| Abstract [eng] |
In this paper, we have reviewed a single-species model of spatiotemporal population dynamics [7] taking into account advection and migration, diffusion due to the random motion of the individuals, and the local growth of the population damped by a strong Allee effect. The model consists of a non-linear partial differential equation of the advection – diffusion – reaction type. Using a suitable change of variables, an exact solution of the equation describing the propagation of a population front has been found. By means of studying the properties of the solution, the interplay between diffusion and different types of advection/migration (density – dependent and density – independent) has been thoroughly investigated. Exact relations between the parameters have been obtained ((29), (41), (44)), which make it possible to forecast whether the interplay between various factors leads to species invasion or to species retreat. Using the method, used in paper [7], a population invasion to a region, evenly settled by a population of the same species, has been investigated. |
