# Evolutionary Dynamics of Biological Games

@article{Nowak2004EvolutionaryDO, title={Evolutionary Dynamics of Biological Games}, author={Martin A. Nowak and Karl Sigmund}, journal={Science}, year={2004}, volume={303}, 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…

## 938 Citations

### Calculating Evolutionary Dynamics in Structured Populations

- BiologyPLoS Comput. Biol.
- 2009

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

- Economics
- 2008

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

- Biology
- 2005

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

- MathematicsProceedings of the International Conference "Mathematical Biology and Bioinformatics"
- 2018

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

- Biology
- 2012

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.

### Integrating Evolutionary Game Theory into Mechanistic Genotype-Phenotype Mapping.

- BiologyTrends in genetics : TIG
- 2016

### Evolutionary dynamics in structured populations

- BiologyPhilosophical Transactions of the Royal Society B: Biological Sciences
- 2010

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.

- MathematicsPhysical 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

- Economics
- 2011

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

- MathematicsBulletin 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.

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