Time evolution of the Partridge-Barton Model

Details Time evolution of the Partridge-Barton Model Time evolution of the Partridge-Barton Model

2000-05-16

arxiv.org/abs/cond-mat/0005265v1

Physics

Condensed Matter

Statistical Mechanics

10 pages, Latex, 1 postscript figure, published in Phys. Rev. E 61, 5664 (2000)

Scientific paper

10.1103/PhysRevE.61.5664

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.

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