Impacts of stand origin, species composition, and stand density on height-diameter relationships of dominant trees in Sichuan Province, China

Schlüsselbegriffe: Bonität, Bestandesqualität, Abies fabri, Picea asperata, Pinus yunnanensis, Pinus massoniana, Cupressus funebris, Cunninghamia lanceolata, Quercus glauca, Betula platyphylla

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Abstract

Analysis of height growth of dominant trees is crucial for accurate evaluation of site quality and how this influences stand characteristics. This study explores, whether stand origin, tree species composition and stand density influence the growth process of stand dominant height. We used forest resource inventory data from 1283 permanent plots in Sichuan Province, China. Three dominant trees were selected from each permanent plot to calculate the average dominant height and diameter at breast height (DBH). The Chapman-Richards equation was used to construct a dominant height prediction model of each tree species based on DBH. The effects of the stand origin, species composition, and stand density on the upper asymptote parameter a, shape parameter b, and growth rate parameter c were analyzed using a dummy variable method. The results show that there was no statistically significant difference in parameters a, b, and c among different stand origins, species composition, and stand density. The upper asymptote parameters of the stand with a natural origin were greater than stands with an artificial origin. Species composition influenced the parameters among different coniferous species but was associated with large coefficients of variation, especially for broadleaf species. Stand density moderatly influenced the model parameters for all species. With an increase in stand density, the influence of stand density on the model parameters decreased gradually. Our results confirm that the relationship between DBH and height of dominant trees is useful to evaluate site productivity. However, this method has to consider stand origin and differences in stand density and species composition, especially for species with DBH-height relations sensitive to stand conditions.

Zusammenfassung

Die Analyse des Höhenwachstums dominanter Bäume ist wichtig für die präzise Beurteilung der Bonität und wie diese die Bestandesstruktur beeinflusst. Hier verwenden wir Waldinventurdaten von 1283 permanenten Plots aus der Provinz Sichuan, China. Drei dominante Bäume wurden ausgewählt, um mittlere Oberhöhe und Brusthöhendurchmesser (DBH) zu berechnen. Die Chapman-Richards-Gleichung wurde verwendet, um ein Oberhöhenschätzmodell für jede Baumart zu erstellen. Wir untersuchten dann den Einfluss von Bestandesursprung, des Mischungsgrads und der Bestandesdichte auf die Parameter a, b und c mittels Dummy-Variablen. Unsere Ergebnisse zeigten keine signifikanten Unterschiede von a, b und c nach Bestandesursprung, Mischungsgrad und Bestandesdichte. Der Parameter a war höher in Beständen mit natürlichen Ursprung im Vergleich zu künstlich begründeten Beständen. Der Mischungsgrad beeinflusste die Modellparameter, aber hatte eine sehr hohe Variabilität, insbesondere für Laubholzbestände. Bestandesdichte hat einen nennenswerten Einfluss auf die Parameter für alle Baumarten. Mit steigender Bestandesdichte nahm der Einfluss von Bestandesdichte auf die Modellparameter ab. Unsere Ergebnisse bestätigen, dass die Durchmesser-Höhenbeziehung hilfreich bei der Beurteilung der Bonität ist. Allerdings müssen bei dieser Methode der Bestandesursprung und Unterschiede in Bestandesdichte und Mischungsgrad berücksichtigt werden, insbesondere für Baumarten, die sensitiv gegenüber Bestandesbedingungen sind.

1 Introduction

The problem of an uneven age structure in mixed forests can be solved by using DBH instead of stand age (Trorey 1932) and the mean height of dominant trees to establish regression models to evaluate site productivity (Meyer 1940; Stout & Shumway 1982; Reinhardt 1982). The height of dominant trees corresponding to a reference DBH is referred to as the site condition (Vanclay & Henry 1988; Weiskittel et al. 2011), similar to the site index, which is the expected height at a certain reference age. As an effective method to evaluate mixed forests and uneven-aged forests (Huang & Titus 1993, 1994; Adeyemi & Adesoji 2016; Kourosh et al. 2017; Moreno-Fernández et al. 2018), the selection of the reference DBH affects the accurate assessment of the site form (Vanclay & Henry 1988). However, the method is quite sensitive to the selection of an index diameter (Goelz & Burk 1992), and Wang (1998a) found it to be an inadequate measure of site quality because it was not related to site index or ecological measures of site quality. This is likely because diameter growth is much more sensitive to stand density than height growth. Site form appears superior for natural secondary forests, whereas site index is superior for plantations, when assessing site quality in Qinling Mountains (Wu et al. 2015). Site index and site form are more accurate than site class in evaluating site quality (Buda & Wang 2006; Beltran et al. 2016; Duan et al. 2018; Fu et al. 2018). Forest formation was taken as the basic unit of site quality evaluation of tropical natural mountain rainforest in Hainan Island, and the vertical topographic guidance curve model was established by applying the average height of the dominant trees as the dependent variable and the average DBH as the independent variable. There was no statistically significant difference between the theoretical and measured values of the compiled site form model (Chen et al. 2000). The reference DBH obtained when the second derivative of the height – DBH equation is zero is the DBH with the maximum continuous growth of tree height.

It is particularly important to analyze the influence of stand origin, species composition and stand density on the relationship between DBH and the height of the dominant tree, when using the relationship to evaluate site quality. There are many studies on the impact of the origin, species composition, and stand density on stand factors (Weiskittel et al. 2011; Fu et al. 2018). Artificial stands, that is, stands originated from planting or sowing, have been reported to have a higher growth limit than natural stands (Weiskittel et al. 2011). Studies on mixed stands of Cunninghamia lanceolata show that different species composition had significant effects on the growth of DBH and the height of individual trees (Fu et al. 2018). The influence of stand density on the height of taller trees is not significant, and the influence of stand density on the average height of stands is also small with certain level of stand density (Stout & Shumway 1982; Huang & Titus 1993). There are further studies that show a significant effect of stand density on the allometric relations between diameter at breast height over bark and tree height (Wang 1998b; Bhandari et al. 2021). Stand density also has a significant effect on average DBH (Weiskittel et al. 2011). Existing studies lack analysis of the influence of stand origin, species composition and stand density on the relationship between DBH and the height of dominant trees by species, which also limits the application of the relationship between DBH and height to evaluate site quality.

It is still controversial to use the height – DBH relationship of dominant trees to evaluate site quality (Molina-Valero et al. 2019); the main reasons are the lack of systematic analysis of stand origin, species composition and stand density and other factors on the height – DBH growth process (Skovsgaard & Vanclay 2008; Peng 2000), which is the aim of this work. Combining a large number of plots with modeling, we use here dummy variables to analyze the different model parameters according to the factor classification, to explore the effect of stand factors on the growth process of dominant trees. This study is relevant for the scientific evaluation of site quality using systematic analysis.

2 Materials and methods

2.1 Research area and data source

Sichuan Province is located in the hinterland of southwestern China, straddling five geomorphic units: Sichuan Basin, Qinghai-Tibet Plateau, Hengduan Mountains, Yunnan-Guizhou Plateau, and Qinba mountains. The soil types are diverse. Yellow soil is the base soil in the eastern basin, while red soil is the base soil in the western basin. Sichuan Province is a transition zone between the eastern monsoon region and the Qinghai-Tibet Plateau in southwestern China. Extensive evergreen broad-leaved forests are distributed in the east and southwest of China. The alpine canyons and subalpine coniferous forests in the west of China are luxuriant. The northwestern plateau is covered with shrubs and meadows adapted to the alpine habitat. The distribution of tree species is shown in Figure 1.

The data used in this paper were obtained from the ninth continuous forest resource inventory data of Sichuan Province, which was established in 1979. Taking the whole province as a whole, the systematic sampling theory was adopted to arrange the plots in alternating intervals of 4 km × 8 km and 8 km × 8 km crossing each other successively. A total of 10,098 permanent plots were set up. The side length of a square plot was 25.82 m, and the area was 0.0667 hectare (ha). Species, size, relative location and other characteristics of each tree were measured in the plots. The diameter of the smallest tree measured was 5 cm. According to the dominant tree species whose stock accounted for the main part of the plot stock, 241 sample plots of Abies fabri, 173 sample plots of Picea asperata, 158 sample plots of Pinus yunnanensis, 127 sample plots of Pinus massoniana, 293 sample plots of Cupressus funebris, 89 sample plots of Cunninghamia lanceolata, 78 sample plots of Quercus semecarpifolia, 46 sample plots of Quercus glauca (also known as Cyclobalanopsis glauca), and 78 sample plots of Betula platyphylla were selected. The average height and DBH of dominant trees were calculated by selecting three dominant trees, which were the two tallest trees and the thickest tree, from each sample plot. In total, 1283 permanent plots were analyzed (Table 1).

2.2 Methods

The Chapman-Richards function (Lee et al. 2021; Nigh 2015) (equation 1), Schumacher function (equation (2) and Hossfeld function (equation 3) were used to fit the relationship between average DBH and average tree height of dominant tree species, and appropriate model fitting results were determined according to the goodness of model fitting (equation 4) and root mean square error (equation 5). Mean error (equation 6) was used for residuals analysis. A dummy variable analysis model was established based on the average DBH and average tree height of dominant trees. Dummy variable analysis has an advantage over other models in parameter comparison. Compared with other models, the Chapman-Richards model had a better fit and each parameter had biological meaning. Thus the Chapman-Richards model was used in the following analysis.

H_D is the mean dominant height; DBH is the mean diameter at breast height of dominant trees; and a, b, c are parameters.

ŷ_i is the predicted value; y_i is the observed value; and n is the number of samples.

Based on the dummy variable method, mixed the differences in the upper limit asymptote parameter a, growth curve shape parameter b and growth rate parameter c among different factors were analyzed.

H_D is the mean dominant height; DBH is the mean diameter at breast height of dominant trees; a_δ in equation (7), b_δ in equation (8), and c_δ in equation (9) are parameters to be solved.

Three factors, i.e., stand origin, species composition, and stand density were selected to analyze the impact on stand dominant height growth. Then, stand origin includes natural forests and artificial forests, and species composition includes the following: Pcs is a pure conifer stand (individual conifer species volume accumulation exceeds the threshold of 90%), Pbs is a pure broadleaf stand (individual broadleaf species volume accumulation exceeds the threshold of 90%), Rpcs is a relatively pure conifer stand (individual conifer species volume accumulation is between the range from 65% to 90%), Rpbs is a relatively pure broadleaf stand (individual broadleaf species volume accumulation is between the range from 65% to 90%), Mcs is a mixed conifer stand (conifer species volume accumulation exceeds the threshold of 65%), Mcbs is a mixed conifer and broadleaf stand (conifer species or broadleaf species volume accumulation is between the range from 35% to 65%), Mbf is a mixed broadleaf stand (broadleaf species volume accumulation exceeds the threshold of 65%), and volume accumulation is the ratio of the dominant species stock to the stock of the whole plot. We used eight stand density classes, including 1–300 ha^-1, 301–600 ha^-1, 601–900 ha^-1, 901–1200 ha^-1, 1201–1500 ha^-1, 1501–1800 ha^-1, 1801–2100 ha^-1, and more than 2101 ha^-1. In total, there were eight stand density levels of dummy variables based on the distribution of stand density of plots in Sichuan Province.

3 Results

3.1 Dominant height growth models

The fitting models for mean DBH and mean tree height of dominant trees are shown in Table 2. Compared with Schumacher and Hossfeld equation, the Chapman-Richards equation has better fitting efficiency. The best fit was found for Picea asperata, whereas Betula platyphylla had the lowest goodness of fit. The fit for coniferous species was better than that for broadleaf species. The root mean square error for Cupressus funebris model fitting was the smallest, compared with the largest for Abies fabri. The dominant height growth of a stand can effectively reflect the tree differentiation caused by site quality differences. 

According to the residual diagram of model fitting results (Figure 2), the residual sum of squares for Abies fabri, Picea asperata, Pinus yunnanensis, Pinus massoniana, Cupressus funebris, Cunninghamia lanceolata, Quercus semecarpifolia, Quercus glauca, and Betula platyphylla were 2745, 1731, 798.7, 923.7, 735.3, 235.8, 387.7, 187.4, and 552.1, respectively. The residuals were evenly distributed, so the mean errors were small, which were –0.0279, –0.0025, 0.0063, –0.0006, –0.0034, 0.0046, –0.0153, 0.0096, and 0.0032, respectively.

According to the scatter diagram of the height growth of dominant trees (Figure 3), Abies fabri, Picea asperata, Pinus yunnanensis, Pinus massoniana, Cupressus funebris, and Cunninghamia lanceolata height increased rapidly as the DBH increased, and the rapid height growth continued until the DBH reached 30 cm, 35 cm, 20 cm, 15 cm, 15 cm, and 15 cm, respectively. Then the height growth rate started to slow down. For Quercus semecarpifolia, Quercus glauca and Betula platyphylla, the rapid height growth continued, which is different from coniferous species. The height growth process of dominant trees of different species can reflect the difference in site productivity. All species are still growing in height with an increase of DBH except for Pinus massoniana based on the selected models.

3.2 Influence of stand conditions on dominant tree height growth

3.2.1 Stand origin

According to the results of parameter fitting by tree species in Table 3, the average value of the upper asymptote parameter a for the natural origin of different tree species was 28.8225, and the average value of parameter a for artificial origin was 20.5043. The mean value of the shape parameter b for the natural origin of different tree species was 0.0916, and the mean value of parameter b for artificial origin was 0.0935. The mean value of the growth rate parameter c for the natural origin of different tree species was 2.1883, and the mean value of parameter c for artificial origin was 2.1818.

The results of Analysis of Variance in Table 4 showed that there was no statistical difference in parameters a, b, and c (p > 0.10) of the DBH – height growth model of dominant trees with different origins. Except for Cunninghamia lanceolata, the upper asymptote parameters of stands with a natural origin were greater than those of artificial origin, which means the origin had an impact on the assessment of the growth potential of the stand. All Quercus semecarpifolia stands were natural.

3.2.2 Species composition

According to the results of parameter fitting with dummy variables, the average values of the upper asymptote parameter a for Pcs, Rpcs, Mcs, Mcbs, Pbs, Rpbs, and Mbf for different tree species were 21.1838, 21.0037, 21.7931, 20.5539, 19.7455, 20.0284, and 21.7698, respectively. the average values of the shape parameter b for pure conifer stands, relatively pure conifer stands, mixed conifer stands, mixed conifer and broadleaf stands, pure broadleaf stands, relatively pure broadleaf stands, and mixed broadleaf stands were 0.1044, 0.1042, 0.1492, 0.0835, 0.0443, 0.0467, and 0.0521, respectively. the average values of the growth rate parameter c for the pure conifer stand, relatively pure conifer stand, mixed conifer stand, mixed conifer and broadleaf stand, pure broadleaf stand, relatively pure broadleaf stand, and mixed broadleaf stand were 2.5895, 2.5873, 2.3965, 2.1507, 1.1439, 1.0764, and 0.9657, respectively.

It was obvious that species composition had an impact on the upper asymptote parameters among different coniferous species accompanied by a large coefficient of variation, while the impact was not statistically significant for broadleaf species (Figure 4A). Species composition had an influence on the upper asymptote parameters for Pinus yunnanensis, Pinus massoniana, Quercus semecarpifolia, and Quercus glauca stands (Figure 4B). Species composition exerted an impact on growth curve shape parameters among different coniferous species accompanied by a large coefficient of variation, while broadleaf species had a slight influence (Figure 4C). Species composition had an influence on the upper asymptote parameters in the Abies fabri stand (Figure 4D). Species composition exerted an impact on the growth rate parameters among different coniferous species accompanied by a large coefficient of variation, while broadleaf species had no influence (Figure 4E). Species composition had an influence on the growth rate parameters of the Pinus yunnanensis, Pinus massoniana, and Cunninghamia lanceolata stands (Figure 4F), which might be related to the artificial management of the main timber species in Sichuan Province.

The results of one-way ANOVA in Table 5 showed that there were no statistical differences in parameter a (p > 0.10), b (p > 0.10), and c (p > 0.10) of the DBH – height growth model of dominant trees with different tree structures. Similar results were obtained in coniferous or broadleaf stands in Table5.

3.2.3 Stand density

According to the results of parameter fitting with dummy variables, the average values of the upper asymptote parameters for various stand densities, i.e., 1–300 trees/hectare, 301–600 trees/hectare, 601–900 trees/hectare, 901–1200 trees/hectare, 1201–1500 trees/hectare, 1501–1800 trees/hectare, 1801–2100 trees/hectare, and more than 2101 trees/hectare, were 20.3781, 20.1081, 20.3864, 20.6253, 20.8844, 22.7359, 20.7427, and 21.8094, respectively. The average values of the shape parameter b for various stand densities were 0.1705, 0.0789, 0.1691, 0.1653, 0.3091, 0.1784, 0.0992, and 0.0949, respectively. The average values of the growth rate parameter c for various stand densities, were 2.7036, 2.4741, 2.2802, 2.1868, 2.0614, 1.9092, 2.1189, and 1.8070, respectively. 

It was obvious that stand density exerted an impact on the upper asymptote parameters among all species accompanied by a large coefficient of variation, although there was no difference in the mean of parameter a between different stand densities (Figure 5A). Stand density had a greater influence on the upper asymptote parameters in the Picea asperata, Pinus massoniana, and Quercus semecarpifolia stands, compared with the other stands (Figure 5B). Stand density exerted an impact on the growth curve shape parameters between 601 and 1800 trees/hectare accompanied by a large coefficient of variation, except for the initial stand density (Figure 5C). Stand density had a greater influence on the upper asymptote parameters in the Abies fabri, Picea asperata, Quercus semecarpifolia, and Quercus glauca stands compared with other stands (Figure 5D). With the increase in stand density, the influence of stand density on growth rate parameters decreased gradually accompanied by the coefficient of variation (Figure 5E). Stand density had a greater influence on the growth rate parameters in the Pinus massoniana and Cunninghamia lanceolata stands compared with other stands (Figure 5F), which might be related to the artificial management of the main timber species in Sichuan Province.

The results of one-way ANOVA in Table 6 showed that there was no statistical difference in parameter a (p > 0.10), b (p > 0.10), and c (p > 0.10) of the DBH – height growth model of dominant trees with different stand densities. Similar results were obtained in coniferous or broadleaf stands in Table 6.

4 Discussion

A wide variety of approaches, such as phytocentric and geocentric, have been used for assessing forest site productivity, each with advantages and disadvantages (Weiskittel et al. 2011). Increasing site productivity produced increasing tree height for a given diameter (Larson 1963). Application of the relationship between DBH and height of dominant trees to evaluate site quality could solve the difficulties in using site index in mixed and uneven aged stands when assessing site quality (Huang & Titus 1993).

Site form for quality evaluation of natural secondary forest is better than the use of site index, and the site quality evaluation of artificial forests is better with the use of site index, which indicates that there are differences in site quality evaluation for stands with different origins (Wu et al. 2015; Buda & Wang 2006; Beltran et al. 2016; Duan et al. 2018). In this paper, there was no statistical difference in the upper asymptote parameters, shape parameters and growth rate parameters between different stand origins, which indicates that there is no statistical difference in stand origin evaluation of site quality when using the site form method (Wang 1998a). The relationship between DBH and height is affected by stand density (Deng et al. 2019; Bhandari et al. 2021). Increasing stand density has been found to reduce both diameter growth and height growth for mixed conifers in the northern Rocky Mountains (Wykoff et al. 1982), implying that the stand density impact on the height and diameter relationship will probably be minimized (Huang & Titus 1993), especially if for dominant trees in the stands (Vanclay & Henry 1988). In this paper, there was no statistical influence on DBH and height of dominant trees with certain different stand densities and tree structure, which might be related to the use of dominance, because dominant trees in the upper canopy are less affected in conifer stands by factors such as tree structure and stand density (Weiskittel et al. 2011; Huang & Titus 1993, 1994). The relationship between DBH and height is sensitive to the selection of reference DBH, but this could not deny the feasibility of the stand quality evaluation by site form. Adoption of DBH of the growth model with the second derivative of zero as the reference DBH is also unreasonable (Chen et al. 2000), because the selection of the reference DBH is the same as the reference age, which needs to be sensitive and can reflect the difference in stand quality (Fu et al. 2018; Chen et al. 2000; Molina-Valero et al. 2019; Skovsgaard & Vanclay 2008).

The accuracy of factor analysis is greatly affected by the sample size and data, that is, the larger the number of plots and the more uniform the plot distribution at different classification levels (Adeyemi & Adesoji 2016; Kourosh et al. 2017; Moreno-Fernández et al. 2018), the more reliable the research conclusion. In this paper, 1283 permanent plots, six coniferous species and three broadleaf species were used to reflect the growth process of DBH and dominant height in real stands. All phytocentric measures of forest site productivity assume that trees are effective representatives of site productivity. However, site and tree genotype interactions are complex and suggest that a variety of factors can influence a tree’s productivity. Despite these drawbacks, these measures are the most commonly used in forestry (Vanclay & Henry 1988; Weiskittel et al. 2011). The relationships between DBH and height of different species (Wang & Hann 1988) have different sensitivity to stand origin, species composition and density, which was highest in pure spruce stand but decreased with increasing Abies fraseri or Betula lutea component (Nicholas & Zedaker, 1992). The mixed effects model seems to be an alternative approach for studying the focus of this paper (Fu et al. 2012), and the stand density index is superior to the number of trees for analysis, However, mixed model with random parameters and dummy variable model approaches are almost same effective (Zeng et al. 2011). The methods used in this paper have to be compared and improved in followup studies.

5 Conclusion

There was no statistical difference in the asymptote parameters, shape parameters, and growth rate parameters between various stand origins, tree structures, and stand densities according to the results. The origin had an impact on the assessment of the growth potential of the stand. Species composition had an influence on parameters among different coniferous species accompanied by a large coefficient of variation, whereas no influence was found in broadleaf species stands. Stand density exerted an impact on parameters among all species. With the increase in stand density, the influence of stand density on the growth rate parameters decreased gradually. Reasonably, the relationship between DBH and the height of dominant trees could be applied in site quality evaluation because the impacts of stand origin, tree structure, and stand density on dominant height growth are limited. The method is feasible for forestry management and practice, and can be applied easily, especially in coniferous stands.

Acknowledgement

This research was funded by the National Natural Science Foundation of China (grant numbers 31560209 and 31760206), the Academician Workstation of Yunnan Province of China (grant number 2018IC066), and the Ten-Thousand Talents Program of Yunnan Province, China (YNWR-QNBJ-2018-184).

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