Universal constraint on nonlinear population dynamics

Abstract

In evolutionary theory, Fisher’s fundamental theorem of natural selection establishes a simple relation between the variance of the growth rate and the temporal increase in the average growth rate. Here, the authors extend the theorem based on statistical physics and information theory and show that the speed in dynamical systems describing nonlinear population dynamics is bounded by Fisher information with universal limit exponents only depending on the kind of bifurcation and not on the specific systems.