Related papers: Multi-type $\Xi$-coalescents from structured popul…
We consider the genealogy of a sample of individuals taken from a spatially structured population when the variance of the offspring distribution is relatively large. The space is structured into discrete sites of a graph G. If the…
The rapid development of sequencing technologies represents new opportunities for population genetics research. It is expected that genomic data will increase our ability to reconstruct the history of populations. While this increase in…
We consider Markov jump processes describing structured populations with interactions via density dependance. We propose a Markov construction with a distinguished individual which allows to describe the random tree and random sample at a…
Coalescent processes, including mutation, are derived from Moran type population models admitting large offspring numbers. Including mutation in the coalescent process allows for quantifying the turnover of alleles by computing the…
Conditional sampling distributions (CSDs), sometimes referred to as copying models, underlie numerous practical tools in population genomic analyses. Though an important application that has received much attention is the inference of…
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…
Consider a structured population consisting of $d$ colonies, with migration rates proportional to a positive parameter $K$. We sample $N_K$ individuals, distributed evenly across the $d$ colonies, and trace their ancestral lineages backward…
Population balance framework is a useful tool that can be used to describe size distribution of droplets in a liquid-liquid dispersion. Breakup and coalescence models provide closures for mathematical formulation of the population balance…
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…
Positive selection distorts the structure of genealogies and hence alters patterns of genetic variation within a population. Most analyses of these distortions focus on the signatures of hitchhiking due to hard or soft selective sweeps at a…
We consider a single genetic locus which carries two alleles, labelled P and Q. This locus experiences selection and mutation. It is linked to a second neutral locus with recombination rate r. If r=0, this reduces to the study of a single…
To understand the effect of assortative mating on the genetic evolution of a population, we consider a finite population in which each individual has a type, determined by a sequence of n diallelic loci. We assume that the population…
We consider a population model where individuals behave independently from each other and whose genealogy is described by a chronological tree called splitting tree. The individuals have i.i.d. (non-exponential) lifetime durations and give…
Compared to a neutral model, purifying selection distorts the structure of genealogies and hence alters the patterns of sampled genetic variation. Although these distortions may be common in nature, our understanding of how we expect…
Studying how diverse human populations are related is of historical and anthropological interest, in addition to providing a realistic null model for testing for signatures of natural selection or disease associations. Furthermore,…
A multi-type neutral Cannings population model with mutation and fixed subpopulation sizes is analyzed. Under appropriate conditions, as all subpopulation sizes tend to infinity, the ancestral process, properly time-scaled, converges to a…
Probability modelling for DNA sequence evolution is well established and provides a rich framework for understanding genetic variation between samples of individuals from one or more populations. We show that both classical and more recent…
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…
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…
Let $\Lambda$ be a finite measure on the unit interval. A $\Lambda$-Fleming-Viot process is a probability measure valued Markov process which is dual to a coalescent with multiple collisions ($\Lambda$-coalescent) in analogy to the duality…