EFFECTS OF COMPETITION ON OPTIMAL PATCH LEAVING - A WAR OF ATTRITION

When resources are patchily distributed, animals have to decide when t o leave a patch to find a new one. We model this leaving decision for any number n greater than or equal to 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 o r not there is interference. Without interference, ah animals should l eave simultaneously according to the marginal value theorem. With inte rference, 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 l eave at different times, and stay longer than is expected from the mar ginal value theorem. As the degree of interference increases more anim als leave simultaneously, and the leaving tendency of the remaining on es increases as well. The only effect of increasing n is that more ani mals 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 tha t is used. When there is no interference, the generalization is straig htforward. When there is interference, however, complications arise in deriving the ESS, since the presence of mutants may change the averag e gain rate in the habitat in such a way that mutants have an advantag e over residents. This type of complication also occurs in other ESS d erivations where local effects have a strong influence. (C) 1994 Acade mic Press, Inc.