Related papers: Continuous approximations for the fixation probabi…
Hypergraphs have been a useful tool for analyzing population dynamics such as opinion formation and the public goods game occurring in overlapping groups of individuals. In the present study, we propose and analyze evolutionary dynamics on…
We propose a model for evolutionary game dynamics with three strategies $A$, $B$ and $C$ in the framework of Moran process in finite populations. The model can be described as a stochastic process which can be numerically computed from a…
We study large fluctuations in evolutionary games belonging to the coordination and anti-coordination classes. The dynamics of these games, modeling cooperation dilemmas, is characterized by a coexistence fixed point separating two…
The appropriate description of fluctuations within the framework of evolutionary game theory is a fundamental unsolved problem in the case of finite populations. The Moran process recently introduced into this context [Nowak et al., Nature…
This work studies the generalized Moran process, as introduced by Lieberman et al. [Nature, 433:312-316, 2005]. We introduce the parameterized notions of selective amplifiers and selective suppressors of evolution, i.e. of networks (graphs)…
Computing the rate of evolution in spatially structured populations is difficult. A key quantity is the fixation time of a single mutant with relative reproduction rate $r$ which invades a population of residents. We say that the fixation…
In stochastic dynamical systems, different concepts of stability can be obtained in different limits. A particularly interesting example is evolutionary game theory, which is traditionally based on infinite populations, where strict Nash…
The probability that the frequency of a particular trait will eventually become unity, the so-called fixation probability, is a central issue in the study of population evolution. Its computation, once we are given a stochastic finite…
We study two of the simple rules on finite graphs under the death-birth updating and the imitation updating discovered by Ohtsuki, Hauert, Lieberman and Nowak [Nature 441 (2006) 502-505]. Each rule specifies a payoff-ratio cutoff point for…
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…
To our knowledge, the populations are generally assumed to be homogeneous in the traditional approach to evolutionary game dynamics. Here, we focus on the inhomogeneous populations. A simple model which can describe the inhomogeneity of the…
This work is a systematic study of discrete Markov chains that are used to describe the evolution of a two-types population. Motivated by results valid for the well-known Moran (M) and Wright-Fisher (WF) processes, we define a general class…
We study stochastic evolutionary game dynamics in a population of finite size. Individuals in the population are divided into two dynamically evolving groups. The structure of the population is formally described by a Wright-Fisher type…
The formula for the probability of fixation of a new mutation is widely used in theoretical population genetics and molecular evolution. Here we derive a series of identities, inequalities and approximations for the exact probability of…
Resources are rarely distributed uniformly within a population. Heterogeneity in the concentration of a drug, the quality of breeding sites, or wealth can all affect evolutionary dynamics. In this study, we represent a collection of…
Population structure can have a significant effect on evolution. For some systems with sufficient symmetry, analytic results can be derived within the mathematical framework of evolutionary graph theory which relate to the outcome of the…
Natural microbial populations often have complex spatial structures. This can impact their evolution, in particular the ability of mutants to take over. While mutant fixation probabilities are known to be unaffected by sufficiently…
We consider the evolution of large but finite populations on arbitrary fitness landscapes. We describe the evolutionary process by a Markov, Moran process. We show that to $\mathcal O(1/N)$, the time-averaged fitness is lower for the finite…
We investigate spatial evolutionary games with death-birth updating in large finite populations. Within growing spatial structures subject to appropriate conditions, the density processes of a fixed type are proven to converge to the…
Fixation probabilities are essential for characterizing stochastic evolutionary dynamics, but analytical results remain limited mainly to systems with two competing types. We develop a perturbative framework to compute fixation…