The Effect of Environmental Variability on Growth

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Abstract
An organism's fitness may depend on either the time that it requires to reach a given size or the organism's size when it reproduces. We consider an organism that has a period of growth in a given habitat. The habitat is characterized by a parameter w that determines the organism's growth. This parameter is a priori unknown, and so is taken to be a random variable W. For different habitats with the same expected value of W, we investigate how the variance of W influences the organism's fitness. Two cases are considered: in the first there is no predation, in the second there is predation that depends on the organism's size. In the first case, maximizing the expected size at a fixed time can require that the variance of W is either maximized or minimized, depending on the growth function; minimizing the expected time to reach a given size always requires that the variance is minimized. In the second case, maximizing the probability of surviving to a fixed time may require variance to be either maximized or minimized, depending on the growth function and the form of the size-dependent predation. The probability of surviving to a critical size is maximized by minimizing variance when mortality is low and by maximizing variance when mortality is high.