Application of joint modeling of competition effects and environmental heterogeneity in Douglas-fir trials using an individual-tree mixed model and Bayesian inference

CAPPA, EDUARDO PABLO; MICHAEL U. STOEHR; CHANG-YI XIE; ALVIN D. YANCHUK

Whistler

Conferencia; Forest Genetics 2013; 2013

British Columbia Ministry of Forests, Lands and Natural Resource Operations

Forest genetic evaluation involves the use of mixed linear models to calculate "best linear unbiased predictors" (BLUP) of tree breeding values (BV). As BLUP depends on the values of the (co)variance matrices for the assumed model, the specification of the dispersion parameters should take into account both the negative correlation caused by competition among individuals, and the positive spatial correlation due to the environmental heterogeneity. Both phenomena, in any given experiment, are dynamic and coexist simultaneously. Therefore, modelling only one of these effects may lead to biases in the estimation of genetic parameters and the prediction of breeding values, and a joint model must be fitted to account for both sources of potential bias. As a first step in the analysis, we used several approaches to identify and quantify the competition effects (at genetic and environmental level) or/and environmental heterogeneity. Then, a joint individual-tree mixed model with direct genetic effects, genetic and environmental competition effects and a two dimensional B-spline smoothing surface to account for environmental heterogeneity (competition + spatial model), was applied to three Douglas-fir (Pseudotsuga meniziessii) progeny tests. This model was compared to three reduced individual-tree mixed models: a standard model with direct genetic effects only, a competition model including direct genetic and genetic and environmental competition effects, and a spatial model with a smoothing surface and direct genetic effects only. Three growth traits: diameter at breast height (DBH), total height (TH), and volume (VOL), were assessed at two ages (12 and 35 years old). This data set was composed of 78 parents and 165 families arranged within 10 diallels and included in a random complete block design with 4 replicates of 4 tree row plots. The traits DBH and VOL at age 35 years revealed strong competition effects at both genetic and environmental levels. There was also evidence of environmental heterogeneity for these traits. In general, the joint competition + spatial model gave a better fit (lower DIC value) than the simpler models on the three test sites. With strong competition genetic effects (i.e., correlation between direct and competition additive genetic effects higher than -0.3) the standard model yielded additive variance estimates that were smaller (from 39.5% to 50.6%) and residual variances that were higher (from 16.3% to 45.0%) than those estimated from the competition + spatial model. Ignoring the genetic and environmental competition effects leads to overestimating environmental heterogeneity; i.e., the spatial model yielded variance estimates of the random knots effects that were higher than those of the competition + spatial model. Ignoring the environmental heterogeneity leads to underestimating genetic and environmental competition effects; i.e., the competition model yielded direct and competition additive correlation estimates that were smaller (from 6.0% to 71.5%) and environmental competition variance that were higher (from 6.3% to 29.4%) than those of the competition + spatial model. The potential impact that the simultaneously adjusting for competition genetic effects and environmental heterogeneity has on the selection will be discussed with respect to the Douglas-fir genetic improvement program.