Hierarchical models for white mould in snap bean

Limitations on the acceptable proportion (incidence) of pods with white mould may lead to the rejection of entire fields of processing snap bean. The low tolerances (no more than 2% to 6% of pods with white mould) are difficult to estimate with sufficient precision in the field when time is limited. These constraints motivated this study of white mould across three spatial hierarchical levels: pods, plants and quadrats consisting of two adjacent plants within rows. Hierarchical relationships are required when designing formal rules for estimating the incidence of pods with white mould from units higher in the spatial hierarchy. Disease assessments were made on all pods from 38 within-row transects of 40 plants each of the snap bean variety Hystyle. Using probability-based principles, equations were derived and fitted to data on the incidence of white mould on pods (ipod), plants (ipad) and quadrats (iq(2)), which led to a function directly linking ipod to iq(2). The variance of ipod increased with iq(2), but that may be of little consequence at the lower values of iq(2) likely to be associated with ipod values at processor-set tolerances. For example, at iq(2)=0.1 there was a 92% probability that ipod was less than 0.02. Assessing iq(2) may be more efficient than directly estimating ipod because iq(2) was about an order of magnitude higher than ipod. Results suggest it may be feasible to design sampling plans for estimating the proportion of pods with white mould from an assessment of the proportion of diseased quadrats. This article is protected by copyright. All rights reserved.