Phase transitions in finite Derrida-Higgs models

• Grant number: 19/13341-7
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: November 01, 2019
• End date: February 29, 2024
• Field of knowledge: Physical Sciences and Mathematics - Physics
• Principal Investigator: Marcus Aloizio Martinez de Aguiar
• Grantee: Vitor Marquioni Monteiro
• Host Institution: Instituto de Física Gleb Wataghin (IFGW). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated scholarship(s): 21/12509-1 - Species abundance distribution in the finite genome Derrida-Higgs model, BE.EP.DR

Abstract

The Derrida-Higgs speciation model, proposed in 1991, became a new paradigm in studies involving neutral evolution processes. One feature of this model, that makes it simple and elegant, is that genomes are represented as an infinite binary chains. This approximation allows the computation of a similarity index between pairs of individuals in the population whose distribution evolution indicates if speciation has happened or not. However, infinite genomes do not exist. In a recent work, we showed by means of simulations with finite genomes that speciation only occurs if the number of genes is indeed pretty large, of the order of $10^5$ for the parameters considered in the 1991 original work. The system equilibrium state presents a phase transition as the number of genes increases, passing from a homogeneous phase (with a single species) to a clusterized phase (with more than only one species). In this project, we intend to analytically study this phase transition, calculating the critical genome size that allows speciation as a function of the population size and the mutation rate. Such expression will enable us to map simulation results in realistic situations, with populations containing thousands of individuals and reduced mutation rates, which are computationally prohibitive. We also intend to approach the problem of interaction between nucleus DNA and mitochondrial DNA. There are evidences that the co-evolution between these two genetic materials influences the speciation process and leads to the “bar-code” mitochondrial property, which would establish a bi-univocal relation between the mitochondrial genome and the species. In this case, an interesting situation appears: infinite genes models does not describe the interaction while few genes models do not describe the speciation. To know the critical sizes at which both phenomena can be observed is an open problem that might have significant implications in population genetics. (AU)

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

MARQUIONI, VITOR M.; DE AGUIAR, MARCUS A. M.. Quantifying the effects of quarantine using an IBM SEIR model on scalefree networks. CHAOS SOLITONS & FRACTALS, v. 138, SEP 2020. (19/13341-7, 16/01343-7)

MARQUIONI, VITOR M.; DE AGUIAR, MARCUS A. M.. Modeling neutral viral mutations in the spread of SARS-CoV-2 epidemics. PLoS One, v. 16, n. 7, JUL 29 2021. (16/01343-7, 19/13341-7, 19/20271-5)

Academic Publications

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

MONTEIRO, Vitor Marquioni. Aplicações do modelo de Derrida-Higgs finito em dinâmica de populações. 2024. Doctoral Thesis - Universidade Estadual de Campinas (UNICAMP). Instituto de Física Gleb Wataghin Campinas, SP.