Genetic Parameter Estimates and Genotype × Environment Interactions of Growth and Quality Traits for Betula alnoides Buch.-Ham. ex D. Don in Four Provenance-family Trials in Southern China

: Betula alnoides is a valuable timber species with wide ecological adaptability in Southeast Asia and southern China. There are more than 150,000 ha of B. alnoides plantations in China until now. However, heavy di ﬀ erentiation in growth and quality traits with low productivity are usually seen in the practice. Elite germplasm are thus urgently needed for this species. Here growth and quality traits for 199 families of 25 provenances were assessed at four sites when 10–15 years old to estimate genetic parameters and reveal genotype by environment (G × E) interaction, and screen out superior provenances and families for plantation forestry of B. alnoides . The growth and quality performances of provenances varied with sites. Signiﬁcant site, provenance, family and provenance-site e ﬀ ects were revealed for most growth and quality traits, while signiﬁcant family-site e ﬀ ects were only observed in crown width (CW) and crown shape (CS), inferring that there existed signiﬁcant G × E interaction. The provenance repeatability ( h 2 p ) and family heritability ( h 2 f ) of all tested traits ranged from 0.026 to 0.636 and 0.148 to 0.578, respectively. Stem volume showed the highest genetic and phenotypic coe ﬃ cients of variation (GCV, PCV) among all traits at each site. The diameter at breast height (DBH), tree height (H), height to live crown base (HCB) and CW were strongly correlated with other traits, and were also under relatively higher genetic control and had stronger discriminating ability on genotype di ﬀ erences. Through biplot analyses of main genotypic e ﬀ ect and G × E interaction (GGE) for these traits, ﬁve provenances and 20 families were screened out with selection ratio of 20 % and 10% at provenance and family level, respectively. The genetic and realized gains at provenance level ranged from 0.25% to 2.01% and 2.43% to 14.84%, and those at family level ranged from 0.85% to 21.22% and 5.76% to 36.71%, respectively. The ﬁndings lay a foundation for subsequent study on genetic improvement and breeding of this species, and application of the superior provenances and families will greatly increase the productivity of its plantations in practice.


Introduction
Betula alnoides Buch.-Ham. ex D. Don is a multiple-ploidy tree species in the genus Betula, family Betulaceae, and is indigenous to the warm subtropical and tropical regions in Southeast Asia and southern China [1]. B. alnoides is a fast-growing valuable tree species, its wood is widely used for floor and furniture-making as well as house decoration due to its beautiful texture, middle density, and excellent processing characteristics [2], and its barks are of medicinal application due to their families of all 25 provenances were involved, respectively. Only 199 half-sib families of 25 provenances existed in all four trials and were mainly analyzed in the present study. All the germplasms were collected from Yunnan and Guangxi, China. Table 1 shows the information of the four trials, and Table A1 shows the localities of 25 provenances. Randomized complete block design was used in each trial with single tree plots and 12 to 19 replicates. The seedlings were planted with 2 m × 3 m spacing.

Measurement of Tree Growth and Quality traits
Stem diameter at breast height (DBH) was measured using diameter tape with a precision of 0.1cm, tree height and height to live crown base (HCB) were measured using Vertex IV Altimeter (Haglöf Sweden AB, Västernorrland, Sverige) with a precision of 0.1 m, and crown width (CW) was measured using sliding staff with a precision of 0.1m. Stem volume (VOL) was calculated with the following equation [20]: where D 1. 3 and H were stem diameter at breast height (DBH) and tree height, respectively. Quality traits including stem form (SF), crown shape (CS) and branchiness (BRA) were evaluated and standardized according to Wang et al. [21].

Statistical Models and Genetic Analysis
Variance analyses (ANOVA) and Duncan's multiple range tests were performed to estimate the variance of traits using univariate restricted maximum likelihood (REML) model in the Genstat 18th software. The following linear mixed models were used for individual site analysis (2) and multi-site analysis (3) at provenance level, respectively [22,23]: (2) y ijkl = µ + S i + B(S) ij + P k + PS ik + PB(S) ijk + PYS ikl + PYB(S) ijkl + e ijklm (3) where y is the observations of traits, µ is the overall mean, S and B(S) are the fixed effects of site and block within site, P, PS, PB(S), PYS and PYB(S) are the random effects of provenance, and provenance-site, provenance-block within site, provenance-year-site, provenance-year-block within site interactions, respectively, and e is residual error. The fixed effects of year and site-year and year-block within site interactions and the random effects of provenance-year interaction were excluded from the models (3) due to non-significant difference. Provenance repeatability (h 2 p ) and variance components of phenotypic (σ 2 ph ) in individual and joint site analyses were estimated using Equations (4) and (6) as well as (5) and (7), respectively. Phenotypic coefficient of variation (PCV, %) and genetic coefficient of variation (GCV, %) were calculated with Equations (8) and (9), respectively [24]: σ 2 ph = σ 2 p + σ 2 ps + σ 2 pb + σ 2 pys + σ 2 pyb + σ 2 e (7) where σ 2 p , σ 2 ps , σ 2 pb ,σ 2 pys , σ 2 pyb , σ 2 e , X are the estimates of variance components for provenance, and provenance-site, provenance-block within site, provenance-year-site and provenance-year-block within site interactions, residual error and mean of traits; and n s , n y , n b are the number of sites, year and the harmonic mean of blocks within sites.
Family models for individual site analysis (10) and multiple sites joint analysis (11) were listed in the following [22,23]: y ijk = µ + B i + P j + PB ij + F(P) jk + F(P)B ijk + e ijkl (10) y ijk = µ + S i + B(S) ij + P k + PS ik + PB(S) ijk + PYS ikl + PYB(S) ijkl + F(P) km + F(P)Y klm + F(P)YS iklm + F(P)YB(S) ijklm + e ijklmn, (11) where y is the observations of traits; µ is the overall mean; S and B(S) are the fixed effects of site and block within site; P, F(P), PS, PB(S) and F(P)S are the random effects of provenance, family, and provenance-site, provenance-block within site and family-site interactions, respectively; F(P)B(S), PYS, PYB(S), F(P)YS and F(P)YB(S) are the random effects of family-block within site, provenance-year-site, provenance-year-block within site, family-year-site and family-year-block within site interactions; and e is residual error. The fixed effects of year, and site-year and year-block within site interactions as well as the random effects of provenance-year, family-site and family-block within site interactions were excluded from the models due to non-significant difference.
Family heritability (h 2 f ) in individual site and multi-site analysis were estimated with the following Equations (12) and (13), respectively [24]: where σ 2 f , σ 2 f y , σ 2 f ys , σ 2 f yb , σ 2 e are variance components of family, and family-year, family-year-site and family-year-block within site interactions, and residual error of trait, respectively; and n s , n y , n b are the number of sites, year and the harmonic mean of blocks within sites. Genetic correlations (r G ) among traits were calculated using the Equation (14) [25]: (14) where Cov G (x, y) is the genotypic co-variances between trait x and y; σ 2 G (x) and σ 2 G (y) are the genotypic variances of trait x and y.
The breeding values of provenances and families were estimated using the method of best linear unbiased prediction (BLUP), and were then used in biplot analysis for main genotypic effects and G × E interaction (GGE) by Genstat 18th software [26]. As described in detail, the breeding values of 25 provenances or 199 families in four sites could be displayed by a rank-two matrix. After the main environmental effects were removed through ANOVA, the main genotypic effect (G) and interaction effect (G × E) were retained in the new matrix. The matrix was then decomposed into its component matrices using the method of singular-value decomposition. The first two principal components (PC1 and PC2) that explained about 85% of the total variation were used to build the biplot [27].
The superiority of provenances and families could be intuitively seen in the biplot graph according to their position in concentric circles, smaller concentric circle referred to better superiority. The superiority could also be ranked by superiority coefficients, smaller coefficients represented better superiority [12]. Based on the ranks of superiority, the desired provenances were then selected with the ratio being 20%, and the excellent families were done with the ratio being 10% regardless of provenances.
Genetic gains (∆G) and realized gains (∆G r )were calculated as follows [25]: where i is selection intensity (the selection rate is 20% and 10% at levels of provenance and family, respectively); h 2 i is heritability of trait; √ σ 2 is standard deviation; x is mean of traits for selected provenances or families; and X is mean of traits for all provenances or families. Table 2 showed the means and ranges of growth and quality traits in each of the four trials. The trees at Mengla site showed the highest levels in the mean annual increment of tree height (MAH), crown width (CW) and branchiness (BRA), which indicated that Mengla was the most suitable for B. alnoids among the four sites. The mean annual increment of diameter at breast height (MABDH), mean annual increment of tree height (MAH), rate of height to live crown base to tree height (HCB·Height −1) , CW and mean annual increment of stem volume (MAVOL) were the lowest at Changning site. The trees at Hua'an site had the highest MADBH and MAVOL, but had the lowest stem form (SF) and BRA. Performance of growth and quality traits of 25 provenances were shown in Table 3, which were presented as means of all four sites for each trait. Significant differences were observed in all traits among provenances. MADBH, MAH, CW and MAVOL of provenance A were nearly the lowest in all 25 provenances, but its SF and BRA were the highest. The highest MAH and CW were observed in provenance P.

Variation of Growth and Quality Traits among Sites and Provenances
The growth and quality performance of 25 provenances differed among four sites (see Tables A2-A5). The lowest MAH, SF, CS, and BRA were observed in provenance O at the Mengla site. MADBH, MAH, MAVOL showed the best performance in provenance V, while the poorest in provenance L at Pingxiang site. At Hua'an and Changning sites, the highest MADBH and MAVOL were seen in provenance P, and the lowest MAH, MAVOL and SF in provenance S.

Genetic Variance, Heritability, and Genotypic Correlation
It was shown from the estimation of variances and genetic parameters for all tested traits at each site ( Table 4) that provenance effects were significant in most of the traits at four sites except SF and BRA at Pingxiang site as well as CS and BRA at Changning site. While significant family effects were mainly observed in growth traits at Mengla and Pingxiang sites. As a whole, the highest provenance repeatability (h 2 p ) of all tested traits were observed at Hua'an site (mean: 0.332), and the highest family heritability (h 2 f ) at Mengla site (mean: 0.164). The genetic (GCV) and phenotypic (PCV) coefficient for variation of all traits at Hua'an site ranged from 3.15% to 15.93% and 20.30% to 70.44%, with their means (9.83% and 44.21%) being the highest in four sites. Volume and quality traits showed higher PCV than most of the other growth traits at each site.
The variances of sources, variance components, and genetic parameters were estimated at four sites together. Significant differences were observed only in CW and CS for family-site interaction, while for other sources of variances, significant differences were seen in most of the traits (Table 5). h 2 p and h 2 f of all traits ranged from 0.026 to 0.636 and 0.148 to 0.578, respectively (Table 6). h 2 p of HCB, SF and BRA showed higher levels than that of other traits. h 2 f of growth, traits were higher than that of quality traits. GCV and PCV of variation ranged from 0.58% to 5.99% and 21.09% to 66.78%, respectively. On the whole, GCV and PCV for quality traits were higher than those for most growth traits.
The genotypic correlation coefficients among all sorts of traits were shown in Table 7. There were moderate to strong positive genotypic correlations between DBH, height, and volume. Strong positive genotypic correlations were observed between SF, HCB, and BRA, while strong negative correlations were seen between these traits and CW.  Notes: DBH, diameter at breast height; HCB, height to live crown base; CW, crown width; SF, stem form; CS, crown shape; BRA, branchiness. Features in parentheses were standard errors. *** P < 0.001; ** 0.001 < P < 0.01; * 0.01 < P < 0.05; ns indicates not significant, level of significance of effects. NE, not estimated and assumed to be zero.
ph ) for provenance, provenance-site, provenance-block within site, provenance-year-site, provenance-year-block within site, family, family-year, family-year-site, family-year-block within site, residual error and phenotypic variance, provenance repeatability (h 2 p ), family heritability (h 2 f ), coefficient of variation at genetic and phenotypic level (GCV, PCV) for various traits in combined analysis of four sites. Notes: DBH, diameter at breast height; HCB, height to live crown base; CW, crown width; SF, stem form; CS, crown shape; BRA, branchiness. The variance analysis at provenance level was estimated in all four sites, while that at family level was estimated in Mengla, Pingxiang and Huanan sites, and the values shown in parentheses were standard errors.. *** P < 0.001; ** 0.001 < P < 0.01; * 0.01 < P < 0.05, level of significance of effects. NE, not estimated and assumed to be zero.

Genotype by Environment (G ×E) Interaction
Provenance-site interactions were significant for all traits except SF, while family-site interaction was significant only for CW and CS (Table 5). There were significantly positive genetic correlations between DBH, Volume, CW and CS as well as between HCB, BRA and SF (Table 7). In addition, it was indicated from Figures 5 and 6 that abilities of DBH, HCB, height, and CW to discriminate provenances and families were stronger than those of other traits. DBH, HCB, and height were thus used to estimate provenance-site interactions by biplot analysis for main genotypic effects and GGE based on the predicted breeding values, and CW was used to estimate the family-site interactions. In the bioplot of GGE, the cosine of the angle between the two environment segments indicated their correlations. Figure 1a showed the biplot of DBH for 25 provenances. There were sharp angles between segments of Changning, Hua'an and Pingxiang sites indicating positive correlations between them. Environment vector represented as an arrow vector joining center and co-ordinates of tested environment, its length indicated the discriminating ability on genotypic differences. Pingxiang showed the most discriminating ability for DBH in the present study. The biplot was divided into eight sectors in polygon view with provenances U, R, P, B, L, C, A and S as the vertexes. Vertex genotypes contributed overall most variation and demonstrated the best performance in each sector. From Figure 1a, it could be deduced that provenances L, B, and K were possible candidates for Mengla, and R and V for Pingxiang and Hua'an, and P for Changning based on DBH. In Figure 1b, the average environment axis (AEA) represented as an arrow vector joining the center and average coordinates of the tested site. Changning site was found to be the most representative environment for the growth of DBH as it has a smaller angle with AEA. The direction of AEA was the trend of the approximate mean for trait in all sites, it could be seen that provenance P showed the highest DBH, followed by W, R, V and Y, and the lowest DBH was observed in A and S. More variations in all four sites were observed in provenances L and U as it has longer perpendicular lines between their co-ordinates and AEX, and little variations for DBH were observed in provenances I, T and Y.  Figure 2a showed the biplot for height, it was indicated that Changning and Hua'an had similar and higher environmental representativeness, and Pingxiang showed a higher ability to discriminate genotypic differences for tree height. Provenances L, C, and H were possible candidates for Mengla, and P for Changning and Hua'an, and V for Pingxiang based on height. Figure 2b showed that height of provenance P was the highest, followed by G, Y, R, I and K, and the lowest height was observed in provenances S and X. Little variations for height were observed in provenances G, I and P, and more variations were observed in L and V.  and P for Changning and Hua'an, and V for Pingxiang based on height. Figure 2b showed that height of provenance P was the highest, followed by G, Y, R, I and K, and the lowest height was observed in provenances S and X. Little variations for height were observed in provenances G, I and P, and more variations were observed in L and V. Figure 3a showed the biplot of HCB for 25 provenances. Provenance C, L, and F were possible candidates for Mengla and Hua'an, and M, G, J and K for Changning and Pingxiang based on HCB. It was indicated from Figure 3b that Changning and Hua'an had similar and higher environmental representativeness, and Mengla showed higher discriminating ability on genotypic differences. HCB of provenance M was the highest, followed by C, G, J, and K, and the lowest HCB was observed in provenance X. Little variations for height were observed in provenances N, S, L and G, and more variations in C and Y.  Figure 2a showed the biplot for height, it was indicated that Changning and Hua'an had similar and higher environmental representativeness, and Pingxiang showed a higher ability to discriminate genotypic differences for tree height. Provenances L, C, and H were possible candidates for Mengla, and P for Changning and Hua'an, and V for Pingxiang based on height. Figure 2b showed that height of provenance P was the highest, followed by G, Y, R, I and K, and the lowest height was observed in provenances S and X. Little variations for height were observed in provenances G, I and P, and more variations were observed in L and V.    Figure 3b that Changning and Hua'an had similar and higher environmental representativeness, and Mengla showed higher discriminating ability on genotypic differences. HCB of provenance M was the highest, followed by C, G, J, and K, and the lowest HCB was observed in provenance X. Little variations for height were observed in provenances N, S, L and G, and more variations in C and Y.  Figure 4a showed the biplot of CW for 199 families. Families K08, P12, and W04 were possible candidates for Mengla, and R04, N20 and H18 for Pingxiang, Hua'an and Changning based on CW. From Figure 4b it was indicated that Changning and Hua'an had similar and higher environmental  Figure 4a showed the biplot of CW for 199 families. Families K08, P12, and W04 were possible candidates for Mengla, and R04, N20 and H18 for Pingxiang, Hua'an and Changning based on CW. From Figure 4b it was indicated that Changning and Hua'an had similar and higher environmental representativeness, and Mengla and Pingxaing showed higher discriminating ability on genotypic differences. Family R04 was the highest, followed by N20, H18, and W04, and the lowest CW was observed in C03. Little variations for CW were observed in families C03, K07 and Q04, and more variations in Y01, L19 and A04.

Superiority Rank and Selection for Provenances and Families
The GGE biplot of which-won-where view at provenance level was presented in Figure 5a. The provenances were divided into seven sectors, P and R were possible candidates for DBH, CW, CS, height and volume, and G and K were for HCB, BRA, and SF. In mean and stability view for trait performances of provenances ( Figure 5B), DBH had the highest environmental representativeness, and height showed higher discriminating ability on genotypic differences. Provenances H, Y and L had little variations for traits, and more variations were seen in provenances X, C, and M. Additionally, provenance P performed the best for all traits, followed by Y and W, the poorest performances were observed in X and S. To rank the provenances based on their position in concentric circles, P was the most desirable provenance to be selected based on overall traits as it was located on the smallest concentric circle, follow by provenances Y, W, K, and R.

Superiority Rank and Selection for Provenances and Families
The GGE biplot of which-won-where view at provenance level was presented in Figure 5a. The provenances were divided into seven sectors, P and R were possible candidates for DBH, CW, CS, height and volume, and G and K were for HCB, BRA, and SF. In mean and stability view for trait performances of provenances (Figure 5b), DBH had the highest environmental representativeness, and height showed higher discriminating ability on genotypic differences. Provenances H, Y and L had little variations for traits, and more variations were seen in provenances X, C, and M. Additionally, provenance P performed the best for all traits, followed by Y and W, the poorest performances were observed in X and S. To rank the provenances based on their position in concentric circles, P was the most desirable provenance to be selected based on overall traits as it was located on the smallest concentric circle, follow by provenances Y, W, K, and R. Figure 6a showed the GGE biplot at family level, families P12, P04 and Y09 were possible candidates for DBH, height, Volume, CW, and CS, and H08, A06, and G11 were possible candidates for HCB, BRA, and SF. Ranking the families in Figure 6b, P12 was the most desirable family to be selected based on overall traits. Y09, W03, D01, and U06 were also desirable families. To rank the provenances and families based on their superiority and stability, excellent provenances and families were then screened out with a selection rate of 20% and 10%, respectively. The means and realized gains of traits were presented in Table 8. It was inferred that not every trait could be positively selected. For example, the genetic and realized gains of HCB·height −1 were negative, while HCB, height, and crown width showed positive genetic and realized gains. These meant longer clear-wood and frondent crown, which were targets of selection in the present study. The genetic and realized gains of all traits except provenances were divided into seven sectors, P and R were possible candidates for DBH, CW, CS, height and volume, and G and K were for HCB, BRA, and SF. In mean and stability view for trait performances of provenances ( Figure 5B), DBH had the highest environmental representativeness, and height showed higher discriminating ability on genotypic differences. Provenances H, Y and L had little variations for traits, and more variations were seen in provenances X, C, and M. Additionally, provenance P performed the best for all traits, followed by Y and W, the poorest performances were observed in X and S. To rank the provenances based on their position in concentric circles, P was the most desirable provenance to be selected based on overall traits as it was located on the smallest concentric circle, follow by provenances Y, W, K, and R.   Figure 6a showed the GGE biplot at family level, families P12, P04 and Y09 were possible candidates for DBH, height, Volume, CW, and CS, and H08, A06, and G11 were possible candidates for HCB, BRA, and SF. Ranking the families in Figure 6b, P12 was the most desirable family to be selected based on overall traits. Y09, W03, D01, and U06 were also desirable families. To rank the provenances and families based on their superiority and stability, excellent provenances and families were then screened out with a selection rate of 20% and 10%, respectively. The means and realized gains of traits were presented in Table 8. It was inferred that not every trait could be positively selected. For example, the genetic and realized gains of HCB·height −1 were negative, while HCB, height, and crown width showed positive genetic and realized gains. These meant longer clear-wood and frondent crown, which were targets of selection in the present study. The genetic and realized gains of all traits except HCB·height −1 ranged from 0.25% to 2.01% and 2.43% to 14.84% at provenance level, and from 0.85% to 21.22% and 5.76% to 36.71% at family level, respectively.

Discussion
Significant variances were observed for most growth and quality traits at levels of provenance and family, which showed good potential for elite germplasm selection of B. alnoides. The performances of growth traits were usually observed not consistent with those of quality traits for the same provenance. For example, the mean annual increment of diameter at breast height (MADBH), crown width (CW), height and volume were the lowest but stem form (SF) and branchiness (BRA) were the highest in provenance A. This discrepancy was also observed in other tree species like Pinus radiate [28], which make it difficult to take equally both growth and quality traits into consideration for selection of elite germplasms. A trade-off between growth and quality traits should thus be done according to the objective in the breeding program of B. alnoides.
Growth and quality traits of trees are mainly impacted by genotype, but also environment condition and physiological age [23]. Significant site effects were observed for all growth and quality traits tested except crown shape in the present study, indicating that B. alnoides trees had high phenotypic plasticity in these traits. Based on biplot analysis of GGE, Mengla and Pingxiang showed high discriminating ability of height, diameter at breast height (DBH), height to live crown base (HCB) and CW on genotypic differences, and similar environmental representativeness of Hua'an and Changning were observed in height, DBH, HCB and CW traits. Site effects reflect the comprehensive reactions of trees to edaphic status, local and regional climatic conditions, etc. [29]. In the present study, the growth performance did not show an obvious trend with such a large range of altitude (275-1250 m), this is closely dependent on geomorphic features in southern China. But anyhow, mean annual air temperature and rainfall may play important roles in growth performance and showed less difference among four trial sites ( Table 1). The relatively poor growth performance of B. alnoides at Changning site may partially be attributed to its shallow soil thickness and low rainfall compared to other sites.
The growth and quality traits varied among provenances and trial sites, which usually could be interpreted from the significant provenance-site interaction [30]. In the previous studies, there existed significant interactions between genotype and environment in tree height, DBH and stem volume for Larix kaempferi (Lamb.) Carriére [25] and in SF for Pinus radiate [28]. In the present study, significant provenance-site and provenance-block within site interactions were observed in most growth and quality traits based on combined variance analysis, demonstrating strong interactions between environment and provenance. While significant family-site interactions were seen only in CW and crown shape (CS). These inferred that the provenance-site interactions were more significant than family-site ones, this was consistent with the study on DBH and SF for Psuedotsuga menziesii (Mirb.) Franco [31].
G × E interaction will usually reduce the genetic gain by reducing the heritability at multi-site trials [12], while there was no significant decline in the heritability of most traits in the present study, which was a foundation for enough genetic gains obtained through selection. Selecting superior and stable for application at different sites was an efficient strategy for dealing with its significant G × E effects, and was also the main breeding program for B. alnoids. The tested traits showed low-to-moderate heritability in multi-site genetic analysis. The estimates of provenance repeatability for SF, BRA, and HCB were higher than those for other traits, this was in accordance with many previous studies such as the high provenance repeatability of stem straightness and branch traits for Pinus radiate [32]. While the estimates of family heritability for growth traits were higher than those for quality traits in the present study. Growth traits were also under more substantial genetic control than quality traits at family levels in the study of Pinus elliottii Engelm., which might be caused by a strong environment effect [23].
The phenotypic and genetic coefficient of variation (GCV, PCV) of volume and DBH were higher than those of height at each site, which indicated that volume and DBH were more sensitive to environmental influence than tree height. This was consistent with the studies on Populus deltoides Bartr. ex Marsh. [33]. The PCV of stem volume and quality traits were higher than other growth traits in both multi-site and single-site analysis, which indicated that G × E interaction of quality traits was stronger than that of most growth traits, and this was consistent with the above-mentioned result that growth traits were under stronger genetic control than quality traits. It was inferred that more genetic gains in terms of quality can be expected from selection at provenance level, and more genetic gains in terms of growth traits like volume can be expected from selection at family level for B. alnoides.
Significant correlations among traits indicated that growth and quality traits were not independent for B. alnoides. Moderate to strong positive genotypic correlations among DBH, height, and volume were observed. The correlations between DBH and volume were higher than those between height and volume, which showed the importance of DBH in selection for high stem volume [34]. The correlations between height with CW, SF and CS were not significant in the present study, while the previous study on clonal selection (3.5 years old unclosed forest) of Betula alnoides × Betula. luminifera H. Winkler hybrids showed that CW, SF, CS, and BRA were significantly correlated to height [21]. This difference could also be interpreted from the unstable growth performance and correlations between traits in the young plantations [20]. As stem volume and SF are the most concerned in plantation forestry of B. alnoides.
SF showed the highest while volume showed the lowest for provenance repeatability, indicating that genetic gain of SF was higher than that of volume in the selection for single trait. DBH, height, and HCB showed strong discriminating ability on provenance differences according to biplot analysis for GGE and were of moderate to strong genotypic correlations with most other traits. These inferred that it was possible to simplify the selected traits to DBH, HCB, and SF, and obtain good provenances with multi-trait. As to the family level, all growth traits had higher family heritabilities than quality traits. In particular, DBH, height, and HCB showed strong discriminating ability on family differences according to biplot analysis for GGE. In addition, moderate to strong cor relations usually existed between growth and quality traits. These inferred that it was possible to simplify the selected traits to volume, DBH, height, and HCB, and obtain good families with multi-trait.
As to methods for the analysis of G × E interaction and selection for excellent germplasms, variance analysis, principal coordinates analysis, and factor analysis as well as index selection and combined selection were widely used in the breeding process of trees [12,35,36]. However, these methods were usually applied to the analysis with a single site, population with simple genetic structure and non-visual form. The BLUP breeding value can be estimated for multi-trait in multi-site based on linear mixed models. Biplot analysis method can show the main genotypic effect (G) and interaction effect (G × E) of multi-site, and both superiority and stability of genotypes and the discriminating ability of traits can be visualized in biplot analysis for GGE according to the BLUP breeding value [26,36]. The present study also showed that the combination of BLUP breeding value and GGE biplot analysis is an appropriate method of multi-site selection for multiple traits.
For selection strategies in the present study, the desired provenances and families have been selected separately from provenances and families regardless of provenances. These germplasm can be applied in the practice. However, the trials were established with a single tree plot so as to evaluate more families. In the further study, multiple trees of a family will be arranged in each plot to reduce the environmental effect and improve the estimation of heritability and realized genetic gains, and these selected families and new families from the natural populations of the desired provenances will be involved in the progeny trials [37,38]. More superior families and individuals in families will thus be screened out for plantation forestry of B. alnoides.

Conclusions
Based on the combined analysis on growth and quality traits of 199 families of 25 provenances of B. alnoides at four sites when 10-15 years old, the genetic variance, heritability, correlation, and G × E interaction were estimated and the provenances and families were ranked. The results showed that there existed a remarkable site, provenance, family, and provenance-site effects for tested traits, indicating the significance of G × E interaction. The provenance repeatability of HCB, SF, and BRA showed higher levels than that of other traits. Growth traits were under moderate and relatively higher genetic control rather than quality traits based on family heritabilities. The DBH, height, HCB, and CW were under relatively higher genetic control, had a stronger discriminating ability on genotype differences, and were also strongly correlated with other traits, they should be paid more attention to in the multi-trait selection. The superior and stable provenances and families selected by GGE biplot analysis should be applied in the practice of B. alnoides plantation forestry.       MAH, mean annual increment of tree height; HCB·Height −1 , rate of height to live crown base to tree height; CW, crown width; MAVOL, mean annual increment of stem volume; SF, stem form; CS, crown shape; BRA, branchiness. Means with standard error in parenthesis were of significant difference at 0.05 level according to Duncan's multiple range tests if followed by wholly different small letters in the same row.