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: impact of chamber disturbance, spatial variability and seasonal evolution. Global Change Biology 6: 907–917. DOI 10.1046/j.1365-2486.2000.00369.x. Matuszkiewicz J.M. 1995. Potencjalna roślinność naturalna Polski. Mapa przeglądowa 1:300 000. Arkusz 8: Wzniesienia Południowomazowieckie i Wyżyna Środkowomałopolska. Polska Akademia Nauk. Warszawa Moncrieff J.B., Fang C. 1999. A model for soil CO 2 production and transport 2: Application to a Florida Pinus elliotte plantation. Agricultural and Forest Meteorology 95: 237–256. DOI 10.1016/S0168

Assessment and Management of Risk for Engineered Systems and Geohazards, DOI: 10.1080/17499518.2013.871189. [14] L umb P., The variability of natural soils , Canadian Geotechnical Journal, 1966, 3(2), 74–97. [15] L umb P., Safety factors and the probability distributions of soil strength , Canadian Geotechnical Journal, 1970, 7(3), 225–242. [16] L umb P., Spatial variability of soil properties , Proc. 2nd Int. Conf. on Appl. of Statistics and Probability in Soil and Struct. Eng. (ICASP) Aachen, 1975, Vol. II, 397–422. [17] P uła W., Zastosowanie teorii

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 (σ2 e), an increase in the posterior means of the additive genetic variance (σ2 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.

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