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.

Spatial analysis of progeny trial data improved predicted genetic responses by more than 10% for around 20 of the 216 variables tested, although, in general, the gains were more modest. The spatial method partitions the residual variance into an independent component and a two-dimensional spatially autocorrelated component and is fitted using REML. The largest improvements in likelihood were for height. Traits that exhibit little spatial structure (stem counts, form, and branching) did not respond as often. The spatial component represented up to 50% of the total residual variance, usually subsuming design-based blocking effects. The autocorrelation tended to be high for growth, indicating a smooth environmental surface, it tended to be small for measures of health, indicating patchiness, and otherwise the autocorrelation was intermediate. Negative autocorrelations, indicating competition, were present in only 10% of diameter measurements for the largest diameter square planted trials, and between nearest trees with rectangular planting at smaller diameters. Bimodal likelihood surfaces indicate that competition may be present, but not dominant, in other cases. Modelling of extraneous effects yielded extra genetic gain only in a few trials with severely asymmetric autocorrelations. Block analysis of resolvable incomplete-block or row–column designs was better than randomized complete-block analysis, but spatial analysis was even better.

This study explores the use of a mixed linear model including spatially correlated residuals in addition to the traditional randomized complete block (RCB) analysis in 12 forest genetic trials. The analysis of early height data from progeny and clonal tests of three species (Picea sitchensis (Bong.) Carr., Pinus pinaster Ait., and Pinus radiata D. Don) showed that there was significant spatial variation in all trials. Adding a basic first-order separable autoregressive error term more effectively modelled the spatial variation than the RCB model and greatly reduced the block and plot variances. There was no evidence that extended spatial modelling was required. The spatial analysis greatly improved the accuracy of genetic value estimation in some trials and was accompanied by large changes in rank of the genetic entries and by greater gains in selection relative to the RCB analysis.

This study assessed the genotype by environment (G × E) interaction for diameter growth in 15 Eucalyptus globulus progeny trials in Australia. Single-site analyses revealed significant subrace and family-withinsubrace variance in all trials. Across-site subrace (b r s ) and family (b r f ) correlations were estimated by linear mixed model analyses of pairs of trials. Using a factor analytic structure for subrace and family random terms in a multi-environment mixed model analysis, best linear unbiased predictions of subrace effects were obtained for each trial. These were then averaged for each of four states (Victoria, Tasmania, South Australia and Western Australia) and across all sites. Statistically significant G × E interaction was detected, and weighted means across states for b r s and b r f were 0.73 and 0.76, respectively. Nevertheless, the three subraces from the Otway Ranges were both fast growing and relatively stable in their ranks over all sites. We evaluated the sensitivity of subraces to changing environmental conditions, on the basis of random coefficient models regressing subrace performance on selected trial climatic variables. The results suggested differential susceptibility of subraces to water, light and (to a less extent) temperature stresses during summer. Moreover, using multivariate techniques to visualize and interpret the across-site correlation structure for subrace effects, we could identify site clusters of reduced G × E interaction related to soil water availability and evaporative demand during summer. A revised site-type classification using these factors should allow a better capture of genetic gains from breeding and deployment.