The study selected four trial sites located in the primary plantation regions of Fujian Province, China: Zhangpu Zhongxi State-owned Forest Farm (ZX), Quanzhou Luoxi State-owned Forest Farm (LX), Nan’an Luoshan State-owned Forest Farm (LS), and Nanping Xiqin Teaching Forest Farm (XQ). These sites were chosen to represent the diverse ecological conditions, including variations in topography and microclimate, typical for Acacia melanoxylon cultivation in southern China. Detailed site conditions, including geographic coordinates, elevation range, soil type, and key climate parameters, are provided in Table 1.

The regional trial involved 47 Acacia melanoxylon families. Families 1 through 17 were derived from seed material collected in 2018 from superior individual trees in Australia (Table 2). Families 18 to 47 originated from a primary clonal seed orchard of A. melanoxylon at Luoxi State-owned Forest Farm, located in Quanzhou City, Fujian Province. This orchard was established by grafting preselected elite trees. Seeds were collected in 2018, germinated at the Zhangpu Zhongxi Forest Farm nursery in the same year, and planted in 2019 across four trial sites in Fujian Province.

The experimental forest uniformly adopts a random complete block design (RCB), setting up 3, 4, 7, and 7 replicates (blocks) respectively in XQ, LS, ZX and LX. Each plot consisted of three trees arranged in a single column (1 row × 3 trees) with spacing of 2 × 3 m. Annual surveys were conducted in the experimental plantation. Diameter at breast height (DBH) was measured at 1.3 meters above ground level using a diameter tape, with an accuracy of 0.1 cm. Tree height was measured using an ultrasonic hypsometer, precise to 0.1 m. The growth data for DBH and tree height from 5-year-old Acacia melanoxylon used in this study consisted of individual tree measurements.

The statistical analysis followed an integrated BLUP-GGE biplot framework to ensure accurate genetic parameter estimation and intuitive visualization. The process began with the estimation of breeding values using a mixed linear model fitted with the lmer() function from the R lme4 package (Gao et al., 2025). The model was specified as follows:

Where X_ijkl represents the observed DBH or tree height of the k-th family in the j-th block at the i-th location (Yuan et al., 2022), μ is the overall mean, L_i is the fixed effect of location, B_j(L_i) is the random block effect nested within location, F_k is the random family effect, L_i×F_k is the random family-by-location interaction effect, and e_ijkl is the residual error.

The model was fitted using the Restricted Maximum Likelihood (REML) algorithm, and the Best Linear Unbiased Predictions (BLUPs) for each family were extracted as the estimated breeding values. Prior to further analysis, the model’s adequacy was rigorously validated; the normality of residuals was assessed using a Q-Q plot, and the assumption of homoscedasticity was verified by plotting residuals against fitted values, with no substantial violations observed. In addition, significance testing for the fixed and random effects in the model was performed using the anova() and ranova() functions from the lmerTest package.

Finally, the validated BLUP values were used as inputs to generate GGE biplots using the GGEBiplotGUI package. The following parameter settings were selected based on the study’s objective to effectively visualize the genetic (G) and genotype-by-environment (GE) interaction patterns: Scaled = 0 (no standardization), Centering = ‘G+GE’ (focused on the GGE model), and singular value partitioning (SVP) = ‘JK’ (symmetric scaling focused on genotype discrimination) (Li et al., 2022).

The output of the mixed model operation displayed “REML criterion at convergence: []”, indicating successful model convergence. This was further verified by the message “Convergence achieved (0)”, confirming convergence. The mixed model residuals satisfied the assumptions of normality (Figure 1) and homoscedasticity (Figure 2). Furthermore, the DBH model demonstrated better performance compared to the tree height model.

Significance testing for fixed effects in the mixed model (Table 3) revealed that location effects were highly significant (P< 0.001). This indicates strong environmental influences on the 5-year-old DBH and tree height. Regarding random effects (Table 4), block effects were non-significant for DBH but highly significant for tree height (P< 0.001). Family and family × location interaction effects were significant or highly significant for both traits (P< 0.05; P< 0.01). These findings demonstrate that DBH and tree height are significantly influenced by genotype and GE interactions.

Using the R lme4 package, we fitted mixed linear models to assess DBH and tree height across four trial sites, as well as for the combined multi-site data, to estimate breeding values (Tables 5 and 6, The complete table can be found in the Supplementary Materials). For ranking purposes, multi-site breeding values were employed to evaluate family growth performance comprehensively. We applied a selection threshold of 20% to pinpoint elite families, ultimately identifying the top nine families with superior DBH and tree height.

The DBH breeding values ranged from −1.27462 to 0.50484, with 25 families registering values above 0. The top performing families were 38, 41, 35, 5, 43, 9, 12, 27, and 24. For tree height, breeding values ranged from −0.42664 to 0.28418, with 23 families showing values greater than 0. The highest-ranking families were 29, 5, 43, 27, 38, 35, 12, 36, and 41. These selected Acacia melanoxylon families demonstrate superior growth traits in both DBH and height, as well as greater genetic potential, making them ideal candidates for large-scale promotion.

The GGE biplots for DBH and tree height (Figures 1-4), constructed from the first two principal components (AXIS1 for genetic and AXIS2 for environmental variation), demonstrated high explanatory power, accounting for 83.38% and 92.21% of the total variation, respectively. This indicates that the key patterns of genotype performance and environmental interaction were effectively captured by the model, ensuring the reliability of the subsequent conclusions regarding family selection and site evaluation (Zhao et al., 2022).

Traditional biplots relying on fixed-effects models face limitations in forestry METs due to their assumptions of homogenous environmental variances and balanced data—conditions rarely met in practice given inherent spatial heterogeneity and occasional missing observations (Gauch et al., 2008). Our study substantiates these challenges, as evidenced by the unbalanced number of replicates across our four test sites. To overcome these constraints, we employed a mixed linear model, from which BLUP breeding values were extracted (Ling et al., 2021). The validity of our model was confirmed through convergence checks and residual diagnostics, ensuring that the BLUPs accurately reflected genetic effects (Piepho et al., 2008). The high discriminative power of sites like ZX and the clear differentiation of stable families (e.g., 38, 35) in our resulting biplots empirically demonstrate that BLUP-based data enhance the reliability of stability assessments and selection accuracy compared to analyses based on raw phenotypic data (Ferreira et al., 2012; Amrate et al., 2024).

The GGE biplots for DBH and tree height in this study explained 83.38% and 92.21% of the total variation, respectively, indicating reliable results, with tree height exhibiting higher reliability than DBH. However, considering the breeding objective for large-diameter timber and uncertainties in volume calculation, along with the inability of the "Discriminiveness vs. representativeness" plot for tree height to effectively identify test sites with both high discriminative power and strong representativeness, the GGE biplot analysis for DBH was ultimately adopted as the primary reference. Furthermore, compared to tree height measurement, DBH measurement offers higher accuracy. Genetic correlations among traits suggest that breeders can select high-productivity individuals based on larger DBH, which is easier to measure and more cost-effective (Adams et al., 2007; Kroon et al., 2008; Munhoz et al., 2021) . This further supports the feasibility of prioritizing the DBH-based GGE biplot analysis.

Acacia melanoxylon has been introduced to China as an important timber species for promotion. As a fast-growing tree species, its rotation period in China is approximately 8 years. Research on tree trials both domestically and internationally suggests that volume growth can be reliably evaluated at 1/3 to 1/2 of the rotation period. Thus, using DBH data from 5-year-old Acacia melanoxylon for evaluation and selection provides valuable reference. Additionally, while this study is based on predictive analysis using 5-year growth data, it should be noted that long-term growth patterns may evolve as trees develop. Continuous monitoring and integration with practical breeding efforts are essential for guiding future promotion and utilization.

Regional METs are a primary and widely used method in forestry research. By analyzing data from multiple sites, METs facilitate the evaluation of genotype adaptability and stability, the identification of genotypes suited to diverse environments, and the delineation of optimal cultivation zones (Sixto et al., 2014; Nelson et al., 2018). On the average environment axis (Figure 4A), Family 12 demonstrated the largest DBH growth but exhibited low stability. In conjunction with breeding value analysis, Family 12 performed optimally at the Luoshan Forest Farm (LS) and moderately well at Zhongxi Forest Farm (ZX), while performing poorly at the other sites. It is recommended for planting in regions with ecological conditions akin to LS and ZX. Notably, stability is only practically significant when it coincides with high yield. For example, although Family 14 showed a “stable” performance, it was categorized as a “stable low-yield” family, making it economically unviable for DBH growth and unsuitable for promotion.

There is a strong correlation among the test sites ZX, LX, and XQ, with the ordering of family performances being similar across these locations, suggesting they may represent a similar mega-environment. This close relationship can be interpreted by examining the environmental data in Table 1.

While the soil types (mountain red soil) are similar between ZX, LX, and XQ, and differ from LS’s sandy loam, the climatic data reveal a more compelling pattern. Site XQ, situated in northern Fujian Province, has the lowest annual average temperature (17.3°C) among the four test sites. Notably, sites ZX and LX also experience relatively moderate average temperatures (20.2°C and 19.5°C, respectively) compared to the overall regional variation. Furthermore, the author's on-site investigations confirmed that Acacia melanoxylon at these sites grows primarily on shady slopes, which likely maintains a cooler microclimate than the broader forest farm averages might suggest. This consistent exposure to comparatively lower temperatures is the most parsimonious explanation for the strong genetic correlation among sites ZX, LX, and XQ.

In contrast, site LS appears independent and shows a weak correlation with the other three sites. Although LS has a reported average temperature of 20°C, it is located at a substantially higher elevation (415–481 m) compared to ZX (140–250 m) and LX (200–350 m). Higher elevation is often associated with greater temperature fluctuations and cooler conditions, which could differentiate its environmental profile. The combined factors of its distinct soil type and potentially unique microclimate at higher elevation may explain its divergence. However, to definitively pinpoint the causative environmental factors, further controlled experiments and more granular environmental monitoring are necessary.

According to the ranking of multi-site breeding values for DBH, a total of 25 families exhibited breeding values greater than 0. Among them, only 7 out of 17 families from the Australian introduced populations were selected, accounting for 41.18%, while 18 out of 30 families from the Luoxi Forest Farm seed orchard performed excellently, representing 60% of this group. This notable difference highlights the critical role of artificial selection in breeding: the proportion of superior genotypes in the locally pre-selected seed orchard population was significantly higher than that in the directly introduced populations. From the perspective of genetic gain, these results demonstrate that scientific selection can effectively enrich superior genotypes, enhance population growth and adaptive potential, and thereby offer more efficient breeding strategies for forest genetic improvement.