2017/01/26 by Elisa Sovrano, Sovrano, Elisa
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · Social Sciences · #34B18 #35K57 #92D25 #Analysis of PDEs (math.AP) #Evolution and Genetic Dynamics #Evolutionary Game Theory and Cooperation #FOS: Biological sciences #FOS: Mathematics #Mathematical Biology Tumor Growth #Mathematical and Theoretical Epidemiology and Ecology Models #Populations and Evolution (q-bio.PE) #math.AP #msc:34B18 #msc:35K57 #msc:92D25 #q-bio.PE
paper · pdf · doi:10.48550/arxiv.1701.07762
18 pages, 5 figures
arxiv created 2017/01/26 · openalex publication_date 2017/01/26 · arxiv updated 2017/01/27 · openalex created_date 2022/09/29 · openalex updated_date 2026/07/28
We deal with the study of the evolution of the allelic frequencies, at a single locus, for a population distributed continuously over a bounded habitat. We consider evolution which occurs under the joint action of selection and arbitrary migration, that is independent of genotype, in absence of mutation and random drift. The focus is on a conjecture, that was raised up in literature of population genetics, about the possible uniqueness of polymorphic equilibria, which are known as clines, under particular circumstances. We study the number of these equilibria, making use of topological tools, and we give a negative answer to that question by means of two examples. Indeed, we provide numerical evidence of multiplicity of positive solutions for two different Neumann problems satisfying the requests of the conjecture.