Implications of the Stochastic Nature of Kuno’s and Green’s Fixed-Precision Stop Lines: Sampling Plans for the Pea Aphid (Homoptera: Aphididae) in Alfalfa as an Example1

Abstract

The fixed-precision sequential sampling plans of Kuno and Green were used to develop monitoring plans for the pea aphid, Acyrthosiphon pisum (Harris), and tested with sequential sampling bootstrap simulations of six independent data sets. For both sampling plans, and population densities from 0.87 to 96.5 aphids per stem, actual precision levels were not fixed at the desired level but fluctuated considerably depending on the particular set of samples selected for any given simulation run. For each set of simulation runs ( n = 100) at the intermediate densities of four and eight aphids per stem, actual precision levels were better than the desired fixed level 99-100% of the time. Corresponding sample sizes for these situations were usually higher than necessary, and the plans were therefore more conservative than stated. Conversely, at the low (0.87 aphids per stem) and high (>24.5 aphids per stem) densities tested, actual precision levels were poorer than the desired level (39-49% of the time). In these situations, too few samples were taken, and the plans were more liberal than stated. These studies clearly demonstrate the stochastic nature of each stop-line plan and emphasize the need for sequential sampling simulations to validate sampling plans before field implementation. As a result of the simulation studies with A. pisum , we used Kuno’s stop-line plan with precision levels (D) = 0.30 for low (≤3/stem) and high (> 1S/stem) aphid densities and D = 0.35 for intermediate densities (3.I-IS/stem). These stop lines were selected to maintain an average actual precision level of D ≅ 0.25 across all density ranges.