Related papers: Duality, Ancestral and Diffusion Processes in Mode…
The distributed genome hypothesis states that the set of genes in a population of bacteria is distributed over all individuals that belong to the specific taxon. It implies that certain genes can be gained and lost from generation to…
A large offspring number diploid biparental multilocus population model of Moran type is our object of study. At each timestep, a pair of diploid individuals drawn uniformly at random contribute offspring to the population. The number of…
Consider a haploid population which has evolved through an exchangeable reproduction dynamics, and in which all individuals alive at time $t$ have a most recent common ancestor (MRCA) who lived at time $A_t$, say. As time goes on, not only…
We consider the evolution of populations under the joint action of mutation and differential reproduction, or selection. The population is modelled as a finite-type Markov branching process in continuous time, and the associated…
The recently discovered correspondence between the distribution of rapidity gaps in electron-nucleus diffractive processes and the statistics of the height of genealogical trees in branching random walks is reviewed. In addition, a new…
The purpose of this work is to describe a duality between a fragmentation associated to certain Dirichlet distributions and a natural random coagulation. The dual fragmentation and coalescent chains arising in this setting appear in the…
We introduce a multi-allele Wright-Fisher model with non-recurrent, reversible mutation and directional selection. In this setting, the allele frequencies at a single locus track the path of a hybrid jump-diffusion process with state space…
We study a model of selection acting on a diploid population (one in which each individual carries two copies of each gene) living in one spatial dimension. We suppose a particular gene appears in two forms (alleles) $A$ and $a$, and that…
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…
Ancestral inference for branching processes in random environments involves determining the ancestor distribution parameters using the population sizes of descendant generations. In this paper, we introduce a new methodology for ancestral…
Cheek and Johnston (Journal of Mathematical Biology, 2023) consider a continuous-time Bienaym\'e-Galton-Watson tree conditioned on being alive at time $T$. They study the reproduction events along the ancestral lineage of an individual…
We consider two versions of stochastic population models with mutation and selection. The first approach relies on a multitype branching process; here, individuals reproduce and change type (i.e., mutate) independently of each other,…
We reconsider the Moran model in continuous time with population size $N$, two allelic types, and selection. We introduce a new particle representation, which we call the labelled Moran model, and which has the same distribution of type…
A density-dependent branching process is a particle system in which individuals reproduce independently, but in a way that depends on the current population size. This feature can model a wide range of ecological interactions at the cost of…
In populations competing for resources, it is natural to ask whether consuming fewer resources provides any selective advantage. To answer this question, we propose a Wright- Fisher model with two types of individuals: the inefficient…
The Moran process, as studied by [Lieberman, E., Hauert, C. and Nowak, M. Evolutionary dynamics on graphs. Nature 433, pp. 312-316 (2005)], is a stochastic process modeling the spread of genetic mutations in populations. In this process,…
We consider weighted particle systems in which new generations are re-sampled from current particles with probabilities proportional to their weights. This covers a broad class of sequential Monte Carlo methods, widely used in applied…
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…
We study the genealogy of a solvable population model with $N$ particles on the real line which evolves according to a discrete-time branching process with selection. At each time step, every particle gives birth to children around $a$…
Widely used models in genetics include the Wright-Fisher diffusion and its moment dual, Kingman's coalescent. Each has a multilocus extension but under neither extension is the sampling distribution available in closed-form, and their…