  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.
