Related papers: Wright-Fisher diffusion bridges
The purpose of this work is to describe a duality between a fragmentation associated to certain Dirichlet distributions and a natural random coagulation. The dual fragmentation and coalescent chains arising in this setting appear in the…
A two-dimensional array of independent random signs produces coalescing random walks. The position of the walk, starting at the origin, after N steps is a highly nonlinear, noise sensitive function of the signs. A typical term of its…
We investigate the nature of genetic drift acting at the leading edge of range expansions, building on recent results in [Hallatschek et al., Proc.\ Natl.\ Acad.\ Sci., \textbf{104}(50): 19926 - 19930 (2007)]. A well mixed population of two…
It is becoming routine to obtain datasets on DNA sequence variation across several thousands of chromosomes, providing unprecedented opportunity to infer the underlying biological and demographic forces. Such data make it vital to study…
Whisking is a rhythmic and adaptive behavior that rodents use to probe and interact with their environment, and the frequency of movement reflects both sensorimotor processing and internal brain states. A robust and traditional method of…
We review the statistical properties of the genealogies of a few models of evolution. In the asexual case, selection leads to coalescence times which grow logarithmically with the size of the population in contrast with the linear growth of…
A popular line of research in evolutionary biology is the use of time-calibrated phylogenies for the inference of diversification processes. This requires computing the likelihood of a given ultrametric tree as the reconstructed tree…
Barrier crossing is a widespread phenomenon across natural and engineering systems. While an abundant cross-disciplinary literature on the topic has emerged over the years, the stochastic underpinnings of the process are yet to be linked…
At time 0, start a time-continuous binary branching process, where particles give birth to a single particle independently (at a possibly time-dependent rate) and die independently (at a possibly time-dependent and age-dependent rate). A…
We examine genetic statistics used in the study of structured populations. In a 1999 paper, Wakeley observed that the coalescent process associated with the finite island model can be decomposed into a scattering phase and a collecting…
We study a class of coalescents derived from a sampling procedure out of N i.i.d. Pareto(alpha) random variables, normalized by their sum, including beta-size-biasing on total length effects (beta < alpha). Depending on the range of alpha,…
Phylogenetic trees represent the evolutionary relationships between extant lineages, where extinct or non-sampled lineages are omitted. Extending the work of Stadler and collaborators, this paper focuses on the branch lengths in…
Consider a population evolving as a critical continuous-time Galton-Watson (GW) tree. Conditional on the population surviving until a large time $T$, sample $k$ individuals uniformly at random (without replacement) from amongst those alive…
Large populations may contain numerous simultaneously segregating polymorphisms subject to natural selection. Since selection acts on individuals whose fitness depends on many loci, different loci affect each other's dynamics. This leads to…
We consider a one dimensional L\'evy bridge x_B of length n and index 0 < \alpha < 2, i.e. a L\'evy random walk constrained to start and end at the origin after n time steps, x_B(0) = x_B(n)=0. We compute the distribution P_B(A,n) of the…
In many biological processes, the size of a population changes stochastically with time, and recent work in the context of cancer and bacterial growth have focused on the situation when the mean population size grows exponentially. Here,…
The dynamics of two liquid droplets coalescing in their saturated vapor phase are investigated by Lattice Boltzmann numerical simulations. Attention is paid to the effect of the vapor phase on the formation and growth dynamics of the liquid…
We introduce a stochastic model of a population with overlapping generations and arbitrary levels of self-fertilization versus outcrossing. We study how the global graph of reproductive relationships, or population pedigree, influences the…
We introduce a new residual-bridge proposal for approximately simulating conditioned diffusions. This proposal is formed by applying the modified diffusion bridge approximation of Durham and Gallant (2002) to the difference between the true…
Accessibility percolation is a new type of percolation problem inspired by evolutionary biology. To each vertex of a graph a random number is assigned and a path through the graph is called accessible if all numbers along the path are in…