Spatial organization and cyclic dominance in asymmetric predator-prey spatial games

TL;DR

This paper investigates how spatial organization influences predator-prey interactions and the stability of coexistence through cyclic dominance, extending a classical model to spatially distributed populations.

Contribution

It extends the Lett-Auger-Gaillard model to include spatial distribution, revealing richer behaviors and stable coexistence driven by cyclic dominance mechanisms.

Findings

Spatial organization leads to richer predator-prey dynamics.

Coexistence of strategies is stabilized by cyclic dominance.

Spatial models differ from mean-field predictions in behavior.

Abstract

Predators may attack isolated or grouped prey in a cooperative, collective way. Whether a gregarious behavior is advantageous to each species depends on several conditions and game theory is a useful tool to deal with such a problem. We here extend the Lett-Auger-Gaillard model [Theor. Pop. Biol. 65 (2004) 263] to spatially distributed populations and compare the resulting behavior with their mean-field predictions for the coevolving densities of predator and prey strategies. Besides its richer behavior in the presence of spatial organization, we also show that the coexistence phase in which collective and individual strategies for each group are present is stable because of an effective, cyclic dominance mechanism similar to a well-studied generalization of the Rock-Paper-Scissors game with four species, a further example of how ubiquitous this coexistence mechanism is.