Testing the Validity of CV for Single-Plant Yield in the Absence of Competition as a Homeostasis Index

Abstract

The coefficient of variation (CV) of yield may functionally be related to the mean. The expected exponential CV decline with increasing mean, i.e., the Taylor’s power law (TPL), is not always valid. Removal of this scale dependency allows for a scale-independent assessment of stability. The objective of this study was to interpret the validity of the homeostasis index (HI), i.e., the inverse CV value, suggested in breeding under nil competition as a selection criterion for progeny lines that oppose the acquired interplant variation. Data concerning the single-plant yield of various crops under a nil-competition regime were studies against the theoretical background of the above hypothesis. Simple correlations between logarithms of variances and respective means were used to assess the reliability of CV as a stability statistic in breeding trials under nil competition. A total of 8 of the 24 case analyses revealed a systematic variance dependence on the mean. The impact was more prevalent in experiments with extensive spatial heterogeneity and high CV scores. Conversion of variance to remove systematic dependence did not validate the CV~mean negative relationship. Because of variance dependence, caution is needed when interpreting the HI as a stability index. Misuse of the HI may entail the risk of bias, upgrading or downgrading a progeny line in its ability to withstand acquired dissimilarity between plants. Testing the validity of the variance seems necessary, and the calculation of HI on a converted variance may enhance the accuracy of identifying the most promising progeny lines.