Detecting amphibian population cycles: The importance of appropriate statistical analyses

Amphibian populations are declining worldwide and understanding their temporal dynamics should be important to separate declines from natural fluctuations. In this study sixteen long-term amphibian time series, lasting 15 years or more, were analysed by means of conventional methods of time series analysis to evaluate the relative importance of exogenous and endogenous factors controlling population dynamics, and in particular to assess the existence of population cycles. There was significant autocorrelation in seven time series, and the autocorrelation function showed no signs of statistical cyclicity, but in one case there was some evidence for weak periodicity. In 12 populations the partial rate correlation function suggested the presence of direct density dependence, while there was no evidence for delayed density dependent regulation. In all time series the global Lyapunov exponent, a statistic that characterises the predictability of a dynamic system, indicated that the population trajectories had a tendency to converge towards a stable dynamics. These results may have conservation implications, because populations with direct density dependence possess high capacity of returning to equilibrium after a perturbation and therefore are less likely to go extinct. In the future, I encourage ecologists to increase the use of statistical time series methods and autoregressive modelling to analyse amphibian population dynamics in the framework of local and global climate variability.