Abstract
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 quasi-species, unless the mutation rate is too high, in which case the asymptotic population becomes de-localized. We introduce a more macroscopic picture of genotypic evolution wherein a random fitness term in the linear model produces features analogous to Anderson localization. When coupled with density dependent non-linearities, which limit the population of any given genotype, we obtain a model whose large time asymptotics display stable genotypic diversity.
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Research partially supported by DARPA under the FUNBIO program and the Francis J. Carey Term Chair.
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Epstein, C.L. Anderson Localization, Non-linearity and Stable Genetic Diversity. J Stat Phys 124, 25–46 (2006). https://doi.org/10.1007/s10955-006-9149-0
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DOI: https://doi.org/10.1007/s10955-006-9149-0