Related papers: Probability that a chromosome is lost without trac…
We consider the Wright-Fisher model for a population of $N$ individuals, each identified with a sequence of a finite number of sites, and single-crossover recombination between them. We trace back the ancestry of single individuals from the…
Recombination is a fundamental evolutionary force, but it is difficult to quantify because the effect of a recombination event on patterns of variation in a sample of genetic data can be hard to discern. Estimators for the recombination…
The correlation among the gene genealogies at different loci is crucial in biology, yet challenging to understand because such correlation depends on many factors including genetic linkage, recombination, natural selection and population…
The transition distribution of a sample taken from a Wright-Fisher diffusion with general small mutation rates is found using a coalescent approach. The approximation is equivalent to having at most one mutation in the coalescent tree of…
Recently, much attention has been given to understanding recombination events along a chromosome in a variety of field. For instance, many population genetics problems are limited by the inaccuracy of inferred evolutionary histories of…
In this paper an exact rejection algorithm for simulating paths of the coupled Wright-Fisher diffusion is introduced. The coupled Wright-Fisher diffusion is a family of multidimensional Wright-Fisher diffusions that have drifts depending on…
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…
The Wright-Fisher model describes a biological population containing a finite number of individuals. In this work we consider a Wright-Fisher model for a randomly mating population, where selection and mutation act at an unlinked locus. The…
The accuracy of the recombination estimation method of Padhukasahasram et al. 2006 can be improved by including additional informative summary statistics in the rejection scheme and by simulating datasets under a fixed segregating sites…
We study a class of processes that are akin to the Wright-Fisher model, with transition probabilities weighted in terms of the frequency-dependent fitness of the population types. By considering an approximate weak formulation of the…
Discrete ancestral problems arising in population genetics are investigated. In the neutral case, the duality concept has proved of particular interest in the understanding of backward in time ancestral process from the forward in time…
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…
Wright-Fisher diffusions and their dual ancestral graphs occupy a central role in the study of allele frequency change and genealogical structure, and they provide expressions, explicit in some special cases but generally implicit, for the…
We develop an iterative global solution scheme for the backward Kolmogorov equation of the diffusion approximation of the Wright-Fisher model of population genetics. That model describes the random genetic drift of several alleles at the…
The formula for the probability of fixation of a new mutation is widely used in theoretical population genetics and molecular evolution. Here we derive a series of identities, inequalities and approximations for the exact probability of…
The Wright-Fisher model and the Moran model are both widely used in population genetics. They describe the time evolution of the frequency of an allele in a well-mixed population with fixed size. We propose a simple and tractable model…
The drift-barrier hypothesis states that random genetic drift constrains the refinement of a phenotype under natural selection. The influence of effective population size and the genome-wide deleterious mutation rate were studied…
The stationary distribution of a sample taken from a Wright-Fisher diffusion with general small mutation rates is found using a coalescent approach. The approximation is equivalent to having at most one mutation in the coalescent tree to…
We develop a global and hierarchical scheme for the forward Kolmogorov (Fokker-Planck) equation of the diffusion approximation of the Wright-Fisher model of population genetics. That model describes the random genetic drift of several…
Understanding patterns of selectively neutral genetic variation is essential in order to model deviations from neutrality, caused for example by different forms of selection. Best understood is neutral genetic variation at a single locus,…