Time evolution of the Partridge-Barton model.
The time evolution of the Partridge-Barton model in the presence of the pleiotropic constraint and deleterious somatic mutations is exactly solved for arbitrary fecundity in the context of a matricial formalism. Analytical expressions for the time dependence of the mean survival probabilities are derived. Using the fact that the asymptotic behavior for large time t is controlled by the largest matrix eigenvalue, we obtain the steady state values for the mean survival probabilities and the Malthusian growth exponent. The mean age of the population exhibits a t-1 power law decayment. Some Monte Carlo simulations were also performed and they corroborated our theoretical results.
Onody
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Departamento de Física e Informática, Instituto de Física de São Carlos, Universidade de São Paulo, Brazil. onody@ifsc.sc.usp.br
de Medeiros
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D005075:Biological Evolution; D017353:Gene Deletion; D008957:Models, Genetic; D009154:Mutation; D011336:Probability; D013995:Time