Variance of the Estimated Population Density from a Presence–Absence Sample

A range of expressions has been proposed for the variance of estimates of pest population densities based on presence-absence samples. An equation of the form ln(m) = a + b ln (−ln p) is used to relate m, the mean density of a sample, to p, the proportion of uninfested sampling units. In this article, the derivation of the variance and the accompanying assumptions are examined. Because many presence-absence samples are not truly random, it is proposed that an adjustment be made to the term in the variance that results from sampling. This adjustment, called the design effect, is illustrated using results for twos potted spider mite, Tetranychus urticae Koch, on strawberries and is shown to be greatest for large values of p.