  Context. So far, theoretical explanations for body-size patterns in periodic
population dynamics have received little attention. In particular, tuning and
testing of allometric models on empirical data and regressions has not been
carried out yet. Here, oscillations expected from a one-species (delayed
logistic) and a two-species (Rosenzweig-MacArthur) model were compared to
cycles observed in laboratory experiments and field surveys for a wide range of
invertebrates and vertebrates. The parameters in the equations were linked to
body mass, using a consistent set of allometric relationships that was
calibrated on 230 regressions. Oscillation period and amplitude predicted by
the models were validated with data taken from literature. Results. The
collected data showed that cycle times of herbivores scaled to species body
mass with a slope up to 1/4 as expected from the models. With exception of
aquatic herbi-detritivores, intercepts were observed at the level calculated by
the two-species model. Remarkably, oscillation periods were size-independent
for predatory invertebrates, fishes, birds and mammals. Average cycles were of
4 to 5 years, similar to those predicted by the one-species model with a
size-independent delay of 1 year. The consistent difference between herbivores
and the carnivores could be explained by the models from the small parameter
space for consumer-resource cycles in generalist predators. As expected,
amplitudes recorded in the field did not scale to size. Observed oscillation
periods were generally within a factor of about 2 from the values expected from
the models. This demonstrates that a set of slopes and intercepts for age and
density parameters applicable to a wide range of species allows a reasonable
estimate of independently measured cycle times.
