Related papers: General triallelic frequency spectrum under demogr…
We consider a general branching population where the lifetimes of individuals are i.i.d.\ with arbitrary distribution and where each individual gives birth to new individuals at Poisson times independently from each other. In addition, we…
We study a universal object for the genealogy of a sample in populations with mutations: the critical birth-death process with Poissonian mutations, conditioned on its population size at a fixed time horizon. We show how this process arises…
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 consider a branching population where individuals live and reproduce independently. Their lifetimes are i.i.d. and they give birth at a constant rate b. The genealogical tree spanned by this process is called a splitting tree, and the…
In population genetics, diffusions on the unit interval are often used to model the frequency path of an allele. In this setting we derive approximations for fixation probabilities, expected hitting times and the expected…
Genetic data are now routinely used to study the history of population size, subdivision, and gene flow. A variety of formal statistical methods is available for testing hypotheses and fitting models to data. Yet it is often unclear which…
In considering evolution of transcribed regions, regulatory modules, and other genomic loci of interest, we are often faced with a situation in which the number of allelic states greatly exceeds the population size. In this limit, the…
Our models for detecting the effect of adaptation on population genomic diversity are often predicated on a single newly arisen mutation sweeping rapidly to fixation. However, a population can also adapt to a new situation by multiple…
A wide range of studies in population genetics have employed the sample frequency spectrum (SFS), a summary statistic which describes the distribution of mutant alleles at a polymorphic site in a sample of DNA sequences. In particular,…
We consider a population model where individuals behave independently from each other and whose genealogy is described by a chronological tree called splitting tree. The individuals have i.i.d. (non-exponential) lifetime durations and give…
Phylodynamics seeks to estimate effective population size fluctuations from molecular sequences of individuals sampled from a population of interest. One way to accomplish this task formulates an observed sequence data likelihood exploiting…
Understanding the population structure and patterns of gene flow within species is of fundamental importance to the study of evolution. In the fields of population and evolutionary genetics, measures of genetic differentiation are commonly…
Splicing sites provide unique statistics in human genome due to their large number and reasonably complete annotation. Analyses of the cumulative SNPs distribution in splicing sites reveal a few interesting observations. While a degree of…
We analyse the statistical properties of genealogical trees in a neutral model of a closed population with sexual reproduction and non-overlapping generations. By reconstructing the genealogy of an individual from the population evolution,…
In large populations, multiple beneficial mutations may be simultaneously spreading. In asexual populations, these mutations must either arise on the same background or compete against each other. In sexual populations, recombination can…
Recurrent mutations are a common phenomenon in population genetics. They may be at the origin of the fixation of a new genotype, if they give a phenotypic advantage to the carriers of the new mutation. In this paper, we are interested in…
As researchers collect increasingly large molecular data sets to reconstruct the Tree of Life, the heterogeneity of signals in the genomes of diverse organisms poses challenges for traditional phylogenetic analysis. A class of phylogenetic…
In many modern applications, including analysis of gene expression and text documents, the data are noisy, high-dimensional, and unordered--with no particular meaning to the given order of the variables. Yet, successful learning is often…
Spatially resolved genetic data is increasingly used to reconstruct the migrational history of species. To assist such inference, we study, by means of simulations and analytical methods, the dynamics of neutral gene frequencies in a…
The stationary sampling distribution of a neutral decoupled Moran or Wright-Fisher diffusion with neutral mutations is known to first order for a general rate matrix with small but otherwise unconstrained mutation rates. Using this…