Related papers: Drift reversal in asymmetric coevolutionary confli…
Coevolutionary dynamics is investigated in chemical catalysis, biological evolution, social and economic systems. The dynamics of these systems can be analyzed within the unifying framework of evolutionary game theory. In this Letter, we…
The entropy rates of the Wright-Fisher process, the Moran process, and generalizations are computed and used to compare these processes and their dependence on standard evolutionary parameters. Entropy rates are measures of the variation…
We study the influence of stochastic effects due to finite population size in the evolutionary dynamics of populations interacting in the multi-person Prisoner's Dilemma game. This paper is an extension of the investigation presented in a…
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,…
We study the coupled dynamics of two populations of random replicators by means of statistical mechanics methods, and focus on the effects of relative population size, strategy correlations and heterogeneities in the respective co-operation…
Many socio-economic and biological processes can be modeled as systems of interacting individuals. The behaviour of such systems can be often described within game-theoretic models. In these lecture notes, we introduce fundamental concepts…
For a population with any given number of types, we construct a new multivariate Moran process with frequency-dependent selection and establish, analytically, a correspondence to equilibrium Lotka-Volterra phenomenology. This…
We consider a trait-structured population subject to mutation, birth and competition of logistic type, where the number of coexisting types may fluctuate. Applying a limit of rare mutations to this population while keeping the population…
Populations of replicating entities frequently experience sudden or cyclical changes in environment. We explore the implications of this phenomenon via a environmental switching parameter in several common evolutionary dynamics models…
Infinitely many distinct trait values may arise in populations bearing quantitative traits, and modeling their population dynamics is thus a formidable task. While classical models assume fixed or infinite population size, models in which…
We study a general setting of neutral evolution in which the population is of finite, constant size and can have spatial structure. Mutation leads to different genetic types ("traits"), which can be discrete or continuous. Under minimal…
The influence of migration on the stochastic dynamics of subdivided populations is still an open issue in various evolutionary models. We develop here a self-consistent mean-field-like method in order to determine the effects of migration…
This paper aims to study how the population size affects the computation time of evolutionary algorithms in a rigorous way. The computation time of an evolutionary algorithm can be measured by either the expected number of generations…
This note is motivated by the article by F. Lutscher, E. Pachepsky, and M. Lewis (2005), The Effect of Dispersal Patterns on Stream Populations SIAM Rev. Vol. 47 No. 4 pp. 749-772 on the drift paradox. We consider the case of a regime…
Evolutionary game dynamics in finite populations provides a new framework to understand the selection of traits with frequency-dependent fitness. Recently, a simple but fundamental law of evolutionary dynamics, which we call {\sigma} law,…
We study the phenomenon of cyclic dominance in the paradigmatic Rock--Paper--Scissors model, as occurring in both stochastic individual-based models of finite populations and in the deterministic replicator equations. The mean-field…
We study the large population limit of the Moran process, assuming weak-selection, and for different scalings. Depending on the particular choice of scalings, we obtain a continuous model that may highlight the genetic-drift (neutral…
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…
We present an explicit unified stochastic model of fluctuations in population size due to random birth, death, density-dependent competition and environmental fluctuations. Stochastic dynamics provide insight into small populations,…
Demographic noise has profound effects on evolutionary and population dynamics, as well as on chemical reaction systems and models of epidemiology. Such noise is intrinsic and due to the discreteness of the dynamics in finite populations.…