Testing Taylor's Power Law association of maize interplant variation with mean grain yield

Abstract

Plant-to-plant variability is a crop stability component. The objective of this study in maize (Zea mays L.) was to test the validity of the theoretical background of the hypothesis that the coefficient of variation (CV) for grain yield per plant and mean yield are connected exponentially, following the Taylor's Power Law (TPL) Model. Field experimentation was conducted across two sites, two seasons, and two planting densities. Densities were the main plots, corresponding to the typical practice of 8.89 plants m–2 (TCD) and the low-input optimal of 5.33 plants m–2 (LCD), while hybrids were the subplots. Data from 26 subplots in the first site averaged CV values of 22.6% at the TCD and 21.9% at the LCD, and mean yields of 19.1 and 13.9 t ha–1, respectively, following the TPL Model. The same was true for the second site, with average CVs and means of 41.5% and 14.3 t ha–1 at the TCD and 36.8% and 11.5 t ha–1 at the LCD. A test was performed on the simple correlation between the logarithms of variances and their respective means to investigate whether there is a systematic variance dependence on mean, thus questioning the reliability of TPL. The validity of TPL was verified in the first site. Nevertheless, there was a systematic dependence of yield variance on mean yield in the second site, implying that the CV-yield correlation might be not biologically meaningful. Conversion of the variance to remove its dependence on the mean did not validate the CV-yield negative relationship, meaning that caution is needed when interpreting the CV as a stability index for intra-crop variation. Whether the determinant factor of invalidity of TPL was the extensive intra-crop variation in the lower yielding second site can be assessed in future research.