Advantage and Disadvantage of Dispersal in Two-Species Competition Models (CSIAM Transactions on Applied Mathematics, 2020)
We consider a two-species competition model in which both populationsare identical except their movement strategies: One species moves upward along thefitness gradient, while the other does not diffuse. While both species can coexist inhomogeneous environment, we show that the species with directed movement hassome advantage over the non-diffusing species in certain measurement. In contrast,if one species moves by random dispersal while the other does not diffuse, then thenon-diffusing population could have advantage. Understanding the full dynamics ofthese ODE-PDE hybrid systems poses challenging mathematical questions.