Genetic Parameter Estimates for the Growth and Morphological Traits of Castanopsis hystrix Families and the Genotype × Environment Interaction Effects

: Castanopsis hystrix , a timber resource from Southeast Asia, is characterized by rapid growth and high yield, but plantation quality and efﬁciency improvements are required. Twenty-year-old C. hystrix experimental forests in Yulin, Liuzhou, and Pingxiang in Guangxi Province, China, comprising 21 open-pollinated half-sib families, were used in this study. Genetic variations in the growth (tree height, diameter at breast height (DBH), and volume (V)) and morphological (height to live crown base (HCB), crown width (CW), and branch angle) traits were assessed, and the genetic parameters were estimated to clarify the genotype × environment interaction effects. The average values for the tree height, DBH, V, HCB, CW, and branch angle were 16.33 m, 17.25 cm, 0.21 m 3 , 6.68 m, 2.15 m, and 45.45 ◦ , respectively. The most important sources of variance for the tree height, DBH, V, and HCB were the block and family, whereas the location, family, and family × location had signiﬁcant impacts on the tree height, DBH, V, and HCB ( p < 0.01). The family heritability for each trait was 0.35, 0.38, 0.62, and 0.19, respectively. Excellent families with strong adaptability and genetic stability were identiﬁed using BLUP–GGE biplots for single and multiple traits. The results provide a theoretical basis for the efﬁcient cultivation of C. hystrix in South China.


Introduction
The genotype × environment interaction effect (G × E) can conceal the authenticity of genetics, reducing selection efficiency and accuracy [1]. Moreover, the G × E can evaluate the genetic stability and adaptability of tree genotypes in various locations [2,3]. Therefore, the G × E has become an essential factor in the selection and popularization of forest tree genotypes. In addition to focusing on the genetic variations of the tested traits, breeders should also pay more attention to the genetic stability and adaptability of genotypes in various environments. Doing so will help them effectively match germplasms and sites. In view of their research, the growth and morphological traits of plant species are not only regulated by their genotypes and the environment but also affected by the interaction between the two [4][5][6]. Due to the G × E, these traits exhibit varying rank and scale effects on tree traits in different locations [1]. Such variances affect the estimation of genetic parameters such as heritability and genetic gains [1,7], which, in turn, affect the formulation of breeding strategies [8].
Breeders in China and overseas have developed various statistical models to evaluate the patterns and scales of the G × E, analyze the relationship between genetic variations

Overview of the Experimental Sites
The three sites used in this study, YL, LZ, and PX, are all on terrains with low hills. The soil is acidic red loam, and the soil layer is more than 1 m deep. The three locations experience a subtropical monsoon climate, which is warm, humid, and with precipitation and heat occurring at the same time. There is little difference between the annual average and the extreme high temperatures, although the extreme low temperatures show large variations. The extreme low temperature at PX is >0 • C, and thus there is no freezing damage throughout the year, whereas at LZ, it is −8 • C, with water freezing easily in the winter, and at YL, freezing occurs occasionally ( Table 2).

Determination of Traits
In August 2022, the Vertex IV ultrasonic altimeter (Haglöf IV, Stockholm, Sweden; accuracy 0.1 m) was used to measure the tree height (H) and the vertical height to the lowest branch from the ground to the tree crown (HCB). The DBH was measured with a DBH ruler (accuracy 0.1 cm) 1.3 m from the ground. The crown width was calculated as the half-sum of the four crown radii, which were measured as the horizontal distances from the center of the tree bole to the greatest extent of the crown from the tree bole [20,21]. When the growth survey and determination of traits were carried out at each location, three plants from each plot in each block were measured, and the measurements were repeated thrice. This was because the preservation rates of the families in YL and PX were <0%. In general, 63 plants were surveyed in each block, and 189 plants survived at every site. A total of 567 tree-growth and morphological-trait data were collected.
The equation for calculating the individual plant V is as follows: where V is the individual plant volume, H is the tree height, DBH is the diameter at breast height, and f is a form factor whose value is 0.421 [22].

Estimation of Genetic Parameters
Microsoft Excel 2010 was used for the statistical compilation of the data. Genstat 18.0 software was used to estimate the variance components and genetic parameters of the growth and morphological traits of the participating families.

Estimations of Single-Location Genetic Variance and Heritability
The single-location genetic statistical model is as follows: where Y ij is the average value of the plot for the jth family in the ith block; X is the average value of the group; B i is the value of the effect for the ith block; F j is the value of the effect for the jth family; B i × F j is the block × family interaction effect; and E ij is a random error. The equation for the single-location family heritability (h 2 F ) is as follows: where σ 2 F , σ 2 F×B , and σ 2 E denote the variance component of the family, variance component of the block × family interaction effect, and variance component of the environment, respectively; and n and b denote the number of families and blocks, respectively.

Estimation of Multiple-Location Genetic Variance and Heritability
The multiple-location genetic statistical model is as follows: where Y ijk is the average value of the plot for the jth family of the ith block at the kth location; X is the average value of the group; S k is the value of the effect at the kth location; S k × B j is the value of the effect of the jth block at the kth location; F j is the value of the effect of the jth family; S k × F j is the value of the interaction effect between the kth location and the jth family; S k × B i × F j is the value of the interaction effect between the ith block and the jth family at the kth location; and E ijk is a random error. The equation for the multiple-location family heritability (h 2 F ) is as follows: where σ 2 F is the variance component of the family; σ 2 S×B×F is the variance of the block × family effect at a location; σ 2 S×F is the variance of the location × family effect; σ 2 E is the variance component of the environment; and n, b, and s represent the number of families, blocks, and locations, respectively.

Estimation of the Genetic Coefficient of Variances and Environmental Coefficient Variances
The genetic coefficient of variance (CV g ) is as follows: The environmental coefficient of variance (CV e ) is: where σ 2 F and σ 2 E represent the variance component of the family and environment, respectively; and X is the average value of the traits.

Estimation of Genetic Gains
The equation for genetic gains (∆G) is as follows: where s i is the selection intensity; δ p is the standard deviation; h 2 is the family heritability; and X is the average value of the traits.

BLUP-GGE Analysis of the Growth and Morphological Traits
The best linear unbiased prediction method was used to estimate the breeding values of the growth and morphological traits of the C. hystrix families. The theoretical model used was as follows: where Z is the breeding value of the quantitative traits; µ is the overall average value; S i is the fixed effect of the environment i; SG ij is the random interaction effect between the jth family and the ith location; and e ij is a random error. Genstat 18.0 software was used to prepare the BLUP-GGE biplots. Specifically, the impacts of the planting environment on the growth and morphological performance of the C. hystrix families were eliminated using analysis of variance (ANOVA). The main effects of the genotype and G × E were retained. The single-value decomposition method was then used to elucidate the principal components.

Genetic Variances in the Growth Traits of C. hystrix
The results of the single-location ANOVA for the growth traits of 20-year-old C. hystrix are shown in Table 3. The block and family effects for the tree height, DBH, and V at each location were either significant (p < 0.05) or extremely significant (p < 0.01). The block × family effects of the three traits were extremely significant at the LZ site (p < 0.01). However, there were no significant differences at PX, and the tree height was only found to have a significant interaction effect at YL (p < 0.05). The interaction effects of the DBH and V were not significant. Analyses of the performances of all families showed that the average annual growth in the height, DBH, and V for the C. hystrix trees at 20 years of age was the smallest at YL, with values of 0.64 m, 0.73 cm, and 0.006 m 3 , respectively. This was followed by LZ and then PX, with values of 0.74 m, 0.92 cm, and 0.0075 m 3 , and 0.94 m, 1.12 cm, and 0.018 m 3 , respectively (Table 4). Among the three experimental forests, the families with the largest growth in tree height were 21, 1, and 9, with values of 18.41, 20.80, and 19.93 m, respectively. The DBH growth for family 21 at YL and LZ was the largest at 20.53 and  (Table 4). The results of the triple-location ANOVA for the growth traits of C. hystrix are shown in Table 5. The results indicate extremely significant differences (p < 0.01) among families and locations for the tree height, DBH, and V, as well as for the family × location effect. These results indicate that the growth performances of the same family under different site conditions were significantly different. The growth performances of different families within the same site were also inconsistent, but there were obvious family × site effects.

Genetic Variances in the Morphological Traits of C. hystrix
The results of the single-location ANOVA for the morphological traits of the 20-year-old C. hystrix are shown in Table 6. The block and family were determined to be the main sources of high HCB variances. However, the block × family effect was only extremely significant at the YL site (p < 0.01). The main sources of CW variances among the C. hystrix families at YL were the block, family, and block × family. Their contributions to the CW variance, however, were not significant at LZ and PX. A descriptive statistical analysis of the morphological traits of the 20-year-old C. hystrix families is shown in Table 7. From the perspective of the families' overall performance, the average HCB, CW, and branch angle were 6.68 m, 2.15 m, and 45.45 • , respectively. The average values for the morphological traits at the PX pilot location were higher than the group average, indicating that the PX pilot plants had the strongest natural adjustment abilities. The CW was relatively small after the large branches from the lower layer were pruned, leading to the maintenance of good crown shapes. The HCB of the C. hystrix families at LZ was the lowest. The thick branches at the sides were not pruned in time, which affected the crown shapes.
The ANOVA results for the morphological traits of the families at the three locations showed that the location, family, and family × location effects were all extremely significant (p < 0.01). This indicated that the pruning abilities of trees in the same family were significantly different under different site conditions, the pruning strength of different families at the same location was different, and the pruning abilities of the various families at the three locations lacked stability. The CW and branch angle were only significantly different between locations (p < 0.01). Variances among families and the family × location effect did not reach a significant or extremely significant level, indicating that site conditions were the main factors Table 8.  Note: ** indicates significant differences at the 0.01 levels. HCB is the height to live crown base, CW is the crown width. Total means total variance.

Estimating the Genetic Parameters for the Growth and Morphological Traits of C. hystrix
The ANOVA results for the CW and branch angle were not significant, and the variance components could not be resolved. Furthermore, the variance components of the family in terms of the tree height, DBH, V, and HCB ranged from 0.00001 to 3.59, indicating that these four traits were all genetically regulated. Relatively speaking, the genetic coefficients of variance for V (ranging from 17.88% to 34.21%) were greater than those for the other traits, indicating that the genetic stability of the individual plant V was weak. The DBH, tree height, V, and HCB of C. hystrix had strong heritabilities. The family heritability was 0.41-0.83, indicating that these traits were strongly regulated by genetics ( Table 9).
The environmental coefficients of variance for the tree height, DBH, individual plant V, and HCB were greater than the genetic coefficients of variance. Relatively speaking, these traits were more affected by the environment of the sites. The family heritabilities of the tree height, DBH, and V were 0.35, 0.38, and 0.62, respectively. These were thus found to be moderately heritable traits, and their values were greater than that of the HCB, indicating that the genetic stability of the growth traits was stronger than that of the morphological traits (Table 10).    Table 11.

GGE-BLUP
The results show that 82.90% of the variance in the tree height was affected by the genotype effect and the G × E (Figures 1a and 2a). Specifically, Principal Components 1 and 2 accounted for 44.87% and 38.3% of the total variances, respectively (Figure 1a). The which-won-where biplots show that the blue circle divided the three pilot sites into two site types: YL and PX were combined into one category and LZ was separate. The C. hystrix families on the outermost edge formed a pentagon based on two-by-two connections and enclosed the rest of the families. The five vertical lines of the pentagon divided the participating families into five different sectors. Among them, family 21 was at the apex of the YL and PX sectors, whereas family 1 was at the apex of the LZ sector. This indicates that family 21 had the greatest growth at YL and PX, whereas family 1 had the greatest growth at LZ (see Figure 1a). The mean vs. stability biplots indicate that the 21 C. hystrix families were divided into three types. Families 10, 14, and 21 were highyielding but unstable, families 16 and 20 were high-yielding and stable, and families 2, 3,4,5,6,7,8,9,11,12,13,15,17,18, and 19 were low-yielding (see Figure 2a).

GGE-BLUP
The results show that 82.90% of the variance in the tree height was affected by the genotype effect and the G × E (Figures 1a and 2a). Specifically, Principal Components 1 and 2 accounted for 44.87% and 38.3% of the total variances, respectively (Figure 1a). The which-won-where biplots show that the blue circle divided the three pilot sites into two site types: YL and PX were combined into one category and LZ was separate. The C. hystrix families on the outermost edge formed a pentagon based on two-by-two connections and enclosed the rest of the families. The five vertical lines of the pentagon divided the participating families into five different sectors. Among them, family 21 was at the apex of the YL and PX sectors, whereas family 1 was at the apex of the LZ sector. This indicates that family 21 had the greatest growth at YL and PX, whereas family 1 had the greatest growth at LZ (see Figure 1a). The mean vs. stability biplots indicate that the 21 C. hystrix families were divided into three types. Families 10, 14, and 21 were high-yielding but unstable, families 16 and 20 were high-yielding and stable, and families 2, 3,4,5,6,7,8,9,11,12,13,15,17,18, and 19 were low-yielding (see Figure 2a).     The GGE biplots for the DBH explained a total of 93.35% of the total variance, of which Principal Components 1 and 2 explained 75.08% and 18.26% of the total variances, respectively (Figures 1b and 2b). Families 21, 2, and 3 had the largest DBH growth at YL, LZ, and PX, respectively ( Figure 1b); families 15 and 20 were high-yielding and stable ( Figure 2b); families 10, 14, and 21 were high-yielding but unstable; and families 1, 2, 3, 4, 5, 6,7,8,9,11,12,13,16,17,18, and 19 were low-yielding.
The sources of 75.55% of the V variance were the genotype effect and the G × E. Principal Components 1 and 2 accounted for 44.11% and 31.44% of the total variance, respectively (Figures 1c and 2c). YL and LZ belonged to the same site type and family 21 had the largest V growth, whereas PX was a separate site type in which family 18 had the largest V growth (Figure 1c). Families 14, 15, and 20 were high-yielding and stable; families 2 and 22 were high-yielding but unstable; and families 1, 3,4,5,6,7,8,9,10,11,12,13,16,17,18, and 19 were low-yielding (Figure 2c).
Principal Components 1 and 2 reflected 82.03% and 14.79% of the total variance, respectively (Figures 1e and 2e). Both principal components reflected 96.85% of the genotype effect and the G × site interaction effect. Family 21 had the best overall performance in terms of the tree height, DBH, individual plant V, and HCB (Figure 1e). Four families (10, 14, 20, and 21) had excellent and stable comprehensive performances (Figure 2e), whereas the remaining 27 families had poor growth and morphological performances overall. The average genetic gains for their growth traits-tree height (H), diameter at breast height (DBH), and volume (V)-and morphological traits-height to live crown base (HCB)-were 21.29%, 22.92%, 21.25%, and −0.14%, respectively (Table 12).

Discussion
Among the C. hystrix families investigated in this study, there were significant differences in their growth and morphological traits. These differences indicate that the traits have great genetic potential among the tested families, and excellent families could potentially be selected. The examined traits were also all found to exhibit significant effects based on the respective site, suggesting that C. hystrix has strong phenotypic plasticity. These findings have also been confirmed in numerous previous studies [15,[23][24][25]. The results of this study, however, have further revealed that the environmental coefficients of variance of the tested traits were greater than the genetic coefficients of variance, and the site factors had a substantial contribution rate to the growth and morphology of the C. hystrix families. These facts indicate that the environmental factor of the planting sites had a stronger impact on the variances in the corresponding traits than the G factor. This phenomenon is also consistent with previous research on conifers (such as Larix kaempferi and Pinus taeda) and broad-leaved species (such as Betula alnoides and B. platyphylla) [6,24,26,27].
According to a survey on natural factors in the original habitat of C. hystrix, the soil pH value ranged from 4.36 to 6.23 [28], which was consistent with the soil acidity among the three sites. Previous studies showed that the correlation between the growth traits of C. hystrxi and the soil pH was weak [29]. So, it can be inferred that the growth differences were basically unrelated to the soil pH in the trials. The growth performance of C. hystrix at the LZ and YL sites was worse than that at the PX site. This was because the first two sites are located close to the Tropic of Cancer and have lower cumulative temperatures, whereas the PX site is located further south with a higher cumulative temperature. Differences in latitude and altitude often lead to corresponding changes in the climate, soil chemical property, and other factors, which, in turn, affects tree growth [30]. In addition, the C. hystrix families at PX had the largest tree-height values, which were 5.90 and 1.29 m taller than those at YL and LZ, respectively. Even though the stand at the PX site maintained a high growth rate, its natural pruning abilities were also the strongest, which promoted the natural pruning of the thick branches. Consequently, the average HCBs of the C. hystrix families at PX were 2.49 and 2.76 m higher than those at YL and LZ, respectively.
The tree height, DBH, V, and HCB of the C. hystrix families presented rank and scale effects at the three investigated sites [1]. This phenomenon was similarly identified during the popularization and utilization of loblolly pine and other tree species [23][24][25][26][27] and is essentially caused by the G × E. When breeding forest trees, it is crucial to determine which environmental factors are the key driving factors for the G × E. Doing so provides an important reference for the division of suitable planting regions to help improve tree species. The geographical differences between YL, LZ, and PX led to differences in the cumulative temperature, precipitation, and soil nutrients of the forest land. For a specific genotype set, the greater the site heterogeneity, the higher the G × E amplitude [31]. In addition, differences in the responses to environmental changes among genotypes constitute the internal driving force generated by the G × E [1]. Therefore, the analysis of the G × E helps to estimate the real genetic parameters of environmental quantitative traits in multiple locations. These analyses also provide a basis for the selection of genotypes with excellent phenotypes and stable genetics, as well as optimizing environmental evaluations. By selecting the best genotypes for the appropriate site, the aim of increasing the production and efficiency of artificial timber forests can be achieved.
In addition to genetic regulations, the impacts of the environmental effects and G × E on the genetic parameter estimations for the measured traits cannot be ignored [32]. The site conditions of the single-location experiments were consistent and the block variances were relatively small, resulting in the overestimation of the heritabilities of the tested traits. Among them, the heritabilities of the tree height, DBH, and V were 0.41-0.72, 0.50-0.83, and 0.54-0.74, respectively. These values revealed genetic regulations at the moderate level or above, which was consistent with the results of Zhu et al. [18] and Fang [19]. However, the ANOVA results of the three locations showed that the high environmental variances and variances in the family × site effects had diluted the genetic potential of the traits.
In contrast to the results of this study, the single-and multiple-location heritabilities of the full-sib families in a third-generation horsetail pine seed garden were found to be similar [33]. This was mainly related to the genetic background of the tested families. In addition, the family heritabilities for the tree height, DBH, and V were higher than that of the HCB, indicating that growth traits were subjected to stronger genetic regulations. This was also consistent with the test results for B. alnoides [6].
Although the economic benefits of timber forests are dependent on their growth traits, the contributions of their morphological traits to their economic value cannot be ignored [32]. Improvements in morphological heritability are thus also considered an important component in the breeding of valuable tree species. The goal of forest tree breeding has thus changed from the selection of single traits to the comprehensive selection of multiple traits. However, owing to the inconsistent performances of the growth and morphological traits, it is often challenging to simultaneously improve the two trait types [4,6]. In the present study, multiple-trait BLUP-GGE biplots were used to select four families with excellent comprehensive performances. These families not only maintained their fast-growing characteristics but their morphological traits also performed well, such that their breeding efficiencies were in line with expectations. Considering that the tested stand was 20 years old and had reached half of the rotation period, the measured traits tended to be stable, and the measured results were accurate and reliable. The final families that were selected can thus be directly promoted and applied by forestry production units. These findings provide a theoretical basis for the efficient cultivation of C. hystrix in commercial forests in South China.

Conclusions
The genetic parameters for various traits of 21 C. hystrix families at 20 years of age located at three sites in China were estimated based on a comprehensive growth (tree height, DBH, and V) and morphological (HCB, CW, and branch angle) trait analysis. The aim was to clarify the impacts of the G × E. The results showed that the tree height, DBH, and average annual growth in the individual plant V of the C. hystrix families was 0.64-0.94 m, 0.73-1.12 cm, and 0.006-0.018 m 3 , respectively. Genetic testing at YL, LZ, and PX revealed that the tested traits were affected by the family, site, and family × site effects. The heritabilities of the tree height, DBH, and V were 0.35, 0.38, and 0.62, respectively, indicating moderate genetic regulation; HCB was under low-intensity genetic regulation with a heritability of 0.19. Considering the extreme significance of the G × E, the targeted cultivation of C. hystrix timber forests should aim to optimize the breeding objectives of improved varieties. Specifically, families 10, 14, 20, and 21 were selected as the four ideal families with comprehensive multiple traits, making them suitable for popularization and planting in various locations. The average genetic gains of the tree height, DBH, V, and HCB were 15.81%, 12.67%, 8.2%, and −0.14%, respectively. The GGE biplots based on BLUP were effectively applied to evaluate the C. hystrix families and their suitable planting sites, thereby providing a theoretical basis for the effective establishment and management of C. hystrix commercial forests in South China.  Data Availability Statement: When needed, data can be uploaded.