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This review appeared in Volume 10(2) of The Semiotic Review of Books.

Life Games

Daniel R Brooks

Evolutionary Game Theory, by Jrgen W Weibull, MIT Press, Cambridge MA, 1997 ISBN 0-262-23181-6

Darwin (1872) believed that evolutionary change resulted from the interaction of two factors, which he called "the nature of the organism" and "the nature of the conditions". Of these two, the nature of the organism ...seems to be much more the important; for nearly similar variations sometimes arise under, as far as we can judge, dissimilar conditions; and, on the other hand, dissimilar variations arise under conditions which appear to be nearly uniform.

This is because Darwin felt it was in the "nature of the organism" to produce offspring that were all highly similar (but not identical) to each other and to their parents and other ancestors. He also postulated that reproduction produced variation without regard for environmental conditions and therefore it was in the "nature of the organism" to produce these offspring in numbers far exceeding the resources available for their support. When this inherent overproduction produced variety in critical characters, natural selection would preserve the versions that were functionally superior in that particular environmental context (adaptations). Whenever an environment changes, those organisms that already had the adaptations necessary to survive would do so, whereas those lacking appropriate adaptations would not. Selection did not create the adaptations, it only determined which ones, if any, would be favored for survival. The production of organismal diversity thus required that organisms be at once autonomous from, and sensitive to, the environment. Darwin's perspective contrasted sharply with Lamarck's proposal that adaptation was an immediate and directed response by organisms to their surroundings. Lamarck believed that the nature of the organism was important in the production of diversity only because all organisms have the same ability to change according to their needs. So while Darwin postulated that the "nature of the organism" included autonomous, self-regulating properties, Lamarck believed that the "nature of the organism" was directly and completely connected to the environment.

Much of the discourse in contemporary evolutionary biology consists of one person asking, "What happens if...?" to which another person answers, "Well, that depends..." Ever since Darwin, "that depends" on the nature of the organism and the nature of the conditions for the particular case being discussed. More than a generation ago, John Maynard Smith began encouraging evolutionary biologists to attempt to integrate the mathematical theory of games into studies of evolution in order to grapple with the complexity and contextual nature of evolution. Weibull seems to pre-suppose knowledge and acceptance of Maynard Smith's perspective in this volume on the subject.

What is involved in viewing evolution as a game? The players are individual organisms displaying one or more inherited "strategies", or options for dealing with their surroundings. These "strategy sets" of options may themselves be complex, including frequency dependent, phylogenetic, and developmental constraints on their expression. The sum total of these inherited constraints is called the bauplan, appearing in games as is the fitness generating function for the species (everything that uses the same strategy set and suffers the same consequences). The Rules of the game are the payoff consequences for using a particular strategy. The Payoff is fitness; i.e. your 'winnings' are converted into copies of yourself. Thus, there are no ultimate winners, just survivors in various frequencies. There can be ultimate losers, of course. The "Gambler's Ruin" is an important part of game theory, stating that no matter how successful you are, you can always lose, even to the point that you cannot make the basic ante, taking you out of the game completely. This leads to different classes of games. Positive-side Games include Kin selection (probability of like interacting with like), Reciprocal altruism (probability of interacting with someone you know), Prudence (probability of acting from habit; probability of getting caught acting from habit). Negative-side games include Disassociative interactions (probability of interacting with unlike); Honor among thieves (I' m only nice to certain people); and Impudence and infamy (I want a reputation for being nasty).

Games theory then makes certain basic Darwinian assumptions: There is heritable variation; There is a struggle for existence; heritable variation influences the struggle; Individuals have fitness and fitness is influenced by your strategy, others around you, frequencies of others. Theexpected outcome of each game is some form of Evolutionary Stable Strategy (ESS), a dynamic steady state in which the fitness generating function of each individual's strategy subset of its species' strategy set is maximized. The game is thus determined by "conflicts of interest" stemming from the nature of the organism under particular conditions; the evolutionary outcome is determined by the way in which those conflicts are resolved. This is A wins, B wins, or A and B accommodate each other in some manner. In biology, the third possibility seems to be the rule rather than the exception, since we see increasing diversity of life over time, punctuated occasionally by large-scale environmental disasters that re-set the stage for a new set of games. I believe this is because it is in the nature of organisms to be adaptable as well as to generate novelty, and this leads to a net accumulation of diversity and complexity. It would appear that games theory incorporates both the nature of the organism and the nature of the conditions. This integration is incomplete, however.

Weibull's text is a master compilation of applications of some very complex and opulent mathematics. It proceeds from the simplest examples through increasingly complex biological interactions, each of which requires increasingly complex mathematical treatments within the theory of games. It is a tour de force of the scope of modern games theory. Having been written somewhat like a recipe book by a master chef for use by other master chefs, this book does not address fundamental questions such as why one would want to be a chef, or would want to prepare the particular dishes included in the recipe book. There are short introductory remarks at the beginning of each recipe, but these are mostly to indicate the history of the recipe. Only occasionally does the author give us some insight into why he is a master chef. These insights, however, are critical to making an informed decision about whether or not you think games theory should be part of your intellectual tool kit. And I think they give insights into an interesting paradox underlying many applications of games theory to biological evolution.

If we need increasing mathematical complexity to explain increasing degrees of biological complexity, are we actually approaching a fundamental goal of basic science, to provide explanations of great generality and power? Is there a meta-game for biology, one explaining why we need increasingly complex mathematical treatments of increasingly complex biological interactions? Weibull does not consider this question Why? I suggest this is not because the meta-game is unknown, but because there are elements of the meta-game that conflict with some of the ideals of those who have adopted games theory. Weibull, like all master chefs, dislikes surprises. He wants his recipes to provide guaranteed, predictable results. "Stable" may occur more often than any other word in this book.

It has been the hope and aim of modern science since the Enlightenment to subjugate and control Nature. Essential to control is the ability to predict the future, to control Time. The framework for achieving this has been called the Newtonian framework. In this framework, the world is deterministic, all phenomena are reversible, and all nature tends to be at rest, in equilibrium. Time can be eliminated from our equations and thus from our explanations. This makes the future behavior of such systems highly predictable (hence they can be controlled); they hold no surprises. Or, as Weibull says (page 93):

For the purpose of making dynamic predictions, asymptotic stability is a more reliable property than Lyapunov stability. For Lyapunov stability does not protect against unmodeled evolutionary drift; occasional small perturbations of the population state may pass unchecked by the dynamics at such a population state. Hence, a sequence of such shocks may carry the population to a state where the replicator dynamics leads it far away. Asymptotic stability, in contrast, guarantees a pull back to status quo after any small perturbation of the population state. Hence, robust evolutionary predictions call for asymptotic stability.
> The passage quoted above expresses fear of the possibility that a system might have its own, uncontrolled, unpredictable evolutionary properties, as well as an intense dislike for anything that disturbs the status quo. In particular, it is highly inconvenient for the nature of the organism to be evolutionary. Since the author makes this statement without discussing its underlying implications, I assume that the games theorists to whom he is talking feel the same way. For them, such a statement is unremarkable. But my reaction is, "What a paradox to find yourself in -- to be fascinated by evolution while at the same time to be afraid of change."

Darwin considered evolution to be "descent with modification", implying some temporal sequence of change, which was the outcome of interactions between the nature of the organism and then nature of the conditions. Evolution is clearly an historical process, something manifested over time. Ever since Ludwig von Boltzmann provided a statistical framework for understanding thermodynamic behavior, there has been an alternative to the Newtonian world view. This alternative applies to systems exhibiting indeterminate, irreversible, non-equilibrium behavior. In direct contrast to classical Newtonian systems, these systems retain much of their history but their future behavior cannot be predicted. This means they cannot be easily controlled, because every attempt we make to control time produces more of it.

If biological evolution is more a statistical mechanical than a Newtonian process, consideration of nonequilibrium, irreversible, complex system behavior may represent the fundamental organizing principle missing in games theory (e.g., Brooks and Wiley, 1988; Brooks et al, 1989; Brooks, 1997; Collier, J. 1986, 1998). In this view, organisms are physical information systems, a type of nonequilibrium thermodynamic system, open to exchanges of matter and energy but maintaining a relatively closed, or isolated, information system internally which functions to reproduce the system, to perpetuate lineages through time. They are able to impose themselves and their functions on their surroundings, and thus are self-stabilizing and self-organizing. They produce organized complexity cheaply (because a small number of chemical templates are used to generate many organisms), variably (because chemical templates are subject to the statistical mechanical vagaries of the Second Law of Thermodynamics), and functionally (because organisms must exchange matter and energy with their surroundings in order to maintain themselves), but without regard for details of the surroundings (because the information system is embodied in relatively autonomous internal chemical production). Organisms are messages embodying this information sent from a genealogical source in the present to itself in the future. As the source and receiver of organized information, populations and species embody the organizing principles for that information. Biological systems thus transmit information through, not to, their surroundings. This supports Darwin's view that it is the (autonomous, selfish, closed, or isolated) nature of the organism that creates the necessary conditions for selection processes to occur.

Treating biological systems as physical information systems provides a causal basis for the origin of selection processes consistent with their well-documented consequences. All organisms are intimately tied together in the structure of the biosphere, because they are all simultaneously parts of larger genealogical and ecological wholes. The significance of the duality of organismal diversity is most apparent in the recognition that new types of organisms are derived from pre-existing organisms, while at the same time, almost all organisms make extensive use of the biodiversity that pre-dated their origins. Newly evolved organisms always have an impact on pre-existing ones. Because it is in the nature of the organism to be relatively autonomous from its surroundings, these interactions are not necessarily positive, often taking the form of "conflicts of interest". The evolutionary resolution of these conflicts of interest has produced an increasingly complex biosphere. Selection processes originate as a result of the necessity that biological systems obtain matter and energy from their surroundings, coupled with the relative autonomy of their information systems, which permits production of organisms regardless of the details of their surroundings. Without the constraints provided by this autonomy, there would be no selection; at the same time, however, constraints provide systems with macroscopic properties that limit the ways in which and the extent to which the system will respond to selection. Each major transition in evolution discussed by Maynard Smith and Szathmary (1995) has been associated with the emergence of organisms, and by extension the entire biosphere, with enhanced abilities to produce, maintain and transmit information cohesively, and also associated with the emergence of novel forms of selection resulting from the evolution of those new organisms. In this way, each newly evolved form of organism becomes intimately involved with both local and global ecology, maintaining the biosphere as a relatively isolated system with its own windows of vitality.

By being afraid of inherent evolutionary dynamics, some games theorists have placed themselves in a position of ignoring the meta-game that provides the rationale for adopting agames theoretical view of evolution. Evolutionary change in the nature of the organism occurs without regard for the nature of the conditions. The nature of the conditions, both biotic and abiotic, will change without regard for the nature of the organism. Thus, evolution may change the payoff, the rules, or the game itself. The meta-game is thus determining the optimal game for the interaction between reproduction (the nature of the organism) and adaptation (the nature of the conditions) in promoting evolutionary change. There are currently two candidates.

The first of these has been advocated most ardently by G.C. Williams. In simple terms, this perspective says that populations should adapt maximally to their local surroundings in order to ensure continuation of the species; i.e. adapt maximally and reproduction (information flow) will take care of itself. Lieberman et al. (1995) have shown that this produces long-term global stasis (because the local information is shared throughout the system by reproduction. This would leave such systems vulnerable to extinction, since each time the adaptive landscape changes, the environment decays with respect to the most fit organisms and you experience local extinctions. If environmental change is too widespread or too rapid for species to adapt, they will go extinct. Collier (1998) has drawn similar conclusions formally using measures of mutual information content to represent the degree of adaptation between organisms and their environments.

The second candidate has been articulated best by Maynard Smith and Szathmary (1995). This perspective says that populations should enhance the efficiency of storing and transmitting information from one generation to the next; i. e. reproduce maximally and adaptation will take care of itself. This is made possible by making information flow more autonomous from particular environmental conditions. And such autonomy is accomplished by making the information systems progressively more abstract representations of their environments. No matter where or in which species enhancements of information storage and transmission evolve, they will be extremely successful globally; thus, they will not be related to any particular external environment. We will not be able to say they were selected for any function other than self-perpetuation. At the same time, these are the conditions under which new forms of selection and thus selection-mediated adaptation will emerge because living systems must always maintain functional causal connection with their surroundings they cannot escape their environments.

It appears then that if evolution is a non-equilibrium process, the optimal game is to enhance the efficiency of the autonomous storage and transmission of information by reproduction. This strategy ensures adaptation as well as reproduction, while the alternative ensures only adaptation. This is in some sense a re-statement of the "ESS Maximum" principle: maximize fitness generating function with respect to the focal individual's particular strategy set subset of the whole species' set. There are more wide-ranging implications, however. This return to Darwin's view of the primacy of the nature of the organism over the nature of the conditions has emerged in other many contexts in other areas of biology (see references). Treating biological systems as physical information systems may hold the key to the next evolutionary synthesis. And the rhetorical structure of games theory may provide a general platform for discourse uniting different disciplines in a truly unified theory of evolution.

References

Brooks, D.R. 1997. "Biological evolution as a microcosm of cosmological evolution." Bridges 4: 9-35.

Brooks, D.R., J. Collier, B.A. Maurer, J.D.H. Smith, and E.O. Wiley. 1989. "Entropy and information in evolving biological systems." Biol. Philos. 4: 407-432.

Brooks, D.R. and D.A. McLennan. 1991. Phylogeny, Ecology and Behavior: A Research Program in Comparative Biology. Chicago: Univ. Chicago Press.

Brooks, D.R. and E.O. Wiley. 1988. Evolution as Entropy: Toward a Unified Theory of Biology. 2nd ed. Chicago: Univ. Chicago Press.

Collier, J. 1986. "Entropy in evolution." Biol. Philos. 1: 5-24.

---. 1998. "Information increase in biological systems: How does adaptation fit?" In Evolutionary Systems: Biological and Epistemological Perspectives on Selection and Self-Organization, ed. G. van de Vijver, S.N. Salthe, and M. Delpos, 129-140. Dordrecht: Kluwer Academic Publishing.

Darwin, C. 1872. The Origin of Species. London: John Murray. 6th edition.

Lieberman, B.S., C.E. Brett, and N. Eldredge. 1995. "A study of stasis and change in two species lineages from the Middle Devonian of New York state." Paleobiology 21: 15-27.

Maynard Smith, J. and E. Szathmary. 1995. The Major Transitions in Evolution. Oxford: W.H.Freeman Spektrum.

Daniel R. Brooks is Professor of Zoology at the University of Toronto. He is an evolutionary biologist with interests in the systematic biology of parasitic helminths, historical ecology, evolutionary theory, and biodiversity and sustainable development. He is currently a member of the International Programme Advisory Boards for the 18th International Congress of Zoology (Athens, 2000) and the International Society of Systematic and Evolutionary Biology. He also serves as the international coordinator of the inventory of eukaryotic parasites of vertebrates of the Area de Conservacion de Guancaste, Guanacaste, Costa Rica. Representative publications include:

Brooks, D.R. and E.O. Wiley. 1988. Evolution as Entropy: Toward a Unified Theory of Biology (1988, co-authored with E.O. Wiley), The Compleat Cladist: A Primer of Phylogenetic Procedures (1991, co-authored with Wiley, E.O., D. Siegel-Causey, D.R. Brooks, and V.A. Funk), Phylogeny, Ecology and Behavior: A Research Program in Comparative Biology (1991, coauthored with D.A. McLennan), Parascript: Parasites and the Language of Evolution (1993, co-authored with D.A. McLennan).


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