Related papers: Continuous approximations for the fixation probabi…
The Moran process is a classic stochastic process that models the rise and takeover of novel traits in network-structured populations. In biological terms, a set of mutants, each with fitness $m\in(0,\infty)$ invade a population of…
Context: The dynamical evolution of binary populations in embedded star clusters shapes the statistical properties of binaries observed in the Galactic field. Accurately modelling this process requires resolving both early cluster dynamics…
One of the most fundamental concepts of evolutionary dynamics is the "fixation" probability, i.e. the probability that a mutant spreads through the whole population. Most natural communities are geographically structured into habitats…
We consider the so called Moran process with frequency dependent fitness given by a certain pay-off matrix. For finite populations, we show that the final state must be homogeneous, and show how to compute the fixation probabilities. Next,…
The evolution of two species with different fitness is investigated on degree-heterogeneous graphs. The population evolves either by one individual dying and being replaced by the offspring of a random neighbor (voter model (VM) dynamics)…
In evolutionary games the fitness of individuals is not constant but depends on the relative abundance of the various strategies in the population. Here we study general games among n strategies in populations of large but finite size. We…
The fixation probability of a mutant in the evolutionary dynamics of Moran process is calculated by the Monte-Carlo method on a few families of clique-based graphs. It is shown that the complete suppression of fixation can be realized with…
We study evolutionary game dynamics in finite populations. We analyze an evolutionary process, which we call pairwise comparison, for which we adopt the ubiquitous Fermi distribution function from statistical mechanics. The inverse…
In population games, a large population of players, modeled as a continuum, is divided into subpopulations, and the fitness or payoff of each subpopulation depends on the overall population composition. Evolutionary dynamics describe how…
The Moran process is a random process that models the spread of genetic mutations through graphs. If the graph is connected, the process eventually reaches "fixation", where every vertex is a mutant, or "extinction", where no vertex is a…
The dynamical mechanisms that can stabilize the coexistence of species (or strategies) are of substantial interest for the maintenance of biodiversity and in sociobehavioural dynamics. We investigate the mean extinction time in the…
We analyze the dynamics of evolutionary games in which fitness is defined as an affine function of the expected payoff and a constant contribution. The resulting inhomogeneous replicator equation has an homogeneous equivalent with modified…
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…
We study the multi-strategy stochastic evolutionary game with death-birth updating in expanding spatial populations of size $N\to \infty$. The model is a voter model perturbation. For typical populations, we require perturbation strengths…
We investigate the dynamics of the voter model in which the population itself changes endogenously via the birth-death process. There are two species of voters, labeled A and B, and the population of each species can grow or shrink by the…
Populations are made up of an integer number of individuals and are subject to stochastic birth-death processes whose rates may vary in time. Useful quantities, like the chance of ultimate fixation, satisfy an appropriate difference…
Birth-death processes (BDPs) are continuous-time Markov chains that track the number of "particles" in a system over time. While widely used in population biology, genetics and ecology, statistical inference of the instantaneous particle…
Continuous-time birth-death-shift (BDS) processes are frequently used in stochastic modeling, with many applications in ecology and epidemiology. In particular, such processes can model evolutionary dynamics of transposable elements -…
Motivated by the question of the impact of selective advantage in populations with skewed reproduction mechanims, we study a Moran model with selection. We assume that there are two types of individuals, where the reproductive success of…
Evolutionary graph theory studies the evolutionary dynamics of populations structured on graphs. A central problem is determining the probability that a small number of mutants overtake a population. Currently, Monte Carlo simulations are…