Population Tracking of Fluctuating Environments and Natural Selection for Tracking Ability

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Abstract
The mathematics of stochastic nonlinear population models is notoriously intractable and has led to the study of linear approximations to make computations easier. Nonlinear models may often better describe biological systems, and linearization may obscure dynamics of biological significance. Various aspects of the dynamics of the logistic population model are clarified with a fluctuating carrying capacity. Average population size [.hivin.N] decreases with an increasing magnitude of variation in K [carrying capacity], but .hivin.N is always less than or equal to .hivin.K. This effect is mediated by the intrinsic rate of increase, r. .hivin.N increases as r increases. This pattern should be general for models where .ovrhdot.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. When the fluctuations in K are large, natural selection may favor forms which are not highly responsive to fluctuations in K.

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