Extension of Fisher's classical result on exponential dynamics of the reproductive value to a wide class of populations

The classical result by R.A. Fisher concerning reproductive value dynamics is expanded to the case of varying vital rates with a constant cohort Lotka's r. Based on the demographic potential approach, 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 the paper fits the classical interpretation by R.A. Fisher as a discounted sum of future births in the general class of models addressed in the paper. Results could be of importance for estimating the fitness of biological populations, aggregate population modeling, and studying the long-term consequences of varying vital rates.