The Implicit Assumptions of Classic Functional Responses and their Multi-Species Extensions

Functional responses are central to describe consumer-resource interactions. Defined as the per capita average feeding rate of consumers, since Hollings seminal papers, they have been widely used in ecology. Hollings central observation was that they often saturate as resource density increases. If the interference between consumers is strong, they also decrease with consumer density. Here we emphasize the stochastic nature of the individual feeding processes and the associated probability distributions of the different behavioral types and show how they control population-averaged feeding rates. We do so by revisiting a classic approach based on the formulation of feeding interactions in terms of individual-based reaction schemes. We highlight the common assumptions underlying the different functional forms and discover a new predator-dependent functional response that should be considered the natural extension of the Holling type II functional response when consumers interference is considered. Our work has clear implications, on the one hand, for both model selection and parameter inference from feeding experiments, and, on the other, for the use of multi-species extensions of these functional responses in population-level food-web dynamic models.