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. These problems are illustrated using data from published insect life-table studies (Bupalus piniarius, Cyzenis albicans, Delia coarctata, Operophtera brumata). Inferences about the presence or absence of chaos in natural insect populations that rely on simple best-fit models are premature. -from Author