| Summary: | The coefficient of variation (<i>CV</i>) of yield may functionally be related to the mean. The expected exponential <i>CV</i> 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 (<i>HI</i>), i.e., the inverse <i>CV</i> 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 <i>CV</i> 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 <i>CV</i> scores. Conversion of variance to remove systematic dependence did not validate the <i>CV</i>~mean negative relationship. Because of variance dependence, caution is needed when interpreting the <i>HI</i> as a stability index. Misuse of the <i>HI</i> 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 <i>HI</i> on a converted variance may enhance the accuracy of identifying the most promising progeny lines.
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