Related papers: Single--crossover recombination and ancestral reco…
Given a set of species whose evolution is represented by a species tree, a gene family is a group of genes having evolved from a single ancestral gene. A gene family evolves along the branches of a species tree through various mechanisms,…
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…
We construct a constant size population model allowing for general selective interactions and extreme reproductive events. It generalizes the idea of (Krone and Neuhauser 1997) who represented the selection by allowing individuals to sample…
We consider a Wright-Fisher diffusion (x(t)) whose current state cannot be observed directly. Instead, at times t1 < t2 < . . ., the observations y(ti) are such that, given the process (x(t)), the random variables (y(ti)) are independent…
We consider a branching random walk with binary state space and index set $T^k$, the infinite rooted tree in which each node has k children (also known as the model of "broadcasting on a tree"). The root of the tree takes a random value 0…
Given a solution to a recursive distributional equation, a natural (and non-trivial) question is whether the corresponding recursive tree process is endogenous. That is, whether the random environment almost surely defines the tree process.…
We investigate the infinitely many demes limit of the genealogy of a sample of individuals from a subdivided population subject to sporadic mass extinction events. By exploiting a separation of timescales property of Wright's island model,…
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 formula for its transition function. In this article we demonstrate that…
We present the first fixed-parameter algorithm for constructing a tree-child phylogenetic network that displays an arbitrary number of binary input trees and has the minimum number of reticulations among all such networks. The algorithm…
Most of major algorithms for phylogenetic tree reconstruction assume that sequences in the analyzed set either do not have any offspring, or that parent sequences can maximally mutate into just two descendants. The graph resulting from such…
We comment on old and new results related to the destruction of a random recursive tree (RRT), in which its edges are cut one after the other in a uniform random order. In particular, we study the number of steps needed to isolate or…
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…
Diffusion theory is a central tool of modern population genetics, yielding simple expressions for fixation probabilities and other quantities that are not easily derived from the underlying Wright-Fisher model. Unfortunately, the textbook…
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…
We examine a discrete random recursive tree growth process that, at each time step, either adds or deletes a node from the tree with probability $p$ and $1-p$, respectively. Node addition follows the usual uniform attachment model. For node…
Diversity patterns of tree species in a tropical forest community are approached by a simple lattice model and investigated by Monte Carlo simulations using a backtracking method. Our spatially explicit neutral model is based on a simple…
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,…
We study a generalized discrete-time multi-type Wright-Fisher population process. The mean-field dynamics of the stochastic process is induced by a general replicator difference equation. We prove several results regarding the asymptotic…
Extinction times in resampling processes are fundamental yet often intractable, as previous formulas scale as $2^M$ with the number of states $M$ present in the initial probability distribution. We solve this by treating multinomial updates…
With novel developments in sequencing technologies, time-sampled data are becoming more available and accessible. Naturally, there have been efforts in parallel to infer population genetic parameters from these datasets. Here, we compare…