Population Tracking of Fluctuating Environments and Natural Selection for Tracking Ability

Abstract

The mathematics of stochastic nonlinear population models is notoriously intractable and has led some investigators to study linear approximations to make computations easier. However, nonlinear models may often better describe biological systems, and linearization may obscure dynamics of biological significance. We clarify various aspects of the dynamics of the logistic population model with a fluctuating carrying capacity. Average population size decreases with an increasing magnitude of variation in K, but N is always less than or equal to K. This effect is mediated by the intrinsic rate of increase, r. In general, N increases as r increases. This pattern should be general for models where N is a concave function of N. In environments where the magnitude of variation in K is not large, natural selection will favor genotypes which are best able to track fluctuations in K. However, when the fluctuations in K are large, natural selection may favor forms which are not highly responsive to fluctuations in K.