Bayesian inference for multi-environment spatial individual-tree models with additive and full-sib family genetic effects for large forest genetic trials

Abstract

The gain in accuracy of breeding values with the use of single trial spatial analysis is well known in forestry. However, spatial analyses methodology for single forest genetic trials must be adapted for use with combined analyses of forest genetic trials across sites. This paper extends a methodology for spatial analysis of single forest genetic trial to a multi-environment trial (MET) setting. A two-stage spatial MET approach using an individual-tree model with additive and full-sib family genetic effects was developed. Dispersion parameters were estimated using Bayesian techniques via Gibbs sampling. The procedure is illustrated using height growth data at age 10 from eight large Tsuga heterophylla (Raf.) Sarg. second-generation full-sib progeny trials from two series established across seven sites in British Columbia (Canada) and on one in Washington (USA). The proposed multi-environment spatial mixed model displayed a consistent reduction of the posterior mean and an increase in the precision of error variances $$ \left( {\sigma _{e}^{2}} \right) $$ than the model with “sets in replicates” or incomplete block alpha designs. Also, the multi-environment spatial model provided an average increase in the posterior means of the narrow- and broad-sense individual-tree heritabilities (h N 2 and h B 2 , respectively). No consistent changes were observed in the posterior means of additive genetic correlations (r Ajj′). Although computationally demanding, all dispersion parameters were successfully estimated from the proposed multi-environment spatial individual-tree model using Bayesian techniques via Gibbs sampling. The proposed two-stage spatial MET approach produced better results than the commonly used nonspatial MET analysis.