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The fitness contribution of an allele at one genetic site may depend on alleles at other sites, a phenomenon known as epistasis. Epistasis can profoundly influence the process of evolution in populations under selection, and can shape the…
Game theoretic tools are utilized to analyze a one-locus continuous selection model of sex-specific meiotic drive by considering nonequivalence of the viabilities of reciprocal heterozygotes that might be noticed at an imprinted locus. The…
In evolutionary dynamics, a key measure of a mutant trait's success is the probability that it takes over the population given some initial mutant-appearance distribution. This "fixation probability" is difficult to compute in general, as…
Stronger selection implies faster evolution---that is, the greater the force, the faster the change. This apparently self-evident proposition, however, is derived under the assumption that genetic variation within a population is primarily…
We study biological evolution in a high-dimensional genotype space in the regime of rare mutations and strong selection. The population performs an uphill walk which terminates at local fitness maxima. Assigning fitness randomly to…
A major goal of molecular evolutionary biology is to identify loci or regions of the genome under selection versus those evolving in a neutral manner. Correct identification allows accurate inference of the evolutionary process and thus…
In subdivided populations, migration acts together with selection and genetic drift and determines their evolution. Building up on a recently proposed method, which hinges on the emergence of a time scale separation between local and global…
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 distribution and heritability of many traits depends on numerous loci in the genome. In general, the astronomical number of possible genotypes makes the system with large numbers of loci difficult to describe. Multilocus evolution,…
The genetic diversity of a species is shaped by its recent evolutionary history and can be used to infer demographic events or selective sweeps. Most inference methods are based on the null hypothesis that natural selection is a weak or…
Neutral evolution assumes that there are no selective forces distinguishing different variants in a population. Despite this striking assumption, many recent studies have sought to assess whether neutrality can provide a good description of…
Understanding the dynamics of genome rearrangements is a major issue of phylogenetics. Phylogenetics is the study of species evolution. A major goal of the field is to establish evolutionary relationships within groups of species, in order…
We study the genealogical distance of two randomly chosen individuals in a population that evolves according to a two type Moran model with mutation and selection. We prove that this distance is stochastically smaller than the corresponding…
The relationship between sequences and secondary structures or shapes in RNA exhibits robust statistical properties summarized by three notions: (1) the notion of a typical shape (that among all sequences of fixed length certain shapes are…
We consider an exactly solvable model of branching random walk with random selection, which describes the evolution of a population with $N$ individuals on the real line. At each time step, every individual reproduces independently, and its…
We consider resequencing studies of associated loci and the problem of prioritizing sequence variants for functional follow-up. Working within the multivariate linear regression framework helps us to account for correlation across variants,…
The contribution to an organism's phenotype from one genetic locus may depend upon the status of other loci. Such epistatic interactions among loci are now recognized as fundamental to shaping the process of adaptation in evolving…
We investigate a continuous time, probability measure-valued dynamical system that describes the process of mutation-selection balance in a context where the population is infinite, there may be infinitely many loci, and there are weak…
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…
We updated the agent based Monte Carlo code HERITAGE that simulates human evolution within restrictive environments such as interstellar, sub-light speed spacecraft in order to include the effects of population genetics. We incorporated a…