© 1996 by The Society for Integrative and Comparative Biology
An Introduction to Risk Sensitivity: The Use of Jensen's Inequality to Clarify Evolutionary Arguments of Adaptation and Constraint1
Department of Biology, University of Pennsylvania Philadelphia, Pennsylvania 19104
I review the basic rationale for risk-sensitive foraging, and present a few of the most common expressions of risk-sensitivity theory. A simple heuristic, the energy-budget rule, and the z-score model are explained. These functional models of risk sensitivity assume or explicitly model fitness as a nonlinear function of an animal's energy state. For such nonlinear relationships, Jensen's inequality predicts that the fitness realized by an animal with a more constant energy state may be higher or lower than the fitness resulting from a variable energy state with the same mean, depending on the shape of the fitness function. Predictive functional models of behavior, like the energy-budget rule and the z-score model, depend on specific features of the function relating energy state to fitness, which may or may not be general features for most organisms. While behavioral ecologist have studied the functional significance of animal responses to variation in foraging rewards, psychologists have long studied the psychological mechanisms by which preferences for variable or constant rewards are expressed. Jensen's inequality is applied here too; psychologists propose nonlinearities in the perception and processing of information. The growing number of different relationships that might account for risk-sensitive behavior is a potential source of confusion. I advocate "returning to the basics," i.e., that hypotheses to explain risksensitive behavior should specify precisely the assumed nonlinear relationships.