Crossover entre ordem e desordem nos modelos do votante e de Moran em populações estruturadas

Author(s)

Gabriella Dantas Franco

• Document type: Master's Dissertation
• Press: Campinas, SP.
• Institution: Universidade Estadual de Campinas (UNICAMP). Instituto de Física Gleb Wataghin
• Defense date: 2019-06-24

Examining board members

Marcus Aloizio Martinez de Aguiar; Leonardo Paulo Maia; Alex Antonelli

• Advisor: Marcus Aloizio Martinez de Aguiar

Abstract

The Moran model describes the dynamics of a biallelic gene in a population with fixed size N in which every pair of individuals can procreate. The mutation rate µ will determine if the systems is in a regime of low or high biodiversity, with a critical point at µc=1/2N. When considering populations with spatial structure, which is represented by a network of interactions, we expect the critical mutation rate to alter, even though mean field approximations show this may not occur. To analyze the effect of the network topology on the critical mutation rate, we first define as the critical point in the system the value which maximizes the Shannon entropy S=-'sigma'm p(m) log[p(m)], in which p(m) is the probability of having m equal alleles in the population for a given mutation rate. The simulations were performed on the voter model with external influencers, which describes an election with two candidates. This model is exactly mapped into the Moran for regular networks. We use ring and lattice networks as standards for the study, varying the number of neighbours with whom it is possible to interact. The results show that the critical mutation rate decreases as the network becomes more structured (lesser number of neighbours), reinforcing previous results (AU)

• FAPESP's process: 16/25271-5 - Conditions for speciation in structured populations
• Grantee: Gabriella Dantas Franco
• Support Opportunities: Scholarships in Brazil - Master