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Comparison of blocking and spatial models

Since the introduction of spatial analysis to field trials (Papadakis, 1937), concepts of blocking and spatial analysis have usually been opposed and mutually exclusive (Edmondson, 2005). Comparative analyses employing both types of models often tended to prove superiority of spatial models either in simulation (Baird and Mead, 1991) or real data analysis (Cullis and Gleeson, 1989). Uniformity trials reveal the impact of plot size and shape on the model efficiency (Wu and Dutilleul, 1999), but even for large scale forestry trials, despite the omnipresence of strong spatial trends, the importance of appropriate blocking scheme is stressed (Dutkowski et al., 2006). Further case studies involving larger array of experiments (Qiao et al., 2000) lead to the conclusion that spatial models should be considered as a useful addition rather than alternative to blocking (Piepho and Williams, 2010). Data used in this study were collected from series of field trials performed within different project frameworks, targeting different objectives, carried out at various environments, and involving two major crops (maize and wheat). All trials were set up in latinized row-column design, using CycDesign software. First step in modelling strategy was reduction of the fixed part of the model, so three different basic fixed models were created by excluding latinized rows/columns and replicates: full (latinized), RCBD and CRD. Three baseline models were then complemented with various random parts, corresponding to different blocking and spatial structures. Fitted models were compared using the three criteria: average standard error of difference for the treatment comparison, likelihood ratio test for added random effects and AIC. Selection of the optimal model was further aided by surface plots of data, fits and residuals. Model were fitted using ASREML software (Gilmour et al., 2009) and visualized using R package ‘agridat’ (Wright, 2011).

field trials; blocking; spatial analysis

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