Probability distributions for marketable pods and white mould on snap bean

Abstract

AbstractWhite mould, caused by Sclerotinia sclerotiorum, is one of the most recalcitrant diseases of snap bean. Probability distributions suitable for describing the total number of marketable pods (hereafter simply referred to as pods) per plant, as well as for the number of pods and stems with white mould per plant, have not been identified. The total number of pods and the number of pods and stems with white mould were measured on a per plant basis in plots of processing snap bean (var. Hystyle) in New York. The total number of pods per plant ranged from 0 to 29, and was best described by the Pólya‐Aeppli distribution. The number of pods and the number of stems with white mould per plant were well‐described by the negative binomial (NB) distribution. A Sarmanov bivariate distribution with NB marginals was derived and fitted to the joint data on the number of pods and stems with white mould per plant, accounting for correlation between pods and stems with white mould on the same plant. The bivariate distribution was used to formulate an empirical equation for the incidence of plants with white mould as a function of the average number of pods and stems with white mould per plant. The results represented a more complete understanding of the distributional properties of white mould in snap bean.