Related papers: An accurate model for genetic hitch-hiking
We explore the connection between evolution and large-deviation theory. To do so, we study evolutionary dynamics in which individuals experience mutations, reproduction, and selection using variants of the Moran model. We show that, in the…
Recent microbial experiments suggest that enhanced genetic drift at the frontier of a two-dimensional range expansion can cause genetic sectoring patterns with fractal domain boundaries. Here, we propose and analyze a simple model of…
The investigation of allele frequency trajectories in populations evolving under controlled environmental pressures has become a popular approach to study evolutionary processes on the molecular level. Statistical models based on…
Many mathematical models of evolution assume that all individuals experience the same environment. Here, we study the Moran process in heterogeneous environments. The population is of finite size with two competing types, which are exposed…
We consider neutral evolution of a large population subject to changes in its population size. For a population with a time-variable carrying capacity we have computed the distributions of the total branch lengths of its sample genealogies.…
A population genetics formulation of Eigen's molecular quasispecies model is proposed and several simple replication landscapes are investigated analytically. Our results show a remarcable similarity to those obtained with the original…
A panel of large number of common Single Nucleotide Polymorphisms (SNPs) distributed across an entire porcine genome has been widely used to represent genetic variability of pig. With the advent of SNP-array technology, a genome-wide…
Evolve and resequence studies provide a popular approach to simulate evolution in the lab and explore its genetic basis. In this context, the chi-square test, Fishers exact test, as well as the Cochran-Mantel-Haenszel test are commonly used…
We examine a model of biological evolution of Eigen's quasispecies in a holey fitness landscape, where the fitness of a site is either 0 (lethal site) or a uniform positive constant (viable site). So, the evolution dynamics is determined by…
We ask the question "when will natural selection on a gene in a spatially structured population cause a detectable trace in the patterns of genetic variation observed in the contemporary population?". We focus on the situation in which…
A very simple event frequency approximation algorithm that is sensitive to event timeliness is suggested. The algorithm iteratively updates categorical click-distribution, producing (path of) a random walk on a standard $n$-dimensional…
In this article, we consider several models of random walks in one or several dimensions, additionally allowing, at any unit of time, a reset (or "catastrophe") of the walk with probability $q$. We establish the distribution of the final…
Genomic regions (or loci) displaying outstanding correlation with some environmental variables are likely to be under selection and this is the rationale of recent methods of identifying selected loci and retrieving functional information…
We study ancestral structures for the two-type Moran model with mutation and frequency-dependent selection under the nonlinear dominance or fittest-type-wins scheme. Under appropriate conditions, both lead, in distribution, to the same…
We study the following model for a diploid population of constant size $N$: Every individual carries a random number of (genetic) elements. Upon a reproduction event each of the two parents passes each element independently with probability…
We consider a neutral dynamical model of biological diversity, where individuals live and reproduce independently. They have i.i.d. lifetime durations (which are not necessarily exponentially distributed) and give birth (singly) at constant…
We show, that the specific distribution of gene's length, which is observed in natural genomes, might be a result of a growth process, in which a single length scale $L(t)$ develops that grows with time as $t^{1/3}$. This length scale could…
We consider the classical Wright-Fisher model with mutation and selection. Mutations occur independently in each locus, and selection is performed according to the sharp peak landscape. In the asymptotic regime studied in [3], a…
The ~4-Mbp basic genome shared by 32 independent isolates of E. coli representing considerable population diversity has been approximated by whole-genome multiple-alignment and computational filtering designed to remove mobile elements and…
Consider a branching Markov process with values in some general type space. Conditional on survival up to generation $N$, the genealogy of the extant population defines a random marked metric measure space, where individuals are marked by…