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.

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Comparison of reflexive vs. non-reflexive behaviour is provided, for the dynamics of globally informed beings in a community with optimal migration. Keywords: population dynamics, optimization migration, global information access, Ferchulst equation. DOI: 10.17516/1997DOI: 10.17516/ -1397DOI: 10.17516/ -2015 1. Reflexive-free model of the dynamics of globally informed beingsWe consider a dynamics of spatially distributed communities where being perform optimal relocation of themselves in space; optimality means maximization of net reproduction [1,2]. We shall suppose a community to consist of two stations (habitation entity) occupied with two species; migration is stipulated to be a transfer from station to station, exclusively. Besides, the beings are supposed to have global access to information/knowledge on environmental conditions, subpopulation density, transfer cost etc. The aim of the paper is to figure out the impact of reflexivity on the dynamics.We start from a single species population subdivided into two subpopulations. Let the dynamics of each subpopulation in migration-free case follows Verchult's equation:where N t and M t are the abundances of the subpopulations in the time moment t, in station I and II , respectively; a and c are Malthusian parameters while b and d describe the density dependent regulation. The functions in the parentheses in (1) are the net reproduction, in the corresponding stations. A migration (between the stations) runs if and only if the living conditions at the immigration station become better than these latter at the habitation station, with respect to transfer cost p. The figure p, (0 p 1) is a probability of a successful transfer from station to station; i. e. the transfer that brings no harm for further reproduction.The migration from station I to station II (and from II to I , respectively) starts, if:a − bN t < p · (c − dM t ) or c − dM t < p · (a − bN t ) .