Evolutionary Dynamics of Biological Games

  title={Evolutionary Dynamics of Biological Games},
  author={Martin A. Nowak and Karl Sigmund},
  pages={793 - 799}
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… 

Calculating Evolutionary Dynamics in Structured Populations

The competition of two strategies in the context of an evolutionary game is studied and which strategy is favored in the limit of weak selection and an intuitive formula for the structure coefficient, σ, is derived and a method for efficient numerical calculation is provided.

Evolutionary Game Theory and Population Dynamics

Stability of equilibria in deterministic dynamics with migration, time-delay, and in stochastic dynamics of well-mixed populations and spatial games with local interactions are discussed.

Evolutionary Game Theory, Natural Selection, and Darwinian Dynamics: List of figures

The evolutionary game theory developed in this book provides the tools necessary for understanding many of Nature’s mysteries, including coevolution, speciation, and extinction as well as the major biological questions regarding fit of form and function, diversity of life, procession oflife, and the distribution and abundance of life.

Mathematical Models of Evolution for Replicator Systems: Fitness Landscape Adaptation

The adaptive landscape metaphor by S. Wright and Fisher's fundamental theorem of natural selection is expanded, combining it with Kimura’s maximal principals to the case of dynamical fitness landscape and is reduced to a series mathematical programming problems or to a first eigenvalue maximization problem.

Evolutionary game dynamics driven by mutations under frequency dependent selection

An evolutionary game theoretic model is proposed, which combines the assumption of infinite alleles and frequency dependent fitness, and the evolutionary dynamics in finite and infinite populations based on this model are investigated.

Evolutionary dynamics in structured populations

The recent advances in evolutionary game dynamics are reviewed with a particular emphasis on stochastic approaches in finite sized and structured populations, and simple, fundamental laws that determine how natural selection chooses between competing strategies are given.

Deterministic evolutionary game dynamics in finite populations.

  • P. AltrockA. Traulsen
  • Mathematics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2009
This work presents a microscopic birth-death process that has a fully deterministic strong selection limit in well-mixed populations of any size and shows that the resulting deterministic dynamics crucially depends on the initial condition in a nontrivial way.

Evolutionary game dynamics

Evolutionary game dynamics is the application of population dynamical methods to game theory. It has been introduced by evolutionary biologists, anticipated in part by classical game theorists. In

Continuous Probabilistic Analysis to Evolutionary Game Dynamics in Finite Populations

  • Meng Gao
  • Mathematics
    Bulletin of mathematical biology
  • 2009
Besides frequency dependent selection, mutation was also included in this study and the equilibrium probability density functions of abundance, expected time to extinction or fixation were derived and their numerical solutions are calculated as illustrations.



Unifying evolutionary dynamics.

This paper shows that apparently very different formulations of the replicator-mutator equation are part of a single unified framework, and obtains as special cases adaptive dynamics, evolutionary game dynamics, the Lotka-Volterra equation of ecology and the quasispecies equation of molecular evolution.

Evolutionary Games and Population Dynamics

In this book the authors investigate the nonlinear dynamics of the self-regulation of social and economic behavior, and of the closely related interactions among species in ecological communities.

Dynamics of Adaptation and Evolutionary Branching

We present a formal framework for modeling evolutionary dynamics with special emphasis on the generation of diversity through branching of the evolutionary tree. Fitness is defined as the long term

Evolutionary Game Theory, Natural Selection, and Darwinian Dynamics

  • J. Fletcher
  • Psychology
    Journal of Mammalian Evolution
  • 2006
Whereas classic evolutionary game theory limits itself to behavioral interactions and phenotypes, this book takes a very broad view of what constitutes a “game” and places natural selection itself firmly within a game-theoretic framework.

Evolutionary dynamics of predator-prey systems: an ecological perspective

A formal framework for this purpose is suggested, extending from the microscopic interactions between individuals through the mesoscopic population dynamics responsible for driving the replacement of one mutant phenotype by another, to the macroscopic process of phenotypic evolution arising from many such substitutions.

Evolutionary cycling in predator-prey interactions: population dynamics and the red queen.

It is shown that evolutionary cycling is a likely outcome of the coevolution of phenotypes in a community comprising a population of predators and of prey, and argues for an extension to a dynamical framework for describing the asymptotic states of evolution.

The dynamical theory of coevolution: a derivation from stochastic ecological processes

It is shown that the coevolutionary dynamic can be envisaged as a directed random walk in the community's trait space and a quantitative description of this stochastic process in terms of a master equation is derived.

No pure strategy is evolutionarily stable in the repeated Prisoner's Dilemma game

It is argued that no pure strategy can be evolutionarily stable in the repeated Prisoner's Dilemma game, which casts doubt on several of Axelrod's conclusions about the evolution of reciprocity.

Darwinian adaptation, population genetics and the streetcar theory of evolution

This paper investigates the problem of how to conceive a robust theory of phenotypic adaptation in non-trivial models of evolutionary biology, and develops a foundation of this theory in the context ofn-locus population genetics.