Binomial sampling plans for the English grain aphid, Sitobion avenae (Homoptera: Aphididae) based on an empirical relationship between mean density and proportion of tillers with different tally thresholds of aphids

Abstract

Field sampling of populations of Sitobion avenae (Fabricius) on spring wheat in the north-western USA from 1988 to 1991 produced a data set consisting of 47 estimates of mean aphid density (m; number of aphids per tiller), variance (s2) and the proportion of tillers (PT) with no more than T = 0, 1, 2, …10, 15, 20, and 25 aphids, respectively; defined as the tally threshold. The average sampling error level of the four-year data set was 0.196 (SE= 0.013). The empirical relationship between m and PT was developed for each T value using the parameters from the linear regression of ln(m) on ln[-ln(Pϒ)] and was satisfactory when T = 2, 3, 4, and 5 (as evidenced by the high r2 values and relatively small mean squared errors from the regression analyses relating to the T values). In comparing the variances estimated from different formulae for predicting m from PT, the variance of Binns & Bostanian (1990b) was found to be more conservative and reliable in estimating the prediction variance. This variance was used in the development of binomial sampling plans for each T and in the determination of associated sampling precision denoted by the half-width of the confidence interval (d). Binomial sample sizes based on the T values of 2–5 were found to be associated with relatively small d values that may actually be reached and thus, are recommended for use in monitoring aphid populations for control decision making. However, at population densities below one aphid per tiller, binomial sampling was found to be feasible only when counts were based on empty tillers (T = 0).