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Perturbation of Equilibria in the Mathematical Theory of Evolution

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Mathematics of Complexity and Dynamical Systems

Article Outline

Glossary

Definition of the Subject

Introduction

Evolution on a Fitness Landscape

Stability of Equilibria on a Fitness Landscape

Perturbation of Equilibria on a Fitness Landscape

Frequency Dependent Fitness: Game Theory

Equilibria in Evolutionary Game Theory

Perturbations of Equilibria in Evolutionary Game Theory

Future Directions

Bibliography

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Abbreviations

Evolutionarily stable equilibria (ESS):

An ESS is a set of frequencies of different types of individuals in a population that can not be invaded by the evolution of a single mutant. It is the evolutionary counterpart of a Nash equilibrium.

Fitness landscape:

A metaphorical description of fitness as a function of individual's genotypes or phenotypes in terms of a multivariable function that does not depend on any external influence.

Genetic locus:

The position of a gene on a chromosome. The different variants of the gene that can be found at the same locus are called alleles.

Nash equilibrium:

In classical game theory, a Nash equilibrium is a set of strategies, one for each player of the game, such that none of them can improve her benefits by unilateral changes of strategy.

Scale free network:

A graph or network such that the degrees of the nodes are taken from a power-law distribution. As a consequence, there is not a typical degree in the graph, i. e., there are no typical scales.

Small-world network:

A graph or network of N nodes such that the mean distance between nodes scales as \({\log N}\). It corresponds to the well-known “six degrees of separation” phenomenon.

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Author information

Authors and Affiliations

  1. Grupo Interdisciplinar de Sistemas Complejos (GISC), Departamento de Matemáticas, Universidad Carlos III de Madrid, Madrid, Spain

    Angel Sánchez

  2. Instituto de Biocomputación y Física de Sistemas Complejos (BIFI), Universidad de Zaragoza, Zaragoza, Spain

    Angel Sánchez

Authors
  1. Angel Sánchez
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Editor information

Editors and Affiliations

  1. RAMTECH LIMITED, 122 Escalle Lane, Larkspur, CA, 94939, USA

    Robert A. Meyers Ph. D. (Editor-in-Chief) (Editor-in-Chief)

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Sánchez, A. (2012). Perturbation of Equilibria in the Mathematical Theory of Evolution. In: Meyers, R. (eds) Mathematics of Complexity and Dynamical Systems. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-1806-1_77

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