Exact solution of an evolutionary model without aging.
We introduce an age-structured asexual population model containing all the relevant features of evolutionary aging theories. Beneficial as well as deleterious mutations, heredity, and arbitrary fecundity are present and managed by natural selection. An exact solution without aging 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 and indicate that the system may exhibit mutational meltdown. The relevance of the model in the context of fissile reproduction groups like many protozoa and coelenterates is discussed.
Onody
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Departamento de Física e Informática, Instituto de Física de São Carlos, Universidade de São Paulo, Caixa Postal 369, 13560-970 São Carlos, São Paulo, Brazil. onody@ifsc.sc.usp.br
de Medeiros
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D000367:Age Factors; D000375:Aging; D000818:Animals; D005075:Biological Evolution; D005828:Genetics, Population; D006801:Humans; D008957:Models, Genetic; D015233:Models, Statistical; D013997:Time Factors