Related papers: The Sampled Moran Genealogy Process
We extend the Moran model with single-crossover recombination to include general recombination and mutation. We show that, in the case without resampling, the expectations of products of marginal processes defined via partitions of sites…
From a continuous-time long memory stochastic process, a discrete-time randomly sampled one is drawn. We investigate the second-order properties of this process and establish some time-and frequency-domain asymptotic results. We mainly…
The paper deals with a certain class of random evolutions. We develop a construction that yields an invariant measure for a continuous-time Markov process with random transitions. The approach is based on a particular way of constructing…
We construct a family of self-similar Markov martingales with given marginal distributions. This construction uses the self-similarity and Markov property of a reference process to produce a family of Markov processes that possess the same…
The entropy rates of the Wright-Fisher process, the Moran process, and generalizations are computed and used to compare these processes and their dependence on standard evolutionary parameters. Entropy rates are measures of the variation…
In genetics the Moran model describes the neutral evolution of a bi-allelic gene in a population of haploid individuals subjected to mutations. We show in this paper that this model can be mapped into an influence dynamical process on…
We investigate a new model for populations evolving in a spatial continuum. This model can be thought of as a spatial version of the Lambda-Fleming-Viot process. It explicitly incorporates both small scale reproduction events and large…
We propose a Markov chain approach for the evolution of a genealogical line of genomes. Our idealized genome has $N$ sites and each site can be in state $0$ or $1$. At each time step we pick a site at random. If the site is in state $0$ we…
We present simple conditions under which the limiting genealogical process associated with a class of interacting particle systems with non-neutral selection mechanisms, as the number of particles grows, is a time-rescaled Kingman…
Genealogical networks, also known as family trees or population pedigrees, are commonly studied by genealogists wanting to know about their ancestry, but they also provide a valuable resource for disciplines such as digital demography,…
We are interested in the evolving genealogy of a birth and death process with trait structure and ecological interactions. Traits are hereditarily transmitted from a parent to its offspring unless a mutation occurs. The dynamics may depend…
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 study the large population limit of the Moran process, assuming weak-selection, and for different scalings. Depending on the particular choice of scalings, we obtain a continuous model that may highlight the genetic-drift (neutral…
We propose a class of evolutionary models that involves an arbitrary exchangeable process as the breeding process and different selection schemes. In those models, a new genome is born according to the breeding process, and then a genome is…
When a beneficial mutation occurs in a population, the new, favored allele may spread to the entire population. This process is known as a selective sweep. Suppose we sample $n$ individuals at the end of a selective sweep. If we focus on a…
Coalescent theory combined with statistical modeling allows us to estimate effective population size fluctuations from molecular sequences of individuals sampled from a population of interest. When sequences are sampled serially through…
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 random walks in dynamic random environments, with an environment generated by the time-reversal of a Markov process from the oriented percolation universality class. If the influence of the random medium on the walk is small in…
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…
A phylogeny describes the evolutionary history of an evolving population. Evolutionary search algorithms can perfectly track the ancestry of candidate solutions, illuminating a population's trajectory through the search space. However,…