A Meta-Analytical Assessment of the Aggregation Parameter of the Binary Power Law for Characterizing Spatial Heterogeneity of Plant Disease Incidence

Abstract

The binary power law (BPL) is often used to characterize spatial heterogeneity of disease incidence. A hierarchical mixed model, coupled with multiple imputation to randomly generate any missing standard errors, was used to conduct a meta-analysis of >200 published values of the estimated aggregation (b) parameter of the BPL. Approximately 50% of estimated b values ranged from 1.1 to 1.3. Moderator-variable analysis showed that the number of individuals per sampling unit (n) had a strong positive effect on b, with a linear relation between estimated b and ln(n). Estimated expected value of b for the population of published regressions at a reference n of 15 was 1.22. The increase in the variance due to the imputations was only 0.03, and the efficiency exceeded 0.98. Results were confirmed with an alternative mixed model that considered a range of possible within-trial correlations of the estimated b values, and with a random-coefficient mixed model fitted to the subset of the data. Cropping system, dispersal mode, and pathogen type all had significant effects on b, with annuals having larger expected value than woody perennials, soilborne and rain-splashed dispersed pathogens having the largest expected values for dispersal mode, and bacteria and Oomycetes having the largest expected values for pathogen type. However, there was considerable variation within each of the levels of the moderators, and the differences of expected values from smallest to largest were small, less than or equal to 0.16. Results are discussed in relation to previously published findings from stochastic simulations.

Does apple canker develop independently on leaf scars of a single apple shoot?

“…It should be noted that the run-test used in the present study is inefficient in detecting association since there were only 10 leaf scars on a single shoot, which may explain why most aggregation cases were for shoots with two canker lesions only. Aggregated spatial disease patterns are commonly observed for numerous pathosystems (Madden et al 2007(Madden et al , 2021, including apple powdery mildew lesions on individual leaves, and number of infected leaves on individual shoots (Xu & Madden 2002), aggregation of pear scab lesions (Li et al 2007), and clustering of apple trees with cankers in orchards (Di Iorio et al 2019). Such aggregation can be usually attributable to localised inoculum dispersal and its gradient, and microclimatic conditions.…”