Spatial analysis methods for forest genetic trials

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Abstract
Spatial analysis, using separable autoregressive processes of residuals, is increasingly used in agricultural variety yield trial analysis. Interpretation of the sample variogram has become a tool for the detection of global trend and "extraneous" variation aligned with trial rows and columns. We applied this methodology to five selected forest genetic trials using an individual tree additive genetic model. We compared the base design model with post-blocking, a first-order autoregressive model of residuals (AR1), that model with an independent error term (AR1η), a combined base and autoregressive model, an autoregressive model only within replicates and an autoregressive model applied at the plot level. Post-blocking gave substantial improvements in log-likelihood over the base model, but the AR1η model was even better. The independent error term was necessary with the individual tree additive genetic model to avoid substantial positive bias in estimates of additive genetic variance in the AR1 model and blurred patterns of variation. With the combined model, the design effects were eliminated, or their significance was greatly reduced. Applying the AR1η model to individual trees was better than applying it at the plot level or applying it on a replicate-by-replicate basis. The relative improvements achieved in genetic response to selection did not exceed 6%. Examination of the spatial distribution of the residuals and the variogram of the residuals allowed the identification of the spatial patterns present. While additional significant terms could be fitted to model some of the spatial patterns and stationary variograms were attained in some instances, this resulted in only marginal increases in genetic gain. Use of a combined model is recommended to enable improved analysis of experimental data.