Related papers: Splitting trees with neutral mutations at birth
In this article we propose a novel method to estimate the frequency distribution of linguistic variables while controlling for statistical non-independence due to shared ancestry. Unlike previous approaches, our technique uses all available…
We revisit the classical population genetics model of a population evolving under multiplicative selection, mutation and drift. The number of beneficial alleles in a multi-locus system can be considered a trait under exponential selection.…
We study a stochastic model based on a modified fragmentation of a finite interval. The mechanism consists in cutting the interval at a random location and substituting a unique fragment on the right of the cut to regenerate and preserve…
We consider a discrete-time Markov chain, called fragmentation process, that describes a specific way of successively removing objects from a linear arrangement. The process arises in population genetics and describes the ancestry of the…
Take a continuous-time Galton-Watson tree. If the system survives until a large time $T$, then choose $k$ particles uniformly from those alive. What does the ancestral tree drawn out by these $k$ particles look like? Some special cases are…
We introduce an individual-based model for structured populations undergoing demographic bottlenecks, i.e. drastic reductions in population size that last many generations and can have arbitrary shapes. We first show that the…
The paper discusses a connection between asymmetric reproduction -- that is reproduction in a parent-child relationship where the parent does not mutate during reproduction --, the fact that all non-viral lifeforms bear genes of their…
The Fleming-Viot process with parent-independent mutation process is one particular neutral population genetic model. As time goes by, some initial species are replaced by mutated ones gradually. Once the population mutation rate is high,…
In this article, discrete and stochastic changes in (effective) population size are incorporated into the spectral representation of a biallelic diffusion process for drift and small mutation rates. A forward algorithm inspired by…
We reconsider the deterministic haploid mutation-selection equation with two types. This is an ordinary differential equation that describes the type distribution (forward in time) in a population of infinite size. This paper establishes…
We investigate two stochastic models of a growing population subject to selection and mutation. In our models each individual carries a fitness which determines its mean offspring number. Many of these offspring inherit their parent's…
We are interested in populations in which the fitness of different genetic types fluctuates in time and space, driven by temporal and spatial fluctuations in the environment. For simplicity, our population is assumed to be composed of just…
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…
Given any regularly varying dislocation measure, we identify a natural self-similar fragmentation tree as scaling limit of discrete fragmentation trees with unit edge lengths. As an application, we obtain continuum random tree limits of…
We study the evolutionary dynamics of a phenotypically structured population in a changing environment , where the environmental conditions vary with a linear trend but in an oscillatory manner. Such phenomena can be described by parabolic…
The first chapter concerns monotype population models. We first study general birth and death processes and we give non-explosion and extinction criteria, moment computations and a pathwise representation. We then show how different scales…
In sexual population, recombination reshuffles genetic variation and produces novel combinations of existing alleles, while selection amplifies the fittest genotypes in the population. If recombination is more rapid than selection,…
Consider a continuous-time binary branching process conditioned to have population size n at some time t, and with a chance p for recording each extinct individual in the process. Within the family tree of this process, we consider the…
We work in the context of the infinitely many alleles model. The allelic partition associated with a coalescent process started from n individuals is obtained by placing mutations along the skeleton of the coalescent tree; for each…
When a beneficial mutation occurs in a population, the new, favored allele may spread to the entire population. This process is known as a selective sweep. Suppose we sample $n$ individuals at the end of a selective sweep. If we focus on a…