Use of covariance structures for temporal errors in the analysis of a three-course wheat rotation and tillage trial
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Crop rotation serves as a mechanism for developing sustainable crop production systems. Crop-rotation trials are used to identify agronomic input factors suitable for use in a cropping system. In crop-rotation trials, experimental errors within the same plot over time are correlated. The form of the covariance structure of the plot errors may be specific to the data from a rotation trial, but is unknown and is generally assumed. Statistical analyses are usually based on the assumption that plot errors are independent, or have constant covariance. An experiment was conducted using wheat-based, three-course rotations containing tillage treatment subplots over 12 years at ICARDA's experimental station at Tel Hadya, a moderately dry area in northern Syria. This study examined several covariance structures for temporal errors arising over the rotation plots and tillage subplots, in order to model wheat yield data. Eighteen covariance structures were examined, and the best pair was selected using the Akaike Information Criterion. The best pair comprised first-order autocorrelation and homogeneous variance for temporal errors in rotation plots, and uniform correlation with heterogeneous variances for temporal errors in tillage subplots. Using the 12 years of data obtained for wheat yield and the best pair of covariance structures, the tillage and rotation effects were found to be statistically significant and to have significant interactions with the cycle of rotation. The precision of the means calculated differed from those calculated using a control structure based on homogeneous error variances and constant correlation. The cumulative yield build-up over time differed significantly over the rotations and the tillage methods. An increasing yield trend was observed for the bread wheat rotation, while a yield decline was observed in durum wheat when the rotation was repeated. When evaluating the effects of input factors in crop rotations, we therefore recommend that the covariance structures be examined and that a suitably chosen structure be used.
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