2016/12/20 by Swati Patel, Sebastian J. Schreiber, Patel, Swati +1 · 2 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · Social Sciences · #37N25 #92D25 #92D40 #Evolution and Genetic Dynamics #Evolutionary Game Theory and Cooperation #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.1612.06554
openalex publication_date 2016/12/20 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
Species experience both internal feedbacks with endogenous factors such as\ntrait evolution and external feedbacks with exogenous factors such as weather.\nThese feedbacks can play an important role in determining whether populations\npersist or communities of species coexist. To provide a general mathematical\nframework for studying these effects, we develop a theorem for coexistence for\necological models accounting for internal and external feedbacks. Specifically,\nwe use average Lyapunov functions and Morse decompositions to develop\nsufficient and necessary conditions for robust permanence, a form of\ncoexistence robust to large perturbations of the population densities and small\nstructural perturbations of the models. We illustrate how our results can be\napplied to verify permanence in non-autonomous models, structured population\nmodels, including those with frequency-dependent feedbacks, and models of\neco-evolutionary dynamics. In these applications, we discuss how our results\nrelate to previous results for models with particular types of feedbacks.\n