Senescence, selection gradients and mortality

Evolutionary explanations of senescence are based on the established fact that the selection gradients (the rate of change of fitness with respect to a trait) on age-specific survival and fertility decline with age. Improvements in survival or fertility at older ages have less of an effect than the same improvements at younger ages. As a result, traits with small positive effects at early ages may accumulate even if they are accompanied by larger negative effects at late ages. It is often claimed that these results imply that additional mortality should make it easier for senescence to evolve, a claim that has led to a great deal of empirical study. However, the actual effect of additional mortality depends on the age dependence of that mortality. We show in detail that age-independent mortality has no effect on the selection gradients in time-invariant, periodic, stochastic and density-dependent life cycles. When the additional mortality is age dependent, its effects on the evolution of senescence depend on where in the life cycle it acts. We develop indices M_p and M_f to measure the shape of the selection gradient on survival and fertility, respectively. These indices give the mean age calculated over the selection gradient; larger values indicate a life history that is more resistant to the evolution of senescence. For several model life tables and for data on human life tables from Sweden, we show that additional early mortality increases M_p and M_f, while mortality later in life has the opposite effect.