Model of Prey-Predator Dynamics with Reflexive Spatial Behaviour of Species Based on Optimal Migration.

We consider the model of spatially distributed community consisting of two species with "predator-prey" interaction; each of the species occupies two stations. Transfer of individuals between the stations (migration) is not random, and migration stipulates the maximization of net reproduction of each species. The spatial distribution pattern is provided by discrete stations, and the dynamics runs in discrete time. For each time moment, firstly a redistribution of individuals between the stations is carried out to maximize the net reproduction, and then the reproduction takes place, with the upgraded abundances. Besides, three versions of the basic model are implemented where each species implements reflexive behaviour strategy to determine the optimal migration flow. It was found that reflexivity gives an advantage to the species realizing such strategy, for some specific sets of parameters. Nevertheless, the regular scanning of the parameters area shows that non-reflexive behaviour yields an advantage in the great majority of parameters combinations.