The functional response is one of the most widely measured attributes of consumers. Phenomenalistic descriptions of how predator attack rates vary with prey density are fundamental components of consumer-resource models. The application of these functions typically assumes continuous foraging by individuals, along with stationarity in their behavioural and physiological processes. Yet most species display a diurnal cycle in foraging and resting, and the impact of this foraging pattern on the functional response is unknown.

We use a physiologically structured or ‘state–space’ approach to examine how the daily foraging cycle affects the temporal dynamics of attack rates and the functional response of parasitoids (Aphytis melinus) and predators (Mantis crassulea and fishes). The state spaces for parasitoids and predators are the number of mature eggs, the eggload, and the satiation level, respectively. The corresponding rates are those of egg maturation and oviposition on one hand, and digestion and prey capture on the other hand.

We show that the length of the foraging period alters both the shape of the functional response and the magnitude of attack rates, compared to a daily functional response proportional to the time spent foraging, as is classically done. Our models reveal how separation of time-scales arises between behavioural or physiological and lifetime processes, and the difficulty in resolving such separation once the new time scale of a foraging cycle is introduced.

Foragers in many environments, either because of exposure to low resource density or constrained by short foraging windows, cannot achieve the behavioural or physiological stationarity assumed in classical analyses. This introduces a fundamental mixture of time-scales that has significant effects on estimates of attack rates. Using a population-level model of predators and prey, we show how restricted periods of daily foraging have important dynamical consequences both in terms of equilibrium levels and return times to these equilibria.