Population genetics and speciation in complex networks

Abstract

The Voter Model with fixed elements defined on complex networks can be mapped exactly into a problem of population genetics where a single biallelic gene is considered. In this proposal we intend to extend this model to the case of individuals with several genes, considered independent initially. This is equivalent to voting in a plebiscite with multiple binary questions. Considering that individuals whose genomes are too different can be incompatible and not be able to produce viable offspring, we shall introduce a parameter measuring the maximum number of genetic differences that two individuals may have in order to be able to reproduce. In the case of plebiscites this implies the impossibility of being convinced to change your mind by a friend whose opinion differs from yours at too many points. This condition couples the genes and can have important consequences for the process of speciation. We intent to study the role of the network topology on the speciation process by doing simulations using several known topologies, like regular, random and scale-free. We also intend to do an analytical study of the simple case of only two genes or one gene with more alleles. (AU)