Related papers: Genetic Demixing and Evolutionary Forces in the On…
By exploiting an analogy between population genetics and statistical mechanics, we study the evolution of a polygenic trait under stabilizing selection, mutation, and genetic drift. This requires us to track only four macroscopic variables,…
A strong demographic Allee effect in which the expected population growth rate is negative below a certain critical population size can cause high extinction probabilities in small introduced populations. However, many species are…
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…
Selection in a time-periodic environment is modeled via the continuous-time two-player replicator dynamics, which for symmetric pay-offs reduces to the Fisher equation of mathematical genetics. For a sufficiently rapid and cyclic…
We study in detail a recently proposed simple discrete model for evolution on smooth landscapes. An asymptotic solution of this model for long times is constructed. We find that the dynamics of the population are governed by correlation…
We consider an asexually reproducing population on a finite type space whose evolution is driven by exponential birth, death and competition rates, as well as the possibility of mutation at a birth event. On the individual-based level this…
Traditionally, frequency dependent evolutionary dynamics is described by deterministic replicator dynamics assuming implicitly infinite population sizes. Only recently have stochastic processes been introduced to study evolutionary dynamics…
Frequency dependent selection and demographic fluctuations play important roles in evolutionary and ecological processes. Under frequency dependent selection, the average fitness of the population may increase or decrease based on…
Some species exhibit very high levels of DNA sequence variability; there is also evidence for the existence of heritable epigenetic variants that experience state changes at a much higher rate than sequence variants. In both cases, the…
We reconsider the deterministic haploid mutation-selection equation with two types. This is an ordinary differential equation that describes the type distribution (forward in time) in a population of infinite size. This paper establishes…
We are concerned with a special form of the (stochastic) Allen-Cahn equation, which can be seen as a model of hybrid zones in population genetics. Individuals in the population can be of one of three types; $aa$ are fitter than $AA$, and…
Population diversity is crucial in evolutionary algorithms as it helps with global exploration and facilitates the use of crossover. Despite many runtime analyses showing advantages of population diversity, we have no clear picture of how…
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…
In this work we develop a microscopic physical model of early evolution, where phenotype,organism life expectancy, is directly related to genotype, the stability of its proteins in their native conformations which can be determined exactly…
In distributed evolutionary algorithms, migration interval is used to decide migration moments. Nevertheless, migration moments predetermined by intervals cannot match the dynamic situation of evolution. In this paper, a scheme of setting…
Population genetic studies have found evidence for dramatic population growth in recent human history. It is unclear how this recent population growth, combined with the effects of negative natural selection, has affected patterns of…
We study the stationary state of a population evolving under the action of random genetic drift, selection and recombination in which both deleterious and reverse beneficial mutations can occur. We find that the equilibrium fraction of…
Background: Speciation corresponds to the progressive establishment of reproductive barriers between groups of individuals derived from an ancestral stock. Since Darwin did not believe that reproductive barriers could be selected for, he…
In the past years, a remarkable mapping has been found between the dynamics of a population of M individuals undergoing random mutations and selection, and that of a single system in contact with a thermal bath with temperature 1/M. This…
Large populations may contain numerous simultaneously segregating polymorphisms subject to natural selection. Since selection acts on individuals whose fitness depends on many loci, different loci affect each other's dynamics. This leads to…