Effects of the prey refuge distribution on a predator-prey system

The existence of prey refuges in a predator-prey system is known to be strongly related to the ecosystem's stability. In this study, we explored how the prey refuge distribution affects the predator-prey system. To do so, we constructed a spatial lattice model to simulate an integrative predator (wolf) - prey (rabbit) - plant (grass) relationship. When a wolf (rabbit) encountered a rabbit (grass), the wolf (rabbit) tended to move to the rabbit (grass) for foraging while the rabbit tended to escape from the wolf. These behaviors were mathematically described by the degrees of willingness for hunting (H) and escaping (E). Initially, n refuges for prey were heterogeneously distributed in the lattice space. The heterogeneity was characterized as variable A. Higher values of A equate to higher aggregation in the refuge. We investigated the mean population density for different values of H, E, and A. To simply characterize the refuge distribution effect, we built an H-E grid map containing the population density for each species. Then, we counted the number of grids, N, with a population density a parts per thousand yen 0.25. Simulation results showed that an appropriate value of A positively affected prey survival while values of A were too high had a negative effect on prey survival. The results were explained by using the trade-off between the staying time of the prey in the refuge and the cluster size of the refuge.