Testing Taylor’s Power Law association of winter wheat variation with mean yield at two contrasting soils

Abstract

Previous research has found that, based on Taylor’s Power Law (TPL), the coefficient of variation (CV) of yield data may functionally be related to the mean, with an exponential mean yield decline with increasing CV. Recent proposals have been made how this scale-dependency can be removed in order to allow a scale-independent assessment of stability. The theoretical background of the hypothesis was studied in wheat (Triticum aestivum L.) throughout data obtained from two fields of the farm of the Mendel University of Brno, Czech Republic. Soils of the two fields were of the contrasting loamy and sandy textures. Yield variation was intense in the sandy field representing a low-input agro-ecosystem. TPL became more obvious when the two fields were considered together, so as to enlarge the range of means and CVs. On the simple correlation between logarithms of variances and respective means, there was a systematic dependence of yield variance on mean yield when the within-block CV was considered. Conversion of variance to remove dependence on mean did not validate the CV ∼ yield negative relationship meaning that caution is needed when interpreting the CV of yield as a stability index. On the other hand, when the genotype CV for yield was considered variance was independent of the mean indicating agronomic essence in the CV∼ yield relationship, and coupled with the POLAR statistic, based on the negative residuals from the linear TPL regression that reflect low variability, revealed genotype cases exhibiting both high yield and stability. The findings corroborated that TPL is not always valid depending on scales and factors structuring the data. Interpreting crop variation via CV may entail a risk of bias due to variance dependence on mean, whereas the POLAR index offers an alternative stability measure that allows straight-forward interpretation providing the basis for developing more stable cropping systems. A trade-off between yield and stability does not exclude genotype cases of simultaneous occurrence of both, pinpointing realism in the pursuit of stable varieties without compromising yield.