Related papers: Fixation Probability for Competing Selective Sweep…
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 large clonal populations, several clones generally compete which results in complex evolutionary and ecological dynamics: experiments show successive selective sweeps of favorable mutations as well as long-term coexistence of multiple…
We study a stochastic differential equation driven by a Poisson point process, which models continuous changes in a population's environment, as well as the stochastic fixation of beneficial mutations that might compensate for this change.…
We investigate the competition between two quasispecies residing on two disparate neutral networks. Under the assumption that the two neutral networks have different topologies and fitness levels, it is the mutation rate that determines…
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…
A key question in evolution is how likely a mutant is to take over. This depends on natural selection and on stochastic fluctuations. Population spatial structure can impact mutant fixation probabilities. We introduce a model for structured…
The growing probabilities of additional offspring with the beneficial reversal allele for various population sizes, $N$, sequence lengths, $L$, selective advantages, $s$, fitness parameters, $k$, and measuring parameters, $C$, were…
We examine the dynamics of an age-structured population model in which the life expectancy of an offspring may be mutated with respect to that of the parent. While the total population of the system always reaches a steady state, the…
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…
In nature, most microbial populations have complex spatial structures that can affect their evolution. Evolutionary graph theory predicts that some spatial structures modelled by placing individuals on the nodes of a graph affect the…
Rock-paper-scissors games metaphorically model cyclic dominance in ecology and microbiology. In a static environment, these models are characterized by fixation probabilities obeying two different "laws" in large and small well-mixed…
We revisit the classical result in finite population sampling which states that in equally-likely "simple" random sampling the sample mean is more reliable when we do not replace after each draw. In this paper we investigate if and when the…
Mutations in a microbial population can increase the frequency of a genotype not only by increasing its exponential growth rate, but also by decreasing its lag time or adjusting the yield (resource efficiency). The contribution of multiple…
Identifying and quantifying the benefits of sex and recombination is a long standing problem in evolutionary theory. In particular, contradictory claims have been made about the existence of a benefit of recombination on high dimensional…
Cumulants and moments are closely related to the basic mathematics of continuous and discrete selection (respectively). These relationships generalize Fisher's fundamental theorem of natural selection and also make clear some of its…
The dynamics of two competing species in a finite size community is one of the most studied problems in population genetics and community ecology. Stochastic fluctuations lead, inevitably, to the extinction of one of the species, but the…
We develop a multi-state model to estimate the size of a closed population from ecological capture-recapture studies. We consider the case where capture-recapture data are not of a simple binary form, but where the state of an individual is…
Numerous traits under migration-selection balance are shown to exhibit complex patterns of genetic architecture with large variance in effect sizes. However, the conditions under which such genetic architectures are stable have yet to be…
We study the limit of many small mutations of a model of population dynamics. The population is structured by phonological traits and is spatially inhomogeneous. The various sub-populations compete for the same nutrient which diffuses…
The Battle of the Sexes describes asymmetric conflicts in mating behavior of males and females. Males can be philanderer or faithful, while females are either fast or coy, leading to a cyclic dynamics. The adjusted replicator equation…