Spatial pattern analysis of hop powdery mildew in the Pacific Northwest: Implications for sampling

The spatial pattern of hop powdery mildew was characterized using 3 years of disease incidence data collected in commercial hop yards in the Pacific Northwest. Yards were selected randomly from yards with a history of powdery mildew, and two to five rows were selected for sampling within each yard. The proportion of symptomatic leaves out of 10 was determined from each of N sampling units in a row. The binomial and the beta-binomial frequency distributions were fit to the N sampling units observed in each row and to SigmaN sampling units observed in each yard. Distributional analyses indicated that disease incidence was better characterized by the beta-binomial than the binomial distribution in 25 and 47% of the data sets at the row and yard scales, respectively, according to a log-likelihood ratio test. Median values of the beta-binomial parameter 0, a measure of small-scale aggregation, were near 0 at both sampling scales, indicating that disease incidence was close to being randomly distributed. The variability in disease incidence among rows sampled in the same yard generally increased with mean incidence at the yard scale. Spatial autocorrelation analysis, used to measure large-scale patterns of aggregation, indicated that disease incidence was not correlated between sampling units over several lag distances. Results of a covariance analysis showed that heterogeneity of disease incidence was not dependent upon cultivar, region, or time of year when sampling was conducted. A hierarchical analysis showed that disease incidence at the sampling unit scale (proportion of sampling units with one or more diseased leaves) increased as a saturation-type curve with respect to incidence at the leaf level and could be described by a binomial function modified to account for the effects of heterogeneity through an effective sample size. Use of these models permits sampling at the sampling unit scale while allowing inferences to be made at the leaf scale. Taken together, hop powdery mildew was nearly randomly distributed with no discernable foci, suggesting epidemics are initiated from a well-distributed or readily dispersible overwintering population. Implications for sampling are discussed.