Related papers: A population model for $\Lambda$-coalescents with …
Coalescents with multiple collisions (also called Lambda-coalescents or simple exchangeable coalescents) are used as models of genealogies. We study a new class of Markovian coalescent processes connected to a population model with…
We define a Markov process in a forward population model with backward genealogy given by the $\Lambda$-coalescent. This Markov process, called the fixation line, is related to the block counting process through its hitting times. Two…
Coalescents with multiple collisions, also known as $\Lambda$-coalescents, were introduced by Pitman and Sagitov in 1999. These processes describe the evolution of particles that undergo stochastic coagulation in such a way that several…
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…
Consider an arbitrary large population at the present time, originated at an unspecified arbitrary large time in the past, where individuals in the same generation reproduce independently, forward in time, with the same offspring…
We investigate a new model for populations evolving in a spatial continuum. This model can be thought of as a spatial version of the Lambda-Fleming-Viot process. It explicitly incorporates both small scale reproduction events and large…
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…
The development of coalescent theory paved the way to statistical inference from population genetic data. In the genomic era, however, coalescent models are limited due to the complexity of the underlying ancestral recombination graph. The…
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,…
Consider a continuous-state branching population constructed as a flow of nested subordinators. Inverting the subordinators and reversing time give rise to a flow of coalescing Markov processes (with negative jumps) which correspond to the…
Kingman derived the Ewens sampling formula for random partitions describing the genetic variation in a neutral mutation model defined by a Poisson process of mutations along lines of descent governed by a simple coalescent process, and…
Consider a population evolving from year to year through three seasons: spring, summer and winter. Every spring starts with $N$ dormant individuals waking up independently of each other according to a given distribution. Once an individual…
We analyse sequential Markov coalescent algorithms for populations with demographic structure: for a bottleneck model, a population-divergence model, and for a two-island model with migration. The sequential Markov coalescent method is an…
We introduce the multiplicative coalescent with linear deletion, a continuous-time Markov process describing the evolution of a collection of blocks. Any two blocks of sizes $x$ and $y$ merge at rate $xy$, and any block of size $x$ is…
We define a multi-type coalescent point process of a general branching process with finitely many types. This multi-type coalescent fully describes the genealogy of the (quasi-stationary) standing population, providing types along ancestral…
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…
The coalescent revolutionised theoretical population genetics, simplifying, or making possible for the first time, many analyses, proofs, and derivations, and offering crucial insights about the way in which the structure of data in samples…
A birth-death-move process with mutations is a Markov model for a system of marked particles in interaction, that move over time, with births and deaths. In addition the mark of each particle may also change, which constitutes a mutation.…
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…
Kingman's coalescent is a widely used process to model sample genealogies in population genetics. Recently there have been studies on the inference of quantities related to the genealogy of additional individuals given a known sample. This…