Emergence of homogamy in a two-loci stochastic population model

This article deals with the emergence of a specific mating preference pattern called homogamy in population. Individuals are characterized by their genotype at two haploid loci, and population dynamics is modelled non-linear birth-and-death process. The first locus codes for phenotype, while second defined respect to locus: individuals more (resp. less) likely reproduce each other if they carry same different) trait locus. Initial resident do not feature homogamy, we interested probability time invasion mutant presenting this characteristic under large assumption. To aim, study trajectory process during three phases: growth mutant, coexistence types, extinction resident. We couple simpler processes, like branching processes or dynamical systems, latter ones order control duration phase.