Related papers: Asymptotic sampling formulae for Lambda-coalescent…
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…
Understanding the interplay between recombination and resampling is a significant challenge in mathematical population genetics and of great practical relevance. Asymptotic results about the distribution of samples when recombination is…
We introduce a general diploid population model with self-fertilization and possible overlapping generations, and study the genealogy of a sample of $n$ genes as the population size $N$ tends to infinity. Unlike traditional approach in…
In this work, we study general Dirichlet coalescents, which are a family of Xi-coalecents constructed from i.i.d mass partitions, and are an extension of the symmetric coalescent. This class of models is motivated by population models with…
The genetic diversity of a species is shaped by its recent evolutionary history and can be used to infer demographic events or selective sweeps. Most inference methods are based on the null hypothesis that natural selection is a weak or…
We consider a ${\Lambda}$-coalescent and we study the asymptotic behavior of the total length $L^{(n)}_{ext}$ of the external branches of the associated $n$-coalescent. For Kingman coalescent, i.e. ${\Lambda}={\delta}_0$, the result is well…
The aim of this article is to establish asymptotic distributions and consistency of subsampling for spectral density and for magnitude of coherence for non-stationary, almost periodically correlated time series. We show the asymptotic…
Assume that individuals alive at time $t$ in some population can be ranked in such a way that the coalescence times between consecutive individuals are i.i.d. The ranked sequence of these branches is called a coalescent point process. We…
The coalescent is a foundational model of latent genealogical trees under neutral evolution, but suffers from intractable sampling probabilities. Methods for approximating these sampling probabilities either introduce bias or fail to scale…
The goal of this paper is to study the lookdown model with selection in the case of a population containing two types of individuals, with a reproduction model which is dual to the $\Lambda$-coalescent. In particular we formulate the…
We describe a new general connection between $\Lambda$-coalescents and genealogies of continuous-state branching processes. This connection is based on the construction of an explicit coupling using a particle representation inspired by the…
Natural populations often show enhanced genetic drift consistent with a strong skew in their offspring number distribution. The skew arises because the variability of family sizes is either inherently strong or amplified by population…
Multiple-merger coalescents, e.g. $\Lambda$-$n$-coalescents, have been proposed as models of the genealogy of $n$ sampled individuals for a range of populations whose genealogical structures are not captured well by Kingman's…
We study an unbiased, discrete time random walk on the nonnegative integers, with the origin absorbing. The process has a history-dependent step length: the walker takes steps of length v while in a region which has been visited before, and…
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,…
The Ancestral Selection Graph (ASG) is an important genealogical process which extends the well-known Kingman coalescent to incorporate natural selection. We show that the number of lineages of the ASG with and without mutation is…
Variation in a sample of molecular sequence data informs about the past evolutionary history of the sample's population. Traditionally, Bayesian modeling coupled with the standard coalescent, is used to infer the sample's bifurcating…
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…
$\Lambda$-coalescents model the evolution of a coalescing system in which any number of blocks randomly sampled from the whole may merge into a larger block. For the coalescent restricted to initially $n$ singletons we study the collision…
We consider the spatial Lambda-Fleming-Viot process model for frequencies of genetic types in a population living in R^d, with two types of individuals (0 and 1) and natural selection favouring individuals of type 1. We first prove that the…