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Analysis of the Association Between the Incidence of Two Spatially Aggregated Foliar Diseases of Strawberry

Association of the incidence of leaf blight (caused by Phomopsis obscurans) and leaf spot of strawberry (caused by Mycosphaerella fragariae) was assessed at multiple scales in perennial plantings at several commercial farms over 3 years (1996 to 1998). For each field, the presence or absence of each disease was recorded from n = 15 leaflets in each of N ≈ 70 evenly spaced sampling units, and the proportion of leaflets with blight, spot, and total disease (blight or spot) was determined. Individual diseases and total disease incidence were all well described by the beta-binomial distribution but not by the binomial distribution, indicating overdispersion of disease. The Jaccard similarity index was used to measure disease co-occurrence at the leaflet, sampling-unit, and field scales. Standard errors of this index for the lower two scales were obtained using the jackknife (resampling) procedure, and data randomizations were used to determine the expected Jaccard index for an independent arrangement of the two diseases, conditioned on the incidence and spatial heterogeneity of the observed disease data. Results based on these statistics showed that only 4 of 52 data sets at the leaflet level and no data sets at the sampling-unit level had Jaccard index values significantly different from that expected under an independent rearrangement of the two diseases. Rank correlation and cross-correlation statistics were calculated to determine the degree of covariation in incidence between the two diseases. Additionally, covariation between diseases was tested using a new procedure in the Spatial Analysis by Distance IndicEs (SADIE) class of tests. Covariation was detected in 21% of the data sets using rank correlation methods and in 15% of the data sets using the SADIE-based approach. The discrepancy between these two methods may be due to the rank correlation procedure not taking into account the effects of spatial pattern of disease incidence. There was no relationship between mean disease incidence per field of spot and blight or between degree of heterogeneity of the two diseases (as measured by θ of the beta-binomial distribution), demonstrating lack of covariation at the field scale. Incidence of leaflets with either disease (total disease incidence) could be well predicted using a linear combination of the estimated probabilities of leaf blight and leaf spot incidence based on independence of the two diseases. Heterogeneity of total disease incidence, measured with the estimated θ parameter of the beta-binomial distribution, could also be well predicted using a linear combination of the weighted θ values for leaf blight and leaf spot, with weights proportional to incidence of the individual diseases.