Definition of the Subject
The importance of evolution can hardly be overstated. As the Jesuit priest Pierre Teilhard de Chardin put it,
Evolution is a general postulate to which all theories, all hypotheses, all systems must hence forward bow and which they mustsatisfy in order to be thinkable and true. Evolution is a light which illuminates all facts, a trajectory which all lines of thought mustfollow – this is what evolution is.
Darwin's evolution theory is based on three fundamental principles: reproduction, mutation and selection, which describe how populations change overtime and how new forms evolve out of old ones. Starting with W. F. R. Weldon, whom at the beginning of the 20th century realized that “the problemof animal evolution is essentially a statistical problem”, and blooming in the 30's with Fisher, Haldane and Wright, numerous mathematicaldescriptions of the resulting evolutionary dynamics have been proposed, developed and studied. Deeply engraved in these frameworks...
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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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Sánchez, A. (2009). Perturbation of Equilibria in the Mathematical Theory of Evolution. In: Meyers, R. (eds) Encyclopedia of Complexity and Systems Science. Springer, New York, NY. https://doi.org/10.1007/978-0-387-30440-3_394
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