Probabilistic ranking of plant cultivars: stability explains differences from mean rank

An alternative to ranking cultivars based on mean and stability of phenotype is evaluating pairs of cultivars and for each pair estimating which cultivar is more likely to perform better across a random subset of target environments. Such pairwise probabilistic order can then be translated into probabilistic ranking of all cultivars that accounts for both mean and stability in a single metric. Mean and probabilistic order will be the same for most cultivar pairs; but the pairs that differ reflect differences in stability and should thus be at least partially explained by existing stability measures. We formulate a classification problem to predict differences between mean and probabilistic order for a pair of cultivars with the predictor variables defined as differences in stability. We then apply a feature selection method to identify the best predictors, that is, the stability measures that are most predictive of the differences in the two orders. The results from applying this method to data observed from multiple crops, namely, rapeseed, sorghum and maize, show that a) existing stability measures explain most of the differences, b) no stability measure explains all differences for all data, and c) stability measures that combine mean with specific type of stability perform the most like probabilistic order. These results support the premise that probabilistic ranking combines mean and stability; but no existing stability measure can completely replace estimating the relevant probabilities to identify the cultivars that are more likely to perform better across their target environments.