On an extension of R.A. Fisher's result on the dynamics of the reproductive value

A classical result by Fisher concerning reproductive value dynamics is extended to the case of varying vital rates with a constant cohort Lotka's r. Based on the demographic potential approach, a generalization of the concept of reproductive value is introduced, which exhibits exponential dynamics both in the classical case of constant vital rates and in a wider class of populations. The generalized reproductive value introduced in this paper fits the classical interpretation by Fisher as a discounted sum of future births in the general class of models addressed here. Our results show when Fisher's classical results may be used as good approximations. They could also be of importance for estimating the fitness of biological populations, aggregate population modeling, and studying the long-term consequences of varying vital rates.