A game-theoretic model of kleptoparasitic behavior in polymorphic populations

Kleptoparasitism, the stealing of food by one animal from another, is a widespread biological phenomenon. In this paper we build upon earlier models to investigate a population of conspecifics involved in foraging and, potentially, kleptoparasitism. We assume that the population is composed of four types of individuals, according to their strategic choices when faced with an opportunity to steal and to resist an attack. The fitness of each type of individual depends upon various natural parameters, for example food density, the handling time of a food item and the probability of mounting a successful attack against resistance, as well as the choices that they make. We find the evolutionarily stable strategies (ESSs) for all parameter combinations and show that there are six possible ESSs, four pure and two mixtures of two strategies, that can occur. We show that there is always at least one ESS, and sometimes two or three. We further investigate the influence of the different parameters on when each type of solution occurs.