Related papers: Muller's ratchet clicks in finite time
When mutation rates are low, natural selection remains effective, and increasing the mutation rate can give rise to an increase in adaptation rate. When mutation rates are high to begin with, however, increasing the mutation rate may have a…
We consider a model of a population of fixed size N in which each individual gets replaced at rate one and each individual experiences a mutation at rate \mu. We calculate the asymptotic distribution of the time that it takes before there…
The forest of mutations associated to a multitype branching forest is obtained by merging together all vertices of its clusters and by preserving connections between them. We first show that the forest of mutations of any mulitype branching…
We consider an infinite asexual population with a mutator allele which can elevate mutation rates. With probability $f$, a transition from nonmutator to mutator state occurs but the reverse transition is forbidden. We find that at $f=0$,…
The mean fixation time of a deleterious mutant allele is studied beyond the diffusion approximation. As in Kimura's classical work [M. Kimura, Proc. Natl. Acad. Sci. U.S.A. Vol.77, 522 (1980)], that was motivated by the problem of fixation…
We consider a stochastic individual-based model of adaptive dynamics for an asexually reproducing population with mutation, with linear birth and death rates, as well as a density-dependent competition. To depict repeating changes of the…
We investigate the process of fixation of advantageous mutations in an asexual population. We assume that the effect of each beneficial mutation is exponentially distributed with mean value $\omega_{med}=1/\beta$. The model also considers…
Using a lattice model based on Monte Carlo simulations, we study the role of the reproduction pattern on the fate of an evolving population. Each individual is under the selection pressure from the environment and random mutations. The…
When beneficial mutations are relatively common, competition between multiple unfixed mutations can reduce the rate of fixation in well-mixed asexual populations. We introduce a one dimensional model with a steady accumulation of beneficial…
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…
We consider the evolution of an asexually reproducing population in an uncorrelated random fitness landscape in the limit of infinite genome size, which implies that each mutation generates a new fitness value drawn from a probability…
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…
In this paper, we review recent results of ours concerning branching processes with general lifetimes and neutral mutations, under the infinitely many alleles model, where mutations can occur either at birth of individuals or at a constant…
We study a family of selection-mutation models of a sexual population structured by a phenotypical trait. The main feature of these models is the asymmetric trait heredity or fecundity between the parents : we assume that each individual…
We study a continuous time model for the frequency distribution of an infinitely large asexual population in which both beneficial and deleterious mutations occur and the fitness is additive. When beneficial mutations are ignored, the exact…
We consider a stochastic individual-based model of adaptive dynamics for an asexually reproducing population with mutation. Biologically motivated by the influence of seasons or the variation of drug concentration during medical treatment,…
Evolutionary branching is analysed in a stochastic, individual-based population model under mutation and selection. In such models, the common assumption is that individual reproduction and life career are characterised by values of a…
In large asexual populations, multiple beneficial mutations arise in the population, compete, interfere with each other, and accumulate on the same genome, before any of them fix. The resulting dynamics, although studied by many authors, is…
Over time, a population acquires neutral genetic substitutions as a consequence of random drift. A famous result in population genetics asserts that the rate, $K$, at which these substitutions accumulate in the population coincides with the…
The accumulation of beneficial mutations on many competing genetic backgrounds in rapidly adapting populations has a striking impact on evolutionary dynamics. This effect, known as clonal interference, causes erratic fluctuations in the…