Related papers: The common ancestor process revisited

We review recent progress on ancestral processes related to mutation-selection models, both in the deterministic and the stochastic setting. We mainly rely on two concepts, namely, the killed ancestral selection graph and the pruned…

We study the large population limit of the Moran process, assuming weak-selection, and for different scalings. Depending on the particular choice of scalings, we obtain a continuous model that may highlight the genetic-drift (neutral…

We consider a branching model in discrete time where each individual has a trait in some general state space. Both the reproduction law and the trait inherited by the offsprings may depend on the trait of the mother and the environment. We…

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…

Using graphical methods based on a `lookdown' and pruned version of the {\em ancestral selection graph}, we obtain a representation of the type distribution of the ancestor in a two-type Wright-Fisher population with mutation and selection,…

We study fixation probabilities for the Moran stochastic process for the evolution of a population with three or more types of individuals and frequency-dependent fitnesses. Contrarily to the case of populations with two types of…

We consider the Moran process, as generalized by Lieberman, Hauert and Nowak (Nature, 433:312--316, 2005). A population resides on the vertices of a finite, connected, undirected graph and, at each time step, an individual is chosen at…

We consider a Moran-type model of cultural evolution, which describes how traits emerge, are transmitted, and get lost in populations. Our analysis focuses on the underlying cultural genealogies; they were first described by Aguilar and…

We consider a population of haploid individuals reproducing sexually, i.e. for which the genome of each individual is a random mixture of the genome of its two parents. We assume that initially one individual carries a mutation at one…

Coalescent processes, including mutation, are derived from Moran type population models admitting large offspring numbers. Including mutation in the coalescent process allows for quantifying the turnover of alleles by computing the…

Evolutionary models for populations of constant size are frequently studied using the Moran model, the Wright-Fisher model, or their diffusion limits. When evolution is neutral, a random genealogy given through Kingman's coalescent is used…

Motivated by the question of the impact of selective advantage in populations with skewed reproduction mechanims, we study a Moran model with selection. We assume that there are two types of individuals, where the reproductive success of…

$\Lambda$-Wright--Fisher processes provide a robust framework to describe the type-frequency evolution of an infinite neutral population. We add a polynomial drift to the corresponding stochastic differential equation to incorporate…

In many models of genotypic evolution, the vector of genotype populations satisfies a system of linear ordinary differential equations. This system of equations models a competition between differential replication rates (fitness) and…

Consider a two-type Moran population of size $N$ with selection and mutation, where the selective advantage of the fit individuals is amplified at extreme environmental conditions. Assume selection and mutation are weak with respect to $N$,…

We consider a Moran model with two allelic types, mutation and selection. In this work, we study the behaviour of the proportion of fit individuals when the size of the population tends to infinity, without any rescaling of parameters or…

Evolutionary graph theory studies the evolutionary dynamics in a population structure given as a connected graph. Each node of the graph represents an individual of the population, and edges determine how offspring are placed. We consider…

The distributions of the times to the first common ancestor t_mrca is numerically studied for an ecological population model, the extended Moran model. This model has a fixed population size N. The number of descendants is drawn from a beta…

Coevolving and competing species or game-theoretic strategies exhibit rich and complex dynamics for which a general theoretical framework based on finite populations is still lacking. Recently, an explicit mean-field description in the form…

This paper is based on the complete classification of evolutionary scenarios for the Moran process with two strategies given by Taylor et al. (B. Math. Biol. 66(6): 1621--1644, 2004). Their classification is based on whether each strategy…