相关论文: Asymptotic genealogies for a class of generalized …

Consider a haploid population of fixed finite size with a finite number of allele types and having Cannings exchangeable genealogy with neutral mutation. The stationary distribution of the Markov chain of allele counts in each generation is…

We propose a general framework for the study of the genealogy of neutral discrete-time populations. We remove the standard assumption of exchangeability of offspring distributions appearing in Cannings' models, and replace it by a less…

Sweepstakes reproduction may be generated by chance matching of reproduction with favorable environmental conditions. Gene genealogies generated by sweepstakes reproduction are in the domain of attraction of multiple-merger coalescents…

The results in this paper provide new information on asymptotic properties of classical models: the neutral Kingman coalescent under a general finite-alleles, parent-dependent mutation mechanism, and its generalisation, the ancestral…

Wright-Fisher diffusions and their dual ancestral graphs occupy a central role in the study of allele frequency change and genealogical structure, and they provide expressions, explicit in some special cases but generally implicit, for the…

Using graphical methods based on a `lookdown' and pruned version of the {\em ancestral selection graph}, we obtain a representation of the type distribution of the ancestor in a two-type Wright-Fisher population with mutation and selection,…

We study the multi-type Cannings population model. Each individual has a type belonging to a given at most countable type space $E$. The population is hence divided into $|E|$ subpopulations. The subpopulation sizes are assumed to be…

We consider the Wright-Fisher model for a population of $N$ individuals, each identified with a sequence of a finite number of sites, and single-crossover recombination between them. We trace back the ancestry of single individuals from the…

We consider a stochastic model describing a constant size $N$ population that may be seen as a directed polymer in random medium with $N$ sites in the transverse direction. The population dynamics is governed by a noisy traveling wave…

We study coalescent processes conditional on the population pedigree under the exchangeable diploid bi-parental population model of \citet{BirknerEtAl2018}. While classical coalescent models average over all reproductive histories, thereby…

Reinforced Galton--Watson processes describe the dynamics of a population where reproduction events are reinforced, in the sense that offspring numbers of forebears can be repeated randomly by descendants. More specifically, the evolution…

Duality plays an important role in population genetics. It can relate results from forwards-in-time models of allele frequency evolution with those of backwards-in-time genealogical models; a well known example is the duality between the…

Star-shaped branching patterns of genealogies are common in marine species. High-fecundity marine populations are characterized by low ratios of effective to actual population size, which reflect high variance in reproductive success among…

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,…

Mathematical models of genetic evolution often come in pairs, connected by a so-called duality relation. The most seminal example are the Wright-Fisher diffusion and the Kingman coalescent, where the former describes the stochastic…

Let $W_1,\ldots,W_N$ be a sample of $\mathrm{Pareto}(\alpha)$ random variables normalized by their sum, such that $\sum_i W_i=1$. The $W_i$ may represent the weights of valleys in a spin glass (if $0<\alpha<1$), or the frequency of…

Consider a continuous-time binary branching process conditioned to have population size n at some time t, and with a chance p for recording each extinct individual in the process. Within the family tree of this process, we consider the…

We study asymptotic properties of supercritical Galton-Watson (GW) branching processes in the asymptotic where the mean of the offspring distribution approaches 1 from above. We show that the population-size distribution of the GW branching…

In a (two-type) Wright-Fisher diffusion with directional selection and two-way mutation, let $x$ denote today's frequency of the beneficial type, and given $x$, let $h(x)$ be the probability that, among all individuals of today's…

Recruitment dynamics, or the distribution of the number of offspring among individuals, is central for understanding ecology and evolution. Sweepstakes reproduction (heavy right-tailed offspring number distribution) is central for…