Related papers: Evolving genealogies for branching populations und…
We study a continuous-time dynamical system that models the evolving distribution of genotypes in an infinite population where genomes may have infinitely many or even a continuum of loci, mutations accumulate along lineages without…
We consider two versions of stochastic population models with mutation and selection. The first approach relies on a multitype branching process; here, individuals reproduce and change type (i.e., mutate) independently of each other,…
The first chapter concerns monotype population models. We first study general birth and death processes and we give non-explosion and extinction criteria, moment computations and a pathwise representation. We then show how different scales…
We consider a discrete model of population with interaction where the birth and death rates are non linear functions of the population size. After proceeding to renormalization of the model parameters, we obtain in the limit of large…
We propose a mathematical framework for natural selection in finite populations. Traditionally, many of the selection-based processes used to describe cultural and genetic evolution (such as imitation and birth-death models) have been…
We model the evolution of two competing populations $U_t, V_t $ by a two-dimensional size-dependent branching process. The population characteristics are assumed to be close to each other, as in a resident-mutant situation. Given that $U_t…
We study the genealogical distance of two randomly chosen individuals in a population that evolves according to a two type Moran model with mutation and selection. We prove that this distance is stochastically smaller than the corresponding…
We introduce a broad class of spatial models to describe how spatially heterogeneous populations live, die, and reproduce. Individuals are represented by points of a point measure, whose birth and death rates can depend both on spatial…
Differential Evolution (DE) is a widely used evolutionary algorithm for black-box optimization problems. However, in modern DE implementations, a major challenge lies in the limited population diversity caused by the fixed population size…
We study the continuous-time evolution of the recombination equation of population genetics. This evolution is given by a differential equation that acts on a product probability space, and its solution can be described by a Markov chain on…
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…
In this paper, we study a two-dimensional process arising as the unique nonnegative solution to a system of two stochastic differential equations (SDEs) with mutually enhancing two-way interactions driven by independent Brownian motions and…
We investigate a simple quantitative genetics model subjet to a gradual environmental change from the viewpoint of the phylogenies of the living individuals. We aim to understand better how the past traits of their ancestors are shaped by…
Phylogenetics uses alignments of molecular sequence data to learn about evolutionary trees relating species. Along branches, sequence evolution is modelled using a continuous-time Markov process characterised by an instantaneous rate…
Consider a branching Markov process with values in some general type space. Conditional on survival up to generation $N$, the genealogy of the extant population defines a random marked metric measure space, where individuals are marked by…
We reconsider the deterministic haploid mutation-selection equation with two types. This is an ordinary differential equation that describes the type distribution (forward in time) in a population of infinite size. This paper establishes…
We consider a metapopulation made up of $K$ demes, each containing $N$ individuals bearing a heritable quantitative trait. Demes are connected by migration and undergo independent Moran processes with mutation and selection based on trait…
We introduce and analyze a general model of a population evolving over a network of selectively neutral genotypes. We show that the population's limit distribution on the neutral network is solely determined by the network topology and…
We consider the evolution of a population of fixed size with no selection. The number of generations $G$ to reach the first common ancestor evolves in time. This evolution can be described by a simple Markov process which allows one to…
The expansion of a population into new habitat is a transient process that leaves its footprints in the genetic composition of the expanding population. How the structure of the environment shapes the population front and the evolutionary…