Exact Solution of an Evolutionary Model without Ageing

Details Exact Solution of an Evolutionary Model without Ageing Exact Solution of an Evolutionary Model without Ageing

1999-08-10

arxiv.org/abs/cond-mat/9908148v1

Physics

Condensed Matter

Statistical Mechanics

LaTeX file, 15 pages, 2 ps figures, to appear in Phys. Rev. E

Scientific paper

10.1103/PhysRevE.60.3234

We introduce an age-structured asexual population model containing all the relevant features of evolutionary ageing theories. Beneficial as well as deleterious mutations, heredity and arbitrary fecundity are present and managed by natural selection. An exact solution without ageing is found. We show that fertility is associated with generalized forms of the Fibonacci sequence, while mutations and natural selection are merged into an integral equation which is solved by Fourier series. Average survival probabilities and Malthusian growth exponents are calculated indicating that the system may exhibit mutational meltdown. The relevance of the model in the context of fissile reproduction groups as many protozoa and coelenterates is discussed.

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