Cooperation

COOPERATION

Mutualism Versus Reciprocity

(Last updated on December 31, 2000)

In a collaboration with Lee Dugatkin, I am using evolutionary game theory to study cooperative behavior among animals. We are working toward a general theory that categorizes cooperative behavior in nature as kin-selected behavior, group-selected behavior, byproduct mutualism or reciprocal altruism. In pursuit of this goal, our current investigations focus on cooperative behaviors that can be excluded on a priori grounds from the first two categories mentioned. Examples of such behaviors are food sharing in ravens and defensive behavior in lions. Accordingly, we focus on reciprocity versus mutualism, and we are developing a mathematical model with the power to discriminate between these two categories of cooperative behavior. Such a model is important, because many examples of reciprocity in nature have been hypothesized, but hardly any have been proven: without such a model, virtually every example is equally interpretable as a case of mutualism.
In other words, the long-term goal of the current project is to determine whether animals can cooperate in nature because they keep score of favors done to, and favors received from, specific individuals; or because acting in their ultimate self-interest coincides with acting in the best interest of their community, even though they do not keep score. From a purely scientific perspective, an answer to this question will advance current knowledge of animal behavior considerably. From a more utilitarian perspective, even though our primary subjects are non-human animals in the wild, our findings may be relevant to achieving cooperation among humans. In particular, our findings may help to solve the the urgent problem of the commons, i.e., the problem of designing cooperative social structures for sustainable management of the global environment.
Nevertheless, in the short term we recognize that mutualism versus recriprocity may be strongly influenced by competition and dominance, whose effects are still not thoroughly understood. In this regard, some of our recent work explores novel aspects of pure competition and dominance, with a view toward understanding their effects on the evolution of cooperation.

This collaboration was funded by the National Science Foundation from August, 1996 until July, 2000 under grants

#9626609	(M. Mesterton-Gibbons)
#9626637	(L. A. Dugatkin)

Publications

M. Mesterton-Gibbons and L.A. Dugatkin. Cooperation and the prisoner's dilemma: toward testable models of mutualism versus reciprocity. Animal Behaviour 54, 551-557 (1997)
ABSTRACT: For the purpose of distinguishing between mutualism and reciprocity in nature, recent work on the evolution of cooperation has both oversimplifed and undersimplified the distinction between these two categories of cooperation. This article addresses the resulting issues of model testability, clarifies the role of time, and argues that the category of "pseudo-reciprocity" is an unnecessary complication.
M. Mesterton-Gibbons and E.S. Adams. Animal contests as evolutionary games. American Scientist 86, 334-341 (1998)
Click here for abstract.
M. Mesterton-Gibbons and E.J. Milner-Gulland. On the strategic stability of monitoring: Implications for cooperative wildlife management programs in Africa. Proceedings of the Royal Society of London B 265, 1237-1244 (1998)
ABSTRACT: Game-theoretic modelling is used to study the design of an agreement among residents to conserve a wildlife resource, by not hunting animals illegally, when the community monitors its own behaviour. The analysis demonstrates that such an agreement may be very much costlier for a government to sustain if its incentive structure avoids the payment of monitoring fees and instead relies on community benefits for conservation with bonuses for reporting poachers. Conditions are identified for the agreement to be stable against both the temptation to avoid monitoring and the temptation to poach, either with guns or by snaring. In particular, the size of the community must exceed a critical value. Implications are discussed for community-based wildlife management programs in Africa.
M. Mesterton-Gibbons. On sperm competition games: raffles and roles revisited. Journal of Mathematical Biology39, 91-108 (1999)
ABSTRACT: In principle there are two approaches to modelling a trade-off between the positive and negative outcomes of a behavior. After suitably defining a value for the behavior in the absence of any trade-off, one can either multiply that value by an appropriate discount or subtract an appropriate cost. In a prospective analysis of sperm competition, Parker (Proc. Roy. Soc. Lond. B 242, pp. 120-126, 1990) adopted a multiplicative approach to model the trade-off between the value of a mating and the cost of its acquisition. He obtained two paradoxical results. First, if two males "know" whether they are first or second to mate, but these roles are assigned randomly, then sperm numbers should be the same for both males whether the "raffle" for fertilization is fair or unfair. Second, if mating order is constant, then a favored male should expend less on sperm. His results are puzzling not only in terms of intuition about nature, but also in terms of his model's consistency. In other words, they present both an external and an internal paradox.
----Parker assumed the fairness of the raffle to a second male to be independent of how much sperm a first male deposits. This article both generalizes Parker's analysis by allowing fairness to decrease with existing sperm expenditure and compares his results to those obtained by the additive approach. In many respects, results are similar. Nevertheless, if the costs of mating are assumed to increase with sperm expenditure but not to depend on the role in which sperm is expended, then the additive approach is more fundamentally correct. In particular, Parker's constant-role paradox is an artifact of his approach. His random-role paradox is internally rationalized in terms of standard microeconomic theory.
----When fairness decreases, however slightly, with existing sperm numbers, both models demonstrate that the evolutionarily stable strategy is for more sperm to be deposited during a first mating than during a second. The lower the costs, the greater the divergence. Thus a possible resolution of the external paradox is that fairness is not constant in nature.
M. Mesterton-Gibbons. On sperm competition games: incomplete fertilization risk and the equity paradox. Proceedings of the Royal Society of London B 266, 269-274 (1999)
ABSTRACT: Evolutionary game theory has been used to predict the effect on sperm expenditure of a trade-off between the value of a mating and the cost of its acquisition. In particular, Parker (Proc. Roy. Soc. Lond. B 242, pp. 120-126, 1990) has predicted that if two males `know' whether they are first or second to mate, but these roles are assigned randomly, then sperm numbers should be the same for both males whether the "raffle" for fertilization is fair or unfair. This prediction relies on the assumption that, in the absence of sperm competition, ejaculates would always contain enough sperm to ensure complete fertilization after mating. The slightest risk of incomplete fertilization, however, is enough to ensure that favored males expend more than disfavored males in the presence of sperm competition, unless the competition is perfectly fair. Divergence of expenditures increases with unfairness until unfairness reaches a critical value, beyond which a disfavored male should no longer compete. The higher the fertilization risk, the lower the critical unfairness. All predictions are independent of the probability of mating first or second. Implications are discussed for the mechanisms that underlie sperm competition.
M. Mesterton-Gibbons and L.A. Dugatkin. On the evolution of delayed recruitment to food bonanzas. Behavioral Ecology10, 377-390 (1999)
ABSTRACT: Whereas food sharing by immediate recruitment to food bonanzas is relatively common, especially among birds, delayed recruitment from overnight roosts is comparatively rare, although it has been studied extensively in the common raven (Corvus corax). Two hypotheses have been advanced to explain the evolution of delayed recruitment. Under the status-enhancement hypothesis, delayed recruiting is favored because the recruiter's social status increases with the number of followers it leads to a food source. The posse hypothesis also focuses on the number of individuals recruited to a site, but in this case aggregation is favored because larger groups are more likely to usurp a carcass defended by a pair of territorial adult ravens. We use a game-theoretic model to explore the logic of immediate versus delayed recruitment in the light of these hypotheses. In particular, we identify three critical values of the probability of immediate recruitment, namely, that below which delayed recruitment is a cooperative strategy, that below which delayed recruitment is an evolutionarily stable strategy, and that below which a mutant strategy of delayed recruitment will invade a population of immediate recruiters to reach fixation. The model demonstrates that either status enhancement or the posse effect may alone suffice for the evolution of delayed recruitment to food bonanzas via mutualistic information sharing at communal roosts.
M. Mesterton-Gibbons. On the evolution of pure winner and loser effects: a game-theoretic model. Bulletin of Mathematical Biology61, 1151-1186 (1999)
ABSTRACT: The persistence of linear dominance hierarchies is often attributed to higher probabilities of a win after a win or a loss after a loss in agonistic interactions, yet there has been no theory on the evolution of such prior-experience effects. Here an analytic model, based on the idea that contests are determined by subjective perceptions of resource holding potential (RHP) which animals may revise in the light of experience, demonstrates that winner and loser effects can evolve through round-robin competition among triads of animals drawn randomly from their population, and that the probability of a hierarchy increases with the strength of the combined effect. The effects are pure, in the sense that a contestant observes neither its own RHP nor its opponent's RHP or RHP perception or win-loss record; and so the strength of an effect is unmodified by the RHPs of particular individuals, but depends on the distribution of RHP among the population at large. The greater the difference between an individual's and its opponent's RHP perception, the more likely it is to win a contest; however, if it overestimates its RHP, then the cost of fighting increases with the overestimate. A winner or loser effect exists only if the fitness gain of the beta individual in a hierarchy, relative to that of the alpha, is less than 0.5. Then a loser effect can exist alone, or it can coexist with a winner effect; however, there cannot exist a winner effect without a loser effect.
M. Mesterton-Gibbons. An Introduction to Game-Theoretic Modelling,second edition (2000). Student Mathematical Library Volume 11, American Mathematical Society.
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