Using response-surface methodology to detect chaos in ecological time series

The performance of Turchin and Taylor's response-surface methodology in characterizing the endogenous dynamics underlying ecological time series is studied for the aphid Phyllaphis fagi. The results are shown to be sensitive to further data from the same population and extra data from a different but comparable population, to the order of the model fitted, and to the functional form of the response-surface model used. We suggest improvements to the estimation procedures and propose some alternative models. We also discuss the possibility of combining data from several populations to overcome the problem of short individual series. Phyllaphis fagi probably has stable, rather than chaotic endogenous dynamics.