Comparison of techniques for modeling mean-proportion relationships with implications for presence-absence sampling

The relationship between mean density and proportion of infested sampling units, an integral component of presence-absence sampling plans for pest management programs, was modeled for a phytophagous mite on avocados, Oligonychus perseae Tuttle, Abatiello and Baker (Acari: Tetranychidae), using four different approaches: 1) an empirical model with linear regression, 2) a negative binomial probability model with a method of moments estimate of dispersion for parameter k, 3) the negative binomial probability model with a maximum likelihood estimate of k, and 4) a modified negative binomial probability model fitted with Taylor’s mean-variance relationship. These procedures were conducted for 6 different infestation thresholds (e.g., 1, 2, 3, 4, 5, 9 mites per leaf). In addition, for modeling approaches 2, 3 and 4, the mean proportion relationship was modeled after the 10th, 50th and 90th quantile estimates of parameter k. The 90th quantile estimates of k gave a better fit to the mean-proportion curve across infestation thresholds than the other evaluated quantile estimates of k. Comparatively, method 1 gave a better fit than the rest of the methods across all infestation thresholds. The implications of these results in the development of presence-absence sampling plans are discussed.