Darwinian fitness and the intensity of natural selection: studies in sensitivity analysis

Darwinian fitness, the capacity of a variant type to establish itself in competition with the resident population, is determined by evolutionary entropy, a measure of the uncertainty in age of the mother of a randomly chosen newborn. This article shows that the intensity of natural selection, as measured by the sensitivity of entropy with respect to changes in the age-specific fecundity and mortality variables, is a convex function of age, decreasing at early and increasing at later ages. We exploit this result to provide quantitative evolutionary explanations of the large variation in survivorship curves observed in natural populations. Previous studies to explain variation in survivorship curves have been based on the proposition that Darwinian fitness is determined by the Malthusian parameter. Hence the intensity of natural selection will be determined by the sensitivity of the Malthusian parameter with respect to changes in the age-specific fecundity and mortality variables. This measure of the selection gradient is known to be a decreasing function of age, with implications which are inconsistent with empirical observations of survivorship curves in human and animal populations. The analysis described in this paper point to the mitigated import of sensitivity studies based on the Malthusian parameter. Our analysis provides theoretical and empirical support for the ecological and evolutionary significance of sensitivity analysis based on entropy, which is the appropriate measure of Darwinian fitness.