Related papers: The coalescent and its descendants
We consider a trait-structured population subject to mutation, birth and competition of logistic type, where the number of coexisting types may fluctuate. Applying a limit of rare mutations to this population while keeping the population…
We review the statistical properties of the genealogies of a few models of evolution. In the asexual case, selection leads to coalescence times which grow logarithmically with the size of the population in contrast with the linear growth of…
A well-established model for the genealogy of a large population in equilibrium is Kingman's coalescent. For the population together with its genealogy evolving in time, this gives rise to a time-stationary tree-valued process. We study the…
Many applications in genetic analyses utilize sampling distributions, which describe the probability of observing a sample of DNA sequences randomly drawn from a population. In the one-locus case with special models of mutation such as the…
We extend our study of a simple model of biological coevolution to its statistical properties. Staring with a complete description in terms of a master equation, we provide its relation to the deterministic evolution equations used in…
Demographic models built from genetic data play important roles in illuminating prehistorical events and serving as null models in genome scans for selection. We introduce an inference method based on the joint frequency spectrum of genetic…
Pervasive natural selection can strongly influence observed patterns of genetic variation, but these effects remain poorly understood when multiple selected variants segregate in nearby regions of the genome. Classical population genetics…
About 45,000 years ago, symbolic and technological complexity of human artefacts increased drastically. Computer simulations of Powell, Shennan and Thomas (2009) explained it through an increase of the population density, facilitating the…
Populations evolving under the joint influence of recombination and resampling (traditionally known as genetic drift) are investigated. First, we summarise and adapt a deterministic approach, as valid for infinite populations, which assumes…
Human populations have a complex history of introgression and of changing population size. Human genetic variation has been affected by both these processes, so that inference of past population size depends upon the pattern of gene flow…
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 study a model of a population with individuals sampled from different species. The Yule-$\Lambda$ nested coalescent describes the genealogy of the sample when each species merges with another randomly chosen species with a constant rate…
In many statistical problems, a more coarse-grained model may be suitable for population-level behaviour, whereas a more detailed model is appropriate for accurate modelling of individual behaviour. This raises the question of how to…
Having a precise knowledge of the dispersal ability of a population in a heterogeneous environment is of critical importance in agroecology and conservation biology as it can provide management tools to limit the effects of pests or to…
We study a universal object for the genealogy of a sample in populations with mutations: the critical birth-death process with Poissonian mutations, conditioned on its population size at a fixed time horizon. We show how this process arises…
Many imaging techniques for biological systems -- like fixation of cells coupled with fluorescence microscopy -- provide sharp spatial resolution in reporting locations of individuals at a single moment in time but also destroy the dynamics…
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…
Using topological summaries of gene trees as a basis for species tree inference is a promising approach to obtain acceptable speed on genomic-scale datasets, and to avoid some undesirable modeling assumptions. Here we study the…
In probability theory and statistics, the IID model represents a single population, and a large, potentially infinite sample from this population. Main theorems, in particular the central limit theorem and laws of large number (LLN) assure…
Population stratification is a problem encountered in several areas of biology and public health. We tackle this problem by mapping a population and its elements attributes into a hypergraph, a natural extension of the concept of graph or…