VARIATION IN SPATIAL PATTERNS OF THE RUSSIAN WHEAT APHID (HOMOPTERA, APHIDIDAE) AMONG SMALL GRAINS IN THE NORTHWESTERN UNITED-STATES

Field sampling of the Russian wheat aphid, Diuraphis noxia (Mordvilko), infesting spring wheat, spring barley, and winter wheat in the northwestern United States from 1988 to 1991 generated a data set of 117 mean aphid density (m) and variance (s2) estimates, based on individual tillers, with an average sampling error level of 0.172. This provided a data set desired for use in spatial analysis and the development of sampling plans. Three regression models-ln(s2) = ln(a) + bln(m) (Taylor's power law), m* = alpha + betam (Iwao's model), and k = c + dm [k = m2/(s2 - m) (a parameter for the negative binomial distribution)-were fit to the data pooled by crop type or growing season. Taylor's power law generally fit the data better than Iwao's model. Taylor's b and Iwao's beta were significantly >1 for all cases (single crop, season, or pooled together), indicating that D. noxia populations were aggregated. The slope d for the summer populations on winter wheat was indistinguishable from 0, indicating the existence of a common k (estimated as 0.003). However, a common k was not detected for the summer populations on spring wheat and barley and the fall populations on winter wheat because their d values were significantly >0, indicating the dependence of k on m. Based on comparisons of intercepts and slopes from the three models, the counts of the summer populations on all three grains could be pooled effectively to generate a more representative data set covering a wide range of variation. However, the fall populations on winter wheat should be treated separately because their spatial pattern apparently is distinct from those of the summer populations. Finally, temporal changes in spatial pattern (represented by the estimates of 1/k) on spring and winter grains are discussed with respect to crop stages and aphid densities.