Introduction

Scientists have proposed many hypotheses about the genetic mechanism of heterosis owing to the extensive genetic information available and the ambiguous nature of genes recombination in cross. Noteworthy among these hypotheses are the classical theories widely acknowledged in scientific discourse, including the “dominance hypothesis”, “over-dominance hypothesis” and “epistasis hypothesis”.

The dominance hypothesis posits that dominant genes are advantageous, contrasting with recessive genes that are considered disadvantageous. The phenomenon of heterosis arises from the dominant synergy between beneficial alleles present in the parental generation F11. The restriction of this hypothesis lies in its exclusive focus on the dominant impacts among alleles while overlooking the interplays involving non-allele genes. Furthermore, it is crucial to note that not all recessive alleles are necessarily detrimental. In 1908, Shull introduced the over dominance hypothesis, positing that heterosis emerges from the interplay among alleles of parental heterogeneity, where heterozygous genotypes exhibit superior performance compared to homozygous genotypes in particular characteristics2. The hypothesis discussed solely pertains to elucidating the benefits associated with single gene characteristics, without considering the interplay between dominant and recessive alleles.

The Epistasis hypothesis posits that the interaction of non-allelic genes in parental organisms leads to the superior performance of the F1 generation in a specific trait. This implies that the gene governing the trait is impacted by one or more additional genes3. Silva et al.’s results argued that the development of favourable epistasis is a key mechanism underlying the genetic divergence of eucalypt species, and epistasis is an important mechanism underlying the evolution of post-zygotic reproductive barriers4. The research had established the veracity of hybrid benefits, particularly evident in enhanced corn5 and rice6 yields, as well as increased arabidopsis biomass7. The proposed hypothesis falls short in elucidating the complete genetic underpinnings of heterosis. Heterosis predominantly arises from the intricate interplay of numerous genes, with its genesis involving extensive gene recombination and interactions. Moreover, its manifestation is subject to the influence of genetic background, trait attributes, and environmental conditions.

Consequently, the regulation of heterosis typically occurs through the concurrent, individual, or dominant operation of the three hypotheses. The genetic network system theory8, genetic balance hypothesis9, gene complementarity theory10, genetic vibration synthesis theory11, heterogeneous combination hypothesis12, and three other hypotheses have collectively contributed to the enhancement of understanding the genetic basis underlying heterosis.

Combining ability serves as a straightforward metric for informing parental selection and forecasting heterosis. This term denotes the assessment of parental impact on the expression of desired traits in the resulting hybrids, including general combining ability (GCA) and special combining ability (SCA). GCA, denoting the mean expression of quantitative characteristics in the initial generation of hybrid originating from one or more parents, is primarily governed by gene additive variance and is deemed heritably constant. Conversely, SCA signifies the extent of departure of hybrid from the average of two particular parents, a manifestation shaped by the gene non-additive variance and is not subject to inheritance.

A study indicated the greater importance of additive gene effects in explaining the phenotypic variation among hybrids13. The extent of parental combining ability exerts a significant influence on the manifestation of heterosis. The creation of superior and productive combinations necessitates parents with elevated levels of both GCA and SCA14. Combining ability provides a guideline for selecting elite parents and desirable cross combinations to be used in formulation of a systematic breeding project for rapid improvement15. Therefore, breeding workers often estimate the GCA and SCA of plant materials in order to estimate whether parents and hybrids have great potential in hybrid breeding, in order to screen parents and predict the heterosis of hybrids16.

Most of studies suggested that heterosis primarily arised from non-additive variance, specifically the interaction between parental genetic factors. The fundamental principle posits that the SCA results from gene non-additive variance, denoting gene interactions. It is observed that parents exhibiting heterosis typically display reduced GCA. Luo’s research findings revealed that the non-additive variance (SCA) in tobacco potassium content surpassed the additive variance (GCA), illustrating a significant impact of non-additive effects on the heterosis of tobacco potassium content17. Similarly, Zhang’s investigation demonstrated a notable prevalence of non-additive effects over additive effects in immune heterosis among yellow catfish18. However, as evidenced by Zhou et al.’s study, the GCA variance in body mass traits of Penaeus vannamei outweighed the SCA variance, indicating variability in the extent of additive and non-additive effects across different species19. Notably, research on corn further supported the notion that additive expression substantially contributes to heterosis20.

The SCA of eucalypt is uncertain because eucalypt hybridization is mainly between purebred species, and there are significant differences in the mating ability effects when a parent is used as the male or female parent. Teixeira et al.’s study showed additive genetic effects and non-additive ones related to ALT, DAP, Vol and IMA of four clones of eucalypt (E. grandis × E. urophylla)21. Therefore, in addition to considering the degree of heterosis, the evaluation of eucalypt SCA should also focus on its internal factors, such as the genetic relationships between tree species and its own genetic characteristics. This is a problem that must be solved when selecting advantageous tree species and combinations based on coordination.

There were more extensive studies on MPH and HPH in evaluating the degree of heterosis in animals and plants. Nie et al.’s research showed that correlation analysis showed a significant association between GD and mid-parent heterosis (MPH) of 1000-grain weight22. Kumar et al.’s research evidenced that SCA, mean general combining ability (MGCA), low parent heterosis (LPH), mid-parent heterosis (MPH) and high-parent heterosis (HPH) exhibited significant positive rank correlations and high coefficients of determination (R-2) with grain yield of F1s (GYF1s)23. Herein high-hybrids of P. deltoides exhibited high-parent heterosis and mid-parent heterosis in growth traits and key enzymes of C–N metabolism24. The new top ranking hybrids displayed up to 250% high-parent heterosis and midparent heterosis for grain yield25. Shrestha et al. have used mid-parent heterosis (MPH) and high-parent heterosis (HPH) for demonstrating biomass yield26. Ndhlela et al.’s study suggested that significant positive correlations were recorded for specific combining ability with mid parent heterosis (MPH), high-parent heterosis (HPH) and per se performance of hybrids27. However, in the field of forestry, there were not many studies evaluating heterosis by combining MPH and HPH. High-parent heterosis and mid-parent heterosis were uesd to assess growth traits in Pinus strobus × P. peuce hybrid by Blada28. Study has employed mid-parent values as a method for determining the heterosis in stem volume and total tree biomass29.

The genetic modification system of eucalypt in China is currently in the preliminary stages, thus making traditional artificial hybridization the predominant approach for developing novel eucalypt cultivars. The judicious exploitation of heterosis stands as a critical determinant for the outcome of hybrid breeding endeavors. dos Santos et al.’s study demonstratd the importance of heterosis to improving adaptability and stability. Genetic complementarity from crosses between different species was the principal process that produced the observed heterosis30. Analysis of variance of E. urophylla showed that there was significant heterosis31. The heterosis of eucalypt is complex. eucalypt mainly obtain excellent hybrids through interspecific hybridization (like E. urophylla, E. grandis, E. pellita and E. tereticornis etc.), which makes the exploration of their heterosis more complex and rich. The overall inheritance of the chemical differences between E. globulus and E. nitens was non-linear. A study on plant secondary metabolites (PSM) of eucalypt hybrid proposed that the inheritance of five of the nine PSMs exhibited significant variations of additivity in F1’s32.

The genetic research on eucalypt, being an exotic tree species, is currently limited, partly due to challenges in creating numerous hybrid populations. There was a scarcity of studies delving into the genetic underpinnings of heterosis in eucalypt, particularly in terms of combining ability. This investigation focused on identifying optimal combinations to enhance specific traits in eucalypt, such as rapid growth (E. urophylla × E. grandis), disease resistance (E. urophylla × E. pellita), and wind tolerance (E. tereticornis × E. urophylla). By examining various tree species pairings, the study extensively analyzed the mechanism behind growth heterosis in eucalypt. This research utilized 124 hybrid combinations of eucalypt as experimental samples to examine the disparities in GCA among female and male progenitors of a specific tree species concerning growth and stem regularity. The investigation focused on identifying the tree species configuration that yields elevated SCA, assessing the advantages of hybrids in relation to mid-parent heterosis (MPH) and high-parent heterosis (HPH), and scrutinizing the correlation between combining ability and heterosis. Through initial investigation into the guidelines of tree species composition for enhancing eucalypt hybrid growth, the study suggests selection tactics for prominent eucalypt parents and superior combinations, with the aim of refining the current eucalypt hybrid population.

Materials and methods

Genetic materials and experimental site

The genetic materials studied in present research were Full-sib hybrid families by controlled pollination, in which 3 families were got in 2018, and 118 families were got in 2019, with DH3229, a widely planted (E. urophylla × E. grandis) hybrid in southern China, as the control. The parent species include E. grandis, E. urophylla, E. pellita, E. tereticornis, E. camaldulensis, E. benthami, E. dunnii, (E. urophylla × E. grandis), (E. urophylla × E. tereticornis), (E. tereticornis × E. urophylla), (E. pellita × E. camaldulensis), (E. tereticornis × E. grandis). Among them, there are 19 female parents and 44 male parents. The hybrid seeds were sown and propagated at the end of 2019, and planted when the seedlings were 30–50 cm tall. Field tests were conducted, and the planted time was mid June 2020.

The experiment was a randomised block design with each hybrid arranged in 10-plant row plots with 3 replications. The planting density was 3 m × 2 m. All blocks were randomised to the same plot to ensure that there was as little variation as possible between sites, and all were operated in the same way to exclude the influence of environmental factors on the results. The study was located at the South China Experiment Nursery (21° 16′ N, 110° 05′ E), with an altitude of about 50 m. The region belongs to the South subtropical maritime monsoon climate, with summer rain type and an average annual rainfall of 1700–1900 mm. The lowest temperature is 1.4 °C, the highest temperature is 38.1 °C, and the average annual temperature is 23.1 °C33. The soil is classified as Rhodi-Udic Ferralosols according to the World Reference Base for Soil Resources, which developed from weathered sediments of basalt. The soil is acidic, with a mean pH value of 4.9 at the 0–80 cm depth34.

Measurements for interesting traits

In the third and fourth year after planted all the trees were investigated. The Vertex IV (Haglof, Sweden) was used to measure the height (HT) of trees, and the diameter at breast height (DBH) of plants was measured with a tree measuring ruler. Manually assign tree stem straightness35 values based on six levels: 6 for extremely curved, 5 for curved, 4 for relatively curved, 3 for average, 2 for relatively straight, and 1 for straight36. To avoid the influence of heterogeneity in the growth environment of parents and hybrids on parent-hybrid comparisons, the trait values of parents were replaced by the mean of hybrids from the same female parent (male parent). The relative volume (Vol, m3) was calculated using the following formula.

$$Vol = \pi \times \left( {DBH/200} \right)^{2} \times HT \times 1/3,\quad \pi = 3.141593$$
(1)

Parameter estimation and data analysis

Combining ability estimation

Use analysis of variance to test whether there is a significant difference in the target trait among hybrid combinations. If the difference is significant, the combining ability will be estimated. Estimation model as follow37:

$$X_{ijk} = \mu + g_{fi} + g_{mj} + S_{ij} + r_{k} + e_{ijk}$$
(2)

Among them, k is replication, Xijk is the mean of female i and male j in k, which is the total mean. gfi and gmj are the GCA of female i and male j, respectively. Sij is the SCA of the combination of female i and male j, rk is the effect of k, and eijk is the random error38.

The calculation formula for coordination force refers to the research39,40. The formulas are as follows:

  • Female parent general combining ability (GCA) effect value:

    $$\hat{g}_{i.} = \overline{{X_{i.} }} - \overline{{X_{..} }}$$
    (3)

  • Male parent general combining ability (GCA) effect value:

    $$\hat{g}_{.j} = \overline{{X_{.j} }} - \overline{{X_{..} }}$$
    (4)

  • Special combining ability (SCA) effect value:

    $$\hat{S}_{ij} = \overline{{X_{ij} }} - \overline{{X_{..} }} - \hat{g}_{i.} - \hat{g}_{.j}$$
    (5)

  • In the formula:

    $$\overline{{X_{ij} }} = \sum\limits_{k = 1}^{b} {ijk/b}$$
    (6)
    $$\overline{{X_{i.} }} = \sum\limits_{j = 1}^{{n_{2} }} {\overline{{X_{ij} }} /n_{2} }$$
    (7)
    $$\overline{{X_{.j} }} = \sum\limits_{i = 1}^{{n_{1} }} {\overline{{X_{ij} }} /n_{1} }$$
    (8)
    $$\overline{{X_{..} }} = \sum\limits_{j = 1}^{{n_{2} }} {\overline{{X_{.j} }} /n_{2} } = \sum\limits_{i = 1}^{{n_{1} }} {\overline{{X_{i.} }} /n_{1} }$$
    (9)

Among them, n1 = 5 is the female number; n2 = 5 is the male number; b is the number of replications; k is replication; \({\text{X}}_{{{\text{ij}}}}\): The mean of a single sample; \({\text{X}}_{{{\text{i}}.}}\): The female parent mean value; \({\text{X}}_{{.{\text{j}}}}\): The male parent mean value; \({\text{X}}_{..}\): The overall mean.

Estimation of heterosis degree

The performance of heterosis is mainly measured by mid-parent heterosis (MPH) and high-parent heterosis (HPH). We adopt the research method of Tang and Zhang et al.41, and the formulas are as follows:

  • Mid-parent heterosis:

    $$MPH(\% ) = \frac{{(F_{1} - MP)}}{MP} \times 100$$
    (10)

  • High-parent heterosis:

    $$HPH(\% ) = \frac{{(F_{1} - HP)}}{HP} \times 100$$
    (11)

Among them, F1 is the mean of traits of hybrids. MP = (P1 + P2)/2: Mean of parental traits. P1 and P2 are the parental trait values, respectively. HP is the optimal parental trait mean. The criteria for determining heterosis are: if the MPH or HPH value is greater than 0, it indicates that the trait exhibits heterosis; If the MPH or HPH value is greater than 50%, it indicates strong heterosis in the trait42.

Genetic parameters and heritability estimation

We mainly refer to the research of Zhang et al.43 for the estimation of heritability and genetic parameters, and the basic formulas are as follows:

  • Estimation of genotype variance of female general combining ability:

    $$\hat{\sigma }_{f}^{2} = \frac{{V_{pf} - V_{fm} }}{{bn_{2} }}$$
    (12)

  • Estimation of genotype variance of male general combining ability:

    $$\hat{\sigma }_{m}^{2} = \frac{{V_{pm} - V_{fm} }}{{bn_{2} }}$$
    (13)

  • Estimation of genotype variance of special combining ability:

    $$\hat{\sigma }_{fm}^{2} = \frac{{V_{fm} - V_{e} }}{{bn_{2} }}$$
    (14)

  • Estimation of Additive variance: \(\hat{\sigma }_{f}^{2} + \hat{\sigma }_{m}^{2}\)

  • Estimation of Explicit variance: \(\hat{\sigma }_{fm}^{2}\)

  • Estimation of Environmental Variance: \(\hat{\sigma }_{e}^{2} = V_{e}\)

  • Variance of GCA:

    $$V_{g} (\% ) = \frac{{\hat{\sigma }_{f}^{2} + \hat{\sigma }_{m}^{2} }}{{\hat{\sigma }_{f}^{2} + \hat{\sigma }_{m}^{2} + \hat{\sigma }_{fm}^{2} }}$$
    (15)

  • Variance of SCA:

    $$V_{s} (\% ) = \frac{{\hat{\sigma }_{fm}^{2} }}{{\hat{\sigma }_{f}^{2} + \hat{\sigma }_{m}^{2} + \hat{\sigma }_{fm}^{2} }}$$
    (16)

  • Broad heritability:

    $$h_{B}^{2} (\% ) = \frac{{\hat{\sigma }_{f}^{2} + \hat{\sigma }_{m}^{2} + \hat{\sigma }_{fm}^{2} }}{{\hat{\sigma }_{f}^{2} + \hat{\sigma }_{m}^{2} + \hat{\sigma }_{fm}^{2} + \hat{\sigma }_{e}^{2} }}$$
    (17)

  • Narrow heritability:

    $$h_{B}^{2} (\% ) = \frac{{\hat{\sigma }_{f}^{2} + \hat{\sigma }_{m}^{2} }}{{\hat{\sigma }_{f}^{2} + \hat{\sigma }_{m}^{2} + \hat{\sigma }_{fm}^{2} + \hat{\sigma }_{e}^{2} }}$$
    (18)

Data statistical analysis and organization

The collation of data in this study was conducted using Excel 2016 and Python 3.11.5. For statistical analysis, SAS was utilized for analyzing variance and multiple comparisons, while SPSS was employed for estimating genetic parameters and heritability. The research involved performing significance tests of multiple comparisons and analysis of variance (ANOVA) (Table 1)37 on the observed values and effect values of five traits from a dataset comprising 124 hybrids, 19 female parents, 44 male parents, and 121 hybrid combinations.

Table 1 ANOVA model.
Full size table

Notably, certain hybrids were found to be represented more than once within each replication, indicating that some hybrids had over 10 plants in a single replication. However, in our subsequent statistical analysis, we selected 10 plants with moderate growth traits for calculation. Hybrid 3229 was the control. The omission of parental measurements for the hybrids 19H12 and 19H39 at age three and four precluded their inclusion in the forthcoming discourse on hybrids. The extensive volume of sample data necessitated a alteration from traditional manual processing methods using only SAS and Excel, as such an approach would elevate the risk of errors, consume considerable time, and potentially affect the accurate assessment of superior hybrid hybrids, as well as lead to misinterpretations regarding high combining ability parents and hybrid combinations.

To mitigate these issues, a combined approach using Python in conjunction with SAS was adopted, with programming code implemented during the data processing phase. Third-party libraries such as pandas, numpy and openpyxl were leveraged in Python for data processing tasks. We developed the survival rate package (Packge S1) to quickly calculate the survival rate trait. The source code incorporated functionalities from the pandas library to read and write Excel data in a two-dimensional format, conducting matrix transformation, traversal loops, merging of identical observations, and debugging the output into a format suitable for direct execution in SAS.

Subsequently, we will import the adjusted data into SAS software and use a two-way ANOVA conducted to analyze the measured parameters of tree height (HT), diameter at breast height (DBH), relative volume (Vol), survival rate (SUR), and stem straightness (SS) for different hybrid species and forest ages, as well as multiple comparative analyses of indicators such as GCA, SCA, MPH and HPH. The study also explored analysis of variance of six factors: samples; age; replication effect; interactions among samples and age (samples × age); interactions among samples and replication effect (samples × replication effect); interactions among age and replication effect (age × replication effect); to assess the impact of age and the experimental design on the aforementioned parameters.

A One-way Analysis of Variance (ANOVA) was employed to assess the alignment of SS, because no investigation was conducted at age 3, thereby omitting age from consideration. Statistical analyses were carried out utilizing the ANOVA procedure in SAS 9.2, with Duncan’s Multiple Range Test used for post hoc multiple comparisons (Package S2 and Package S3). For multiple comparisons with 26 letters that could not be labeled, we changed PROC ANOVA to PROC GLIMMIX as well as means to lsmeans. If there are program errors caused by too many insignificant groups, change the multiple comparison method to Student Maximum Modular Test (SMM). The statistical difference was set at the significance level of 0.05.

We have developed Whole table splitting—normalization package to process the analysis of variance results from SAS (Package S4). We have developed Multiple comparisons package and Dictionary search on demand package to process the multiple comparison results from SAS (Package S5 and Package S6). The source code leverages the numps library for streamlined array operations and matrix computations, the openpyxl library for data transformation, validation, and automated task configurations, along with the functionalities of the aforementioned pandas library. These facilitate various data manipulation tasks such as data slicing, indexing, iterative reordering, capitalization conversion, sorting (Package S5), dictionary key-value pair retrieval, conditional evaluations, and other operations (Package S6). The purpose of these three packages is to improve data conversion efficiency, ensure the accuracy of significance testing, enhance the credibility of the results, and obtain the display results in the final article and supplementary material.

The genetic parameters were determined using the Whole table splitting—naming by tree species package (Package S7) to analyze a total of 10 female varieties of trees and 17 male varieties of trees in order to calculate the parental GCA. Use Whole table splitting—delete the unique tree species of the variety and name them according to the tree species package (Package S8) to process hybrid combinations of 26 varieties of trees. Calculate the SCA of hybrid combinations, perform data cleaning, feature selection, and extract data subsets, and organize them into a format (Package S7 and Package S8) that can be imported and read into SPSS for analysis of variance. Finally, use One way ANOVA of SPSS to calculate five traits’s Additive variance, Non-additive variance, Environmental variance, Variances of GCA (Vg/%), Variances of SCA (Vs/%), narrow heritability/% and Broad heritability/% of overall and each pair of tree species hybrid combinations.

The SAS code showcased herein is extracted verbatim from the system log, maintaining identical color and format. Conversely, Python code cannot be simply copied and pasted to achieve the final code package presentation. To maintain the legibility of Python code, the SublimeText4 editor equipped with the Sublime highlight package (Package S9) is employed. This tool ensures the preservation of color highlighting form of Python code, enhancing clarity, comprehension, while safeguarding the original format and structure of the code.

Because we added comments to each line when writing Python code, a custom plugin Code comment deletion package (Package S10) was developed to the SublimeText4 editor, which enables the elimination of all comments within a code file by adhering to syntax highlighting conventions. By executing the command view.run_command (‘remove_comments’), users can efficiently eradicate multi-line comments at once with a single click.

Result

The growth variations of 124 eucalypt hybrids

Analysis of variance was performed on the four growth traits of 124 hybrids, each with three replications from the two distinct ages that were observed. The analysis revealed significant disparities in all traits among the various hybrids, the two ages and hybrids × replication effect, with all results meeting the threshold p value < 0.0001. These three factors were recognized as the primary contributors to variations in growth. And among the three replications of each trait, P < 0.01 was met (HT, p < 0.0001; DBH, p = 0.0023; SUR, p = 0.0026; Vol, p < 0.0001). The 124 hybrids with all traits at age three and four tree showed significant differences among the three replications. Hybrids × age satisfied p < 0.01 (HT, p < 0.0001; DBH, p = 0.0014; SUR, p < 0.0001; Vol, p < 0.0001). The significant differences in the interaction between hybrids × age for all traits indicate that these two factors were also the most important sources of differences. There was a highly significant interaction effect between the two traits of HT and Vol in the hybrids, which age × replications (HT, p < 0.0001; DBH, p = 0.1643; SUR, p = 0.0664; Vol, p = 0.0029) satisfied p < 0.01 (Table S1).

The maximum DBH mean values were 19H83, 19H45, 19H56 and 18H167. In addition, the DBH mean values of 18H30, 19H52 and 19H92 were also relatively large, and there were significant differences among these hybrids. The HT mean values of the five hybrids 19H45, 19H52, 19H92, 19H83 and 18H30 were the highest. In addition, the HT mean values of 18H167 and 19H56 were also relatively large, and there are significant differences among these hybrids. The Vol mean values of the hybrids 19H45, 19H83, 19H56, 19H52 and 18H167 exhibited highestly. Furthermore, the Vol mean values of 18H30 and 19H92 were notably substantial. Nevertheless, there was no statistically significant difference between hybrids 19H45 and 19H83, as well as between 19H56 and 19H52. The SUR of 19H97 was the highest, 19H116 followed.

The overall performance of hybrids 19H45, 19H83, 18H30, 19H56, 18H167 and 19H92 demonstrated superiority. Utilizing the Dictionary search on demand package, their survival rates and importance were identified as 0.4000bcdefghijk, 0.4333abcdefghiyz, 0.7750cdefghijkl, 0.1417q, 0.4500abcdefghxyz and 0.6833hijklmnopq, respectively. With the exception of 18H30, the survival rates of other well-developed hybrids were suboptimal. Further research was warranted to explore methods for enhancing the survival rate of these superior hybrids.

The minimum DBH mean values observed were 19H32, 19H85, 19H133, 19H38, 19H115, 19H37 and 19H31, with the exception of the hybrids 19H115 and 19H37, which did not exhibit a significant difference. The average HT measurements for the hybrids 19H85, 19H32, 19H38 and 19H37 exhibited the lowest values. Similarly, the HT mean values for 19H115, 19H33, 19H75, and 19H133 were comparatively modest. However, there was no significant difference between the two hybrids 19H38 and 19H37, and between the two hybrids 19H115 and 19H33. The lowest Vol mean values were 19H32, 19H85, 19H38, 19H37, 19H115, 19H133, 19H75, 19H31 and 19H33. There was no significant difference between the three hybrids 19H38, 19H37, and 19H115, and there was no significant difference between the two hybrids 19H31 and 19H33. The SUR of 19H97 was the lowest, and the SUR of 19H85, 19H38, and 19H115 were also very low.

In summary, the growth of several hybrid varieties 19H32, 19H85, 19H38, 19H115, 19H37, and 19H133 were the worst. Using the Dictionary search on demand package, their survival rates and significance were found to be 0.275klnnopq, 0.23333mnopq, 0.25lmnopq, 0.25lmnopq, 0.33333ghijklmno, and 0.51667abdtuvwxyz, respectively. In addition to the decent survival rate of 19H133, the survival rates of 19H32, 19H85, 19H38, 19H115, and 19H37 were also very low (Table 2).

Table 2 121 Growth performance and multiple comparison of hybrids (α = 0.05, Top 10 and bottom 10 sorted by DBH in descending order. See Table S2 for full data.)
Full size table

Use the Dictionary search on demand package to find the best performing hybrids 19H45, 19H83, 18H30, 19H56, 18H167 and 19H92 in terms of growth traits. The female and male parents were U1101 × 3229, U3423 × 3327, U1240 × G425486, U1617 × H253, T15 × U3423, and U952 × C2232, respectively. The corresponding varieties were (E. urophylla) × (E. urophylla × E. grandis), (E. urophylla) × (E. urophylla × E. grandis), (E. urophylla) × (E. grandis), (E. urophylla) × (E. pellita × E. tereticornis), (E. tereticornis) × (E. urophylla) and (E. urophylla) × (E. camaldulensis). The female and male parents of the hybrids 19H32, 19H85, 19H38, 19H115, 19H37 and 19H133, which performed the worst in terms of growth traits, were 06H16 × DN4, U3423 × T131, 06H16 × E. camaldulensis, U6 × open pollination, 06H16 × U6 and H0733 × G6BS, respectively. The corresponding varieties were (E. tereticornis × E. urophylla) × (E. dunnii), (E. urophylla) × (E. tereticornis), (E. tereticornis × E. urophylla) × (E. camaldulensis), (E. urophylla × E. tereticornis) × (open pollination), (E. tereticornis × E. urophylla) × (E. urophylla × E. tereticornis) and (E. tereticornis × E. urophylla) × (E. grandis). The complete table of growth performance and multiple comparisons of 121 hybrids is Table S2, which lists the top 10 and bottom 10 in descending order of DBH.

GCA of 19 female parents

Analysis of variance was conducted on the GCA of 19 female parents from the two ages, and it was found that there were very significant differences in the GCA of all traits among different female parents, all of which met the criteria of p < 0.0001. However, there was no significant difference in the female parent GCA with different traits of the different ages (HT, p = 0.6811; DBH, p = 0.5562; SUR, p = 0.8217; Vol, p = 0.4764) and the interaction between female parents × age (HT, p = 0.9730; DBH, p = 0.9830; SUR, p = 0.9941; Vol, p = 0.9318) (Table S3). Age of the female parents did not have a substantial impact on the GCA.

Among the different genotypes studied, U1101 exhibited the highest DBH mean effect value, followed by U1240. Furthermore, U1240 demonstrated the highest HT mean effect value, with H64 as the next highest. Genotypes U1101 and U1240 were associated with the greatest Vol and optimal growth conditions. Conversely, genotypes H33 and 06H16 exhibited the smallest effect values of the mean for these traits and were characterized by the poorest growth conditions. U1240 had the highest SUR, followed by H23, and H33 and U1617 had the lowest SUR.

In summary, U1101 (E. urophylla) and U1240 (E. urophylla) had the highest female parent GCA and significant differences, while 06H16 (E. tereticornis × E. urophylla) and H33 (E. pellita × E. tereticornis) had the lowest GCA. The two had significant differences in the performance of the other three traits except DBH (Table 3). The multiple comparisons of the GCA of various female traits are shown in the following table:

Table 3 GCA and Multiple Comparisons of 19 female parents (α = 0.05).
Full size table

GCA of 44 male parents

Analysis of variance was conducted on the GCA of 44 male parents from the two ages, and it was found that there were very significant differences in the GCA of all traits among different male parents, all of which met the criteria of p < 0.01 (HT, p = 0.0002; DBH, p < 0.0001; SUR, p < 0.0001; Vol, p = 0.0005). However, there was no significant difference in the male parent GCA with different traits of the different ages (HT, p = 0.7993; DBH, p = 0.8872; SUR, p = 0.8079; Vol, p = 0.7857) and the interaction between male parents × age (HT, p = 0.9997; DBH, SUR and Vol, p = 1.0000) (Table S4). Similarly, there was no significant age effect on the male parent GCA.

The DBH mean effect value was highest for U3423, followed by U1101, and Vol was also the highest among the two. In addition, the DBH and Vol of 3229 were also relatively large. The HT mean effect value of P1510 was the highest, followed by 3229. And the three traits with the smallest effect values of the mean were DN4 and G6BS, both had the worst growth conditions. The SUR of br29 was the highest, followed by P440, and T131 and DH3226 had the lowest SUR.

In brief, U3423 (E. urophylla) and 3229 (E. urophylla × E. grandis) exhibited superior male parent GCA, whereas U1101 (E. urophylla) also demonstrated high male parent GCA, presenting significant differences among the three. Notably, U3423 and U1101 both pertained to the species E. urophylla, while 3229 represented a hybrid involving E. urophylla. Hence, it could be inferred that E. urophylla potentially possessed heightened male parent GCA. DN4 (E. dunni) and G6BS (E. grandis) exhibited the lowest male GCA, with significant differences observed in their GCA values across four distinct phenotypic traits (Table 4). The multiple comparisons of the GCA of various male traits are shown in the following table:

Table 4 GCA and Multiple Comparisons of 44 male parents (α = 0.05).
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SCA of parents in 121 hybrid combinations

Analysis of variance was conducted on the SCA of 121 hybrid combinations from the two ages, and it was found that there were very significant differences in the SCA of all traits among different hybrid combinations, all of which met the criteria of p < 0.0001. Among the SCA of hybrid combinations with the different ages, except SUR, the SCA of the other three traits all satisfied P < 0.05 (HT, p = 0.0022; DBH, p = 0.0420; SUR, p = 0.2021; Vol, p = 0.0009). There was a significant age effect on the SCA of HT, DBH and Vol in 121 hybrid combinations. The study found that the interaction effect between hybrid combinations × age was not statistically significant (Vol, p = 0.9999; HT, DBH and SUR, p = 1.0000) (Table S5). Specifically, there was no notable interaction effect observed between hybrid combinations × age regarding the SCA of hybrid combinations.

The hybrid combinations with the highest DBH effect values of the mean were U3423 × 3327, 06H16 × LL131, H0733 × U6, and U3423 × LY4, but there was no significant difference between the H0733 × U6 and U3423 × LY4 hybrid combinations. The hybrid combinations with the highest HT effect values of the mean were U3423 × E. camaldulensis, U3423 × 3327, 06H16 × LL131 and H0733 × U6, but there was no significant difference between the three hybrid combinations of U3423 × 3327, 06H16 × LL131 and H0733 × U6. The highest Vol effect values of the mean were U3423 × 3327, 06H16 × LL131, and U3423 × LY4, and U3423 × E. camaldulensis was also relatively large. There were significant differences in Vol traits among the four hybrid combinations. The three traits with the smallest effect values of the mean were U952 × EC106 and U1101 × 3229. In addition, the growth of U2223 × P9060 and U1101 × open pollination was also poor. U3423 × H253 had the highest SUR, H0733 × U6 also had a higher SUR, EC106 × LL131 had the lowest SUR, and U2223 × P9060 also had a lower SUR.

In summary, U3423 × 3327, 06H16 × LL131, H0733 × U6, U3423 × LY4 and U3423 × E. camaldulensis had the highest SCA. Use the Dictionary search on demand package to find the corresponding tree species as (E. urophylla) × (E. urophylla × E. grandis), (E. tereticornis × E. urophylla) × (E. urophylla), (E. tereticornis × E. urophylla) × (E. urophylla × E. tereticornis), (E. urophylla) × (E. exserta) and (E. urophylla) × (E. camaldulensis).

The SCA forces of U952 × EC106, U1101 × 3229, U2223 × P9060 and U1101 × open pollination were the lowest. Use the Dictionary search on demand package to find the corresponding tree species as (E. urophylla) × (E. tereticornis × E. grandis), (E. urophylla) × (E. urophylla × E. grandis), (E. urophylla) × (E. pellita) and (E. urophylla) × (open pollination). There was a significant differences observed in the HT effect value of the mean when comparing the U952 × EC106 and U1101 × 3229 hybrid combinations, in contrast to the U2223 × P9060 and U1101 × open pollination hybrid combinations where no significant differences was identified. However, a distinct contrast emerged in the HT effect values of the mean between the former and latter pairings. Significant differences were observed in the characteristics of DBH, SUR and Vol among the hybrid combinations U2223 × P9060 and U1101 × open pollination. Notably, the former hybrid combinations demonstrates marked distinctions in both DBH and Vol compared to the hybrid combinations U952 × EC106 and U1101 × 3229. Specifically, only the U2223 × P9060 hybrid combination exhibited significant differences in SUR (Table 5). The complete table for SCA and multiple comparisons of 121 hybrid combinations parents is Table S6, and Table 5 shows the top 10 and bottom 10 in descending DBH order.

Table 5 SCA and multiple comparisons of 121 hybrid combinations parents (α = 0.05, Top 10 and bottom 10 sorted by DBH in descending order. See Table S6 for full data.)
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Analysis of heterosis in 121 hybrid combinations

Analysis of variance was conducted on the MPH and HPH of 121 hybrid combinations of two ages, and it was found that there were significant differences in the MPH and HPH of all traits among different hybrid combinations, with P < 0.0001. Among the MPH of different traits and ages hybrid combinations, only the MPH of HT satisfied P < 0.05 (HT, p = 0.0302; DBH, p = 0.1572; SUR, p = 0.7979; Vol, p = 0.1375) (Table S7). The difference between HPH was not significant (HT, p = 0.0503; DBH, p = 0.1697; SUR, p = 0.0536; Vol, p = 0.2329) (Table S8). There was no significant age effect observed in the 121 hybrid combinations studied, except for MPH of HT. The interaction between hybrid combinations × age showed that the P-values for the four traits of MPH and HPH in 121 hybrid combinations were all 1, indicating that heterosis was not related to the interaction effect between hybrid combinations × age.

Analysis of MPH in 121 hybrid combinations

The highest DBH effect values of the mean were observed in (E. urophylla × E. grandis) × 06H241 and H0733 × U6, while H0733 × P9060 and C254 × H07 also had larger DBH effect values of the mean. However, only (E. urophylla × E. grandis) × 06H241 showed significant differences from the latter three. The highest HT effect values of the mean were H0733 × U6, H0733 × P9060, (E. urophylla × E. grandis) × 06H241, C254 × H07 and H0733 × G6BS. But there was no significant difference between these 5 hybrid combinations. The the highest Vol effect values of the mean were (E. urophylla × E. grandis) × 06H241, H0733 × P9060, H0733 × U6, C254 × H07 and H0733 × G6BS. Except for the two hybrid combinations H0733 × P9060 and H0733 × U6, which did not show significant differences, there were significant differences among the other three hybrid combinations. The SUR of H0733 × U6 was the highest, and the SUR of H0733 × P9060 and C254 × H07 were also high. There were significant differences among the three hybrid combinations.

The hybrid combinations H0733 × U6, H0733 × P9060, (E. urophylla × E. grandis) × 06H241, C254 × H07 and H0733 × G6BS exhibited the most significant MPH concerning growth traits. By utilizing the Dictionary search on demand package, the corresponding tree species were identified as (E. tereticornis × E. urophylla) × (E. urophylla × E. tereticornis), (E. tereticornis × E. urophylla) × (E. pellita), (E. urophylla × E. grandis) × (E. urophylla × E. grandis), (E. camaldulensis) × (E. tereticornis × E. urophylla) and (E. tereticornis × E. urophylla) × (E. grandis).

The smallest DBH effect values of the mean were noted in the hybrid combinations T15 × DN4, U6 × br22 and U952 × EC106, indicating significant differences among these three hybrid combinations. The least HT effect values of the mean were found in T15 × DN4, H37 × open pollination, U952 × EC106 and U6 × br22. No significant difference was observed between the hybrid combinations U952 × EC106 and U6 × br22. The Vol values of the mean of T15 × DN4 and U6 × br22 were relatively diminutive, with a significant difference between the two. The lowest SUR was seen in T15 × DN4, while H37 × open pollination also exhibited a lower SUR, with a significant difference between the two (Table 6).

Table 6 MPH and multiple comparisons of 121 hybrid combinations (α = 0.05, Top 10 and bottom 10 sorted by DBH in descending order. See Table S9 for full data.)
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The analysis demonstrated that the hybrid combinations T15 × DN4, H37 × open pollination, U952 × EC106 and U6 × br22 exhibited the least advantageous growth traits when considering the MPH. Through utilization of the Dictionary search on demand package, the involved tree species were identified as (E. tereticornis) × (E. dunnii), (E. pellita × E. camaldulensis) × (open pollination), (E. urophylla) × (E. tereticornis × E. grandis) and (E. urophylla × E. tereticornis) × (E. brassiana). The complete table of MPH and multiple comparisons of 121 hybrid combinations is Table S9, and Table 6 shows the top 10 and bottom 10 in descending order of DBH.

Analysis of HPH in 121 hybrid combinations

The hybrid combinations U3423 × 3327 and (E. urophylla × E. grandis) × 06H241 exhibited the highest DBH effect values of the mean. Furthermore, (E. urophylla × E. grandis) × G243237 and U952 × C2232 also showed relatively large DBH effect values of the mean, with significant differences observed among these four hybrid combinations. Regarding the HT effect, the top mean values were found in U3423 × 3327, U952 × C2232, and H0733 × U6, while H0733 × P9060 also displayed a notable HT effect value of the mean. Notably, there were no significant differences between U3423 × 3327 and U952 × C2232, as well as between H0733 × U6 and H0733 × P9060, but significant differences existed between the first two pairs and the last two pairs of hybrid combinations. For the Vol effect, the highest mean values were recorded in U3423 × 3327 and (E. urophylla × E. grandis) × 06H241, with significant differences in Vol effect values of the mean also observed in U952 × C2232 and (E. urophylla × E. grandis) × G243237 among the four hybrid combinations. The SUR was highest in H0733 × U6, followed by H0733 × P9060, with a significant difference between the two.

The HPH for growth traits were determined to be U3423 × 3327, U952 × C2232, (E. urophylla × E. grandis) × 06H241 and H0733 × U6. Through the utilization of the Dictionary search on demand package, the specific tree species involved were identified as (E. urophylla) × (E. urophylla × E. grandis), (E. urophylla) × (E. camaldulensis), (E. urophylla × E. grandis) × (E. urophylla × E. grandis) and (E. tereticornis × E. urophylla) × (E. urophylla × E. tereticornis).

The smallest DBH effect values of the mean were T15 × DN4 and U6 × br22. In addition, the DBH effect values of the mean of U1101 × open pollination, H64 × open pollination, and H37 × open pollination were also relatively small. There was no significant difference between the three hybrid combinations of U6 × br22, U1101 × open pollination, and H64 × open pollination. The HT effect values of the mean of T15 × DN4, H37 × open pollination, and H64 × open pollination were the smallest. In addition, the HT effect values of the mean of U6 × br22 and U1101 × open pollination were also relatively small. There was no significant difference between the three hybrid combinations of H37 × open pollination, H64 × open pollination, and U6 × br22. The Vol effect values of the mean of T15 × DN4, U6 × br22, and H64 × open pollination were also relatively small, and there are significant differences among the three hybrid combinations. The SUR of T15 × DN4 and U1101 × open pollination were the lowest, and the SUR of H37 × open pollination was also low. There were significant differences among the three hybrid combinations (Table 7).

Table 7 HPH and multiple comparisons of 121 hybrid combinations (α = 0.05, Top 10 and bottom 10 sorted by DBH in descending order. See Table S10 for full data.)
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In summary, the five hybrid combinations T15 × DN4, H37 × open pollination, H64 × open pollination, U6 × br22 and U1101 × open pollination had the weakest HPH in terms of growth traits. Using the Dictionary search on demand package, the corresponding tree species were found to be (E. tereticornis) × (E. dunnii), (E. pellita × E. camaldulensis) × (open pollination), (E. tereticornis × E. pellita) × (open pollination), (E. urophylla × E. tereticornis) × (E. brassiana) and (E. urophylla) × (open pollination). The complete table of HPH and multiple comparisons of 121 hybrid combinations is Table S10, and Table 7 shows the top 10 and bottom 10 in descending order of DBH.

Analysis of variance in SS for combining ability, MPH and HPH of 121 hybrids

The study encompassed a variance analysis involving 121 hybrids, evaluating the GCA of 19 female parents, 44 male parents, and the SCA of the 121 hybrid combinations. Additionally, the MPH and HPH were assessed across three replications of four age. Remarkably, the observed differences in SS traits across different hybrids were found to be highly significant (p < 0.0001). Furthermore, the interaction between hybrids × replications exhibited significant differences (p = 0.0009 < 0.01), underscoring their pivotal roles as the primary sources of variation. It was also noted that the SS trait of hybrids varied significantly among the three replications (p = 0.0231 < 0.05), indicating significant differences among the 121 four age hybrids across replications, with replication identified as another contributing factor to the observed differences. Significant differences in GCA were observed among different female SS traits (p = 0.0017 < 0.01). The MPH (P < 0.0001) and HPH (P = 0.0447) of SS traits displayed significant differences across 121 hybrid combinations, meeting the significance threshold of P < 0.05. Conversely, no disparity was detected in GCA among different male SS traits (p = 0.4377). Furthermore, the SCA of the SS trait did not differ among the 121 hybrid combinations (p = 0.0668) (Table S11). Consequently, the analysis of SCA of the 121 hybrid combinations and GCA of the male parents with respect to SS was not conducted.

The highest SS among the top 10 hybrids included 19H84, 19H52, 19H107, 19H62, 19H151, 19H161, 19H125, 19H108, 19H56 and 19H26. These hybrids were derived from various combinations such as U3423 × DH3226, U1101 × open pollination, 3229 × open pollination, U2223 × E. camaldulensis, (E. urophylla × E. grandis) × G243237, (E. urophylla × E. grandis) × U6, H33 × G243237, 3229 × open pollination, U1617 × H253 and H64 × open pollination, with the corresponding tree species (E. urophylla) × (E. urophylla × E. grandis), (E. urophylla) × (open pollination), (E. urophylla × E. grandis) × (open pollination), (E. urophylla) × (E. camaldulensis), (E. urophylla × E. grandis) × (E. grandis), (E. urophylla × E. grandis) × (E. urophylla × E. tereticornis), (E. pellita × E. tereticornis) × (E. grandis), (E. urophylla × E. grandis) × (open pollination), (E. urophylla) × (E. pellita × E. tereticornis) and (E. tereticornis × E. pellita) × (open pollination) identified using the Dictionary search on demand package. There was no significant difference between 19H84, 19H52, 19H107 and 19H62, nor between 19H125 and 19H108, nor between 19H56 and 19H26.

The lowest SS among the top 10 hybrids included 19H75, 19H85, 19H115, 19H86, 19H81, 19H145, 19H72, 19H63, 19H37 and 19H49. These hybrids were derived from various combinations such as U3423 × BM1, U3423 × T131, U6 × open pollination, U3423 × H37, U3423 × LY4, 13H231 × open pollination, U3423 × T105, U2223 × P9060, 06H16 × U6 and U1101 × H37, with the corresponding tree species (E. urophylla) × (E. benthami), (E. urophylla) × (E. tereticornis), (E. urophylla × E. tereticornis) × (open pollination), (E. urophylla) × (E. pellita × E. camaldulensis), (E. urophylla) × (E. exserta), (E. urophylla × E. grandis) × (open pollination), (E. urophylla) × (E. tereticornis), (E. urophylla) × (E. pellita), (E. tereticornis × E. urophylla) × (E. urophylla × E. tereticornis) and (E. urophylla) × (E. pellita × E. camaldulensis) identified using the Dictionary search on demand package. There was a lack of statistically significant variance observed between hybrids 19H85 and 19H115, as well as between hybrids 19H145, 19H72 and 19H63 (Table 8). The complete multiple comparison table of SS of 121 hybrids and corresponding parental hybrid combinations is shown in Table S12.

Table 8 Multiple comparison among the top 10 and bottom 10 hybrids with the highest and lowest SS, as well as their corresponding parent hybrid combinations (α = 0.05).
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The top 5 hybrid combinations with the highest degree of MPH SS were H0733 × P1812, H0733 × G6BS, H0733 × P2111, H0733 × G2BS and H0733 × C1117. Use the Dictionary search on demand package to find the corresponding tree species: (E. tereticornis × E. urophylla) × (E. pellita), (E. tereticornis × E. urophylla) × (E. grandis), (E. tereticornis × E. urophylla) × (E. pellita), (E. tereticornis × E. urophylla) × (E. grandis) and (E. tereticornis × E. urophylla) × (E. camaldulensis). There was no significant difference between the two hybrid combinations H0733 × P2111 and H0733 × G2BS. What were the 5 hybrid combinations with the lowest degree of SS in the MPH were U1101 × open pollination, U2223 × E. camaldulensis, U952 × 3327, T15 × DN4 and U3423 × DH3226. Use the Dictionary search on demand package to find the corresponding tree species: (E. urophylla) × (open pollination), (E. urophylla) × (E. camaldulensis), (E. urophylla) × (E. urophylla × E. grandis), (E. tereticornis) × (E. dunnii) and (E. urophylla) × (E. urophylla × E. grandis). And there was no significant difference between U952 × 3327, T15 × DN4 and U3423 × DH3226 (Table 8).

The top 5 hybrid combinations with the highest degree of SS in the HPH were 13H231 × open pollination, U952 × T105, 06H16 × DH3226, U3423 × C2232 and T15 × U1101. Use the Dictionary search on demand package to find the corresponding tree species: (E. urophylla × E. grandis) × (open pollination), (E. urophylla) × (E. tereticornis), (E. tereticornis × E. urophylla) × (E. urophylla × E. grandis), (E. urophylla) × (E. camaldulensis) and (E. tereticornis) × (E. urophylla). There was no significant difference between 13H231 × open pollination and U952 × T105. What were the 5 hybrid combinations with the lowest degree of SS in the HPH were U1101 × open pollination, U2223 × E. camaldulensis, U3423 × DH3226, H64 × open pollination and T15 × DN4. Use the Dictionary search on demand package to find the corresponding tree species: (E. urophylla) × (open pollination), (E. urophylla) × (E. camaldulensis), (E. urophylla) × (E. urophylla × E. grandis), (E. tereticornis × E. pellita) × (open pollination) and (E. tereticornis) × (E. dunnii). There were significant differences between the first two hybrid combinations and the last three hybrid combinations (Table 8).

Based on the aforementioned traits, the developments and SS of 19H56 (U1617 × H253) were notably commendable. In contrast, the developments and SS of 19H85 (U3423 × T131), 19H115 (U6 × open pollination) and 19H37 (06H16 × U6) exhibited subpar performance. H0733 × G6BS displayed the most significant MPH across all five traits, while T15 × DN4 demonstrated the least MPH in these traits. Moreover, H64 × open pollination, U1101 × open pollination, and T15 × DN4 manifested the weakest HPH in the five traits under consideration. Notably, the inclusion of trunk SS as an artificial measurement trait carried considerable importance when evaluating the growth traits of four age eucalypt.

We observed that despite the C254 × 06H241 hybrid combination exhibiting the greatest SS trait, it did not demonstrate any heterosis, as indicated by both MPH and HPH being zero. Consequently, this particular hybrid combination was omitted from the analysis of the minimum individual trait effects outlined in the preceding results pertaining to hybrid combinations.

When considering SS characteristics, hybrids U3423 and 13H231 exhibited the highest female parent GCA, while hybrids H64 and 3229 demonstrated the least, displaying statistically significant distinctions between the pairs (Table S13).

Genetic parameter analysis of 5 growth traits

The estimation of genetic parameters for five growth traits in this study showed that the variances of GCA for DBH, HT, Vol, SUR, and SS were 28.97%, 27.94%, 57.75%, 62.97%, and 47.32, respectively. The variances of SCA were 71.03%, 72.06%, 42.25%, 37.03%, and 52.68%, respectively. Except for SS, there were significant differences in GCA and SCA for other traits. The narrow heritability of DBH, HT, and SS was less than 50%, indicating that they were mainly controlled by non additive genetic effects and less controlled by additive effects genetically. And Vol and SUR were mainly controlled by additive effects. Except for SS, the broad heritability of other four growth traits reached 90%, indicating that these traits can be genetically improved through controlled pollination (Table 9). These results indicated that it is necessary to simultaneously consider the GCA of the parents and the SCA of the parent combinations in combined selection for interesting traits, so as to achieve the goal of scientific utilization of eucalypt heterosis.

Table 9 Estimation of overall genetic parameters for 5 growth traits.
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Subsequently, we analyzed the genetic parameters of 5 growth traits in the hybrid combinations of 26 tree species in this study (Tables S14–S39). We found that when it came to specific tree species, the five growth traits of hybrid combinations of different tree species were greatly influenced by additive and non-additive variance. All traits completely controlled by non-additive effect were (E. tereticornis × E. urophylla) × (E. urophylla), (E. urophylla) × (open pollination) and (E. urophylla × E. grandis) × (open pollination). Completely controlled by additive effect were (E. tereticornis × E. urophylla) × (E. camaldulensis), (E. tereticornis × E. urophylla) × (E. grandis), (E. urophylla) × (E. pellita × E. tereticornis), (E. urophylla × E. grandis) × (E. pellita) and (E. urophylla × E. grandis) × (E. tereticornis). The Vol and SUR of individual hybrid combinations of tree species were subject to additive variance, akin to the overall genetic parameters. Findings suggest that, with the exception of the broad heritability observed in certain hybrid combinations involving (E. tereticornis) × (E. urophylla) and (E. urophylla) × (E. pellita × E. camaldulensis), most traits in hybrid combinations of other tree species exhibited significant heritability. The study underscored the pivotal roles of GCA and SCA in shaping the traits of hybrid tree species, emphasizing their importance in harnessing heterosis and selecting superior hybrids.

Discussion

The origins of hybrids exhibiting superior growth traits

Studies had shown that the E. grandis × E. camaldulensis hybrid had lower straightness44. Theoretically, notable variations were anticipated in the hybrids resulting from the interbreeding of distinct parental species. The hybrids with superior growth traits and SS had the highest number of occurrences of the female parent E. urophylla (i.e. the female parent was E. urophylla or a hybrid of E. urophylla with other tree species). The female parent of the hybrid with the highest SS was mostly U3423. In addition, the combination of (E. urophylla) × (E. tereticornis) and (E. urophylla) × (E. pellita × E. camaldulensis) tree species could produce hybrids with the best SS.

When the female parent exhibited a hybrid of E. urophylla and E. tereticornis, the resulting hybrids tended to display inferior growth traits. The male parent of the hybrid with the lowest SS was mostly open pollination. The female species contributing to hybrids with suboptimal SS were typically E. urophylla, E. urophylla × E. grandis and E. tereticornis × E. pellita. Notably, employing the orthogonal breeding design of (E. tereticornis) × (E. urophylla) had shown potential in producing hybrids with commendable growth traits. Conversely, the reciprocal cross design of (E. urophylla) × (E. tereticornis) tended to yield hybrids with inferior growth traits.

Our initial findings suggested that the hybridization of tree species (E. urophylla) × (E. urophylla × E. grandis) yields hybrids exhibiting exceptional growth traits. The absence of a significant differences in Vol between the U1101 × 3229 and U3423 × 3327 hybrids in prior findings might be attributed to the identical parentage of the tree species (E. urophylla) × (E. urophylla × E. grandis), resulting in the superior growth traits observed in the hybrids of these two hybrid combinations. The growth traits of the hybrids resulting from the female parent of E. tereticornis × E. urophylla exhibited suboptimal traits, suggesting a potential strong dominant influence from the former hybrid. Notable observations included the lack of significant differences in Vol among the hybrids of 06H16 × E. camaldulensis, 06H16 × U6, and U6 × open pollination. Additionally, variations in HT were insignificant between hybrids of the first two, while DBH did not significantly differ in hybrids of the latter two. This consistency could be attributed to the common female parent of 06H16 in the first two and the common female species of E. tereticornis and E. urophylla in the three combinations. For E. urophylla × E. grandis hybrids, dominance genetic effects accounted for nearly 60% of the total genetic variance. It seemed that the most appropriate breeding strategy might be exploits non-additive variance, such as the reciprocal recurrent selection scheme or reciprocal recurrent selection with forward selection45.

The relationship between the level of combining ability and tree species

We found that U1101 had a high level of parental coordination at this time. But when U1101 was used as the female parent, its SCA with the hybrid combinations of 3229 and open pollination was the lowest. When the female parent 06H16 was utilized, it exhibited the lowest GCA, while displaying the highest SCA when combined with the LL13-1 male parent. In contrast, the male parent 3229 demonstrated the highest GCA. However, its SCA was at its lowest when paired with the female parent U1101. Moreover, when 3229 served as the female parent, it displayed the lowest GCA in terms of SS traits. On the other hand, the male parent U3423 showcased the highest GCA. Particularly, U3423 displayed the highest SCA as a female parent when used with hybrid combinations involving 3327, LY4, and E. camaldulensis. Furthermore, in terms of SS traits, U3423 also demonstrated the highest GCA when utilized as the female parent. When 13H231 was employed as the female parent, it typically exhibited a high GCA of SS, whereas when H64 was the lowest.

As a result, the GCA of a tree species as both a parent and a progenitor might not consistently exhibit a positive correlation with its SCA. The association between the GCA and SCA levels of a particular tree species didn’t follow a distinct pattern. Combining ability represented the inherent potential of parents to produce superior hybrids46. It was important to noted that the pairing of parents with high GCA didn’t always result in hybrids with high SCA47, just as the combination of parents with low GCA didn’t necessarily yield low SCA48,49,50,51.

The SCA of U3423 × 3327 was the highest, while the parents of other hybrids with good growth performance did not show any special performance in SCA. Notably, among the 12 parents of the top-performing hybrid, four of them—U1101 (E. urophylla), U1240 (E. urophylla), U3423 (E. urophylla) and 3229 (E. urophylla × E. grandis)—consistently demonstrated high GCA. This suggested that parents displaying SCA were more likely to yield outstanding hybrids, highlighting the importance of enhancing parental combining ability as a crucial strategy for achieving heterosis. The effect of E. tereticornis male variance was significant for 2.5- and 4-year-old growth except for H (4), and E. urophylla × E. tereticornis interaction was significant for 0.5- and 1.5-year-old growth, whereas E. urophylla female effect was not significant for the majority of traits analyzed. Both additive and dominance gene action were present in the genetics of all the traits measured at most ages52.

The GCA was responsible for most of the variations between the hybrids53. Through the analysis of GCA, we found that E. urophylla had a higher GCA, but there were also differences due to different varieties. Because U1101, U1240 (the highest female parent GCA), U3423, U1101 (the highest male parent GCA) were all E. urophylla. And 3229, which had the highest GCA in the male line, was also a hybrid of E. urophylla. The tree species demonstrated the lowest GCA include hybrids of (E. tereticornis × E. urophylla), (E. pellita × E. tereticornis) (the lowest female parent GCA), E. dunni and E. grandis (the lowest male parent GCA). Notably, E. tereticornis was anticipated to exhibit the lowest GCA, primarily due to the two varieties with the lowest GCA of the female parents were usually hybrids of E. tereticornis with other tree species. Moreover, the variances of GCA and SCA in E. urophylla and E. tereticornis varied significantly based on the specific tree species combinations, indicating that the genetic effects on growth from these two tree species can be influenced by their respective breeding partners.

Through analysis of SCA, we found that there was no significant difference in the HT trait between (E. urophylla) × (E. urophylla × E. grandis), (E. tereticornis × E. urophylla) × (E. urophylla), (E. tereticornis × E. urophylla) × (E. urophylla × E. tereticornis). There was no significant difference in DBH traits between (E. tereticornis × E. urophylla) × (E. urophylla × E. tereticornis), (E. urophylla) × (E. exserta). There was no significant difference in the SUR trait between (E. urophylla) × (E. tereticornis × E. grandis), (E. urophylla) × (E. urophylla × E. grandis) and (E. urophylla) × (open pollination), while there was no significant difference in the DBH and Vol traits between the SCA of the first two. There was no significant difference in the HT trait between the special coordination abilities of (E. urophylla) × (E. pellita) and (E. urophylla) × (open pollination).

The research revealed that U3423 (E. urophylla) exhibited the greatest SCA when employed as the female parent in hybridization with other parental varieties. Furthermore, (E. tereticornis × E. urophylla) also displayed notable SCA levels as the female parent in crosses with other parental varietie. Conversely, E. urophylla acted as the female parent in hybrid combinations displaying the lowest SCA, indicating discernible variations in SCA growth attributes among distinct varieties within the same tree species. Thus, it was tentatively inferred that diverse cultivars of a singular tree species manifest significant disparities in SCA traits. The outcomes of the analysis of variance suggested that female parents of hybrid combinations exhibiting insignificant differences in SCA growth traits predominantly consist of E. urophylla and E. tereticornis × E. urophylla, with varying male parent species. Hence, there was an indication that E. urophylla and E. tereticornis × E. urophylla potentially exhibited strong dominant influences, a notion reinforced by our genetic parameter evaluations for the ultimate tree species, as both were capable of significantly modulating variance deviation when employed as female parents. Notably, despite the impact of non-additive effects on (E. urophylla) × (E. urophylla × E. grandis), the SCA levels among distinct varieties within this tree species amalgamation differed, underscoring the necessity to meticulously considered the specific varieties of the parents when determining SCA levels.

Research indicated that non-additive genetic variation explained the majority of the total genetic variation in E. grandis × E. urophylla seedling and clonal populations54. Subsequently, they indicated that the majority of the pre-eminence of non-additive genetic variation was explained by the proportion of dominance variance55. E. urophylla exhibited the highest GCA and the most pronounced SCA among the tree species studied. The female parents, particularly the species E. urophylla and E. tereticornis × E. urophylla, significantly impacted the expression of SCA. Analysis of genetic parameters, including growth traits and SS, revealed that the growth patterns of eucalypt were influenced by non-additive genetic effects due to their low narrow heritability. Notably, there was minimal disparity in the variations of GCA and SCA concerning SS, suggesting a potential joint influence of both GCA and SCA on this trait. Alternatively, the insignificance of variance effects in the context of SS could imply that this trait was artificially constrained to a narrow range, diminishing the magnitude of its genetic variance.

The differences in Vol and SUR variations between GCA and SCA were notably more pronounced, with additive variation potentially exerting a prominent influence on these growth traits. Particularly noteworthy was the significantly higher additive variance observed in Vol compared to non-additive variance. This disparity could be attributed to Vol being an indirect trait derived from the integration of DBH and HT, both having substantial numerical values, thus leading to distinct additive and non-additive variances. This observation might suggest that the overall growth trait Vol was predominantly influenced by additive variation, while the individual growth traits DBH and HT were more impacted by non-additive variation. This might indicate that high genetic correlations between growth traits HT and DBH, controlling by the same class of genes in an organism, e.g., 0.87 in 9-year-old E. urophylla56 and 0.71–0.96 at ages 5 and 8 in P. caribaea var. hondurensis × P. tecunumanii and P. caribaea var. hondurensis × P. oocarpa57.

The relationship between heterosis and tree species and tree species combinations

Possible explanations for hybrid superiority included heterosis, complementarity, and greater allelic diversity58. In Liang’s case, the female species E. urophylla grew usually faster than the male E. tereticornis, and the better growth of their hybrids than E. urophylla OP families might indicate the effect of heterosis59. Research demonstrated that while the male E. tereticornis exhibited generally higher wood basic density than the female E. urophylla, it seemed that their hybrid mean of wood density was intermediate between the parental species60.

We believed that the hybrid combinations of E. tereticornis × E. urophylla (especially variety H0733) as the female parent had the strongest MPH in terms of growth and SS, and might have a dominant genetic effect. There was no significant difference in the MPH of the 5 hybrid combinations (E. tereticornis × E. urophylla) × (E. urophylla × E. tereticornis), (E. tereticornis × E. urophylla) × (E. pellita), (E. camaldulensis) × (E. tereticornis × E.urophylla), (E. urophylla × E. grandis) × (E. urophylla × E. grandis) and (E. tereticornis × E. urophylla) × (E. grandis) in HT, the MPH of the first three combinations in DBH, and the MPH of the first two combinations in Vol. This was because the female parents in the first two hybrid combinations were both H0733, which might also indicated that there was no significant difference in MPH between H0733 and C254 when they were used as female parents in the hybrid combinations. In addition, there was no significant difference in SS between H0733 × P2111 and H0733 × G2BS. Peng et al. mentioned superior growth of E. urophylla × E. tereticornis hybrids earlier61. The basic density was good within the range of some popularly cultivated hybrid clones of E. urophylla × E. grandis and E. urophylla × E. tereticornis38.

(E. urophylla) × (E. urophylla × E. grandis) and (E. urophylla) × (E. camaldulensis) was no significant difference in the HPH in HT, and in addition, there was no significant difference in the HPH in SS between (E. urophylla × E. grandis) × (open pollination) and (E. urophylla) × (E. tereticornis). This might be because the female species of both hybrid combinations were either E. urophylla or its hybrid. The investigation of the hybrid combinations exhibiting the least HPH revealed that when the male parent displayed open pollination, the HPH of the hybrid combinations with respect to growth traits and SS were notably poor. Genetic correlations were mostly favorable for simultaneous improvement on growth and wood traits. Additive and non-additive genetic effects should be considered in making a hybrid breeding strategy62. Particularly, the combination of parent species (E. urophylla) × (E. camaldulensis) demonstrated an exceptionally pronounced HPH in terms of SS, wherein the influence of both additive and non-additive effects was distributed almost evenly across the highest and lowest values, indicative of a substantial overall heritability. Consequently, it was imperative to devote increased consideration to the specific genetic composition of the parent varieties in order to optimize the HPH.

Significant female and male genetic effects were found in HT and DBH of single-site trials of E. urophylla × E. pellita by Bouvet and Vigneron. (mating design R90-10;63) and E. urophylla × E. camaldulensis by Gan et al.64. Non-significant female × male interactions were also observed in other hybrid populations, such as E. urophylla × E. grandis (mating design R89-20) and E. urophylla × E. pellita (mating design R89-21) for HT and DBH at age 4 and earlier63. The findings indicated that the presence of E. urophylla in the female parent, whether it was a pure E. urophylla or a hybrid with other tree species, consistently resulted in higher broad heritability compared to other tree species combinations. This underscored the robust hereditary influence of E. urophylla, and highlights the MPH and HPH in growth traits exhibited by its hybrids. The distinctions among female parent varieties within hybrids exhibiting the most pronounced MPH were negligible, despite the specific varieties. Furthermore, within hybrids displaying lowest MPH of SS, the predominant female parents were predominantly E. urophylla, with the exception of one female parent, E. tereticornis, which exhibited a statistically insignificant difference in this trait.

The findings suggested that E. urophylla held considerable research significance in the realm of heterosis. There was no significant difference in the MPH of the two hybrid combinations (E. urophylla) × (E. tereticornis × E. grandis) and (E. urophylla × E. tereticornis) × (E. brassiana) in terms of HT, which further indicated the pivotal involvement of E. urophylla in the genetic transmission of MPH. The vertical stature of the female parent of E. urophylla exhibited variability. Nevertheless, research reported low narrow-sense heritability and dominance effect for DBH (ages 2–10) and Pilodyn-based wood density (age 6), respectively, in an E. globulus factorial mating population65. However, extremely high narrow-sense heritability values were described elsewhere, especially for Klason lignin content at age 14 in E. urophylla (a factorial mating population of 33 full-sib families;66) and 0.84 for cellulose content at age 11 in E. globulus (35 open-pollinated families;67).

Parental selection based on combining ability and heterosis

The study revealed that the hybrid combination of (E. tereticornis × E. urophylla) × (E. urophylla × E. tereticornis) exhibited notable SCA, MPH and HPH in growth and enhanced SS traits. This might indicate that when parents were hybrids of reciprocal cross of the same tree species, they might have pronounced SCA and heterosis. (E. urophylla × E. grandis) × (E. urophylla × E. grandis) demonstrated strongest MPH and HPH in growth traits, suggesting the potential for generating hybrids with pronounced heterosis through self-pollination. Furthermore, the SCA and HPH observed in (E. urophylla) × (E. urophylla × E. grandis) and (E. urophylla) × (E. camaldulensis) were notably significant. Notably, hybrid combinations displaying reduced MPH which HPH was also generally lower, consistently manifest heterosis in terms of SS. Thus far, great success in heterosis exploitation in E. urophylla × E. grandis has been achieved in tropical and sub-tropical plantation forestry in South America, Asia and South Africa68,69.

The SCA and heterosis exhibited by H0733 × U6 were deemed optimal. Despite the fact that the GCA of the parental lines was not particularly strong, their performance post-hybridization remained impressive, resulting this hybrid combination might confer the most robust genetic advantage. Conversely, the hybrid combination U3423 × 3327 displayed the most pronounced SCA and HPH. (E. urophylla × E. grandis) × 06H241 exhibited robust heterosis, while the GCA performance of H0733 and 06H241 was not notably remarkable. The hybrid combination of H0733 × G6BS demonstrated exceptional MPH. Their hybrids might have significant differences in growth traits from one of their parents, which could become a source of variation.

The SCA of U952 × EC106 was the lowest, and the MPH in growth traits was the weakest. The three hybrid combinations T15 × DN4, H37 × open pollination and U6 × br22 had the worst heterosis in terms of growth traits. Based on the preceding discourse, T15 × DN4 displayed minimal heterosis with respect to SS, whereas H64 × open pollination and U1101 × open pollination exhibited the least HPH concerning growth and straightness. The analysis indicated notable underestimation in GCA or SCA for DN4, H64 and U1101.

In addition to the calculation indicators such as GCA, SCA, MPH, and HPH selected in this article, many other indicators could also be used to evaluate heterosis and conduct breeding of superior varieties. Nikles and newton proposed the concepts of general and specific hybridizing ability (GHA and SHA, respectively) to measure the parental additive and non-additive genetic effects, respectively, for interspecific hybrid crosses70. So far, GHA and SHA have been evaluated in a number of forest tree taxa, e.g. European larch (Larix decidua MILL.) and Japanese larch (L. kaempferi (LAMB.) CASUR.)71 as well as flooded gum (E. grandis HILL ex MAIDEN) and Timor mountain gum (E. urophylla S. T. BLAKE)72. Research suggested the potential utility of GDIA (GDs based on effect-increasing) and GDDA (effect-decreasing alleles) for molecular prediction of hybrid performance, SHA (specific hybridizing ability), and heterosis in eucalypt and might have implications for hybrid breeding in other plants73. Studies have shown low correlations between EST-SSR-based GD and MPH for all the four traits in the E. urophylla × E. tereticonis analyzed in wheat74.

Python assisted genetic variation research in forest trees

The genetic materials studied in present research comprised 121 hybrids, 19 female parents and 44 male parents, which involved a large amount of traits data. It needed classified hybrids and their parents, parental combinations, and tree species repeatedly in the evaluating for parental combining ability and heterosis, which required a large amount of screening and classification work and was prone to errors. So we written Python languages and used it for data classification and statistics, greatly improving the efficiency and accuracy of data analysis. Given the inherent potential for human-induced inaccuracies in manual measurements of tree growth parameters (such as tree height), the application of Python software to model and estimate tree growth could greatly improve the efficiency and accuracy of evaluating target species, thereby assisting in the genetic improvement of trees.

For example, a research used optical data from plantation to estimate the biomass of different tree species in high-density plantation by selecting decision trees, random forests, and calibrating models based on support vector machines and eXtreme gradient boosting algorithms75. A B/S application developed by Python and Django, could help breeders find useful knowledge and patterns more quickly using data analysis and optimized result generated from decision tree and spectral biclustering algorithm, and improve the accuracy and efficiency of crop breeding76. There was research on the deployment of an improved adaptive parallel genetic algorithm (IAPGA) based on Python language, which reduced the inbreeding level and was used to improve the poor genetic gain, genetic diversity, and low seed setting rate in crops77. Ghimire focused on the analysis of seed traits using a Python algorithm78. Bayesian optimization was implemented using the BoTorch module of Python to optimize budget allocations to the PIC and each stage of the VDP79. The above studies all indicated that Python could be used for genetic improvement research in agriculture and forestry.