Related papers: Colonization times in Moran process on graphs
The dynamical mechanisms that can stabilize the coexistence of species (or strategies) are of substantial interest for the maintenance of biodiversity and in sociobehavioural dynamics. We investigate the mean extinction time in the…
Our goal is to study the genetic composition of a population in which each individual has 2 parents, who contribute equally to the genome of their ospring. We use a biparental Moran model, which is characterized by its xed number N of…
A key question in evolution is how likely a mutant is to take over. This depends on natural selection and on stochastic fluctuations. Population spatial structure can impact mutant fixation probabilities. We introduce a model for structured…
Population structure can have a significant effect on evolution. For some systems with sufficient symmetry, analytic results can be derived within the mathematical framework of evolutionary graph theory which relate to the outcome of the…
Many exotic species combine low probability of establishment at each introduction with rapid population growth once introduction does succeed. To analyze this phenomenon, we note that invaders often cluster spatially when rare, and…
Evolutionary game dynamics describes the spreading of successful strategies in a population of reproducing individuals. Typically, the microscopic definition of strategy spreading is stochastic, such that the dynamics becomes deterministic…
We explore the connection between evolution and large-deviation theory. To do so, we study evolutionary dynamics in which individuals experience mutations, reproduction, and selection using variants of the Moran model. We show that, in the…
In large clonal populations, several clones generally compete which results in complex evolutionary and ecological dynamics: experiments show successive selective sweeps of favorable mutations as well as long-term coexistence of multiple…
We study two models of population with migration. We assume that we are given infinitely many islands with the same number r of resources, each individual consuming one unit of resources. On an island lives an individual whose genealogy is…
Natural microbial populations often have complex spatial structures. This can impact their evolution, in particular the ability of mutants to take over. While mutant fixation probabilities are known to be unaffected by sufficiently…
The growth of a population divided among spatial sites, with migration between the sites, is sometimes modelled by a product of random matrices, with each diagonal elements representing the growth rate in a given time period, and…
We consider a Moran model with recombination in a haploid population of size $N$. At each birth event, with probability $1-\rho_N R$ the offspring copies one parent's chromosome, and with probability $\rho_N R$ she inherits a chromosome…
In this paper, we consider certain linear-fractional branching processes with immigration in varying environments. For $n\ge0,$ let $Z_n$ counts the number of individuals of the $n$-th generation, which excludes the immigrant which enters…
In evolutionary game theory, an important measure of a mutant trait (strategy) is its ability to invade and take over an otherwise-monomorphic population. Typically, one quantifies the success of a mutant strategy via the probability that a…
The Moran process is one of an basic mathematical structure in the evolutionary game theory. In this work, we introduce the formulation of the path integral approach for evolutionary game theory based on the Moran process. We derive the…
Understanding how natural selection unfolds across space and time is a central problem in evolutionary biology. Classic models such as the Moran process capture stochastic birth-death dynamics in structured populations, while…
In subdivided populations, migration acts together with selection and genetic drift and determines their evolution. Building up on a recently proposed method, which hinges on the emergence of a time scale separation between local and global…
The Moran process is a foundational model of genetic drift and mutation in finite populations. In its standard two-allele form with population size $n$, allele counts, and hence allele frequencies, change through stochastic replacement and…
We study the dynamics of colonization of a territory by a stochastic population at low immigration pressure. We assume a sufficiently strong Allee effect that introduces, in deterministic theory, a large critical population size for…
The influence of migration on the stochastic dynamics of subdivided populations is still an open issue in various evolutionary models. We develop here a self-consistent mean-field-like method in order to determine the effects of migration…