Related papers: When evolution realizes large deviations of fitnes…
The interplay between space and evolution is an important issue in population dynamics, that is in particular crucial in the emergence of polymorphism and spatial patterns. Recently, biological studies suggest that invasion and evolution…
Genetic drift is stochastic fluctuations of alleles frequencies in a population due to sampling effects. We consider a model of drift in an equilibrium population, with high mutation rates: few functional mutations per generation. Such…
We consider a trait-structured population subject to mutation, birth and competition of logistic type, where the number of coexisting types may fluctuate. Applying a limit of rare mutations to this population while keeping the population…
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…
We consider a integro-differential nonlinear model that describes the evolution of a population structured by a quantitative trait. The interactions between traits occur from competition for resources whose concentrations depend on the…
Understanding the time evolution of fragmented animal populations and their habitats, connected by migration, is a problem of both theoretical and practical interest. This paper presents a method for calculating the time evolution of the…
Large sets of genotypes give rise to the same phenotype because phenotypic expression is highly redundant. Accordingly, a population can accept mutations without altering its phenotype, as long as thegenotype mutates into another one on the…
Positive selection distorts the structure of genealogies and hence alters patterns of genetic variation within a population. Most analyses of these distortions focus on the signatures of hitchhiking due to hard or soft selective sweeps at a…
In genetics the Moran model describes the neutral evolution of a bi-allelic gene in a population of haploid individuals subjected to mutations. We show in this paper that this model can be mapped into an influence dynamical process on…
We consider an asexual population under strong selection-weak mutation conditions evolving on rugged fitness landscapes with many local fitness peaks. Unlike the previous studies in which the initial fitness of the population is assumed to…
We consider an individual-based spatially structured population for Darwinian evolution in an asexual population. The individuals move randomly on a bounded continuous space according to a reflected brownian motion. The dynamics involves…
The inheritance of characteristics induced by the environment has often been opposed to the theory of evolution by natural selection. Yet, while evolution by natural selection requires new heritable traits to be produced and transmitted, it…
In many biological processes, the size of a population changes stochastically with time, and recent work in the context of cancer and bacterial growth have focused on the situation when the mean population size grows exponentially. Here,…
A new approach to understanding evolution [Val09], namely viewing it through the lens of computation, has already started yielding new insights, e.g., natural selection under sexual reproduction can be interpreted as the Multiplicative…
Large deviation theory quantifies the occurence of events that deviate from the average behavior of a system. Such events arise from non-typical trajectories of the dynamics. In this note we derive the time evolution of these rare…
We consider a fitness-structured population model with competition and migration between nearest neighbors. Under a combination of large population and rare migration limits we are particularly interested in the asymptotic behavior of the…
We study using large deviation theory the fluctuations of time-integrated functionals or observables of the unbiased random walk evolving on Erd\"os-R\'enyi random graphs, and construct a modified, biased random walk that explains how these…
The interrelationships of the fundamental biological processes natural selection, mutation, and stochastic drift are quantified by the entropy rate of Moran processes with mutation, measuring the long-run variation of a Markov process. The…
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…
On rugged fitness landscapes where sign epistasis is common, adaptation can often involve either individually beneficial "uphill" mutations or more complex mutational trajectories involving fitness valleys or plateaus. The dynamics of the…