{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/interpreting-how-nonlinear-diffusion-affects","title":"Interpreting how nonlinear diffusion affects the fate of bistable populations using a discrete modelling framework","arxiv_id":"2112.10989","date":"2021-12-21","proceeding":null,"authors":["Yifei Li","Pascal R. Buenzli","Matthew J. Simpson"],"abstract":"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.","url_abs":"https://arxiv.org/abs/2112.10989v2","url_pdf":"https://arxiv.org/pdf/2112.10989v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"interpreting-how-nonlinear-diffusion-affects","repo_url":"https://github.com/oneflyli/yifeinonlieardiffusion2021","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[{"method_slug":"diffusion","method_name":"Diffusion"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}