SYSTEMATIC APPROXIMATIONS FOR GENETIC DYNAMICS

Christopher R. Stephens () and Adolfo Zamora ()
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Christopher R. Stephens: Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, A. Postal 70-543, México 04510 D.F., Mexico;
Adolfo Zamora: Centro de Ciencias de la Complejidad, Universidad Nacional Autónoma de México, Torre de Ingenierí a, México 04510 D.F., Mexico;

Advances in Complex Systems (ACS), 2009, vol. 12, issue 06, 583-618

Abstract: Although much progress has been made in recent years in describing the dynamics of genetic systems, both in population genetics and evolutionary computation, there is still a conspicuous lack of tools with which to derive systematic, approximate solutions to their dynamics. In this article, we propose and study perturbation theory and the renormalization group as potential tools to fill this gap. We concentrate mainly on selection–mutation systems, showing different implementations of the perturbative framework, developing, for example, perturbative expansions for the eigenvalues and eigenvectors of the transition matrix. The main focus, however, is on diagrammatic methods, taken from physics, where we show how approximations can be built up using a pictorial representation generated by a simple set of rules, and how the renormalization group can be used to systematically improve the perturbation theory.

Keywords: Genetic dynamics; mutation; selection; perturbation theory; renormalization group (search for similar items in EconPapers)
Date: 2009
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DOI: 10.1142/S0219525909002350

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