Metapopulation models with temperature- and density-dependent growth and dispersal rates

In this study, we create a set of ordinary differential equations to model population dynamics of a wildlife species living in a patchy habitat. We prove existence and uniqueness for a general model. We then develop several specific models that include temperature- and density-dependent growth and dispersal rates. Each of these models is a special case of the general model, and therefore has a unique solution. The models we develop include metapopulation models that track the population size in each patch and models exhibiting the Allee effect, which is a type of density-dependent per-capita growth rate. We also create a metapopulation model with temperature-dependent birth and migration rates. We generate numerical solutions for each model and analyze population dynamics for the system. For the temperature-dependent model, two years of local temperature data is utilized. We apply a best-fit polynomial to approximate and smooth the temperature data curve. This temperature polynomial is used to generate solutions for the temperature-dependent model. The result of this study shows that changing birth parameter values changes the strength of the Allee effect, which has consequences for wildlife preservation. Finally, the temperature-dependent model shows that population size is small during the winter and early spring at low temperatures and large during the summer at higher temperatures.