Using machine learning algorithms to estimate stand volume growth of Larix and Quercus forests based on national-scale Forest Inventory data in China

Huiling Tin, Jinhu Zhu,b,＊, Xio H, Xinyun Chn, Zunji Jin, Chnyu Li,Qingxin Ou, Qi Li, Guoshng Hung, Chngfu Liu,b, Wnf Xio,b,＊＊

a Ecology and Nature Conservation Institute, Chinese Academy of Forestry, Key Laboratory of Forest Ecology and Environment of National Forestry and Grassland Administration, Beijing, 100091, China

b Co-Innovation Center for Sustainable Forestry in Southern China, Nanjing Forestry University, Nanjing, 210037, China

c Institute of Forest Resource Information Techniques, Chinese Academy of Forestry, Key Laboratory of Forest Management and Growth Modeling, National Forestry and Grassland Administration, Beijing, 100091, China

d Academy of Forest Inventory and Planning, National Forestry and Grassland Administration, Beijing, 100714, China

e School of Forestry and Landscape Architecture, Anhui Agricultural University, Hefei, 230036, Anhui, China

Keywords:Stand volume growth Stand origin Plant functional type National forest inventory data Random forest algorithms

ABSTRACT

1. Introduction

Forests are the largest part of terrestrial carbon pools and play irreplaceable roles in regulating climate change and mitigating greenhouse impacts around the world (Pan et al., 2011; Reich et al., 2014). Wood volume in forests that refers to the total volume of all standing trees in a certain area is often used as an indicator of, or reference for, forest resource management and regional forestry planning and policy creation.Forest volume has a strong correlation with forest biomass and carbon storage,and,as a result,it is a direct manifestation of the distribution of carbon sequestration in space (Zhang et al., 2003; Mura et al., 2018).Therefore, estimating volume growth accurately is very important for understanding the trend of forest carbon sequestration and achieving carbon neutrality goals in the future.

Generally, the simulation models of volume growth can be divided into single-tree volume-based growth models and stand volume-based growth models. There is a lot of research that has been carried out on the single-tree volume-based growth models (Zhang et al., 2003; Hasenauer,2006;Luo et al.,2016).Xu et al.(1996)used tree age,diameter at breast height (DBH), and tree height to fit the optimal models of the single-tree growth rate of Chinese firs and Masson pines,and concluded that tree age was the most important factor affecting the tree growth rate.Ma et al.(2018)established the single-tree volume growth rate models of fir, spruce, and cypress in the natural forests of Tibet, China and found that the volume growth rate of these species gradually decreased with the increase of DBH. Although these single-tree volume growth models can provide detailed single-tree information for predicting the stand volume growth,this data is relatively complicated among various tree species in a given stand and would probably lead to the accumulation of errors(Qin et al.,2006;Zhang et al.,2010).Instead,the stand volume-based growth models can be used to describe the volume growth process and are crucial for the development and execution of a sustainable forest management plan (Masota et al., 2014; Wallacy et al., 2014). In various studies or applications of stand volume-based growth models,the stand average age and stem density are usually included as independent variables(Matney et al.,1982;Pienaar et al.,1984).For instance,Tian et al.(2011)found that the stand volume in plantations of Populus × euramericana ‘Neva’first increased and then decreased with the increase of stand density,and Sampson et al.(2015)concluded that stand age had the greatest impact on stand volume growth in Pinus taeda forests. Moreover, previous studies also established climate-sensitive volume growth models,such as the Climate-FVS model(Crookston et al.,2010)and the CSMatrix model(Liang et al., 2011). For example, Zhao et al. (2015) found that the hydrothermal conditions of thick soil on shady slopes were better than those of thin soils on sunny slopes and were more conducive to the growth of Larix principis-rupprechtii. However, the current research has focused more on statistical models related to stand attributes(e.g.,DBH and tree height)rather than environmental factors(e.g.,climate,soil,and topography)(Lu et al.,2019).In fact,stand volume growth is a complex process, which is determined by multiple factors such as stand, site condition, climate, and their interactions (Lei, 2019). Accordingly, estimating stand volume growth accurately requires taking various environmental factors into account;however,such studies are still lacking.

Although traditional statistical models, such as linear and nonlinear regression models,mixed effect models,and other statistical models are widely used to simulate stand volume growth, they cannot accurately represent the complex relationships of these environmental factors such as stand, site condition, climate and their interactions (Lei, 2019). Machine learning algorithms (e.g., support vector machine, decision tree,and random forest) have been used to estimate stand growth in recent years (Ahmed et al., 2015; Gao et al., 2018; Zhang et al., 2018). The random forest(RF)can not only be used for regression,classification,and prediction, but it can also quantify the relative importance of each independent variable to the dependent variable and then obtain the partial dependence of the dependent variable as the independent variable changes (Breiman, 2001). Consequently, the RF models have been successfully applied to various tasks in forest ecology. Based on the RF algorithms, for example, Weiskitte et al. (2011) studied climate-driven forecasts of the status index and gross primary productivity across forests of the western United States under the impact of future climate changes.Bond-Lamberty et al.(2013)analyzed the effects of climate and disturbance on the diameter growth of Canadian boreal coniferous forests, and Jevˇsenak and Skudnik (2021) predicted the basal area increment using Slovenia's National Forest Inventory(NFI)data.These studies provided efficient information on the application of the RF algorithms for forest growth simulations and predictions.Because forest ecosystems are established at the environmental heterogeneity, whether the RF algorithms can be applied in various site conditions is still needs to be well-understood.

Larix and Quercus forests,which were widely distributed across China(Fig. 1), accounted for 6.02% and 9.21% of the national forest area in China,respectively(State Forestry and Grassland Administration,2019).Previous studies reported had higher average biomass densities of the Larix (126.2 Mg?ha-1) and Quercus (122.2 Mg?ha-1) forests (Guo et al.,2010),indicating an important carbon sink(Pan et al.,2011).Thus,the estimation of stand volume growth of these two species groups is important to understand their dynamics within the context of global change. However, previous research about the volume growth of these two species had been concentrated primarily on its response to stand attributes at a regional scale(Zhao et al.,2015;Lei et al.,2016;Yan et al.,2019) rather than on the comprehensive influence of environmental factors (e.g., topography, soil, climate and stand) at a national scale. In this study,therefore,the RF algorithm was used to estimate the volume growth in Larix and Quercus forests based on the NFI data in China and to evaluate the effects of environmental factors on the volume growth.Specifically,the aims of this study were(1)to estimate volume growth in both planted and natural Larix and Quercus forests in relation to stand,climate, soil, and topography variables using the RF algorithms, (2) to identify the relative importance of various variables on the stand volume growth,and(3)to explore the partial dependence of the key variables on the stand volume growth.

2. Materials and methods

2.1. Data collocation

2.1.1. Stand volume growth data

The stand volume data was collected from the permanent plots in the 7th (2004–2008), 8th (2009–2013), and 9th (2014–2018) NFI data of China, including 1311 plots of Larix forests and 1438 plots of Quercus forests,respectively(Fig.1).The plots are generally square with an area of 0.0667 or 0.06 ha and are monitored every 5 years.The volume of the individual trees was calculated based on its DBH, and the stand volume was the sum of all trees in each plot.The stand volume growth was then calculated as the difference between the two consecutive stand volume measurements. Notably, only alive trees that were remeasured at least once in both periods were included(Jevˇsenak and Skudnik,2021),and,consequently, the stand volume growth refers to living trees in a given permanent plot.Moreover,these plots were divided into two parts based on their stand origins(natural versus planted)due to obvious differences in site conditions (Guo and Ren, 2014). In this study, the stand volume growth data was represented in the two inventory periods(Jevˇsenak and Skudnik,2021),i.e.,the period from 7th to 8th and the period from 8th to 9th, and then was normalized and transformed into an annual value(m3?ha-1?yr-1).That is to say,the observations of annual growth of stand volume were the sum of these two inventory periods.Accordingly,there are a total of 1074 and 1547 observations of natural and planted Larix forests,respectively,and a total of 2504 and 369 observations of natural and planted Quercus forests,respectively.

2.1.2. Edaphic variables

In this study, seven edaphic variables were chosen as candidate variables for model fitting, including alkali-hydrolyzable nitrogen (AN),available phosphorus(AP),available potassium(AK),bulk density(BD),pH value (pH), gravel content (GRAV) and soil organic matter (SOM)(Table 1). These soil indicators were derived from the database of “Soil properties of land surface in China”(Shangguan et al.,2013)released by the platform of Tibet Plateau Science Data Center (http://tdpc.ac.cn).Based on 8979 soil profiles and the soil map of China(1:1000,000),the database was established using the polygon linkage method with the spatial resolution of 30 × 30 arc-seconds. It has been widely used in related research(Hengl et al.,2014;Zheng et al.,2015).

Fig. 1. The Larix and Quercus sample plot distributions of the study area in China.

Table 1 Candidate variables for stand volume growth modeling.

2.1.3. Bioclimatic factors

The bioclimate data were derived from the temperature and precipitation data of 2456 meteorological stations from 1995 to 2015 released by the China Meteorological Data Science Sharing Platform(http://data.cma.cn),combined with elevation and aspect data,through Co-Kring to obtain (with a resolution of 1000 m × 1000 m). Based on the raster where the sample plot was located, (if there is no corresponding coordinate point,take the raster closest to the sample plot),the climate data corresponding to the permanent plot was obtained from the database,including 16 bioclimatic factors(Table 1).

2.1.4. Site conditions

The site conditions (i.e., altitude, slope, aspect, slope position, soil thickness, and land classification) (Table 1) of each plot were collected from the NFI data in China.

2.2. Random Forest algorithm

The RF algorithm,an ensemble method based on regression trees(Ou et al., 2019), includes a series of base learners (e.g., classification and regression trees) from bootstrap. During the construction of each base learner,a few variables were randomly selected from all variables at the tree node, and then the most sensitive variable was found out of all of them (Breiman, 2001). The superior predictive power of the RF algorithm arises from a randomized regression tree construction for each bootstrap sample. And, then, only a subset of all independent variables was considered to split at each tree node. This subset is set with the“mtry” parameter. The portion of data that was not drawn into the sample was composed of the“out-of-bag”data,which was used to assess the generalization errors of the selected regression tree trained with the bootstrap sample (Zhou, 2016). The RF predictions are the averaged predictions on every tree (Ou et al., 2019). However, the RF algorithm cannot intuitively provide the relationships between predictor variables and response variables, thereby reducing its interpretability. It is necessary to increase the interpretability of the RF algorithm in the actual application process (Kuhn et al., 2013; Ou et al., 2019). The relative importance and the partial dependence plots of predictor variables are proposed to improve the interpretability(Breiman,2001;Friedman et al.,2001). In this study, the node purity enhancement method was used to determine the relative importance of each predictor variable (Strobl et al., 2008). We measured the increase of the purity of the nodes that were caused by the splitting of variables at the node, and the relative importance of each variable was normalized to 100% for comparison.The partial dependence plot helps to visualize the dependence of the dependent variable on one or two independent variables. When the independent variable is one, the partial dependence plot is a two-dimensional line graph in which the dependent variable (ordinate)changes with the independent variable (abscissa); when there are two independent variables, a partial dependence plot is a three-dimensional surface plot of the dependent variable as the independent variable changes(Goldstein et al.,2015).It is worth pointing out that the partial dependence of a dependent variable on an independent variable is not calculated by ignoring the influence of other variables on the dependent variable,but by considering the average effect of other variables on the dependent variable (Zhang et al., 2014). The RF algorithm was performed using the“randomForest”package(Liaw and Wiener,2002)in R 4.0.4(R Development Core Team,2021).

2.3. Model building

In this study, a total of 29 predictors (Table 1) were used as independent variables to simulate the stand volume growth based on the RF algorithm. In the model building process, two important tuning parameters were required:the number of decision trees(ntree)and the number of predictive variables selected randomly by the tree nodes (mtry)(Freeman et al., 2016). In general, the overall error rate tended to be stable when the ntree was greater than 500 (Zhang et al., 2016).Therefore, the default value of ntree was 500, but it still needs to be further specified based on specific data. In order to ensure that the reliability of the prediction results did not affect the computational efficiency,the value of ntree in this study was set at 1000(Ou et al.,2019).The default value of mtry is recommended to be the number of total predictor variables divided by three in the regression context(Breiman,2001). However, the default value of mtry was not always able to be ascertained for the optimal model.It is necessary to tune the parameters.Since 29 predictive variables were used in this study(1 ≤mtry ≤29),a resampling technique(i.e.,10-fold cross-validation)was implemented to train and evaluate these 29 RF models(ntree=1000;mtry=1,2,3,…,29).The“caret”package in R was used to tune these models(Kuhn et al.,2013).The model with the best generalization ability was selected as the optimal model.The impacts of mtry on the model performance of stand volume growth in planted and natural forests of Larix and Quercus were explored(Figs.S1–S4)and then the optimal parameters for each species and origin were selected(Table 2).

2.4. Model evaluation

In a machine learning algorithm,the error of the learner of the training set is called a“training error”,and the error of the new samples is called a“generalization error”. In general, a learner with a small generalization error is an ideal model. The k-fold cross-validation, one of the main methods for evaluating machine learning models,was used to evaluate the performance of all RF models in this study. The k parts were used as a testing dataset and the remaining k-1 parts were used as the training dataset.Therefore,the model was done k times in total and k error values were obtained.In this study,the average value of k error values was used as an evaluation index of the RF model.Usually,the 10-fold cross-validation(Lei, 2019) was widely applied with spatial and/or temporal structures(Bergmeir and Benítez,2012).Three evaluation metrics for the RF model performance were computed for each fold:the coefficient of determination(R2), the root mean square error (RMSE), and the mean absolute error(MAE).And,then,the 10 resampled validation measurements of the model performance were averaged as follows:for each species independently,the model with the mtry value that returned the highest R2for the independent validation data was selected and used for further analysis.

Coefficient of determination of cross-validation (R2cv):

Table 2 10-fold cross-validation results for different origins of two selected species.

3. Results

3.1. RF model performance of stand volume growth

The optimal RF models of Larix and Quercus in different origins were tested (Table 2). For the Larix forests, the value of R2in natural forests(0.65) was obviously higher than that in planted forests (0.44), and the values of RMSE and MAE in natural forests(0.61 and 0.46,respectively)were obviously lower than those in planted forests (2.33 and 1.79,respectively). Similar RF model performances were found in Quercus forests: the values of R2, RMSE, and MAE in natural forests were 0.66,0.73,and 0.51,respectively;and 0.40,1.64,and 1.25 in planted forests,respectively.For both the Larix and the Quercus forests,three evaluation metrics of the RF model in natural forests demonstrated better performance than those in the planted forests(Table 2).But these values were comparable among the Larix and the Quercus in both natural and planted forests (Table 2). Overall, a small stand volume growth difference was noted between measured values and predicted values(Fig.2).

3.2. Relative importance of predictor variables

For both natural Larix and Quercus forests,the stand age was the most important predictor for stand volume growth and its relative importance in these forests was 66.2% (Fig. 3) and 62.9% (Fig. 4), respectively;while,bioclimatic factors,edaphic variables,and topographic features in natural forests showed limited relative importance,which was less than 6%for each variable(Figs.3 and 4).Similarly,the stand age was the most important predictor for stand volume growth in planted Larix forests,with high relative importance(14.3%;Fig.3).In contrast,the dominant factor was the altitude with high relative importance in the planted Quercus forests (18.2%; Fig. 4). Bioclimatic factors, edaphic variables,and other topographic features in planted forests of both Larix and Quercus showed considerable relative importance, which ranged from 1.2%to 7.4%(Figs. 3 and 4). Overall, the most important edaphic variable and topographical feature were the soil thickness(1.2%–4.5%)and aspect (3.5%–7.4%), respectively; whereas, the relative importance of bioclimatic factors differed in different origins of these two species groups(Figs.3 and 4).

3.3. Partial dependence relationships of predictor variables

With the increase of stand age, the average annual volume growth(ΔV) in natural Larix and Quercus forests increased at the beginning,decreased at 50 years and gradually stabilized after 120 years (Figs. S5 and S6). Obviously, the precipitation in the driest quarter (＜100 mm,Bio14)between 0 and 100 mm had a positive effect on ΔV in the natural forests of Quercus (Fig. S6). But, there were no obvious relationships between other variables and ΔV in natural forests(Figs.S5 and S6).

The response of ΔV in planted forests to stand age differed:binomial effects at a turning point of 15 years in Larix forests(Fig.5)and positive effects from 0 to 50 years in Quercus forests (Fig. 6). Overall, in the planted Larix forests, the altitude and bioclimatic factors (e.g., Bio12,Bio14, and Bio16) had a positive impact on ΔV at the initial ranges(altitude ＜2500 m, Bio12 ＜10 mm,Bio14 ＜100 mm,and Bio16 ＜35 mm), but edaphic variables (e.g., thickness and pH) had a negative impact on ΔV at the thickness ranging from 0 to 50 cm and the pH ranging from 5.5 to 8.0 (Fig. 5). And, the impact of slope and soil AP content on ΔV fluctuated. In contrast,the slope and temperature (Bio5)showed an obvious positive impact on ΔV, and the altitude (＜1000 m)had a negative impact in the planted Quercus forests. Similarly, bioclimatic factors(e.g.,Bio6,Bio8,and Bio11)had positive impacts on ΔV for Bio6 higher than 22.5°C, Bio8 higher than 24 mm, and Bio11 greater than 150 mm.Edaphic variables had different impacts on ΔV(Fig.6).

Fig. 2. Validated prediction of Random Forest (RF) regression models.

Fig.3. Relative importance of each variable in the Larix forests found by the random forest was normalized to 100%.The explanations of each factor were presented in Table 1.

Fig. 4. Relative importance of each variable in Quercus forests found by the random forest was normalized to 100%.The explanations of each factor were presented in Table 1.

Fig. 5. Stand volume growth simulations in relation to the most important predictor variables of Larix plantations.

4. Discussion

4.1. RF model evaluation

The RF model has the 10-fold cross-validation system, which is an effective set of modeling tools for stand volume growth(Lei,2019)and is commonly applied on data sets with spatial and/or temporal structures(Roberts et al., 2017). The results showed good performance (R2=0.40–0.66) for estimating stand volume growth in Larix and Quercus forests of different origins throughout China (Table 2; Fig. 2). A similar RF model performance(R2=0.29–0.57)to predict basal area increments in mixed-species forests in Slovenia was found (Jevˇsenak and Skudnik,2021). Interestingly, the squared correlation coefficient calculated for independent variables data in natural forests (R2= 0.65 for Larix and 0.66 for Quercus, respectively) was better than those in planted forests(R2=0.44 for Larix and 0.40 for Quercus,respectively)(Table 2).These results might be related to the age structure of different forest origins:high percentage for near-mature and mature natural forests(e.g.,62.4%for Larix)and high percentage for young and middle-age planted forests(e.g., 65.5% for Larix) (State Forestry and Grassland Administration,2019). A previous study showed that adult trees with comparatively larger basal areas are easier to predict than younger, suppressed trees(Jevˇsenak and Skudnik,2021).In other words,near-mature and mature forests grow more slowly and are less affected by the environment,while young and middle-age forests grow more quickly and are sensitive to environmental changes (Regos et al., 2019), thereby determining the model performance for prediction volume growth of different forest origins. Moreover, China's afforestation has often been used to develop different ecological services and it has been conducted at various site conditions. As a result, high heterogeneity of geographic locations and soil nutrients in planted forests suggests that the complex interaction of various variables might influence the model accuracy. Undoubtedly,some variables such as stand DBH, stand density, insect outbreaks, fire,and drought,should be considered in the future to increase the predictability of stand volume growth models.

The interpretability of the RF model can be done through the relative importance of the predictor variables and the partial dependence graph.This study found that the partial dependence of certain variables on ΔV is highly correlated with the relative importance of the same variable on ΔV(Figs. 3–6; Figs. S5–S6). In other words, the greater the relative importance of the variable to ΔV, the greater the partial dependence relationship of ΔV with this variable.This is manifested as the greater degree of ΔV changes with the change of this variable.Conversely,if the relative importance of a variable decreases,ΔV will change more gradually with the change of the variable.

4.2. Differences in predictors for volume growth between natural and planted forests

For both the Larix and Quercus natural forests,the stand age was the most important variable for stand volume growth simulation and it had the highest relative importance (66.2% and 62.9%, respectively), while both edaphic and climatic variables had limited effects (relative importance with less than 6.0%) (Figs. 3 and 4). For the planted forests, the stand age and altitude were the dominant factors for stand volume growth simulation in Larix and Quercus forests, respectively (relative importance of 14.4%and 18.2%,respectively)(Figs.3 and 4).Moreover,the bioclimatic factors, edaphic variables and topographic features in both planted Larix and Quercus forests showed considerable relative importance, which ranged from 1.2% to 18.2% (Figs. 3 and 4). The differences in predictors for volume growth between natural and planted forests were related to the altered niches.In the natural distribution area,the natural selection process of the species during the long-term forest succession has created similar site conditions (e.g., climate and soil),which may have slightly affected tree growth. On the contrary, afforestation selects the adapting region and forms high heterogeneity of site conditions,which obviously affects tree growth.

Fig. 6. Stand volume growth simulations in relation to the most important predictor variables of Quercus plantations.

4.3. Relevant explanatory variables for simulation of Larix's volume growth

For both natural forests and planted forests, our results underlined that the stand age was the most important predictor (Fig. 3) and had binomial impacts on Larix volume growth(Figs.5 and S5),with a turning point of 45 years and 15 years, respectively. This result confirmed previous findings again (Qi et al., 2011, 2015). However, Larix volume growth stabilized from being in natural forests for 150 years and being in planted forests for 45 years, respectively. The average annual volume growth of young and medium-aged forests was greater than that of near-mature,mature and over-mature in natural forests(Fig.S5),which was consistent with the findings of other studies(Hutchison et al.,1990;Fujimoto et al., 2006; Rosenthal et al., 2010). Higher stand volume growth in the young and middle-aged forests was due to sufficient light and heat and less competition (Rosenthal et al., 2010). Although the stand volume growth increased slowly in the near-mature, mature and over-mature forests, its fluctuating trend was mainly caused by self-thinning (Ma et al., 2010). Under such conditions, the forest gaps provided light, and the decomposition of fallen trees provided efficient nutrients to promote tree growth (Forrester et al., 2021). Similarly, the decreased stand volume growth in planted Larix forests with increased stand ages, starting from 15 years, may be mostly explained by select thinning. Unfortunately, it is impossible to know the growing trend of stands over 60 years due to insufficient information on mature and over-mature plantations.

Below 2000 m, the altitude had a positive impact on stand volume growth in planted Larix forests (Fig. 5). This result was related to the changes in water and heat conditions caused by the increase of altitude(Devi et al., 2010; Moser et al., 2010; Wang et al., 2020). The planted Larix forests are located primarily at the lower altitude areas in northeastern China (Fig. 1), where there are high temperatures and low precipitation.As a result,precipitation was the main factor that limited the Larix growth,which was confirmed by the positive relationships between precipitation indices (e.g., Bio12, Bio14 and Bio16) and stand volume growth (Fig. 5) and was consistent with previous findings (Dulamsuren et al., 2010). As the altitude increased, the precipitation also gradually increased but the temperature decreased. Therefore, the temperature(i.e., Bio5) became the limiting factor and had a positive impact on the Larix growth (Fig. 5). When altitudes increased continuously, the temperature and precipitation declined,and,consequently,the stand volume growth became limited and showed a flat trend at 2500 m. In fact, as found in previous studies (Cienciala et al., 2016; Rohner et al., 2018),bioclimatic factors also played minor roles in Larix forests (Fig. 3).However,previous studies indicated that the differences in hydrothermal conditions between the shady slope and the sunny slope had a significant impact on stand growth(Song et al.,2016).In this study,the aspect also had obvious effects on stand volume growth in planted Larix forests(Fig. 5). But the interactions of aspect and bioclimatic factors on stand volume growth in Larix forests need to be further studied.

Soil plays a vital role in tree growth, but estimating stand growth mainly depends on the stand attributes and climatic factors and ignores the role of soil indicators in previous studies (Ibanez et al., 2014;L'evesque et al., 2016). In this study, the relative importance of edaphic variables in Larix forests was not generally high at a national scale(Fig.3),in line with the previous finding(Leng et al.,2007).Notably,the soil thickness and pH value were the potential predictors that affected Larix growth.For example,stand volume growth in planted Larix forests declined when the soil thickness was between 0 and 75 cm(Fig.6).One explanation may be the shallow root traits of this species and vertical distributions of its root systems. Therefore, taking soil variables into account can improve the estimation of stand volume growth in Larix forests.

4.4. Relevant explanatory variables for simulation of Quercus volume growth

Our analysis also highlighted that the stand age was the most important predictor for stand volume growth in Quercus forests, especially in planted forests (Fig. 4). Obviously, the annual stand volume growth increased firstly with increasing stand age (less than 45–50 years), and then it fluctuated after 45 years in natural Quercus forests(Fig.S6)and stabilized after 50 years in planted Quercus forests(Fig.6).These changing trends of stand volume growth over stand ages were consistent with prior research (Kappelle et al., 1996), where the stand volume of Quercus forests rapidly rose throughout the early and middle age stages and reached the highest value at an age from 30 to 50 years.For the decreased trends of stand volume growth in the near-mature Quercus forests, the mechanism may be decreased tree density due to the self-thinning processes or the interspecific competition (Kappelle et al.,1996; Forrester et al.,2021).

Topographic features (e.g., altitude and aspect)play important roles for affecting stand growth (Ndiaye et al., 1993; Robert et al., 2003;Glennr et al., 2010). In this study, the altitude had strong relative importance for stand volume growth in planted Quercus forests (Fig. 4)and showed a negative impact (altitude ＜1000 m; Fig. 6), which was similar to previous reported results (Slavík, 1981; Lebourgeois et al.,2004). The Quercus forests are mainly distributed in eastern China(Fig. 1), where they have enough hydrothermal conditions (especially precipitation). As the altitude increased, the temperatures decreased,which subsequently resulted in limited tree growth. Therefore, the temperature indices(e.g.,Bio5 and Bio6)had positive impacts on stand volume growth in the planted Quercus forests (Fig. 6). Meanwhile, the high relative importance of four bioclimatic factors(i.e.,Bio5,Bio6,Bio8 and Bio11; Fig. 4) indicated that the hydrothermal conditions in the spring and summer played an important role in determining stand volume growth in planted Quercus forests. Similar findings were found in other studies (Wang et al., 1992; Hacke et al., 1996; Rozas et al., 2001;Lebourgeois et al., 2004). Under good hydrothermal conditions (e.g.,increased temperature and precipitation), the mobilized carbohydrates(i.e.,starch and sugars)during the spring and summer periods(Lacointe et al., 2000; Barbaroux et al., 2002) can make the reactivation of tree growth during the same periods in planted Quercus forests.As suggested by a previous study(Ou et al., 2019), accordingly, although bioclimatic factors showed a weak relative importance in this study (Fig. 4), they should be used as predictors for estimating stand volume growth in forest ecosystems.Moreover,the relative importance of aspect was up to 6.3%in planted Quercus forests (Fig. 4), indicating that the aspect was an important predictor for stand volume growth.Overall,the stand volume growth on shady slopes was greater than that on sunny slopes (Fig. 6)because the shady slope can keep the better soil more moist(Song et al.,2016).Furthermore,due to a strong tolerance of Quercus trees to infertile soil (Skiadaresis et al., 2021), the edaphic variables often showed the minor impacts on stand volume growth(Figs.4 and 6).

4.5. Limitation and implications of this study

Overall, these results revealed the fundamental roles of stand,topography,soil and climate factors on the stand volume growth in Larix and Quercus forests of different origins across China. Nevertheless, the edaphic and bioclimatic variables were obtained from the established databases with a spatial resolution of 1000 m × 1000 m, but the stand volume growth data represented a small plot with an area of 0.0667 ha or 0.06 ha.This can result in the low relative importance(Figs.3 and 4)and weak partial dependence (Figs. 5 and 6; Figs. S5 and S6) of these variables on stand volume growth. Thus, the fact that these variables especially edaphic factors were measured in permanent plots suggests that they can improve the estimation of stand volume growth.

Our results also provided a good framework for site-specific recommendations regarding the management practices necessary to maintain the volume growth in planted Larix and Quercus forests. Stand age was the most important factor affecting stand volume growth in these two species forests(Figs.3 and 4).The annual stand volume growth increased in the young and middle age forests,and then decreased in Larix forests(Figs.5 and S5)and stabilized in Quercus forests(Figs.6 and S6).These results suggest that we should strengthen the management of nearmature and mature forests of Larix and Quercus forests in China to improve their stand volume growth. Similarly, altitude was one of the main predictors for stand volume growth in planted Quercus forests(Fig. 4) and the annual stand volume growth was stable at a low value(approximately 2.3 m3?ha-1?yr-1) when the altitude was more than 2000 m (Fig. 6). Thus, afforestation of Quercus forests is no more than 2000 m to maintain stand productivity.

5. Conclusions

Estimating stand volume growth will be important for forest management and climate change mitigation in the future. Based on China's NFI data of Larix and Quercus forests and environmental factors, the relative importance and dependence of these environmental factors on the annual stand volume growth was evaluated using the RF algorithm.The performances of the RF model were relatively stable and showed good results(R2=0.40–0.66).In both natural forests and planted forests,the stand age was the main predictor for annual stand volume growth,with a relative importance of 8.6%–66.2% and a positive effect at the younger and middle years, indicating that we should strengthen the management of near-mature and mature forests of Larix and Quercus in China to improve their stand volume growth. The annual stand volume growth was stable at a low value over altitude of more than 2000 m in planted Quercus forests,suggesting that afforestation of Quercus forests is no more than 2000 m to maintain stand productivity. Moreover, bioclimatic factors, edaphic variables and topographical features had a more significant role on stand volume growth in planted forests than those in natural forests, which demonstrated that there were diverse effects of environmental factors on volume growth among stand origins and plant functional types.Our results highlighted that the RF model has a certain statistical reliability and can be applied to stand growth and yield predictions. However, the model performance in natural forests was better than that in planted forests due to some limitations(e.g.,low resolution of data)in RF algorithms,suggesting that the RF model is still required to further refine the applications in different forest ecosystems.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This work was supported by the Major Program of the National Natural Science Foundation of China(No. 32192434), the Fundamental Research Funds of Chinese Academy of Forestry (No.CAFYBB2019ZD001) and the National Key Research and Development Program of China (2016YFD060020602). We thank our colleagues,Yanyan Ni,Yu Tian,for their assistance in providing relevant factor data and data sorting.We thank Shuyi Guo,Rui Wang,staff of the Academy of Forest Inventory and Planning,National Forestry and Grassland Administration, for help with data provision. We also thank the Zigui Forest Ecosystem Research Station for their help.

Appendix A. Supplementary data

Supplementary data to this article can be found online at https://do i.org/10.1016/j.fecs.2022.100037.