Effects of competition on optimal patch leaving: A war of attrition

Abstract When resources are patchily distributed, animals have to decide when to leave a patch to find a new one. We model this leaving decision for any number n≥2 of animals per patch as a new version of the war of attrition. First, we consider a particular patch and assume that the animals get a fixed gain rate after leaving this patch. In this case, the optimal leaving strategy depends on whether or not there is interference. Without interference, ah animals should leave simultaneously according to the marginal value theorem. With interference, only n − K animals leave simultaneously, where K is a certain number independent of n , and the evolutionarily stable strategy (ESS) of the remaining K animals is stochastic. As a consequence, they may leave at different times, and stay longer than is expected from the marginal value theorem. As the degree of interference increases more animals leave simultaneously, and the leaving tendency of the remaining ones increases as well. The only effect of increasing n is that more animals leave simultaneously. Finally, we discuss in a heuristic way how to use these results in case the gain rate that the animals get after leaving the patch is not fixed but depends on the leaving strategy that is used. When there is no interference, the generalization is straightforward. When there is interference, however, complications arise in deriving the ESS, since the presence of mutants may change the average gain rate in the habitat in such a way that mutants have an advantage over residents. This type of complication also occurs in other ESS derivations where local effects have a strong influence.