The evolutionary advantage of controlled chaos

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Abstract
In a chaotic system, many different patterns of motion are simultaneously present. Very small changes in the initial conditions can greatly alter the system's trajectory. Here a one-dimensional difference equation is used to explain how these properties can be exploited to control the chaotic dynamics of a population. Applying small perturbations according to a simple rule drives the density of the population to a stable state. Moreover, the population can inflict these perturbations on itself: it can exert self control. Under some circumstances, such a mechanism confers an evolutionary advantage. A mutant exerting self control can invade an uncontrolled but otherwise equal resident population. Invasion of the mutant stabilizes the previously fluctuating population density. The system considered here is a subject to a form of K selection. Even if the mutant's K value is less than that of the resident, self control can still make invasion possible, but in that case invasion does not stabilize the system. It may instead lead to intermittent chaos.