Spatial heterogeneity,incidence-incidence and incidence-lesion density relationship of apple scab (<Emphasis Type="Italic">Venturia inaequalis</Emphasis>) in managed orchards

The spatial pattern of apple scab was characterized using 10 years of disease incidence and lesion density data collected in managed orchards located in Quebec, Canada. Distributional analyses indicated that scab incidence was better characterized by the beta-binomial than the binomial distribution in 53 and 65% of the data sets at the leaf and shoot scales, respectively. Median values of the beta-binomial parameter θ, a measure of small-scale aggregation, were near 0 (0.003 and 0.028) at both sampling scales, indicating that disease incidence was close to being randomly distributed (low degree of aggregation). For lesion density, the negative binomial distribution fitted the data better than the Poisson distribution in 86% of the data sets at the leaf scale. The median value of the index of dispersion k was 0.068, indicating that aggregation was present. For all apple scab measurements, the power law models provided a good fit to the data. The estimated slope and intercept parameters were significantly greater than 1 and 0, respectively, suggesting that spatial heterogeneity changed systematically with disease incidence. Results of a covariance analysis showed that spatial heterogeneity of scab incidence at both scales and lesion density was not dependent upon shoot type but that spatial heterogeneity of scab incidence and lesion density at the leaf scale was influenced by the sampling period. A hierarchical analysis showed that scab incidence at the tree scale increased as a saturation-type curve with respect to incidence at the leaf or shoot scales. A similar relationship was observed for incidences at the shoot and leaf scales. An effective sample size model based on the binary power law parameters (Madden and Hughes, Phytopathology 89:770–781, 1999) gave the best fit to the leaf and shoot data, respectively. The incidence-lesion density relationship at both scales was well described by a complementary log-log (CLL) and log transformation model ( R_adj² = 0.97 and R_adj² = 0.94 ) \left( {R_{{adj}}^2 = 0.97\,and\,R_{{adj}}^2 = 0.94} \right) , however, the models tended to underestimate lesion density. The information of the spatial relations of apple scab within and between hierarchical scales acquired from this study can be used in developing and evaluating practical disease management strategies and to improve apple scab assessments for fungicide or cultivar susceptibility trials.