Spatial analysis and incidence-density relationships for downy mildew on hop

The spatial pattern of downy mildew (Pseudoperonospora humuli) on hop (Humulus lupulus) was characterized over 4 years to aid in deriving an appropriate incidencedensity relationship. From 472 disease assessments (datasets), discrete distributions were fitted to the datasets to determine aggregation of disease density. Where distributions were able to be fitted, the Poisson distribution fitted 4% of the datasets and the negative binomial distribution fitted 87% of the datasets. Larger-scale patterns of disease were assessed by autocorrelation and runs analysis; both indicated aggregation of diseased plants was less common than aggregation of disease within plants. Taylors power law indicated disease density was aggregated and related to mean disease density in all years. Disease incidence and density were linked by saturation-type relationships based on the zero term of the negative binomial distribution or an empirical regression. Certain individual datasets were not described well by any incidencedensity model, particularly when disease density was greater than about 0.8 diseased shoots per plant with the cultivar Cascade. When applied to 56 validation datasets, 88% of the variation in observed disease incidence was explained by the incidencedensity models. Under conditions where sampling would be implemented for disease management, the requisite conditions appear to be in place for a binomial sampling plan for downy mildew.