Ecological implications of a latitudinal gradient in inter-annual climatic variability: a test using fractal and chaos theories

Although measures of seasonality are common, ecologists have seldom measured inter-annual variation or tested for the presence of a latitudinal gradient. Yet, species diversity and range size may be influenced by latitudinal gradients in climatic variability. Fractal and chaos theories offer new techniques to measure climatic unpredictability by analyzing the dynamics of nonlinear time-series data. We analyzed data on the number of freezing degree-days and date of first permanent ice from 12 weather stations (43–83°N) in Canada to describe latitudinal gradients in the timing of seasonal events. Time-series (ca 30 yr) of climatic variables were found to be nonlinear dynamic systems that were neither stochastic nor cyclic. The analyses reveal a latitudinal gradient in system memory length, with high latitude locations displaying shorter memory length (R/S fractal analysis and Lyapunov exponent). This latitudinal gradient is also characterized by more random and irregular fractal patterns (Hurst exponent) associated with higher latitudes. Both of these patterns may be due to the simpler climatic systems in high latitudes as indicated by fewer dynamic variables (lower correlation dimension). Application of fractal and chaos theories show that the timing of seasonal events (i.e. inter-annual variation) comprises a chaotic-dynamic system of comparatively low dimension.