Related papers: Wright-Fisher diffusion bridges
Identifiability of evolutionary tree models has been a recent topic of discussion and some models have been shown to be non-identifiable. A coalescent-based rooted population tree model, originally proposed by Nielsen et al. 1998 [2], has…
Sweepstakes reproduction may be generated by chance matching of reproduction with favorable environmental conditions. Gene genealogies generated by sweepstakes reproduction are in the domain of attraction of multiple-merger coalescents…
Consider a population of fixed size that evolves over time. At each time, the genealogical structure of the population can be described by a coalescent tree whose branches are traced back to the most recent common ancestor of the…
Near the beginning of the century, Wright and Fisher devised an elegant, mathematically tractable model of gene reproduction and replacement that laid the foundation for contemporary population genetics. The Wright-Fisher model and its…
We present a robust method which translates information on the speed of coming down from infinity of a genealogical tree into sampling formulae for the underlying population. We apply these results to population dynamics where the genealogy…
We analyze the diffusion processes associated to equations of Wright-Fisher type in one spatial dimension. These are defined by a degenerate second order operator on the interval [0, 1], where the coefficient of the second order term…
The measure-valued Fleming-Viot process is a diffusion which models the evolution of allele frequencies in a multi-type population. In the neutral setting the Kingman coalescent is known to generate the genealogies of the "individuals" in…
We consider a non-Gaussian stochastic process where a particle diffuses in the $y$-direction, $dy/dt=\eta(t)$, subject to a transverse shear flow in the $x$-direction, $dx/dt=f(y)$. Absorption with probability $p$ occurs at each crossing of…
Coalescence processes have received a lot of attention in the context of conditional branching processes with fixed population size and non-overlapping generations. Here we focus on similar problems in the context of the standard…
It is known that the time until a birth and death process reaches a certain level is distributed as a sum of independent exponential random variables. Diaconis, Miclo and Swart gave a probabilistic proof of this fact by coupling the birth…
We provide a class of diffusion processes for continuous time-varying multivariate angular data with explicit transition probability densities, enabling exact likelihood inference. The presented diffusions are time-reversible and can be…
We consider an expanding population on the plane. The genealogy of a sample from the population is modelled by coalescing Brownian motion on the circle. We establish a weak law of large numbers for the site frequency spectrum in this model.…
The correlation among the gene genealogies at different loci is crucial in biology, yet challenging to understand because such correlation depends on many factors including genetic linkage, recombination, natural selection and population…
Consider the Markov process taking values in the partitions of N such that each pair of blocks merges at rate one, and each integer is eroded, i.e., becomes a singleton block, at rate d. This is a special case of exchangeable…
We consider a family of models describing the evolution under selection of a population whose dynamics can be related to the propagation of noisy traveling waves. For one particular model, that we shall call the exponential model, the…
Branching processes and Fleming-Viot processes are two main models in stochastic population theory. Incorporating an immigration in both models, we generalize the results of Shiga (1990) and Birkner et al. (2005) which respectively connect…
The interface formation model is applied to describe the initial stages of the coalescence of two liquid drops in the presence of a viscous ambient fluid whose dynamics is fully accounted for. Our focus is on understanding (a) how this…
In a series of recent works it has been shown that a class of simple models of evolving populations under selection leads to genealogical trees whose statistics are given by the Bolthausen-Sznitman coalescent rather than by the well known…
Compared to a neutral model, purifying selection distorts the structure of genealogies and hence alters the patterns of sampled genetic variation. Although these distortions may be common in nature, our understanding of how we expect…
We consider a system of particles which perform branching Brownian motion with negative drift and are killed upon reaching zero, in the near-critical regime where the total population stays roughly constant with approximately N particles.…