The Effects Of Allee Effect On Predator-Prey System With Niche Construction

As ecology basic core theory, Niche construction enriches the existing theory of evolution, provides a new theoretical basis for the study of species adaptability and provides an effective mechanism mode for explaining ecological phenomena at different scales. Species affected by the Allee effect, its density being lower than a critical value, will become extinct. The importance of Allee effect in population dynamics is gradually recognized by people. However, Most of the research is focused on the Allee effect of local population or Allee-like effect on the metapopulation, the research of Allee effect having a niche role in constructing model is limited.This paper based on predator-prey system of niche construction discusses the effect of the Allee effect on the number of species and their spatial distribution, and understands the effect on the control and regulation of ecological system, which will further enrich and develop niche construction theory and existing conclusions Allee effect. Two methods will be used in the study. One is the constructed differential dynamic systems model.using the stability theory of differential equations, the equilibrium and stability of the system will be described, namely the time dynamic; the other is the spatially explicit model of reaction-diffusion equation and by using Matlab software simulation, spatial pattern, structure, dynamics will be explicitly demonstrated, namely the spatial dynamic.Through numerical simulation study, the thesis draws the following three conclusions:(1) The enhancement of Allee effect reduces the density of the predator at equilibrium; (2) Allee effect can make an effect on the density variation of the species in the predator prey system with ecological niche construction behavior; (3) The Allee effect enhances the spatial diffusion capacity of the species, and promotes the rapid migration of construction species into the space habitat which is favorable for their survival to be Stable species. Allee effect on other systems having a niche role in the the number of changes of the species and its spatial extension is worth further study.This thesis is divided into four parts:Chapter one will summarize the frontiers and development of niche construction, as well as the Allee effect model that will be used in the following; Chapter two will establish the ordinary differential dynamic model with the Allee effect, and discusses the effect of the prey system of the Allee effect through numerical simulation on the density change of different species in the positive equilibrium point and the population density map of predator with prey over time; Chapter three will construct the partial differential prey predator model with Allee effect based on the predator prey system with the ecological niche construction behavior, and discusses the influence of Allee effect on the spatial diffusion of the system through numerical simulation analysis. In the last chapter, the main conclusions summary and future prospect of the research work are proposed.