Is food worth fighting for? ESS's in mixed populations of Kleptoparasites and Foragers

We extend the game theoretic model of kleptoparasitism discussed in Broom et al. (2004), by considering a population of foragers consisting of two groups with different behaviours--those who forage and steal from other feeders, and those who only forage. We a sume that those who do not steal have a better foraging rate than those who are also looking out for opportunities to steal. We also allow either type to resist an attack or not resist. We look for Evolutionary Stable States, of either a mixture of the two behaviours, or where the whole population has just one of these behaviours. We find nine such ESS's, dependent on the environmental parameters, although in fact only five of these are distinguishable. In general, we find that if the overall population density is low, food-stealing becomes less viable, and there is an ESS consisting of only foragers. Conversely, when there are many animals looking for, and finding, food, there is an ESS consisting of just kleptoparasites (which are also foraging). In between, an ESS will contain both pure-foragers and stealers. There is some empirical evidence of such behaviours. We find that when there is a mixture of the two types, they must both have the same resistive behaviour. We can thus have some individuals challenging for food but not resisting challenges, and others not challenging and not resisting. This shows how aggressive behaviour may be context-dependent, as seen in practice.