Anderson Localization, Non-linearity and Stable Genetic Diversity

Details Anderson Localization, Non-linearity and Stable Genetic Diversity Anderson Localization, Non-linearity and Stable Genetic Diversity

2006-02-28

arxiv.org/abs/q-bio/0602027v1

Biology

Quantitative Biology

Populations and Evolution

25 pages, 8 Figures

Scientific paper

10.1007/s10955-006-9149-0

In many models of genotypic evolution, the vector of genotype populations satisfies a system of linear ordinary differential equations. This system of equations models a competition between differential replication rates (fitness) and mutation. Mutation operates as a generalized diffusion process on genotype space. In the large time asymptotics, the replication term tends to produce a single dominant quasispecies, unless the mutation rate is too high, in which case the populations of different genotypes becomes de-localized. We introduce a more macroscopic picture of genotypic evolution wherein a random replication term in the linear model displays features analogous to Anderson localization. When coupled with non-linearities that limit the population of any given genotype, we obtain a model whose large time asymptotics display stable genotypic diversity

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