Population Dynamics Model With a Carrying Capacity Driven Diffusion
My research project is concerned with investigating a reaction-diffusion model for the dynamics of a population. I consider a model with a carrying capacity driven diffusion as oppose to the random diffusion most commonly assumed in reaction-diffusion models of a growing population. We have shown that this type of diffusion implies that the density of a population converges with time to the carrying capacity, which means that the species match the recourses perfectly. Recently, we have established that the population that uses the proposed diffusion strategy has an evolutional advantage over a population that diffuses randomly. More precisely, the first population cannot be invaded by the second but can in turn invade the second even if it has established on some territory. We hope to further investigate this problem of evolutional stability by introducing mutations and considering a broader range of dispersal strategies for the second population.