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Journal Articles ALEA : Latin American Journal of Probability and Mathematical Statistics Year : 2021

Emergence of homogamy in a two-loci stochastic population model

Camille Coron
Manon Costa
Fabien Laroche
Hélène Leman

Abstract

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 non-linear 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 branching processes or dynamical systems, and study the latter ones in order to control the trajectory and duration of each phase.
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Dates and versions

hal-02043536 , version 1 (21-02-2019)

Identifiers

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Camille Coron, Manon Costa, Fabien Laroche, Hélène Leman, Charline Smadi. Emergence of homogamy in a two-loci stochastic population model. ALEA : Latin American Journal of Probability and Mathematical Statistics, 2021, 18, pp.469-508. ⟨10.30757/ALEA.v18-21⟩. ⟨hal-02043536⟩
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