Blowflies as a Case Study in Non-Linear Population Dynamics

Time series have provided the stimulus for generating the central hypotheses in population ecology (regulation by endogenous factors vs. exogenous control; stability vs. instability; equilibria vs. cycles vs. chaos etc.). Time-series analysis also provides the first (and sometimes the sole) approach to testing competing hypotheses (Turchin and Ellner, this volume). Yet the last five years have shown that there is no simple means of characterising complex dynamic behaviour such as chaos in real ecological data (i.e. data sets that are short by physicists’ standards and noisy by any standards), despite early optimism about approaches such as non-linear forecasting (Sugihara and May, 1990; Ellner and Turchin, 1995). Most ecological time series are doubly flawed from a scientific point of view - they are insufficiently long and detailed for modern dynamical analysis, and they are unreplicated. Advances in computation have helped to alleviate the first problem, for example cross- validation has provided a very powerful aid to model selection (Turchin and Ellner, this volume); the universality of noise in ecology, however, renders interpretation of point estimates of any aspect of dynamics dubious.