Poverty, gender, and youth : working paper ...

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