Nonlinearity of a Generic Variance–Mean Equation for Stored-Grain Insect Sampling Data

Abstract

Equations predicting the variance for a mean insect density have been widely used to calculate the precision of density estimates. Traditionally, the logarithm of the variance is regressed against the logarithm of the mean giving a linear equation. We fit a single nonlinear variance-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 sampling methods, and the 6 most commonly encountered species. The asymptotic slope of this generic nonlinear regression equation increased with 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, respectively. This density-dependent change in the asymptotic slope explains the differences among studies in the slopes of linear regression equations. 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 distributions could be the result of random dispersal, and that the mechanism underlying 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 lower insect densities. This generic nonlinear regression equation can be used to calculate the precision of mean insect density estimates over a 0.025-100 insects per sample unit density range and thus reduce the cost of developing new sampling programs.