4.1. Factors and Their Influence
The growth of trees is influenced by factors such as climate and stand conditions [
12]. In this study, climatic factors had a large effect on all tree species, indicating that climate is the main driver of regional forest growth in Beijing, and these findings are consistent with previous studies [
47,
48]. Combining the elevation distribution in
Figure 1 and the results shown in
Figure 6, the tree growth distribution in Beijing is clearly correlated with the elevation gradient, which is probably due to the differences in temperature, precipitation, and topography brought about by the differences in elevation. In Beijing, there is a decrease in temperature of 1 °C for every elevation increase of approximately 167 m, and a corresponding change in precipitation [
49,
50]; the distribution of MAP and MAT is shown in
Figure 7. Studies by other researchers of the climatic response relationships for large-scale tree growth have found that the upper limit of forest distribution at high elevations or high latitudes is mainly limited by temperature, while forest growth at low elevations is more sensitive to moisture [
51,
52]. The elevation of Beijing’s plains ranges from 20 to 60 m, and the mountains generally range from 1000 to 1500 m above sea level—relatively low elevations. In this study, MAT and Prec_sm were variables with a strong influence on tree growth, ranking in the top three positions for all species, which was consistent with the findings of others.
For the MAT factor, except for
Pinus tabulaeformis Carr. and
Robinia pseudoacacia Linn., all species showed that the higher the temperature, the greater the partial dependence value. The experimental results indicated that MCMT is an important factor affecting tree growth. According to the results of the partial dependence plot, the larger the MCMT value of the tree species, the larger the effect [
53]. This is similar to the results of most previous studies—warm winters favor tree growth in northern forests [
54,
55,
56]. Previous studies have shown that temperature has a lesser effect on trees as elevation decreases [
54], while MWMT, which first promoted and then inhibited tree growth with increasing temperature (probably because high summer temperatures cause drought stress and decreased net photosynthesis, which negatively affects tree growth at lower elevations), and precipitation, especially summer precipitation (Prec_sm), have a significant effect on growth [
57]. Prec_wt affects tree growth by influencing soil water content in spring [
58]. Precipitation generally has a positive effect on tree growth, but in this study, the areas with more precipitation were mountainous, and the temperature and topographic conditions were not conducive to storing water and nutrients for tree growth, so the partial dependent values instead show a decreasing trend with increasing MAP, peaking at 550 mm. This was probably because the overall environmental conditions in areas of Beijing under this precipitation condition are more favorable for tree growth.
The annual heat:moisture index (AHM) [
29] is used to indicate annual climatic water deficits. Larger values of AHM indicate dry conditions due to high evaporative demand relative to the available moisture, while lower values of AHM indicate relatively wet conditions [
59]. In this study, the highest value of partial dependence, at approximately 42, is considered high for AHM, and this was a different result from other studies [
53], probably due to the use of other topographic conditions and anthropogenic control. According to the AHM distribution, areas with an index of 42 were mainly in the Daxing, Fangshan, and Changping districts, where the temperature conditions are better, and in accordance with the data, these are the areas of Beijing’s plain afforestation, where the other stand conditions are relatively superior and the management and care factors are strong, so tree growth is optimal.
Among the topographic factors, other researchers have found that slope has an effect on soil preservation and water storage, as well as surface runoff after rainfall [
60], with gently sloping soils having better preservation and water accumulation; mountain soils being more water-scarce and barren compared to flatlands, and evergreen tree species being more suitable for barren environments [
60]. Therefore, coniferous forests have a relatively larger range of suitable habitat. This is consistent with the present study. According to the prediction and partial dependence maps of the suitability zones for each tree species,
Pinus tabulaeformis Carr. and
Platycladus orientalis (Linn.) Franco can be grown in most areas. In this study, the remaining topographic factors showed less significant effects on tree growth, probably because the Beijing area is dominated by plains and low mountains, as shown in the geomorphological data. Some tree species, especially some broad-leaved species, are planted mainly on flatlands in Beijing, so the effects of slope aspect, slope position, and slope degree of these species are weak in comparison to the effects of these factors on tree species growing at higher elevations.
The general effect from the soil data was small. For
Platycladus orientalis (Linn.) Franco,
Pinus tabulaeformis Carr. and
Robinia pseudoacacia Linn., soil thickness was secondary to climatic factors, and all three species can grow at higher elevations in mountainous areas as well. Some studies have reported a strong relationship between species distribution and soil thickness, but they point out that this relationship is indirectly achieved through the soil thickness affecting the soil moisture [
61,
62]. The data relating to GWL, HLT, and BRP showed similar values for most plots, and therefore had a only a small effect on the classification results.
4.2. Implications for Matching Species with the Site
Different combinations of site conditions have different degrees of influence on the growth of trees. Within the same area, there are differences in the relative importance of the influencing factors for each tree species, which further affects the growth of the trees, so it is important to conduct research using suitable trees in the right place. Therefore, when managing plantation forests, we should objectively consider the degree of influence of each site factor, so that the growth environment can be in the best possible condition to achieve the highest benefits.
Beijing is divided into plains, shallow mountains, and steep mountains according to elevation. The “Beijing shallow mountains protection plan (2017–2035)” classifies elevations of 100–300 m as shallow mountains, areas below 100 m as plains, and areas above 300 m as steep mountains. According to the results of this study, geographically, the plain areas are suitable for the growth of almost all tree species in this study; of the six studied tree species, five were suitable for growth in shallow mountainous areas (all species except Sophora japonica Linn.); and the tree species suitable for growth in steep mountainous areas were Pinus tabulaeformis Carr., Robinia pseudoacacia Linn., and Salix matsudana Koidz. Although the southwest area of Yanqing is higher in elevation, the terrain is flat, and this part of the Beijing area is also suitable for the growth of Pinus tabulaeformis Carr., Platycladus orientalis (Linn.) Franco, and Robinia pseudoacacia Linn.
The distribution map showed that the predicted distribution range of each tree species gradually decreased according to the elevation, which is similar to the actual situation in Beijing. In general, higher elevation results in lower temperatures and a more barren environment. Most tree species are suitable for growth on the plains due to better topography and temperature conditions, while the number of suitable species decreases gradually from southeast to northwest, with the increasing elevation. The six tree species selected for the study were all native species suitable for afforestation and greening in Beijing, according to the Beijing afforestation protocol. This study predicted the suitable areas for distribution of these species through random forest modelling, demonstrating which of them can be selected for planting, where, which provides a reference for afforestation work.
4.3. Strengths and Limitations
In this study, two stand variables, mean age and mean tree height, were studied using data from the 2014 Beijing forest management inventory. These two variables are generally included in forest survey data. Compared with the variable of stand dominant height required by the site index method, the average tree height of the stand used in this study is easier to obtain. Applicable to heterogeneous stands, the quantile approach converts the problem of growth volume at different ages into a homogeneous stand growth volume according to the different quantile distributions.
We used the random forest model and selected the optimal combination of parameters by genetic algorithm, which had the advantages of being a simple algorithm with easy calculation. It can improve the accuracy of classification and prediction, it can deal with nonlinearities and interactions, and it can be used for variable importance assessment; the model itself has algorithmic advantages and is easy to compute.
At the same time, there are some shortcomings in this study. The study area was Beijing, which has extensive plains and a relatively low overall elevation, resulting in some tree species, especially broad-leaved species, being mainly distributed on flatlands, and so there are limitations to the study relating to stand factors. In this study, only climate, soil, and topography-related environmental factors were considered, and no anthropogenic factors were taken into account. A future study could be extended to areas with richer landforms for more in-depth investigation.