NONLINEARITY OF A GENERIC VARIANCE-MEAN EQUATION FOR STORED-GRAIN INSECT SAMPLING DATA

Equations predicting the variance for a mean insect density have been widely used to calculate the precision of density estimates. Tradition ally, the logarithm of the variance is regressed against the logarithm of the mean giving a linear equation. We fit a single nonlinear varia nce-mean regression equation to 4 stored-product insect sampling data sets. This generic nonlinear regression equation described the stored- product insect sampling data for 25 additional studies, 3 different sa mpling methods, and the 6 most commonly encountered species. The asymp totic slope of this generic nonlinear regression equation increased wi th insect density, and at mean densities of 0.01, 0.1, 1, 10, and 100 insects per sample unit was 1.06, 1.32, 1.64, 2.05, and 2.55, respecti vely. This density-dependent change in the asymptotic slope explains t he differences among studies in the slopes of linear regression equati ons. We generated a similar regression equation by randomly assigning insects to sampling units to simulate random dispersal of insects in a grain mass. This suggests that the observed insect sampling distribut ions could be the result of random dispersal, and that the mechanism u nderlying the regression equation is fairly general. Compared with the predictions of the generic nonlinear regression equation, the linear regression equation overpredicted the 95% CL within the 0.3-3 insects per sample unit density range, and underpredicted them at higher or lo wer insect densities. This generic nonlinear regression equation can b e used to calculate the precision of mean insect density estimates ove r a 0.025-100 insects per sample unit density range and thus reduce th e cost of developing new sampling programs.