Modelling habitat loss with partial differential equations
It is well known that habitat loss is a leading cause of species extinctions worldwide. It is therefore important to better understand how, exactly, different forms of habitat loss affect interacting species. In the context of reaction-diffusion equations, we formulate some models aiming to describe the impacts of habitat degradation and habitat destruction. We can then fully describe the outcomes of a competition model under each form of habitat loss. We are also able to prove a robust connection between these two formulations in a limiting process. Motivated by these efforts, we then seek to develop some new tools to better understand habitat fragmentation, and the relative impacts it will have on species' populations. This is joint work with my supervisors, Dr. Hao Wang and Dr. Zhongwei Shen.