Single-species models for many-species food webs

Most species live in species-rich food webs; yet, for a century, most mathematical models for population dynamics have included only one or two species(1-3). We ask whether such models are relevant to the real world. Two-species population models of an interacting consumer and resource collapse to one-species dynamics when recruitment to the resource population is unrelated to resource abundance, thereby weakening the coupling between consumer and resource(4-6). We predict that, in nature, generalist consumers that feed on many species should similarly show one-species dynamics. We test this prediction using cyclic populations, in which it is easier to infer underlying mechanisms(7), and which are widespread in nature(8). Here we show that one-species cycles can be distinguished from consumer-resource cycles by their periods. We then analyse a large number of time series from cyclic populations in nature and show that almost all cycling, generalist consumers examined have periods that are consistent with one-species dynamics. Thus generalist consumers indeed behave as if they were one-species populations, and a one-species model is a valid representation for generalist population dynamics in many-species food webs.