Stochastic difference equation predictors of population fluctuations.

This paper studies the effectiveness of a class of linear statistical estimators called autoregressive and autoregressive-moving averages equations for mimicking and predicting the abundance fluctuations of three species of Drosophila censused at a pine plantation near Bogota, Colombia. A short introductory justification for the use of linear estimators is given followed by a brief discussion of the theoretical basis of statistical prediction. The assumptions of the method, fitting techniques, and use of the equations in forecasting are discussed. The mimicking ability of the equations is tested by comparing monte carlo simulations employing the fitted models to the observed fluctuations of the three species. Of the autoregressive equations fitted to each species two are judged successful and one less than successful. Autoregressive-moving averages models were found to be significantly worse predictors than the simpler autoregressive equations for these three species. The parameter estimates given by the preliminary estimation techniques are compared with the statistically efficient least squares estimates. The estimates compare well for most of the autoregressive models, but the parameter estimates for the autoregressive-moving averages models were misleading.