Related papers: Asymptotic genealogies for a class of generalized …
Based on the multivariate saddle point method we study the asymptotic behavior of the characteristic polynomials associated to Wishart type random matrices that are formed as products consisting of independent standard complex Gaussian and…
We study the following model for a diploid population of constant size $N$: Every individual carries a random number of (genetic) elements. Upon a reproduction event each of the two parents passes each element independently with probability…
We study a class of evolution models, where the breeding process involves an arbitrary exchangeable process, allowing for mutations to appear. The population size $n$ is fixed, hence after breeding, selection is applied. Individuals are…
We investigate the infinitely many demes limit of the genealogy of a sample of individuals from a subdivided population subject to sporadic mass extinction events. By exploiting a separation of timescales property of Wright's island model,…
Widespread sharing of long, identical-by-descent (IBD) genetic segments is a hallmark of populations that have experienced recent genetic drift. Detection of these IBD segments has recently become feasible, enabling a wide range of…
We analyse a family of two-types Wright-Fisher models with selection in a random environment and skewed offspring distribution. We provide a calculable criterion to quantify the impact of different shapes of selection on the fate of the…
The simple Galton--Watson process describes populations where individuals live one season and are then replaced by a random number of children. It can also be viewed as a way of generating random trees, each vertex being an individual of…
We review recent progress in the understanding of the role of multiple- and simultaneous multiple merger coalescents as models for the genealogy in idealised and real populations with exceptional reproductive behaviour. In particular, we…
We consider the classical Wright-Fisher model with mutation and selection. Mutations occur independently in each locus, and selection is performed according to the sharp peak landscape. In the asymptotic regime studied in [3], a…
Study sample sizes in human genetics are growing rapidly, and in due course it will become routine to analyze samples with hundreds of thousands if not millions of individuals. In addition to posing computational challenges, such large…
In this paper, we study a Galton-Watson process $(Z_n)$ with infinitely many types in a random ergodic environment $\bar{\xi}=(\xi_n)_{n\geq 0}$. We focus on the supercritical regime of the process, where the quenched average of the size of…
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…
We introduce a multi-allele Wright-Fisher model with non-recurrent, reversible mutation and directional selection. In this setting, the allele frequencies at a single locus track the path of a hybrid jump-diffusion process with state space…
Many popular Bayesian nonparametric priors can be characterized in terms of exchangeable species sampling sequences. However, in some applications, exchangeability may not be appropriate. We introduce a {novel and probabilistically coherent…
We study the iterated Galton-Watson process (IGW), possibly with thinning, introduced by Gawe{\l}and Kimmel to model the number of repeats of DNA triplets during some genetic disorders. If the process involves some thinning, then extinction…
We consider a single genetic locus with two alleles $A_1$ and $A_2$ in a large haploid population. The locus is subject to selection and two-way, or recurrent, mutation. Assuming the allele frequencies follow a Wright-Fisher diffusion and…
We study an extension of the so-called defective Galton-Watson processes obtained by allowing the offspring distribution to change over the generations. Thus, in these processes, the individuals reproduce independently of the others and in…
The number of extant individuals within a lineage, as exemplified by counts of species numbers across genera in a higher taxonomic category, is known to be a highly skewed distribution. Because the sublineages (such as genera in a clade)…
In this article, we focus on Bienaym\'e-Galton-Watson processes with linear-fractional offspring distributions. At a fixed generation, we consider a sample of the individuals alive, drawn in two different ways: either through Bernoulli…
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 $N$,…