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# Conditions for speciation in structured populations

 Grant number: 16/25271-5 Support type: Scholarships in Brazil - Master Effective date (Start): July 01, 2017 Effective date (End): June 30, 2019 Field of knowledge: Physical Sciences and Mathematics - Physics - General Physics Cooperation agreement: Coordination of Improvement of Higher Education Personnel (CAPES) Principal researcher: Marcus Aloizio Martinez de Aguiar Grantee: Gabriella Dantas Franco Home Institution: Instituto de Física Gleb Wataghin (IFGW). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil Associated scholarship(s): 18/01896-1 - Critical mutation rates in structured populations, BE.EP.MS Abstract Understanding the different mechanisms that lead to speciation is still an open question and has motivated the formulation of several theoretical models. The Moran model is a classic evolutionary model that represents a finite population where individuals die and are replaced by offspring of other individuals. In its simplest version a single biallelic gene subjected to mutations is considered and both births and deaths are random. The allelic frequencies are determined by the mutation rate and the critical value that determines the transition between the regimes of low and high diversity is $\mu_c = 1/2N$ where $N$ is the population size. More complex versions of the model, with more genes, sexual assortative mating and spatially structured populations allow for the study of speciation. The limit of infinitely many genes is particularly important and can be described with the Derrida-Higgs theory.In this proposal we will study the transition between the regimes of high and low diversity in structured populations using ring networks. In this description each individual is represented by a node in the network and each node has exactly the same number $k$ of neighbors, that are the possible mates for reproduction. Initially we will characterize the transition and study the behavior of the critical mutation as a function of the number of neighbors, mu_c(k) in the case of a single gene. Next we will consider the case of multiple genes with assortative mating to determine the maximum number of neighbors k_{max} and the minimum mutation mu_{min}(k) for speciation, comparing this value with mu_c(k). We will study, in particular, the limit of infinitely many genes with an extension of the Derrida-Higgs model. (AU)
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