of ecosystems
This is a subject that has been introduced recently by evolutionary modelers,
and which we have begun to explore with the current investigation.
4. Hypothesis: Ecological homeostasis as a system-level adaptation
The present work is inspired by the insight that the success of modeling #5 (predatorprey dynamics) may be leveraged to offer insights into #1-4 as well, and that #6 may
provide the link. Predator-prey population dynamics may be generalized to
ecosystem dynamics, in which many species may form mutual dependencies. Within
such a system, unrestrained population growth can be deadly to the stability of the
system, and therefore to each species that depends on it. The inability of individuals
to maximize their reproductive potential without destroying their ecosystem has broad
implications because it may help us to understand why “weaker” evolutionary forces
are not overwhelmed by the imperative to maximize reproduction.
5. Description of our model
We have explored a world consisting of two evolving (animal) species and one nonevolving plant : “foxes, rabbits and grass”, arrayed on an n*n cartesian grid of sites
Is Ecological
Stability an Adaptation?
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(16<n<32). Individual animals with individual genomes interact with others at their
home grid site, and have a finite probability in each time step of migrating to any of
the von Neumann neighbor sites. Biomass is created by the grass, and traced through
two more trophic levels. The system is dissipative in two ways: each animal species
has a finite probability of (accidental) death in each time step ; and each animal
spends a portion of its biomass (energy) in surviving each time step.
Grass is governed by a logistic difference equation, with an added term for grazing by
rabbits. Well below the saturation density, grass biomass grows by a constant
multiplicative factor in each time step, while rabbits feed on the grass in proportion to
their appetite. Thus when grass is plentiful, a site can support a large population of
rabbits sustainably. At low levels, grass biomass is presumed never to fall below a
minimal level, so it cannot become extinct, even locally. Different model dynamics
are observed if this level is set too low to support a single rabbit, or higher so that
rabbit populations are not punished so
Each animal carries five genes, implemented as floating point numbers that are
initialized in a triangular distribution, and are passed to the offspring with a finite
chance of mutation. Mutation consists in multiplication by (1+ where  is a
random number scaled by a parameter of the model. The five genes are :
Appetite – controls the intensity of predation, for either rabbits or foxes. Higher
appetite means greater growth rate and reproduction rate, but also greater
exploitation of food resources.
Aging rate – death from old age increases at an exponential rate (a Gompertz
function) scaled by this factor. The speed (of flight or pursuit) that determines
the outcome when a fox hunts a rabbit also declines exponentially at this rate.
Reproductive threshold – an accumulation of this much biomass triggers
reproduction. Lower threshold means a faster reproduction.
Incidental mortality – a death rate per time step independent of all other factors.
Metabolic rate – has two effects: (1) the rate per time step at which biomass is
consumed as a cost of living, and (2) scales the “speed” of both foxes and
rabbits, and thus determines the outcome of the hunt.
An unusual feature of this model system is the presumed relationship between aging
and predation. A “speed” is attributed to each fox and each rabbit, based on its
metabolic rate and its age. In each time step, at each site, the foxes and rabbits at that
site engage in a tournament. The fastest foxes are paired with the slowest rabbits.
The foxes that win their race earn a meal (biomass), and the rabbits that lose, lose
their lives. Speed of young animals is proportional to metabolic rate; both rabbits
and foxes slow with age, giving an advantage to the young foxes over the old rabbits.
Specifically, speed declines with age at an exponential rate equal to the animal’s gene
for aging rate.
The source code (Delphi Pascal) and GUI excecutable (for Windows platforms) with
many user-specifiable parameters are publicly available as
http://www.mathforum.org/~josh/ecsys2ge.zip and
http://www.mathforum.org/~josh/ecsys2ge.exe, respectively.
Is Ecological Stability an Adaptation?
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5.1. Dynamics of the model
Individual selection tends to push appetite higher, aging rate, reproductive threshold,
and incidental mortality lower. High metabolic rate is disadvantageous to an
individual, because it represents a loss of biomass in each time step; however in our
model, rabbits and foxes are locked in a speed race that derives from the dynamics of
predation. This effect dominates, and pushes metabolic rate higher for both species.
Predation and local population dynamics complicate this picture and make the model
interesting. If foxes become too successful in their hunt, they push the rabbits to local
extinction, and the site remains vacant until it is re-seeded through migration. If
rabbits become too numerous at a site, the grass biomass drops to a level that cannot
support them. A high reproductive threshold for foxes allows them to store biomass
and survive through a famine; while a low reproductive threshold for rabbits enables
them to reproduce quickly, before they can be hunted. Other combinations of
individual genetic traits contribute to stabilizing or destabilizing the ecosystem as a
whole, and may evolve in combinations that promote homeostasis.
5.2. Other options in the model
The model allows provision for three other options:
 Territoriality: If selected, then an animal will not migrate to a site that is
occupied by other animals of the same species. Rabbits or foxes or both can
be territorial.
 Random predation: The system described above for pairing fast foxes with
slow rabbits can be replaced by a random hunt, independent of age or
metabolic rate.
 Closed-loop ecosystem: If this option is selected, then the presence of foxes
at a site enhances the growth rate of the grass. This is a crude way to model
the fact that ecosystems often include mutual dependencies, in addition to
trophic dependencies.
 Sexual reproduction: An option is available for combining genes from
two (hermaphroditic) individuals in creating each offspring.
6. Preliminary Results

Limited appetite evolves in both foxes and rabbits, conserving their food
species.
Is Ecological
Stability an Adaptation?
8
 One striking finding is that our implementation of a hunt based on speed of
flight that declines with age dramatically stabilizes the system. With hunting
based on random probability of success and equal vulnerability of all rabbits,
the system invariably evolves toward a rabbit victory (foxes become extinct) or
a fox victory (rabbits become extinct, followed by foxes). But when foxes hunt
the slowest rabbits preferentially, the foxes and rabbits co-evolve a solution,
whereby foxes are too slow to catch the young rabbits, and rabbits age
sufficiently that eventually they are all consumed by the foxes.
 Prey are observed to evolve shorter life spans (faster aging) than predators.
This stabilizes the ecology, and agrees with a general observation that predators
in nature have longer life spans than their prey.
 Prey populations may become dependent on predators for stability. The rabbits
can evolve a set of life history traits that efficiently use the grass, in the
presence of predation by foxes. If the foxes are suddenly (artificially) removed,
the rabbit population overgrazes, and quickly plummets. It may take a long
while for selection to find a better set of life history parameters in the absence
of predation.
 The closed loop option stabilizes the 3-species system, and enhances the
evolution of cooperative solutions between predator and prey.
7. Summary
We have begun the exploration of a promising new paradigm for explaining four
general phenomena of the biosphere which are not easily treated by the standard
paradigm of population genetics. We hypothesize that ecosystem interactions blunt
the force of selection for reproductive potential (r) that overwhelms the higher level,
longer-term mechanisms that are capable of selecting for aging, diversity, and sexual
dimorphism.
References
Cropp, R., & Gabric, A. 2002. Ecosystem adaptation: Do ecosytems maximize resilience?
Ecology 83(7):2019-2026
Fisher, R.A. 1930, (repr 2000). The genetical theory of natural selection. Oxford University
Press. New York.
Gilpin, M. 1975. Group selection in predator-prey communities. Princeton University Press.
Princeton, NJ.
Mitteldorf, J. 2004. Aging Selected for its Own Sake. Evol. Ecol. Res, In press.
Pels, B.; deRoos, A.M.; & Sabelis, M.W. 2002. Evolutionary dynamics of prey exploitation in a
metapopulation of predators. Am Nat 159:172-189.
Pepper, J.W. 2002. The evolution of evolvability in genetic linkage patterns. BioSystems
69:115-126 link
Pepper, J & Smuts, B. 2002, A mechanism for the evolution of altruism among non-kin:
Positive assortment through environmental feedback. Am Nat 160:205-213