Related papers: Coalescence in a random background
We present a novel approach for generating minority samples that live on low-density regions of a data manifold. Our framework is built upon diffusion models, leveraging the principle of guided sampling that incorporates an arbitrary…
Diffusion theory is a central tool of modern population genetics, yielding simple expressions for fixation probabilities and other quantities that are not easily derived from the underlying Wright-Fisher model. Unfortunately, the textbook…
Genome-wide patterns of genetic divergence reveal mechanisms of adaptation under gene flow. Empirical data show that divergence is mostly concentrated in narrow genomic regions. This pattern may arise because differentiated loci protect…
We consider the Moran model in continuous time with two types, mutation, and selection. We concentrate on the ancestral line and its stationary type distribution. Building on work by Fearnhead (J. Appl. Prob. 39 (2002), 38-54) and Taylor…
Sweepstakes reproduction refers to a highly skewed individual recruitment success without involving natural selection and may apply to individuals in broadcast spawning populations characterised by Type III survivorship. We consider an…
Population genetics theory has laid the foundations for genomics analyses including the recent burst in genome scans for selection and statistical inference of past demographic events in many prokaryote, animal and plant species.…
We derive exact formulae for the allele frequency spectrum under the coalescent with mutation, conditioned on allele counts at some fixed time in the past. We consider unlinked biallelic markers mutating according to a finite sites, or…
Study sample sizes in human genetics are growing rapidly, and in due course it will become routine to analyze samples with hundreds of thousands if not millions of individuals. In addition to posing computational challenges, such large…
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…
Comparing allele frequencies among populations that differ in environment has long been a tool for detecting loci involved in local adaptation. However, such analyses are complicated by an imperfect knowledge of population allele…
We are interested in the long-time behavior of a diploid population with sexual reproduction, characterized by its genotype composition at one bi-allelic locus. The population is modeled by a 3-dimensional birth-and-death process with…
We review the statistical properties of the genealogies of a few models of evolution. In the asexual case, selection leads to coalescence times which grow logarithmically with the size of the population in contrast with the linear growth of…
Kingman's model describes the evolution of a one-locus haploid population of infinite size and discrete generations under the competition of selection and mutation. A random generalisation has been made in a previous paper which assumes all…
Deep generative models produce data according to a learned representation, e.g. diffusion models, through a process of approximation computing possible samples. Approximation can be understood as reconstruction and the large datasets used…
We consider a Moran model with recombination in a haploid population of size $N$. At each birth event, with probability $1-\rho_N R$ the offspring copies one parent's chromosome, and with probability $\rho_N R$ she inherits a chromosome…
Diffusion has been widely used to describe a random walk of particles or waves, and it requires only one parameter -- the diffusion constant. For waves, however, diffusion is an approximation that disregards the possibility of interference.…
The Yule model and the coalescent model are two neutral stochastic models for generating trees in phylogenetics and population genetics, respectively. Although these models are quite different, they lead to identical distributions…
Understanding the statistical properties of a collection of individuals subject to random displacements and birth-and-death events is key to several applications in physics and life sciences, encompassing the diagnostic of nuclear reactors…
We consider an extension of the noisy $N$-Branching Random Walk that models the evolution of a population subject to natural selection. We show the existence of a critical value for the noise which separates the limiting genealogical…
Having a precise knowledge of the dispersal ability of a population in a heterogeneous environment is of critical importance in agroecology and conservation biology as it can provide management tools to limit the effects of pests or to…