The patch distributed producer–scrounger game

Grouping in animals is ubiquitous and thought to provide group members antipredatory advantages and foraging efficiency. However, parasitic foraging strategy often emerges in a group. The optimal parasitic policy has given rise to the producer–scrounger (PS) game model, in which producers search for food patches, and scroungers parasitize the discovered patches. The N  -persons PS game model constructed by Vickery et al. (1991. Producers, scroungers, and group foraging. American Naturalist 137, 847–863) predicts the evolutionarily stable strategy (ESS) of frequency of producers (q^) that depends on the advantage of producers and the number of foragers in a group. However, the model assumes that the number of discovered patches in one time unit never exceeds one. In reality, multiple patches could be found in one time unit. In the present study, we relax this assumption and assumed that the number of discovered patches depends on the producers’ variable encounter rate with patches (λ  ). We show that q^ strongly depends on λ within a feasible range, although it still depends on the advantage of producer and the number of foragers in a group. The basic idea of PS game is the same as the information sharing (parasitism), because scroungers are also thought to parasitize informations of locations of food patches. Horn (1968) indicated the role of information-parasitism in animal aggregation (Horn, H.S., 1968. The adaptive significance of colonial nesting in the Brewer's blackbird (euphagus cyanocephalus). Ecology 49, 682–646). Our modified PS game model shows the same prediction as the Horn's graphical animal aggregation model; the proportion of scroungers will increase or animals should adopt colonial foraging when resource is spatiotemporally clumped, but scroungers will decrease or animals should adopt territorial foraging if the resource is evenly distributed.