Characterizing time-evolution of allele frequencies in a population is a fundamental problem
in population genetics. In the Wright–Fisher diffusion, such dynamics is captured by the …

The trajectory of the frequency of an allele which begins at x at time 0 and is known to have
frequency z at time T can be modelled by the bridge process of the Wright–Fisher diffusion …

A number of discrete time, finite population size models in genetics describing the dynamics
of allele frequencies are known to converge (subject to suitable scaling) to a diffusion …

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 …

Abstract The Wright–Fisher family of diffusion processes is a widely used class of
evolutionary models. However, simulation is difficult because there is no known closed-form …

Abstract 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 …

A coalescent dual process for a multi-type Moran model with genic selection is derived using
a generator approach. This leads to an expansion of the transition functions in the Moran …

We investigate the properties of a Wright–Fisher diffusion process starting at frequency x at
time 0 and conditioned to be at frequency y at time T. Such a process is called a bridge …

We present a series of elementary stochastic models arising from population genetics.
Various mathematical aspects are investigated at the intuitive level. Special emphasis is put …