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Conference Papers Year : 2010

ESS versus cooperative behaviour in a consumer-resource model


In this work we consider a system of two interacting populations of consumers and resources. It is assumed that the two populations interact during a season of length T and die at the end of it. Reproductive processes occurring during the season determine the size of the populations at the beginning of the next season, what corresponds to a 'semi-discrete' model [1,2]. We assume that the resource population behaves passively and the consumers have some control on their reproduction: they must choose between investing their time in foraging the resources, what increases their reproductive capacities, or in reproducing. Assuming that consumers agree to cooperate, we first study the maximization of the consumers fitness (strictly speaking their number of descendants in the next generation) as a dynamic problem of energy allocation and investment [3]. We show that such an 'optimal' strategy is not evolutionarily stable (ESS) as a population using such a strategy might be invaded by some mutants that take advantage of their small density and non-cooperative behaviour. We then look for an ESS, using the first condition for ESS (or "Nash condition" or rather "Wardrop condition" [4,5]) for the consumers population which does not allow any mutant to invade. We show how such a strategy can be obtained as the solution of a zero-sum differential game. Moreover, we compare these two reproductions strategies in terms of their influence on the dynamics of the system through many seasons. Though not ESS, the optimal strategy leads to a stable situation in a long-term perspective. On the contrary, the prevention strategy is ESS but it is not long-term stable and leads to an instance of the so-called "Tragedy of the Commons".
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hal-00850412 , version 1 (06-08-2013)


  • HAL Id : hal-00850412 , version 1


Anderi R. Akhmetzhanov, Frédéric Grognard, Ludovic Mailleret, Pierre Bernhard. ESS versus cooperative behaviour in a consumer-resource model. Conference on Computational and Mathematical Population Dynamics, 2010, Bordeaux, France. ⟨hal-00850412⟩
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