Related papers: The fixation time of a strongly beneficial allele …
Cellular differentiation and evolution are stochastic processes that can involve multiple types (or states) of particles moving on a complex, high-dimensional state-space or "fitness" landscape. Cells of each specific type can thus be…
The environment in which a population evolves can have a crucial impact on selection. We study evolutionary dynamics in finite populations of fixed size in a changing environment. The population dynamics are driven by birth and death…
Evolutionary game theory has proved to be a powerful tool to probe the self-organisation of collective behaviour by considering frequency-dependent fitness in evolutionary processes. It has shown that the stability of a strategy depends not…
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 study the fixation and stationary behavior of the Lambda-Wright-Fisher process with parent-independent mutation and finitely many types, a jump-diffusion model for allele frequency dynamics in large populations with potentially large…
Resource are often not uniformly distributed within a population. Spatial variations of concentration of a resource, change the fitness of competing strategies locally. The notion of fitness varying with respect to both genotype and…
We study fixation probabilities for the Moran stochastic process for the evolution of a population with three or more types of individuals and frequency-dependent fitnesses. Contrarily to the case of populations with two types of…
When a beneficial mutation occurs in a population, the new, favored allele may spread to the entire population. This process is known as a selective sweep. Suppose we sample $n$ individuals at the end of a selective sweep. If we focus on a…
Studies of fixation dynamics in Markov processes predominantly focus on the mean time to absorption. This may be inadequate if the distribution is broad and skewed. We compute the distribution of fixation times in one-step birth-death…
The fixation probability of a single mutant invading a population of residents is among the most widely-studied quantities in evolutionary dynamics. Amplifiers of natural selection are population structures that increase the fixation…
Different evolutionary models are known to make disparate predictions for the success of an invading mutant in some situations. For example, some evolutionary mechanics lead to amplification of selection in structured populations, while…
For a class of Cannings models we prove Haldane's formula, $\pi(s_N) \sim \frac{2s_N}{\rho^2}$, for the fixation probability of a single beneficial mutant in the limit of large population size $N$ and in the regime of moderately strong…
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…
Consider a genetic locus carrying a strongly beneficial allele which has recently fixed in a large population. As strongly beneficial alleles fix quickly, sequence diversity at partially linked neutral loci is reduced. This phenomenon is…
The stage of evolution is the population of reproducing individuals. The structure of the population is know to affect the dynamics and outcome of evolutionary processes, but analytical results for generic random structures have been…
It has been a puzzling question why some organisms reproduce sexually. Fisher and Muller hypothesized that reproducing by sex can speed up the evolution. They explained that in the sexual reproduction, recombination can combine beneficial…
A multiplicative identity in law connecting the hitting times of completely asymmetric $\alpha-$stable L\'evy processes in duality is established. In the spectrally positive case, this identity allows with an elementary argument to compute…
This paper is based on the complete classification of evolutionary scenarios for the Moran process with two strategies given by Taylor et al. (B. Math. Biol. 66(6): 1621--1644, 2004). Their classification is based on whether each strategy…
Temporal environmental variations are ubiquitous in nature, yet most of the theoretical works in population genetics and evolution assume fixed environment. Here we analyze the effect of variations in carrying capacity on the fate of a…
A population protocol *stably elects a leader* if, for all $n$, starting from an initial configuration with $n$ agents each in an identical state, with probability 1 it reaches a configuration $\mathbf{y}$ that is correct (exactly one agent…