Detecting chaotic dynamics of insect populations from long-term survey data

1. Estimates of the Lyapunov exponent, a statistic that measures the sensitive dependence of the dynamic behaviour of a system on its initial conditions, are used to characterize several sets of insect time series. 2. A new method is described to overcome the difficulty of defining the dynamics of an observed, noisy, short ecological time series. This method provides two test statistics for the estimated Lyapunov exponent. 3. This method is applied to forty-six time series comprising six aphid species from five sites and four moth species from six sites. There are few positive Lyapunov exponents and none is sufficiently large to characterize its time series as chaotic. 4. Two methods to estimate the Lyapunov exponent are compared; that based on logarithmically transformed counts yields less variable estimates for highly variable insect data than that based on untransformed counts.