Spatial analysis enhances modelling of a wide variety of traits in forest genetic trials

Abstract

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.

Efficiency of using spatial analysis for Norway spruce progeny tests in Sweden

“…Variables recorded as counts were not transformed as it was observed that transformation using the square root for counts did not further normalize the distribution (Dutkowski et al 2006). …”

“…The large physical area needed for a progeny trial usually exhibits considerable variation in environmental conditions (Bian et al 2017;Dutkowski et al 2006;Chen et al 2017). To reduce such environmental heterogeneity, an experimental design subdividing the trial into blocks is usually used (Williams et al 2002).…”

“…While various blocking methods used for forest genetic trials may be effective in reducing global (trend) variation, spatial analysis was introduced, initially for crops and recently for trees, to account for both global and local microsite variations and therefore further improve the accuracy of breeding value prediction (Cullis et al 1998;Ye and Jayawickrama 2008). Even with traditional RCB design, implementation of spatial analysis could still improve the model by detecting microsite variations within or between block variations, covering the type of changes in soil depth and nutrition that exist in most trials (Dutkowski et al 2006;Ye and Jayawickrama 2008).…”

“…Recently, the competition effect between neighboring trees has been described in several papers (Cappa and Cantet 2008;Cappa et al 2015Cappa et al , 2016Dutkowski et al 2002;Dutkowski et al 2006;Ye and Jayawickrama 2008). Dutkowski et al (2006) reported that 10% of diameter variables showed competition effects, represented by negative first-order autocorrelation coefficients in both column and row directions at a residual level.…”

“…Dutkowski et al (2006) reported that 10% of diameter variables showed competition effects, represented by negative first-order autocorrelation coefficients in both column and row directions at a residual level. Ye and Jayawickrama (2008) reported that eight negative autocorrelations from a total of 1135 variables were observed, either in one direction or in both directions of row and column.…”