Diet Selection as a Differential Foraging Game

An important issue addressed by Behavioural Ecology is that of the evolutionary relevance of foraging strategies adopted by animals in quest of a patchily distributed resource, both in terms of diet selection and patch-leaving decisions under competition. We revisit the classical model of diet selection concerning an isolated—not subject to competition— forager; it yields a zero-one rule —a type of resource should be always accepted, or always rejected— that appears to be more the exception than the rule, as partial preferences are commonly observed in many species. Thus arises the question of its robustness to uncertainties concerning the time available to enjoy a patch before a perturbating event occurs. We mean any event that would affect its gain with respect to what it would obtain by enjoying alone the patch as long as it wants. For instance, the sudden presence of a predator could force it to flee the patch or the arrival of a conspecific would deprive it of some good resources. By taking into account the potentially imminent arrival of a conspecific —but also any event that would suddenly shorten patch exploitation—, we show that the classical policy of diet selection no longer holds —as it changes the qualitative aspect of the optimal foraging strategies. Qualitatively, the optimal strategy is close to, but less greedy than, the evolutionarily stable strategy that concerns foragers actually competing for resources. It consists in accepting only the most profitable resource until it is depleted down to a given level, after which time both resources are accepted. The underlying mathematical technique involves the solution of non-zero-sum differential games and synthesis techniques.