Functional Response and Stability in Predator-Prey Systems

We propose two measures of how stabilizing a functional response is. We suggest that predation be regarded as stabilizing at a prey density of H if the predation rate is increasing then-i.e., if f(H)/H is increasing where f is the functional response. This is equivalent to asking that an increase in prey density results in an increased chance of a given prey being killed by the predator. With Hmas the maximum value of H for which this criterion holds, our measures are Hmand f(Hm). We relate this criterion and these measures to local stability and also to structural stability in a modified Lotka-Volterra model and a general multispecies model. The criteria will be used in detailed models of switching in predators (in the following paper in this issue) and of patchiness.