Related papers: EWF : simulating exact paths of the Wright--Fisher…
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…
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 Wright-Fisher model and the Moran model are both widely used in population genetics. They describe the time evolution of the frequency of an allele in a well-mixed population with fixed size. We propose a simple and tractable model…
A forward diffusion equation describing the evolution of the allele frequency spectrum is presented. The influx of mutations is accounted for by imposing a suitable boundary condition. For a Wright-Fisher diffusion with or without selection…
A generalised one-dimensional Fisher-Wright diffusion process with mutations is considered. This is a well-known model in population genetics. An exponential recurrence is established for the process, which also implies an exponential rate…
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…
Wright-Fisher diffusions describe the evolution of the type composition of an infinite haploid population with two types (say type $0$ and type $1$) subject to neutral reproductions, and possibly selection and mutations. In the present…
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…
We study a generalization of the Wright--Fisher model in which some individuals adopt a behavior that is harmful to others without any direct advantage for themselves. This model is motivated by studies of spiteful behavior in nature,…
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…
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…
In a (two-type) Wright-Fisher diffusion with directional selection and two-way mutation, let $x$ denote today's frequency of the beneficial type, and given $x$, let $h(x)$ be the probability that, among all individuals of today's…
One-dimensional Fisher-Wright diffusion process on the interval $(0,1)$ with mutations is considered. This is a widely known model in population genetics. The goal of the paper is an exponential recurrence of the process, which also implies…
Coupled Wright-Fisher diffusions have been recently introduced to model the temporal evolution of finitely-many allele frequencies at several loci. These are vectors of multidimensional diffusions whose dynamics are weakly coupled among…
With a view to statistical inference for discretely observed diffusion models, we propose simple methods of simulating diffusion bridges, approximately and exactly. Diffusion bridge simulation plays a fundamental role in likelihood and…
Diffusion coefficients are essential microphysics input for modeling white dwarf evolution, as they impact phase separation at crystallization and sedimentary heat sources. Present schemes for computing diffusion coefficients are accurate…
We consider diffusion processes x_{t} on the unit interval. Doob-transformation techniques consist of a selection of x_{t}-paths procedure. The law of the transformed process is the one of a branching diffusion system of particles, each…
To model discrete sequences such as DNA, proteins, and language using diffusion, practitioners must choose between three major methods: diffusion in discrete space, Gaussian diffusion in Euclidean space, or diffusion on the simplex. Despite…
The recently introduced two-parameter Poisson-Dirichlet diffusion extends the infinitely-many-neutral-alleles model, related to Kingman's distribution and to Fleming-Viot processes. The role of the additional parameter has been shown to…
We provide a general theorem bounding the error in the approximation of a random measure of interest--for example, the empirical population measure of types in a Wright-Fisher model--and a Dirichlet process, which is a measure having…