A model for Mendelian populations demogenetics

Abstract

Abstract. This proceeding introduces and studies a diffusion process that models the demogenetic behavior of a diploid population with sexual Mendelian reproduction. This process is defined as the slow limit of a slow-fast dynamics derived from the rescaling of a birth-and-death process with interactions.Résumé. Cet acte de conférence introduit et étudie un processus de diffusion modélisant le comportement démo-génétique d'une population diploïde à reproduction sexuée. Ce processus est obtenu comme la limite lente d'une dynamique stochastique lente-rapide obtenue par changement d'échelle d'un processus de naissance et mort avec interactions.

Effects of demographic stochasticity and life-history strategies on times and probabilities to fixation: an individual-based model

“…Individual mortality can be natural or due to competition with other individuals (therefore allowing for density-dependence and limiting population size). Here we assume that death rates do not depend on genotypes, in order to focus on a small number of parameters (but see [11] for a more general model). If the population is at a state z = (z 1 , z 2 , z 3 ), the rate…”

Effects of demographic stochasticity and life-history strategies on times and probabilities to fixation

“…Contrary to previous models, where individuals were haploid (Champagnat et al 2006;Champagnat and Lambert 2007;Parsons et al 2010), we consider a sexually reproducing diploid population, with general dominance relationships between alleles, the possibility of self-fertilization and allow for extinction in finite time. In this probabilistic model (which is properly defined with a more general form of selection but without the possibility of fertilization in Coron (2016Coron ( , 2015) both the demography and genetics of a given population are defined through the stochastic dynamics of each individual within the population, which themselves are dependent on demographic parameters that can be estimated (Moran 1953). As population size is directly determined by frequent birth and death events, it changes stochastically with time, and can also depend on the population's genetic composition.…”