Trial design and measurement
Two large progeny trials, F1146 (trial 1) and F114 (trial 2) (Chen et al. 2014), were established in 1990, in southern Sweden, with 1373 and 1375 open-pollinated families, respectively. A randomized incomplete block design with single-tree plot was used for both trials. Six healthy trees were sampled for each of 524 families representing 112 provenances. Two cores per tree were sampled at breast height from a total of 5618 trees (2973 and 2645 from trial 1 and trial 2, respectively). Details on characteristics of plant materials, soil type, climate, field design, and sampling method have been reported elsewhere (Chen et al. 2014).
One increment core from each tree was previously used for the determinations and analysis of growth and solid-wood traits from pith to bark with the SilviScan instrument at Innventia, Stockholm, Sweden (Chen et al. 2014). The first core was also used for determination of fiber-dimension traits.The second core was used for our FL determinations and data analysis, as follows. The SilviScan measurements provided data on variations from pith to bark in wood density, and RFW, TFW, FWT, and FC measured as averages for consecutive 25 μm radial intervals, as well as in MFA and MOE for 5 mm intervals (Evans 1994, 2006; Evans et al. 1995). All rings were identified and their property averages were calculated. Also, property averages for stem cross sections at the ends of each growth season were calculated, through weighting each ring value with the cross-sectional area of the ring and assuming that the ring is circular around the pith. The data for all samples have been checked for weather-induced false rings to ensure that all rings correspond to one full growth season, so that the ring number equals the cambial age.
In the investigations of age trends and “age-age” correlations (between different ring numbers from the pith), the investigated span was restricted to 3–15 years, even though ca. 30 % had more rings. These cores originate from fast-grown trees, which reached breast height at a lower age than the rest. Thus, data for ring numbers (“cambial ages”) >15 available only for the fastest-growing trees were excluded. Further, close to the pith, the rings are too curved for accurate measurement based on X-ray transmission and diffraction, and the data quality is not as good as further from the pith. Therefore, also data from rings 1–2 were excluded in the age-age correlation analysis. However, data from all the rings were used when heritabilities, genetic correlations, and genetic gains were estimated for the tree as a unit.
FL was determined from the second core for each of three randomly selected trees per family per site, 3217 trees in total. The wood of the rings 8 to 11 from pith was cut out, macerated, and analyzed with the Kajaani Fiber Lab 3.5 at the Wood Fiber Lab at SLU, Umeå, Sweden, as described elsewhere (Chen et al. 2016). In order to correct for the fiber-cutting unavoidable when sampling by wood increment cores and for sampling error (Bergqvist et al. 1997; Mörling et al. 2003), the measured FL distribution data, including large numbers of cut fibers, was mathematically converted into an estimate of the FL at the wood sampling area within the tree by applying the expectation-maximization algorithm (Chen et al. 2016; Svensson and Sjöstedt-de Luna 2010; Svensson et al. 2006). The approach was recently shown to give more accurate FL estimates than length-weighing or length2-weighing algrithms implemented in the Kajaani Fiber Lab 3.5 (Chen et al. 2016).
Statistical analysis
Variance and covariance components for genetic analyses were estimated using ASReml 3.0 (Gilmour et al. 2009) based on the following linear mixed model for joint-site analysis:
$$ {y}_{ijklm}=\mu +{S}_i+{B}_{j(i)}+{P}_k+{F}_{l(k)}+{SF}_{il(k)}+{e}_{ijklm} $$
(1)
where y
ijklm
is the observation on the mth tree from the lth family within the kth provenance in the jth block within the ith site. μ is the general mean; S
i
is the fixed effect of the ith site; B
j(i) the fixed effect of the jth block within the ith site; P
k
is the fixed effect of the kth provenance; F
l(k) is the random effect of the lth family within the kth provenance; SF
il(k) is the random interaction effect of the ith site and the lth family within the kth provenance; and e
ijklm
is the random residual effect. Based on mixed-model assumptions, the random family-within-provenance effects are ~NID(0, \( {\upsigma}_{\mathrm{f}\left(\mathrm{p}\right)}^2 \)), the random site-by-family within provenance effects are ~NID(0, \( {\upsigma}_{sf\left(\mathrm{p}\right)}^2 \)), while the random residual effects are ~NID(0, \( {\upsigma}_{\mathrm{e}}^2\Big). \) Preliminary analyses indicated that there was no significant effect for the provenance-by-site interaction for any trait, and consequently, this effect was removed in the final model. The analogous model is applied also for individual rings. Significance of the fixed effects was tested by Wald F test.
Expanding Eq. 1, a bivariate model was constructed to estimate age-age genetic correlations and type-B (between-sites) genetic correlations, and multivariate analysis was used to estimate genetic parameters for different selection scenarios.
Estimates of heritability were obtained for each trait using variance components from the univariate joint-site analysis. Approximate standard errors were calculated using the Taylor series expansion method (Gilmour et al. 2009).
The individual-tree narrow-sense heritability for each trait was estimated by
$$ {\hat{h}}_{\mathrm{i}}^2\approx \frac{4{\hat{\upsigma}}_{\mathrm{f}\left(\mathrm{p}\right)}^2}{{\hat{\upsigma}}_{\mathrm{f}\left(\mathrm{p}\right)}^2+{\hat{\upsigma}}_{sf\left(\mathrm{p}\right)}^2+{\hat{\upsigma}}_{\mathrm{e}}^2} $$
(2)
where \( {h}_{\mathrm{i}}^2 \) is the narrow-sense heritability; \( {\sigma}_{\mathrm{f}\left(\mathrm{p}\right)}^2 \) is the family-within-provenance variance;\( {\sigma}_{sf\left(\mathrm{p}\right)}^2 \) is the site-by-family-within-provenance variance; and \( {\sigma}_{\mathrm{e}}^2 \) is the residual variance.
Genotype-by-environment interaction
To evaluate the extent of gentotype-by-environment interaction (G × E) for each trait, between-site type-B genetic correlations were used (Burdon 1977), and their approximate standard errors were estimated using the Taylor series expansion method in ASReml (Gilmour et al. 2009). The type-B genetic correlation of additive effects across sites is calculated as
$$ {r_B}_{=}\frac{{\hat{Cov}}_{\left({\mathrm{a}}_1,{\ \mathrm{a}}_2\right)}}{\sqrt{{\hat{\upsigma}}_{{\mathrm{a}}_1}^2 \times {\hat{\upsigma}}_{{\mathrm{a}}_2}^2}} $$
(3)
where \( {Cov}_{\left({\mathrm{a}}_1,{\mathrm{a}}_2\right)} \) is the covariance between additive effects of the same traits in different sites and \( {\upsigma}_{{\mathrm{a}}_1}^2 \)and \( {\upsigma}_{{\mathrm{a}}_2}^2 \) are estimated additive variances for the same traits in trial 1 and trial 2, respectively (cf Falconer and Mackay 1996). A one-tailed likelihood ratio test (LRT) against the null hypothesis of genetic correlations of +1 was used to check the significant of G × E interaction (Gilmour et al. 2009).
Phenotypic and genetic correlations
Phenotypic and genetic correlations (type-A) between traits and age-age genetic correlations for individual traits were estimated as
$$ {r}_{\left(x,y\right)}=\frac{{\hat{Cov}}_{\left(x,y\right)}}{\sqrt{{\hat{\upsigma}}_{(x)}^2\times {\hat{\upsigma}}_{(y)}^2}} $$
(4)
where \( {\upsigma}_{(x)}^2 \) and \( {\upsigma}_{(y)}^2 \) are the estimated phenotypic or genetic variances for traits x and y or the same trait variances at two different ages, respectively, and Cov(x, y) is the estimated phenotypic or genetic covariance between traits x and y or between early age and reference age. For the sake of comparison, genetic correlations between traits were estimated for the mean values across rings 8–11. Correlations were also recalculated among all traits (except FL) based on cross-sectionally-weighted average values from pith to bark.
The efficiency (E) of early selection relative to reference age was calculated as
$$ {\hat{E}}_{gen}={r}_A\times \frac{i_E\times {\hat{h}}_E}{i_R\times {\hat{h}}_R} $$
(5)
where r
A
is the additive genetic correlation between early and reference ages; i
E
and i
R
are the selection intensities at the early age and reference age, respectively; and h
E
and h
R
are the square roots of individual-tree narrow-sense heritability estimates at early and reference ages (White et al. 2007). Selection intensities at early age (i
E
) and the reference age (i
R
) were assumed to be equal.
The correlated response to early selection was calculated as
$$ {\hat{CR}}_y=i{\hat{h}}_x{\hat{h}}_y{r}_A{\hat{\sigma}}_{Py} $$
(6)
where i is the selection intensity (standardized selection differential); h
x
and h
y
are the square roots of individual-tree narrow-sense heritabilities for direct-selection x trait and correlated y trait; r
A
is the estimated additive genetic correlation between traits x and y; and σ
Py
is the phenotypic standard deviation for trait y (Falconer and Mackay 1996).
To study whether there were negative effects on fiber traits when selection was based on diameter or MOE separately or based on selection indices combining growth and stiffness, we constructed selection indices based on single or multiple traits and with or without restriction on fiber traits. A total of six different selection scenarios were considered: (A) Selection based on diameter alone; (B) selection based on MOE alone; (C) selection based on diameter and MOE using an economic weight (increasing 1 GPa in MOE is 10 times as profitable as an increase of 1 mm in diameter, when average tree height is assumed to be 10 m and average diameter at breast height is 110 mm at 21 years of age; Chen et al. 2014). Economic weights for Norway spruce have not been estimated using production-system parameter estimates. Therefore, this index is mainly based on published genetic-parameter estimates for radiata pine (Ivković et al. 2006); (D) selection based on diameter, but with the restriction of no change to FL; (E) selection based on MOE, but with the restriction of no change to FL; and (F) selection based on diameter and MOE using an economic weight, but with the restriction of no change to FL (Mrode and Thompson 2005).
The index coefficients were obtained from
$$ \mathbf{b}={\mathbf{P}}^{-1}\mathbf{Ga} $$
(7)
where P is the phenotypic variance-covariance matrix for selection traits, G is the additive genetic variance-covariance matrix between selection traits and objective traits, and a is the vector of economic weights for each of objective traits (Mrode and Thompson 2005).
For a restricted selection index, Eq. 7 could be modified as
$$ {\mathbf{b}}^{*}={\left[\begin{array}{cc}{\mathbf{P}}^{*}& {\mathbf{G}}^{*}\\ {}{\mathbf{G}}^{*}\prime & 0\end{array}\right]}^{-1}\left[\begin{array}{c}{\mathbf{G}}^{\mathbf{x}}\\ {}0\end{array}\right]\left[\mathbf{v}\right] $$
(8)
where P* is the phenotypic variance-covariance matrix for selection traits, excluding the restricted trait; G* is the additive genetic variance-covariance matrix between selection traits and traits excluding restricted traits; G
X is the additive genetic variance-covariance matrix for selection traits excluding restricted traits; v is the vector of economic weights of all traits; 0 is the zero vector (Cunningham et al. 1970). Genetic gain was calculated using mass selection for a single trait. Profitability was calculated using diameter and MOE as
$$ \Pr =1{G}_d+10\ {G}_{M.} $$
where Pr is the profitability; G
d
is the genetic gain of diameter (mm); and G
M
is the genetic gain of MOE. The coefficients of 1 and 10 for G
d
and G
M
are the economic weights.