%0 Journal Article
%T Time evolution of the Partridge-Barton Model
%A Roberto N. Onody
%A Nazareno G. F. de Medeiros
%J Quantitative Biology
%D 2000
%I arXiv
%R 10.1103/PhysRevE.61.5664
%X 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.
%U http://arxiv.org/abs/cond-mat/0005265v1