Influences of migrations from local competitive pressures on populations between patches

Abstract

A mathematical model of two competitive populations with migrations between two patches is proposed, which incorporates the dispersals produced by local competitive pressures. It is shown that the density-dependent migrations enhance the persistence of the two competitive populations. Compared with constant migrations, the dispersals from local competitive pressures induce dramatic changes of dynamical behavior of the model. First, the model admits a transition from one stable positive equilibrium to bistable positive equilibria. Second, the model exhibits bifurcations with the existence of seven positive steady states, in which two stable positive equilibria coexist with two stable boundary equilibrium points. These changes alter the distribution of the two populations in the two patches and increase their survival possibilities.

Population dispersal and Allee effect

“…Figures 2 and 7 demonstrate that a moderate migration rate to the better patch is beneficial to all members, whereas a larger migration rate is harmful because positive equilibrium could be lost, which results in the abandon of the worse patch and the high competition pressure in the better patch. This phenomenon is quite different from those in the models of population dispersals without Allee effect [2,12,17,21,22,24,31,32], where population dispersals do not decrease the population persistence. …”