Determining the Functional Form of Density Dependence: Deductive Approaches for Consumer-Resource Systems Having a Single Resource

Consumer-resource models are used to deduce the functional form of density dependence in the consumer population. A general approach to determining the form of consumer density dependence is proposed; this involves determining the equilibrium (or average) population size for a series of different harvest rates. The relationship between a consumer's mortality and its equilibrium population size is explored for several one-consumer/ one-resource models. The shape of density dependence in the resource and the shape of the numerical and functional responses all tend to be "inherited" by the consumer's density dependence. Consumer-resource models suggest that density dependence will very often have both concave and convex segments, something that is impossible under the commonly used v-logistic model. A range of consumer-resource models predicts that consumer population size often declines at a decelerating rate with mortality at low mortality rates, is insensitive to or increases with mortality over a wide range of intermediate mortalities, and declines at a rapidly accelerating rate with increased mortality when mortality is high. This has important implications for management and conservation of natural populations.