Related papers: Single--crossover recombination and ancestral reco…
Our motivation comes from the large population approximation of individual based models in population dynamics and population genetics. We propose a general method to investigate scaling limits of finite dimensional population size Markov…
The coupled Wright-Fisher diffusion is a multi-dimensional Wright-Fisher diffusion for multi-locus and multi-allelic genetic frequencies, expressed as the strong solution to a system of stochastic differential equations that are coupled in…
The diffusion approximation of the Wright-Fisher model of population genetics leads to partial differentiable equations, the so-called Kolmogorov equations, with an operator that degenerates at the boundary. Standard tools do not apply, and…
We show that an algorithmic construction of sequences of recursive trees leads to a direct proof of the convergence of random recursive trees in an associated Doob-Martin compactification; it also gives a representation of the limit in…
A two-types, discrete-time population model with finite, constant size is constructed, allowing for a general form of frequency-dependent selection and skewed offspring distribution. Selection is defined based on the idea that individuals…
We study the continuous-time evolution of the recombination equation of population genetics. This evolution is given by a differential equation that acts on a product probability space, and its solution can be described by a Markov chain on…
We develop a global and hierarchical scheme for the forward Kolmogorov (Fokker-Planck) equation of the diffusion approximation of the Wright-Fisher model of population genetics. That model describes the random genetic drift of several…
We study a class of processes that are akin to the Wright-Fisher model, with transition probabilities weighted in terms of the frequency-dependent fitness of the population types. By considering an approximate weak formulation of the…
We consider a population evolving under mutation and selection. The genotype of an individual is a word of length $\ell$ over a finite alphabet. Mutations occur during reproduction, independently on each locus; the fitness depends on the…
Binary trait data record the presence or absence of distinguishing traits in individuals. We treat the problem of estimating ancestral trees with time depth from binary trait data. Simple analysis of such data is problematic. Each homology…
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…
We consider catalytic branching populations. They consist of a catalyst population evolving according to a critical binary branching process in continuous time with a constant branching rate and a reactant population with a branching rate…
I describe an analytical approximation for calculating the short-term probability of loss of a chromosome under the neutral Wright-Fisher model with recombination. I also present an upper and lower bound for this probability. Exact…
In this work we model the dynamics of a population that evolves as a continuous time branching process with a trait structure and ecological interactions in form of mutations and competition between individuals. We generalize existing…
Moran or Wright-Fisher processes are probably the most well known model to study the evolution of a population under various effects. Our object of study will be the Simpson index which measures the level of diversity of the population, one…
Recently, much attention has been given to understanding recombination events along a chromosome in a variety of field. For instance, many population genetics problems are limited by the inaccuracy of inferred evolutionary histories of…
The entropy rates of the Wright-Fisher process, the Moran process, and generalizations are computed and used to compare these processes and their dependence on standard evolutionary parameters. Entropy rates are measures of the variation…
We are interested in the evolving genealogy of a birth and death process with trait structure and ecological interactions. Traits are hereditarily transmitted from a parent to its offspring unless a mutation occurs. The dynamics may depend…
We study a family of n-dimensional diffusions, taking values in the unit simplex of vectors with nonnegative coordinates that add up to one. These processes satisfy stochastic differential equations which are similar to the ones for the…
In a deterministic or random tree, a notion of ancestral diversity can be defined as follows. Sample independently $n$ groups of $k$ leaves and count the number $N_n(k)$ of distinct most recent common ancestors of each of the groups. As $n$…