Noise, cycles, and noisy cycles in finite populations

Periodic predator-prey dynamics in constant environments are usually taken as indicative of deterministic limit cycles. It is known, however, that demographic stochasticity in finite populations can also give rise to regular population cycles, even when the corresponding deterministic models predict a stable equilibrium. The existence of quasi-cycles substantially expands the scope for natural patterns of periodic population oscillations caused by ecological interactions, thereby complicating the conclusive interpretation of such patterns. It is, however, feasible and straightforward to accurately distinguish between the two types of cycle through the combined analysis of autocorrelations and marginal distributions of population sizes. By confronting these results with real ecological time series even short and imperfect time series allow quasi-cycles and limit cycles to be distinguished reliably. This work has been published in: Pineda-Krch M, Blok HJ, Dieckmann U, Doebeli M. 2007. A tale of two cycles - Distinguishing between true limit cycles and quasi-cycles in finite predator-prey populations. Oikos 116: 53-64