Although individual species persist within a web of interactions with other species, data are usually gathered only from the focal species itself. We ask whether evidence of a species' interactions be detected and understood from patterns in the dynamics of that species alone. Theory predicts that strong coupling between a prey and a specialist predator/parasite should lead to an increase in the dimensionality of the prey's dynamics, whereas weak coupling should not. Here we describe a rare test of this prediction. Two natural enemies were added separately to replicate populations of a moth. For biological reasons that we identify here, the prediction of increased dimensionality was confirmed when a parasitoid wasp was added (although this increase had subtleties not previously appreciated), but the prediction failed for an added virus. Thus, an imprint of the interactions may be discerned within time-series data from component species of a system.