A generic model of undesired biodiversity: Temporal and spatio-temporal bifurcations

Journal article, 2006

The human activity (e.g. fish farming) may result in the supply of undesired species (with poor heredity) to the wild, which may deteriorate the quality of the wild species of the same kind or even cause their extinction. We present a generic three-variable model focused on this problem. The model includes wild and cultivated preys and predators. The coexistence of these species is predicted to be possible provided that the supply of the cultivated preys is below the critical value. If this condition is not fulfilled, the wild preys asymptotically disappear. In the case of temporal mean-field kinetics, this transition representing mathematically a saddle-node bifurcation depends on the rate constants of the steps describing the interplay of the species. In the spatio-temporal case with the supply of undesired species at the boundary of the habitat, the situation depends also on the rate of migration of species and the habitat size.