Mathematical Models of Population Dynamics in Discrete Heterogeneous Space

Habitat fragmentation remains the severest threat to biodiversity globally, making it the focus of research for more than two decades. However, due to the issue's complexity, there are still various matters that are yet to be understood, especially how the habitat's fragmented spatial structure and intersite coupling in habitats with randomly distributed attributes impact population persistence or extinction. This thesis addresses the two problems by developing a population dynamics model that combines dynamic demographic noise with 'frozen' environmental noise and conducting numerical simulations respectively. In the simulations, an idealized single-species spatially-discrete system is used. Since it is well documented that global climate change promotes habitat fragmentation, this thesis argues that the two issues must not be disjointed but addressed together. The study also postulates that the two stochastic processes interact in an entangled and counterintuitive manner and argues that although unbiased demographic noise increases the chances of extinction, its effect may be reversed by a biased noise. Through the simulations, the study illustrates the impact of increased intersite coupling on the population distribution, which forms persistence domains bounded by extinction domains.