Trait evolution in two-sex populations

2014/08/24 by Paweł Zwoleński, Zwoleński, Paweł
Mathematics · #34G20 #47J35 #60K35 #92D15 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:34G20 #msc:47J35 #msc:60K35 #msc:92D15

paper · pdf · doi:10.48550/arxiv.1408.5587

arxiv created 2015/02/21 · arxiv updated 2015/02/24

Abstract

We present an individual-based model of phenotypic trait evolution in two-sex populations, which includes semi-random mating of individuals of the opposite sex, natural death and intra-specific competition. By passing the number of individuals to infinity, we derive the macroscopic system of nonlinear differential equations describing the evolution of trait distributions in male and female subpopulations. We study solutions, give criteria for persistence or extinction, and state theorem on asymptotic stability, which we apply later to particular examples of trait inheritance.

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