Covariance Structures in Conventional and Organic Cropping Systems

Guidelines are needed to develop proper statistical analyses procedures and select appropriate models of covariance structures in response to expected temporal variation in long-term experiments. Cumulative yield, its temporal variance, and coefficient of variation were used in estimating and describing covariance structures in conventional and organic cropping systems of a long-term field experiment in a randomized complete block design. An 8-year database on 16 treatments (conventional and organic cropping systems, crop rotations, and tillage) was subjected to geostatistical, covariance structure, variance components, and repeated measures multivariate analyses using six covariance models under restricted maximum likelihood. Differential buildup of the cumulative effects due to crop rotations being repeated over time was demonstrated by decreasing structured and unstructured variances and increasing range estimates in the geostatistical analyses. The magnitude and direction of relationships between cumulative yield and its temporal variance, and coefficient of variation shaped the covariance structures of both cropping systems, crop rotations, and phases within crop rotations and resulted in significant deviations of organic management practices from their conventional counterparts. The unstructured covariance model was the best to fit most factor-variable combinations; it was the most flexible, but most costly in terms of computation time and number of estimated parameters. 1. Introduction Long-term experiments (LTEs) that include fixed and random factors are valuable tools in understanding the effects of spatiotemporal variation and in developing guidelines for proper management practices [1, 2]. Moreover, LTEs can delineate risks and stability of cropping practices due to year-to-year variability in biotic and abiotic stresses [3]. A major advantage of an LTE over short-term experiment is that it provides insight into the causes of the changes in the slope of the responses, the causes of the inflection points, and the magnitude of the long-term change in crop yield and its variance, whereas a short-term experiment focuses only on the initial trajectories of variables under study [4]. In addition, there is more interest in examining not only treatment main effects but also, more importantly, the treatment × time interaction through which cumulative effects of treatments can be quantified and contrasted [5]. Crop yield in LTEs with repeated measures involving diverse cropping systems and crop rotations can be expressed as a function of large-scale