Demographic Parameters and Natural Selection

This paper introduces two new demographic parameters, the entropy and the reproductive potential of a population. The entropy of a population measures the variability of the contribution of the different age classes to the stationary age distribution. The reproductive potential measures the mean of the contribution of the different age classes to the growth rate. Using a relation between these measures and the Malthusian parameter, it is shown that in a random mating population in Hardy-Weinberg equilibrium, and under slow selection, the rate of change of entropy is equal to the genetic variance in entropy minus the genetic covariance of entropy and reproductive potential. This result is an analogue of Fisher's fundamental theorem of natural selection.