Problems in Detecting Chaotic Behavior in Natural Populations by Fitting Simple Discrete Models

In order to predict the long—term qualitative dynamics of natural populations with discrete generations, ecologists have used short—term field data to estimate the parameters of simple difference—equation models whose behaviors are then examined. Three problems complicate the model—fitting approach: (1) the parameter estimates, and hence the predicted dynamics, may be sensitive to the estimation procedure used; (2) different models may fit the data equivalently well and yet make different predictions about population behavior; and (3) even when the best—fit parameters are used, a simple model may fail to capture the observed dynamics of the field population. I illustrate these problems using data from published insect life—table studies. I then discuss the limitations these problems impose upon the prediction of the qualitative behavior of natural populations by means of simple best—fit models. I conclude that, given these limitations, inferences about the presence or absence of chaos in natural insect populations that rely on simple best—fit models and premature.