Related papers: A population model for $\Lambda$-coalescents with …
Consider a population of fixed size that evolves over time. At each time, the genealogical structure of the population can be described by a coalescent tree whose branches are traced back to the most recent common ancestor of the…
We consider an asexually reproducing population on a finite type space whose evolution is driven by exponential birth, death and competition rates, as well as the possibility of mutation at a birth event. On the individual-based level this…
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…
We introduce a continuous-time Markov chain describing dynamic allelic partitions which extends the branching process construction of the Pitman sampling formula in Pitman (2006) and the birth-and-death process with immigration studied in…
The star-shaped $\Lambda$-coalescent and corresponding $\Lambda$-Fleming-Viot process where the $\Lambda$ measure has a single atom at unity are studied in this paper. The transition functions and stationary distribution of the…
A simplified model for the growth of a population is studied in which random effects arise because reproducing individuals have a certain probability of surviving until the next breeding season and hence contributing to the next generation.…
We propose an extension of the classical $\Lambda$-Fleming-Viot model to intrinsically varying population sizes. During events, instead of replacing a proportion of the population, a random mass dies and a, possibly different, random mass…
Changes in population size influence genetic diversity of the population and, as a result, leave a signature of these changes in individual genomes in the population. We are interested in the inverse problem of reconstructing past…
A Markovian model of group-structured (two-level) population dynamics features births, deaths, and migrations of individuals, and fission and extinction of groups. These models are useful for studying group selection and other evolutionary…
Markov combination is an operation that takes two statistical models and produces a third whose marginal distributions include those of the original models. Building upon and extending existing work in the Gaussian case, we develop Markov…
Kingman Coalescent was first proposed by Kingman [7] in population genetics to describe population's genealogical structure. Now it becomes a bench-mark model for coalescent process. Extensive studies have been conducted on Kingman…
We consider a stochastic individual-based population model with competition, trait-structure affecting reproduction and survival, and changing environment. The changes of traits are described by jump processes, and the dynamics can be…
In this paper, we review recent results of ours concerning branching processes with general lifetimes and neutral mutations, under the infinitely many alleles model, where mutations can occur either at birth of individuals or at a constant…
In this paper, we study consistent and partially exchangeable sequences of Markov chains on a finite state space. We provide a characterisation of the admissible transition rates via a decomposition into individual and coordinated motion of…
We present a model for evolving population which maintains genetic polymorphism. By introducing random mutation in the model population at a constant rate, we observe that the population does not become extinct but survives, keeping…
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…
We provide new connections between multitype $\Lambda$-coalescents and multitype continuous state branching processes via duality and a homeomorphism on their parameter space. The approach is based on a sequential sampling procedure for the…
We propose a class of continuous-time Markov counting processes for analyzing correlated binary data and establish a correspondence between these models and sums of exchangeable Bernoulli random variables. Our approach generalizes many…
We are interested in modelling Darwinian evolution, resulting from the interplay of phenotypic variation and natural selection through ecological interactions. Our models are rooted in the microscopic, stochastic description of a population…
We apply recently developed inference methods based on general coalescent processes to DNA sequence data obtained from various marine species. Several of these species are believed to exhibit so-called shallow gene genealogies, potentially…