Conditions for speciation in structured populations

• Grant number: 16/25271-5
• Support Opportunities: Scholarships in Brazil - Master
• Start date: July 01, 2017
• End date: June 30, 2019
• Field of knowledge: Physical Sciences and Mathematics - Physics - General Physics
• Agreement: Coordination of Improvement of Higher Education Personnel (CAPES)
• Principal Investigator: Marcus Aloizio Martinez de Aguiar
• Grantee: Gabriella Dantas Franco
• Host 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)

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

FRANCO, Gabriella Dantas. Crossover entre ordem e desordem nos modelos do votante e de Moran em populações estruturadas. 2019. Master's Dissertation - Universidade Estadual de Campinas (UNICAMP). Instituto de Física Gleb Wataghin Campinas, SP.