Related papers: An explicit transition density expansion for a mul…
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 stationary distribution of the diffusion limit of the 2-island, 2-allele Wright-Fisher with small but otherwise arbitrary mutation and migration rates is investigated. Following a method developed by Burden and Tang (2016, 2017) for…
We develop an iterative global solution scheme for the backward Kolmogorov equation of the diffusion approximation of the Wright-Fisher model of population genetics. That model describes the random genetic drift of several alleles at the…
We apply a Lindeberg principle under the Markov process setting to approximate the Wright-Fisher model with neutral $r$-alleles using a diffusion process, deriving an error rate based on a function class distance involving fourth-order…
The two-parameter Poisson-Dirichlet diffusion takes values in the infinite ordered simplex and extends the celebrated infinitely-many-neutral-alleles model, having a two-parameter Poisson-Dirichlet stationary distribution. Here we identify…
The Moran discrete process and the Wright-Fisher modelare the most popular models in population genetics. It is common tounderstand the dynamics of these models to use an approximating diffusionprocess, called Wright-Fisher diffusion. Here,…
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…
In this paper we introduce a multilocus diffusion model of a population of $N$ haploid, asexually reproducing individuals. The model includes parent-dependent mutation and interlocus selection, the latter limited to pairwise relationships…
In the context of population genetics, active information can be extended to measure the change of information of a given event (e.g., fixation of an allele) from a neutral model in which only genetic drift is taken into account to a…
The recently introduced two-parameter infinitely-many neutral alleles model extends the celebrated one-parameter version, related to Kingman's distribution, to diffusive two-parameter Poisson-Dirichlet frequencies. Here we investigate the…
Consider a two-type Moran population of size $N$ with selection and mutation, where the selective advantage of the fit individuals is amplified at extreme environmental conditions. Assume selection and mutation are weak with respect to $N$,…
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…
A new class of time-dependent Dirichlet priors is introduced as a generalisation of the Wright-Fisher diffusion, allowing discontinuities in the trajectories, as well as non-Markovian memory. This class is obtained as a simple stochastic…
Convective counterparts of variants of the nonlinear Fisher equation which describes reaction diffusion systems in population dynamics are studied with the help of an analytic prescription and shown to lead to interesting consequences for…
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…
We consider Taylor dispersion for tracer particles in micro-fluidic planar channels with strong confinement. In this context, the channel walls modify the local diffusivity tensor and also interactions between the tracer particles and the…
Fleming-Viot diffusions are widely used stochastic models for population dynamics which extend the celebrated Wright-Fisher diffusions. They describe the temporal evolution of the relative frequencies of the allelic types in an ideally…
In this paper an exact rejection algorithm for simulating paths of the coupled Wright-Fisher diffusion is introduced. The coupled Wright-Fisher diffusion is a family of multidimensional Wright-Fisher diffusions that have drifts depending on…
We study the population genetics of two neutral alleles under reversible mutation in the \Lambda-processes, a population model that features a skewed offspring distribution. We describe the shape of the equilibrium allele frequency…
In the present review we survey the properties of a transcendental function of the Wright type, nowadays known as M-Wright function, entering as a probability density in a relevant class of self-similar stochastic processes that we…