Asymptotic behavior of mean fixation times in the Moran process with frequency-independent fitnesses.

We derive asymptotic formulae in the limit when population size N tends to infinity for mean fixation times (conditional and unconditional) in a population with two types of individuals, A and B, governed by the Moran process. We consider only the case in which the fitness of the two types do not depend on the population frequencies. Our results start with the important cases in which the initial condition is a single individual of any type, but we also consider the initial condition of a fraction [Formula: see text] of A individuals, where x is kept fixed and the total population size tends to infinity.

Predicting the evolution of the COVID-19 epidemic with the A-SIR model: Lombardy, Italy and São Paulo state, Brazil.

The presence of a large number of infected individuals with few or no symptoms is an important epidemiological difficulty and the main mathematical feature of COVID-19. The A-SIR model, i.e.

Fixation probabilities for the Moran process with three or more strategies: general and coupling results.

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. Contrary to the case of populations with two types of individuals, in which fixation probabilities may be calculated by an exact formula, here we must solve a large system of linear equations. We first show that this system always has a unique solution.

Fixation probabilities for the Moran process in evolutionary games with two strategies: graph shapes and large population asymptotics.

This paper is based on the complete classification of evolutionary scenarios for the Moran process with two strategies given by Taylor et al. (Bull Math Biol 66(6):1621-1644, 2004. https://doi.

Evolution of cooperation in a particular case of the infinitely repeated prisoner's dilemma with three strategies.

We study a population of individuals playing the infinitely repeated prisoner's dilemma under replicator dynamics. The population consists of three kinds of individuals adopting the following reactive strategies: ALLD (individuals which always defect), ATFT (almost tit-for-tat: individuals which almost always repeat the opponent's last move) and G (generous individuals, which always cooperate when the opponent cooperated in the last move and have a positive probability q of cooperating when their opponent has defected). Our aim is studying in a mathematically rigorous fashion the dynamics of a simplified version for the computer experiment in Nowak and Sigmund (Nature 355:250-253, 1992) involving 100 reactive strategies.

Extremely rare interbreeding events can explain neanderthal DNA in living humans.

Considering the recent experimental discovery of Green et al that present-day non-Africans have 1 to [Formula: see text] of their nuclear DNA of Neanderthal origin, we propose here a model which is able to quantify the genetic interbreeding between two subpopulations with equal fitness, living in the same geographic region. The model consists of a solvable system of deterministic ordinary differential equations containing as a stochastic ingredient a realization of the neutral Wright-Fisher process. By simulating the stochastic part of the model we are able to apply it to the interbreeding of the African ancestors of Eurasians and Middle Eastern Neanderthal subpopulations and estimate the only parameter of the model, which is the number of individuals per generation exchanged between subpopulations.

Detailed analysis of an Eigen quasispecies model in a periodically moving sharp-peak landscape.

The Eigen quasispecies model in a periodically moving sharp-peak landscape considered in previous seminal works [M. Nilsson and N. Snoad, Phys.