Delayed Logistic and Rosenzweig - MacArthur Models with Allometric Parameter Setting Estimate Population Cycles Well

Abstract

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.