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Spatial environmental heterogeneity are well known characteristics of field forest genetic trials, even in small experiments (&lt;1ha) established under seemingly uniform conditions and intensive site management. In such trials, it is commonly assumed that any simple type of experimental field design based on randomization theory, as a completely randomized design (CRD), should account for any of the minor site variability. However, most published results indicate that in these types of trials harbor a large component of the spatial variation which commonly resides in the error term. Here we applied a two-dimensional smoothed surface in an individual-tree mixed model, using tensor product of linear, quadratic and cubic B-spline bases with different and equal number of knots for rows and columns, to account for the environmental spatial variability in two relatively small (i.e., 576 m 2  and 5,705 m 2 ) forest genetic trials, with large multiple-tree contiguous plot configurations. In general, models accounting for site variability with a two-dimensional surface displayed a lower value of the deviance information criterion than the classical RCD. Linear B-spline bases may yield a reasonable description of the environmental variability, when a relatively small amount of information available. The mixed models fitting a smoothed surface resulted in a reduction in the posterior means of the error variance (σ 2 e ), an increase in the posterior means of the additive genetic variance (σ 2 a ) and heritability ( h 2 HT ), and an increase of 16.05% and 46.03% (for parents) or 11.86% and 44.68% (for offspring) in the accuracy of breeding values, respectively in the two experiments.

silvae genetica/silvae genetica

Two-dimensional penalized splines via Gibbs sampling to account for spatial variability in forest genetic trials with small amount of information available