Related papers: The peripatric coalescent
We consider a population with non-overlapping generations, whose size goes to infinity. It is described by a discrete genealogy which may be time non-homogeneous and we pay special attention to branching trees in varying environments. A…
We present a robust method which translates information on the speed of coming down from infinity of a genealogical tree into sampling formulae for the underlying population. We apply these results to population dynamics where the genealogy…
In large populations, multiple beneficial mutations may be simultaneously spreading. In asexual populations, these mutations must either arise on the same background or compete against each other. In sexual populations, recombination can…
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…
The strong Allee effect plays an important role on the evolution of population in ecological systems. One important concept is the Allee threshold that determines the persistence or extinction of the population in a long time. In general, a…
If one goes backward in time, the number of ancestors of an individual doubles at each generation. This exponential growth very quickly exceeds the population size, when this size is finite. As a consequence, the ancestors of a given…
Population dynamics is constrained by the environment, which needs to obey certain conditions to support population growth. We consider a standard model for the evolution of a single species population density, that includes reproduction,…
We construct a continuum model for biological aggregations in which individuals experience long-range social attraction and short range dispersal. For the case of one spatial dimension, we study the steady states analytically and…
We study a spatially explicit harvesting model in periodic or bounded environments. The model is governed by a parabolic equation with a spatially dependent nonlinearity of Kolmogorov--Petrovsky--Piskunov type, and a negative external…
This article considers a model of genealogy corresponding to a regular exchangeable coalescent (also known as Xi-coalescent) started from a large finite configuration, and undergoing neutral mutations. Asymptotic expressions for the number…
Consider a population of fixed size that evolves over time. At each time, the genealogical structure of the population can be described by a coalescent tree whose branches are traced back to the most recent common ancestor of the…
We consider a system of interacting Moran models with seed-banks. Individuals live in colonies and are subject to resampling and migration as long as they are $active$. Each colony has a seed-bank into which individuals can retreat to…
Source-sink systems are metapopulations of habitat patches with different, and possibly temporally varying, habitat qualities, which are commonly used in ecology to study the fate of spatially extended natural populations. We propose new…
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 give a short overview on our work on ancestral lineages in spatial population models with local regulation. We explain how an ancestral lineage can be interpreted as a random walk in a dynamic random environment. Defining regeneration…
We are interested in modelling Darwinian evolution, resulting from the interplay of phenotypic variation and natural selection through ecological interactions. Our models are rooted in the microscopic, stochastic description of a population…
We analyze the long-term stability of a stochastic model designed to illustrate the adaptation of a population to variation in its environment. A piecewise-deterministic process modeling adaptation is coupled to a Feller logistic diffusion…
We consider a periodic extension of the classical Kingman non-linear model (Kingman, 1978) for the balance between selection and mutation in a large population. In the original model, the fitness distribution of the population is modeled by…
We study a class of coalescents derived from a sampling procedure out of N i.i.d. Pareto(alpha) random variables, normalized by their sum, including beta-size-biasing on total length effects (beta < alpha). Depending on the range of alpha,…
We model an enclosed system of bacteria, whose motility-induced phase separation is coupled to slow population dynamics. Without noise, the system shows both static phase separation and a limit cycle, in which a rising global population…