Coexistence of Species

Joon Kang (Mathematics)

Coexistence of species of animals residing in the same environment

A prominent subject of study and analysis in mathematical biology concerns the interaction of two or more species of animals in the same environment.  Especially important areas of investigation include the conditions under which the species can coexist, as well as the conditions under which any one of the species becomes extinct, that is, one of the species is excluded by the others. A general ecological tenet is that competing species can coexist if their rates of reproduction and self-limitation are relatively larger than their rates of competition. In other words, every species can survive if the members of each interact strongly with themselves and interact weakly with the members of other species. In my study, I investigate this phenomenon from a mathematical point of view, modeling it using reaction-diffusion equations with various boundary conditions. In this research I ask two sets of questions:

Question 1: Under what conditions do two interacting species coexist?  Under what conditions do they have a unique positive steady state?  Under what conditions does either of the species become extinct?

Question 2: Assuming that the two species can coexist and that the coexistence state is unique at fixed rates of reproduction, self-limitation, and interaction, can the species still coexist despite slight changes (perturbations) in the rates? In other words, can all of the species still survive if they “relax” ecologically-speaking?

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