Are classical predator-prey models relevant to the real world?

Mathematical models of predator-prey population dynamics are widely used for predicting the effect of predators as biocontrol agents, but the assumptions of the models are more relevant to parasite-host systems. Predator-prey systems, at least in insects, substantially differ from what is assumed by these models. The main differences are: (i) Juveniles and adults have to be considered as two different entities, as the former stay within a patch and do not reproduce, while the latter move between patches of prey and reproduce there. (ii) Because of their high mobility, food availability is likely to be less restrictive for adults than juveniles, which are confined to one patch. Therefore, a functional response to prey abundance may not be important for adults. (iii) Egg and larval cannibalism are common in insect predators. Therefore, the quality of patches of prey for their larvae determines the reproductive strategy of adult predators more than the availability of food for the adults. Here we develop a new model, based on the above considerations, which is suitable for modelling these interactions. We show that selection should favour mechanisms that enable predators to avoid reproducing in patches with insufficient prey and those already occupied by predators.