2021/12/21 by Yifei Li, Li, Yifei, Pascal R. Buenzli +3
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · #92B05 #Evolution and Genetic Dynamics #FOS: Biological sciences #Mathematical Biology Tumor Growth #Mathematical and Theoretical Epidemiology and Ecology Models #Populations and Evolution (q-bio.PE)
paper · pdf · doi:10.48550/arxiv.2112.10989
openalex publication_date 2021/12/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Understanding whether a population will survive and flourish or become extinct is a central question in population biology. One way of exploring this question is to study population dynamics using reaction-diffusion equations, where migration is usually represented as a linear diffusion term, and birth-death is represented with a bistable source term. While linear diffusion is most commonly employed to study migration, there are several limitations of this approach, such as the inability of linear diffusion-based models to predict a well-defined population front. One way to overcome this is to generalise the constant diffusivity, D, to a nonlinear diffusivity function D(C), where C>0 is the density. While it has been formally established that the choice of D(C) affects long-term survival or extinction of a bistable population, working solely in a classical continuum framework makes it difficult to understand precisely how the choice of D(C) affects survival or extinction. Here, we address this question by working with a simple discrete simulation model that is easy to interpret. The continuum limit of the discrete model is a nonlinear reaction-diffusion equation, where the flux involves a nonlinear diffusion term and the source term is given by the strong Allee effect bistable model. We study population extinction/survival using this very intuitive discrete framework together with numerical solutions of the reaction-diffusion continuum limit equation. This approach provides clear insight into how the choice of D(C) either encourages or suppresses population extinction relative to the classical linear diffusion model.