Topic
Moran process
About: Moran process is a research topic. Over the lifetime, 229 publications have been published within this topic receiving 13453 citations.
Papers published on a yearly basis
Papers
TL;DR: In this article, the authors consider a class of matrix games in which successful strategies are rewarded by high reproductive rates, so become more likely to participate in subsequent playings of the game, thus, over time, the strategy mix should evolve to some type of optimal or stable state.
Abstract: We consider a class of matrix games in which successful strategies are rewarded by high reproductive rates, so become more likely to participate in subsequent playings of the game. Thus, over time, the strategy mix should evolve to some type of optimal or stable state. Maynard Smith and Price (1973) have introduced the concept of ESS (evolutionarily stable strategy) to describe a stable state of the game. We attempt to model the dynamics of the game both in the continuous case, with a system of non-linear first-order differential equations, and in the discrete case, with a system of non-linear difference equations. Using this model, we look at the notions of stability and asymptotic behavior. Our notion of stable equilibrium for the continuous dynamic includes, but is somewhat more general than, the notion of ESS.
3,491 citations
Book•
29 Sep 2006
TL;DR: This chapter discusses games in Finite Populations, fitness Landscapes and Sequence Spaces, and the evolution of Virulence, as well as the Evolutionary Dynamics of Cancer and Language Evolution.
Abstract: Preface 1. Introduction 2. What Evolution Is 3. Fitness Landscapes and Sequence Spaces 4. Evolutionary Games 5. Prisoners of the Dilemma 6. Finite Populations 7. Games in Finite Populations 8. Evolutionary Graph Theory 9. Spatial Games 10. HIV Infection 11. The Evolution of Virulence 12. The Evolutionary Dynamics of Cancer 13. Language Evolution 14. Conclusion Further Reading References Index
2,128 citations
TL;DR: It is shown that a single cooperator using a strategy like ‘tit-for-tat’ can invade a population of defectors with a probability that corresponds to a net selective advantage.
Abstract: To explain the evolution of cooperation by natural selection has been a major goal of biologists since Darwin. Cooperators help others at a cost to themselves, while defectors receive the benefits of altruism without providing any help in return. The standard game dynamical formulation is the 'Prisoner's Dilemma', in which two players have a choice between cooperation and defection. In the repeated game, cooperators using direct reciprocity cannot be exploited by defectors, but it is unclear how such cooperators can arise in the first place. In general, defectors are stable against invasion by cooperators. This understanding is based on traditional concepts of evolutionary stability and dynamics in infinite populations. Here we study evolutionary game dynamics in finite populations. We show that a single cooperator using a strategy like 'tit-for-tat' can invade a population of defectors with a probability that corresponds to a net selective advantage. We specify the conditions required for natural selection to favour the emergence of cooperation and define evolutionary stability in finite populations.
1,543 citations
TL;DR: This paper focuses on frequency-dependent selection, and argues that game-theoretic arguments are more appropriate than optimization algorithms for studying frequency- dependent selection.
Abstract: Darwinian dynamics based on mutation and selection form the core of mathematical models for adaptation and coevolution of biological populations. The evolutionary outcome is often not a fitness-maximizing equilibrium but can include oscillations and chaos. For studying frequency-dependent selection, game-theoretic arguments are more appropriate than optimization algorithms. Replicator and adaptive dynamics describe short- and long-term evolution in phenotype space and have found applications ranging from animal behavior and ecology to speciation, macroevolution, and human language. Evolutionary game theory is an essential component of a mathematical and computational approach to biology.
1,197 citations
TL;DR: A simple closed formula is derived that determines the feasibility of cooperation in finite populations, whenever cooperation is modeled in terms of any symmetric two-person game, and is valid at all intensities of selection and for any initial condition.
Abstract: 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 temperature in this process controls the intensity of selection, leading to a unified framework for evolutionary dynamics at all intensities of selection, from random drift to imitation dynamics. We derive a simple closed formula that determines the feasibility of cooperation in finite populations, whenever cooperation is modeled in terms of any symmetric two-person game. In contrast with previous results, the present formula is valid at all intensities of selection and for any initial condition. We investigate the evolutionary dynamics of cooperators in finite populations, and study the interplay between intensity of selection and the remnants of interior fixed points in infinite populations, as a function of a given initial number of cooperators, showing how this interplay strongly affects the approach to fixation of a given trait in finite populations, leading to counterintuitive results at different intensities of selection.
626 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2022 | 1 |
| 2021 | 12 |
| 2020 | 20 |
| 2019 | 21 |
| 2018 | 27 |
| 2017 | 15 |