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

E. P. Cappa 1 , M. Lstiburek 2 , A. D. Yanchuk 3 , 4 ,  und Y. A. El-Kassaby 4
  • 1 Instituto Nacional de Tecnología Agropecuaria (INTA), Instituto de Recursos Biológicos, 1686, Buenos Aires, Argentina
  • 2 Department of Dendrology and Forest Tree Breeding, Faculty of Forestry and Wood Sciences, Czech University of Life Sciences Prague, 165 21, Praha
  • 3 British Columbia Forest Service, Tree Improvement Branch, V8W 9C2, Victoria, Canada
  • 4 Department of Forest Sciences, Faculty of Forestry, University of British Columbia, V6T 1Z4, Canada

Abstract

Spatial environmental heterogeneity are well known characteristics of field forest genetic trials, even in small experiments (<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 m2 and 5,705 m2) 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 (σ2e), an increase in the posterior means of the additive genetic variance (σ2a) and heritability (h2HT), 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.

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