University of Miami
Joint work with Don DeAngelis, Jerry Ault, and Don Olson.
This talk will describe a mechanistic approach to the derivation of functional response terms in mean field predator-prey models which takes into account the spatial distribution of predators and/or prey. This approach can produce prey-dependent, ratio-dependent, Hassell-Varley, and various other forms of functional responses depending on the assumptions about the spatial distribution of predators and/or prey. Roughly speaking, functional responses which involve predator as well as prey densities tend to correspond to scenarios where there is significant aggregation of predators. This is in agreement with some empirical results and simulations. These results suggest that ratio-dependent, Hassell-Varley, or similar sorts of functional responses may sometimes be appropriate models for predator-prey interactions, but only in the presence of some fairly specific features of the systems under consideration.
In many predator-prey models the presence of a functional response which depends only on the prey density leads to a prediction that the equilibrium population of the prey is determined by the predation rate and the death rate of the predator but not by the growth rate or carrying capacity of the prey. This implies that enriching the environment for the prey will not increase the prey density but will increase the predator density. If the functional response depends on the predator density as well, then in many cases both predator and prey densities will increase in response to increased carrying cacpacity for the prey. Dependence of the functional response on the predator density can also have a stabilizing effect on population oscillations in the sense of reducing their amplitude, provided the dependence reflects some type of mutual interference by the predators.