Related papers: A conditional coalescent for diploid exchangeable …
The goal of this paper is to prove rigorous results for the behavior of genealogies in a one-dimensional long range biased voter model introduced by Hallatschek and Nelson [25]. The first step, which is easily accomplished using results of…
We explore a Boltzmann scheme for studying the evolution of compact binary populations of globular clusters. We include processes of compact-binary formation by tidal capture and exchange encounters, binary destruction by dissociation and…
In a geographically distributed population, assortative clustering plays an important role in evolution by modifying local environments. To examine its effects in a linear habitat, we consider a one-dimensional grid of cells, where each…
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…
Bertoin and Le Gall (2003) introduced a certain probability measure valued Markov process that describes the evolution of a population, such that a sample from this population would exhibit a genealogy given by the so-called…
The mapping between genotype and phenotype is encoded in the complex web of epistatic interaction between genetic loci. In this rugged fitness landscape, recombination processes, which tend to increase variation in the population, compete…
Environmental changes greatly influence the evolution of populations. Here, we study the dynamics of a population of two strains, one growing slightly faster than the other, competing for resources in a time-varying binary environment…
Given a gene tree topology and a species tree topology, a coalescent history represents a possible mapping of the list of gene tree coalescences to associated branches of a species tree on which those coalescences take place. Enumerative…
In most biological studies and processes, cell proliferation and population dynamics play an essential role. Due to this ubiquity, a multitude of mathematical models has been developed to describe these processes. While the simplest models…
Spatial models where growth is limited to the edge of the expansions have been instrumental to understand the population dynamics and the clone size distribution in growing cellular populations, such as microbial colonies and avascular…
We review models of biological evolution in which the population frequency changes deterministically with time. If the population is self-replicating, although the equations for simple prototypes can be linearised, nonlinear equations arise…
The reconstruction of a species phylogeny from genomic data faces two significant hurdles: 1) the trees describing the evolution of each individual gene--i.e., the gene trees--may differ from the species phylogeny and 2) the molecular…
Our results characterize the long-term behavior for a broad class of $\Lambda$-Wright--Fisher processes with frequency-dependent and environmental selection. In particular, we reveal a rich variety of parameter-dependent behaviors and…
We give a short overview on our work on ancestral lineages in spatial population models with local regulation. We explain how an ancestral lineage can be interpreted as a random walk in a dynamic random environment. Defining regeneration…
Consider two ancestral lineages sampled from a system of two-dimensional branching random walks with logistic regulation in the stationary regime. We study the asymptotics of their coalescence time for large initial separation and find that…
Forward-time models of diversification (i.e., speciation and extinction) produce phylogenetic trees that grow "vertically" as time goes by. Pruning the extinct lineages out of such trees leads to natural models for reconstructed trees…
This paper deals with the stochastic modeling of a class of heterogeneous population in a random environment, called birth-death-swap. In addition to demographic events, swap events, i.e. moves between subgroups, occur in the population.…
We consider the mutation--selection differential equation with pairwise interaction (or, equivalently, the diploid mutation--selection equation) and establish the corresponding ancestral process, which is a random tree and a variant of the…
A probabilistic reconstruction of genealogies in a polyploid population (from 2x to 4x) is investigated, by considering genetic data analyzed as the probability of allele presence in a given genotype. Based on the likelihood of all possible…
In subdivided populations, migration acts together with selection and genetic drift and determines their evolution. Building up on a recently proposed method, which hinges on the emergence of a time scale separation between local and global…