Two large progeny trials, S21F9021146 aka F1146 (trial1) and S21F9021147 aka F1147 (trial 2), were established in 1990 in southern Sweden, with 1373 and 1375 open pollinated half-sib families, respectively. A randomized incomplete block design using single-tree plot was used in both trials. Detailed descriptions about field design, soil type, and climate condition were given in the previously published paper (Chen et al. 2014). The current study is based on a subset of 524 families. Diameter at breast height (DBH) was assessed at age 12 and 21 (DBH12 and DBH21), and height was measured at age 7 (Ht7) in both trials (Table 1).
Table 1 Description of measured and calculated traits
SilviScan data
The details of sampling for increment cores, measurements of density, MFA, and MOE with SilviScan and calculations of area-weighted averages representing cross sections were shown in the paper (Chen et al. 2014). In the current work, area-weighted mean wood properties of density, MOE, and MFA for each increment cores were calculated based on all rings of the increment cores, 24 % of the cores having 15 or less rings, 65 % having 16–17 rings, and about 11 % having 18 to 19 rings. In Chen et al. (2014), however, all calculations were based on area-weighted averages for 15 rings for consistency and as the outermost rings are sometimes influenced by the sampling. This resulted in higher heritabilities of 0.52, 0.23, and 0.38 for wood density, MFA, and MOE, respectively. Our reason for including also the outermost rings in the current study was that the Pilodyn and Hitman measurements are performed from the outside of the stem.
Measurement of Pilodyn penetration depth in standing trees
Pilodyn penetration depth was measured in September 2011 at age 22 (Pilo22), using a Pilodyn 6J Forest (PROCEQ, Zurich, Switzerland) with a 2.0-mm diameter pin, without removing bark. To keep consistence, Pilodyn measurement was made at approximate 1.3 m above the ground for each tree and on the same side for all trees.
Measurement of acoustic velocity
The Hitman ST300 tool (Fiber-gen, Christchurch; New Zealand) was used to determine acoustic velocity at age 24 (AV 24), at the tree side with fewer branches. The branches of the trees below approximately 2 m were removed before the measurement. To avoid knots as much as possible, the upper probe was usually inserted just below the higher branch whorl and the lower probe was placed just above the lower whorl. All measurements were conducted within the consecutive 3 weeks from middle October and early November 2013. For each tree, 16 or 24 readings were made, and the average of the readings was used.
Estimate of dynamic acoustic MOE
In this study, Pilodyn data (Pilo22) were used as surrogate for standing tree wood density data. Based on observed high correlation between Pilodyn penetration and wood density in one previous Norway spruce studies (Costa-e-Silva et al. 2000), the dynamic MOE was estimated using the following model:
$$ {\mathrm{MOE}}_{\left({\mathrm{AV}}^2+\mathrm{Pilo}\right)}=\left(1/\mathrm{Pilo}\right)*10,000*{\mathrm{AV}}^2 $$
(2)
where Pilo is the Pilodyn penetration depth (mm) (Pilo22) and AV is the velocity of the wave through the material (km ∙ s− 1) (AV24). The inverse of Pilo was used since it is inversely correlated with wood density, but a scale parameter of 10,000 was used to adjust its value to the same scale as wood density and consequently also the prediction of wood stiffness to the typical level of MOE of wood.
For comparison, the acoustic MOE has been estimated also with use of wood density from SilviScan as follows:
$$ MO{E}_{\left(A{V}^2+D\right)}=D*A{V}^2 $$
(3)
where D is the area-weighted air-dry density (Density21) determined from the increment core sample (kg ∙ m− 3) and AV is the velocity (AV24) of the wave through the material (km ∙ s− 1). In Norway spruce, the applicability of this equation has been verified in a previous study (Haines and Leban 1997).
Statistical analyses
Variance and covariance components for genetic analyses were estimated using ASREML3.0 (Gilmour et al. 2009), and the following linear mixed model for joint-site analysis was fitted as follows:
$$ {Y}_{ijklm}=\mu +{S}_i+{B}_{j(i)}+{P}_k+S{P}_{iK}+{F}_{l(k)}+S{F}_{il(k)}+{e}_{ijklm} $$
(4)
where Y
ijklm
is the observation on the mth tree from the lth family within the kth stand (plus tree selection stand) in the jth block within the ith site, μ is the general mean, S
i
, B
j(i), P
k
, and SP
iK
are the fixed effects of the ith site, the jth block within the ith site, and the kth stand, the ith site by the kth stand interaction, respectively, F
l(k) and SF
il(k) are the random effects of the lth family within the kth stand and the random interactive effect of the ith site and the lth family within the kth stand, respectively, and e
ijklm
is the random residual effect. The effect will be dropped if it is not significant.
Estimates of heritability were obtained for each trait using variance components from the univariate joint-site analysis. Standard errors were estimated by using the Taylor series expansion method (Gilmour et al. 2009).
The individual-tree narrow-sense heritability for each trait was estimated by
$$ {\widehat{\mathrm{h}}}_{\mathrm{i}}^2=\frac{{\widehat{\upsigma}}_{\mathrm{A}}^2}{\widehat{{\widehat{\sigma}}_{\mathrm{p}}^2}}=\frac{4\times {\widehat{\sigma}}_{\mathrm{f}}^2}{{\widehat{\sigma}}_{\mathrm{f}}^2+{\widehat{\sigma}}_{\mathrm{f}\mathrm{s}}^2+{\widehat{\sigma}}_{\mathrm{e}}^2} $$
(5)
where ĥ
2i
, \( {\widehat{\sigma}}_{\mathrm{A}}^2 \), \( {\widehat{\sigma}}_{\mathrm{f}}^2 \), \( {\widehat{\sigma}}_{\mathrm{fs}}^2 \), \( {\widehat{\sigma}}_{\mathrm{e}}^2 \), and \( {\widehat{\sigma}}_{\mathrm{p}}^2 \) are the narrow-sense heritability and additive genetic, family within stand, family within stand by site, residual, and phenotypic variance components, respectively.
Phenotypic and genetic correlations between traits were calculated as
$$ {r}_{\left(x,y\right)}=\frac{{\widehat{\sigma}}_{\left(x,y\right)}}{\sqrt{{\widehat{\sigma}}_{(x)}^2\times {\widehat{\sigma}}_{(y)}^2}} $$
(6)
where \( {\widehat{\sigma}}_{\left(\mathrm{x}\right)}^2 \) and \( {\widehat{\sigma}}_{\left(\mathrm{y}\right)}^2 \) are the estimated phenotypic or genetic variances for traits x and y, respectively, \( {\widehat{\sigma}}_{\left(\mathrm{x},\mathrm{y}\right)} \) is the estimated phenotypic or genetic covariance between traits x and y.
Genetic gain (G
A
) was calculated using a selection intensity of 1 % (i = 2.67):
$$ {G}_A=i\times C{V}_p\times {h}_i^2 $$
(7)
where CVp is the coefficient of variation of phenotypic effect (calculated as the phenotypic standard deviation divided by the mean of a specific trait) and h
2
i
is the individual heritability.
The efficiency of selection for one trait on another trait was estimated as
$$ {E}_{ind}={r}_{A\left(x,y\right)}\times \frac{h_x}{h_y} $$
(8)
where r
(x,y) is the additive genetic correlation between trait x on which selection is made (indirect) and trait y on which the effect is evaluated (direct), and h
x
and h
y
are the square roots of individual-tree narrow-sense heritability of these two traits (White et al. 2007).