期刊名称：Latin American Journal of Probability and Mathematical Statistics
电子版ISSN：1980-0436
出版年度：2021
卷号：18
期号：1
页码：469
DOI：10.30757/ALEA.v18-21
出版社：Instituto Nacional De Matemática Pura E Aplicada
摘要：This article deals with the emergence of a specific mating preference pattern called homogamy in a population. Individuals are characterized by their genotype at two haploid loci, and the population dynamics is modelled by a nonlinear birth-and-death process. The first locus codes for a phenotype, while the second locus codes for homogamy defined with respect to the first locus: two individuals are more (resp. less) likely to reproduce with each other if they carry the same (resp. a different) trait at the first locus. Initial resident individuals do not feature homogamy, and we are interested in the probability and time of invasion of a mutant presenting this characteristic under a large population assumption. To this aim, we study the trajectory of the birth-and-death process during three phases: growth of the mutant, coexistence of the two types, and extinction of the resident. We couple the birth-and-death process with simpler processes, like multidimensional branching processes or dynamical systems, and study the latter ones in order to control the trajectory and duration of each phase.
其他关键词：Birth and death processes with interactions, multitype branching processes, large population limits, mating preferences.
