Bayesian estimation of a surface to account for a spatial trend using penalized splines in an individual-tree mixed model.

EDUARDO P. CAPPA, RODOLFO J.C. CANTET

CANADIAN JOURNAL OF FOREST RESEARCH

National Research Council Research Press

Lugar: Ottawa, On.; Año: 2007 vol. 37 p. 2677 - 2688

0045-5067

Unaccounted spatial variability leads to bias in estimating genetic parameters and predicting breeding values from forest genetic trials. Previous attempts to account for large scale continuous spatial variation employed spatial coordinates in the direction of the rows (or columns). In this research, we use an individual tree mixed model and the tensor product of B-spline bases with a proper covariance structure for the random knot effects to account for spatial variability. Dispersion parameters were estimated using Bayesian techniques via the Gibbs sampling. The procedure is illustrated with data from a progeny trial of E. globulus. Four different models were used in the sequel. The first model included block effects and the three other models included a surface on a grid of either 8 × 8, 12 × 12, or 18 × 18 knots. The three models with B-splines displayed a sizeable lower value of the Deviance Information Criterion than the model with blocks. Also, the mixed models fitting a surface displayed a consistent reduction in the posterior mean of , an increase in the posterior means of and h2DBH, and an increase of 66 % (for parents) or 60% (for offspring) in the accuracy of breeding values.