  In this paper we introduce a formal method for the derivation of a predator's
functional response from a system of fast state transitions of the prey or
predator on a time scale during which the total prey and predator densities
remain constant. Such derivation permits an explicit interpretation of the
structure and parameters of the functional response in terms of individual
behaviour. The same method is also used here to derive the corresponding
numerical response of the predator as well as of the prey.
