POPULATION ecology typically focuses on particular species or pairs of species within webs of interacting species to understand variations in their abundance. Classical theory(1-3) predicts multigeneration cycles in predator and prey abundance. These cycles have received considerable attention(3-6), although there is an alternative possibility, of prey generation-length cycles in predator-prey interactions(7-9). Does observation of either of these patterns depend on how firmly predators and prey are embedded in their web of interactions? Concurrent investigations of predator-prey dynamics both in isolation and within a larger web have been lacking. Here we report observations of the population dynamics of a simple predator-prey system, and also of a three-species system including predator and prey. The dynamic patterns exhibited by both systems are cyclic, but the increase from two to three species gives rise to a marked shift in cycle peroid from one to several host generation lengths.