Two-level Numerical Sampling Plans and Optimal Subsample Size Computations for Urophora affinis and Urophora quadrifasciata (Diptera: Tephritidae) on Spotted Knapweed

Abstract

Taylor's power law analysis was performed on among- and within-subsample mean and variance estimates of the number of Urophora affinis Frauenfeld and Urophora quadrifasciata (Meigen) galls per spotted knapweed seed head. Highly significant correlation coefficients suggested that Taylor's power relationship fits the data well. A comparison of the b parameters from Taylor's analyses suggested that the spatial dispersion of U. affinis was more clumped than that of U. quadrifasciata. The spatial dispersion of U. quadrifasciata appeared to become more uniform in the presence of U. affinis. Means and estimated variances (among and within subsamples) were used to develop numerical sampling equations for the two fly species. A cost (work effort) analysis was performed on the among- and within-subsample units. Optimal subsample sizes calculated for overall mean gall densities of U. affinis and U. quadrifasciata (averaged over all sampling sites) were 18.95 and 21.86 seed heads per subsample, respectively. To protect against sampling low population sites, it is recommended that 15 subsamples of 25 seed heads each be collected per sampling site and used to assess population levels of the two fly species. Information presented in this paper should improve accuracy and efficiency in future sampling of U. affinis and U. quadrifasciata and aid in determining those sites warranting future releases of the flies.