Living on the Edge of Chaos: Population Dynamics of Fennoscandian Voles
Peter Turchin, Stephen P. Ellner
Although ecologists were among the first scientists to study the implications of chaotic dynamics, there is still no widely accepted example of chaos in a field population. If current developments in nonlinear dynamics are to be of relevance to population ecology, however, it is necessary to determine whether chaos occurs in nature. Here we bring together two lines of evidence suggesting that the dynamics of vole populations in northern Fennoscandia may be chaotic: nonlinear analysis of time-series data, and a model based on biological mechanisms. We review how a mechanistic population model can be used to produce short-term population forecasts, even when one of the species is not observed, and then use this benchmark of model accuracy to support our choice of a mechanistic population model for vole dynamics. By adjusting model parameters to optimize the forecasting accuracy on the vole time series, we can obtain parameter estimates for the model. In tests on simulated data, this new approach to parameter estimation for stochastic dynamic models yields parameter estimates such that the fitted model produces dynamics qualitatively and quantitatively similar to those observed. However, some parameters are poorly identified (i.e., many different parameter combinations yield nearly identical model dynamics). For the best-fit parameters, the model dynamics are characterized by quasi-chaotic behavior; the global Lyapunov exponent is very close to (and statistically undistinguishable from) zero, but the median local Lyapunov exponent is significantly positive. Our findings of recurrent short-term chaos suggest that vole dynamics in northern Fennoscandia are characterized by a blend of order and irregularity. The irregularity is the same type as would occur in a noisy chaotic system (i.e., exogenous noise amplification by sensitive dependence on initial conditions) but only occurs during specific portions of the oscillation.