Population data collected from 132 trees during a 3-year period were used to simulate spots of K trees (1 k 50) infested by the attacking adult stage of
Dendroctonus frontalisZimmerman. The total number of beetles on the K trees was then estimated by sampling k trees (1 k 10). The k trees were chosen at random and by selecting those of largest diameter and largest infested area. Within-tree populations were estimated at two levels of precision and within-spot populations were then estimated by scaling the sum of the k within-tree estimates according to the proportion of the tree numbers, tree diameters, or infested phloem areas included in the sample. The various combinations of tree selection, within-tree precision, and scaling produced 10 procedures which were evaluated for bias, precision, and cost as estimators of within-spot populations. Bias was calculated as the mean of the proportional errors in estimating the true numbers, and the standard deviation of the proportional errors was used as a measure of precision.
The procedures in which trees were randomly selected provided unbiased estimates of the within-spot populations. Selecting the largest trees tended to overestimate the true number with the bias diminishing to zero as k K. However, separate analyses of trees sampled on the same date within actual spots showed no reason to reject the hypothesis of no difference in beetle density (insects/diameter and insects/area) between the largest and smallest trees.
When k = K = 1, the precision of all within-spot estimators was equivalent to the precision of the within-tree estimate. For larger k = K, the precision improved approximately as (K). No attempt was made to derive functional relationships of precision for k < K. For each procedure, precision improved as k K. Sampling the k trees at two sample heights (3.5 and 6.5 m, 4100 cm2 disks/height) was more precise than single level sampling (4 disks at 5 m), but equally precise estimates could be obtained by single level sampling of just one or two additional trees in the spot. Random selection of the k trees with scaling by the number of infested trees was the least precise of the estimating procedures; scaling by diameter and by infested surface area increased the precision. Best precision was obtained by selecting the k trees of greatest infested phloem area, but selecting the largest diameter trees was nearly as precise. The least costly procedure for obtaining a desired level of precision consists of selecting the k trees of largest diameter and extracting 4 disks/tree at 5 m.