1. Introduction
The relationships between forest structural characteristics, biodiversity indicators, and forest productivity have been investigated in recent studies for different forest conditions and forest regions, and it has generally been shown that biodiversity has a profound positive effect on the services produced by forest ecosystems, especially on a global scale [
1,
2]. However, the relationship between tree diversity and ecosystem functions in many cases depends on local environmental conditions [
3]. For example, the structure of a forest ecosystem, its plant and animal diversity, and the conditions of a site affect the productivity of a forest ecosystem [
4]. However, Ouyang et al. [
5] noted that the relationship between diversity and productivity may not differ along a gradient of the environment and that stand age and tree density may be more important than biodiversity in describing productivity. Tilman et al. [
6] offered two main hypotheses to elucidate the positive impact of forest biodiversity on productivity: the niche complementary effect and the selection-probability effect. Thus, as a result of the niche complementary effect, it is assumed that by differentiating and facilitating niches, increased biodiversity can enhance productivity. In contrast, the selection-probability effect suggests that increasing species richness increases productivity in a forested community by improving the chances of having highly productive species [
7]. These two effects can also have a positive, simultaneous effect on biodiversity and forest ecosystem services [
7].
As mentioned above, the relationship between forest biodiversity and productivity varies among different studies. In some studies, this relationship has been positive and significant [
2,
8,
9,
10,
11]. In others, negative relationships were observed [
12], and in some cases, a nonsignificant relationship was reported [
13]. Therefore, it can be concluded that biodiversity conditions might influence the growth and productivity of trees, depending on the situation, by affecting the characteristics of environmental resources, especially water and soil [
14,
15]. As a result, the relationship between diversity and productivity largely depends on these factors [
5,
9,
12].
In this study, we employed species richness, Shannon Wiener, and Simpson indices to estimate biodiversity. Even though there may be a broader set of biodiversity indicators, because some indicators are based on similar or common concepts, in most studies, especially in modeling, to prevent the production of large amounts of data, the most important and widely used indicators are used. Peet [
16] suggests that a combination of species counts (richness, such as Margalef index) and relative species abundance, which together form heterogeneity indices (such as Shannon Wiener and Simpson index), can be used to estimate beneficially the diversity of an ecosystem. As a result, the Shannon Wiener and Simpson indices have been used often in forest research, while other biodiversity indicators are used less often [
17,
18].
Moreover, there are several indicators that might help estimate the productivity of mixed and uneven-aged forests. In some studies, the heights of dominant trees at different elevations above sea level were considered as a productivity index, and in others, the above ground biomass increment or annual volume increment (ton, kg/hectare/year) have been used to determine the productivity in the forest [
2,
8,
19,
20]. Nevertheless, measuring indices based on height of trees is costly and time consuming; therefore, it is preferable and reasonable to determine the productivity using indicators that are based on diameter at breast height, such as biomass estimates and annual volume increment [
21]. Therefore, to determine productivity, in the current study, we used the annual volume increment. In mountain forests, there are many biotic and abiotic factors, which may affect biodiversity and productivity, based on the results of previous research [
22,
23,
24,
25,
26,
27,
28,
29,
30]. These indicators included topographic wetness index (TWI), wind velocity, elevation, and basal area of the largest trees (BAL) [
31]. Huang, Chen, Castro-Izaguirre, Baruffol, Brezzi, Lang, Li, Härdtle, Von Oheimb, and Yang [
19] also showed that the effect of species richness on tree yield was positive for a large-scale tropical forest in China. They conducted this study at two different sites with different species composition and different factors such as functional traits leaf duration, specific leaf area, and wood density. This study, like our study, examined a combination of tree species. Paquette and Messier [
8] examined the effect of biodiversity on tree productivity across a gradient from boreal to temperate forests. They used abiotic factors that included average annual temperature, organic layer depth, intensity of competition, and BAL, along with biodiversity indices that included functional diversity, phylogenic diversity, species richness, and phylogenic species variability. Compared to Paquette and Messier [
8], our current study used more abiotic factors, such as slope, aspect, elevation, and azimuth. Further, we used stepwise regression and artificial intelligence (ANN) methods combined to explore the biodiversity–productivity relationships. Prior studies indicate that both productivity and biodiversity of a forest can be affected by many factors, such as local climatic conditions, soil characteristics, biodiversity, and even the type of management practices employed. Environmental factors are key variables that can help determine the diversity and distribution of plant species, and in our research, the following factors were considered: solar radiation, air temperature, topographic wetness index (TWI), and wind velocity. Solar radiation is one of main abiotic factors that can affect the growth and distribution of tree species. Air temperature in the lower troposphere is one of the important factors that controls the growth and metabolism of plants. As a result, plant growth is related to annual heat input indicators. However, soil water requirements and tolerances vary by tree species. Wind was assumed an important and influential nonbiological factor in plant production [
32,
33]. Wind speed exerts both positive and negative physiological and biomechanical effects on plants. In low wind velocity environments, large boundary-layer resistances between the air and leaf surface can hinder the transfer of carbon dioxide to plants [
34], leading to a decreased growth rates in the plants [
35].
Forest variables such as productivity, mortality, tree survival, and diversity have been modeled with regression analysis to help understand forest dynamics [
32,
36]. However, these models often assume a linear or nonlinear relationship exists between the dependent variable and the independent variables, and they may not adhere well to regression assumptions such as normally distributed sample data and others. Machine learning methods such as artificial neural networks (ANNs) have largely overcome these problems and, in recent years, have proven to be a good alternative to regression methods for estimating environmental conditions [
37]. ANNs are an alternative to traditional regression modeling approaches [
38], they have the ability to model nonlinear and complex relationships between different parameters, and they are more flexible than regression models in solving problems related to multiple interacting variables [
39]. ANNs are more generalizable than regression models and can be less sensitive to the effects of outliers and noise in data. Therefore, in this study, some specific issues were investigated: (i) the relationships between tree species diversity and forest productivity using different variables in the Hyrcanian forests of northern Iran (the main objective); (ii) the potential use of parametric and nonparametric models for describing these relationships; (iii) the potential use of two artificial neural networks (i.e., the multilayer perceptron (MLP) and radial basis function (RBF) networks) to, for the first time, describe these relationships; and (iv) whether biotic and abiotic factors (solar radiation, topographic wetness index, wind velocity, seasonal air temperature, basal area, number trees per hectare, and basal area in largest trees) had an effect on forest productivity.
4. Results
Across the sample plots, there was quite a lot of variation in tree density per ha, but interestingly, much less variation in basal area per ha. The diameter distribution of trees sampled in the study area for the first and second measurement periods describes the typical reverse J-shaped frequency distributions of uneven-aged forests (
Figure 4 and
Figure 5). The volume distribution by diameter class in the study area during both measurement periods indicated that oriental beech had the greatest footprint from a tree volume perspective, particularly in the higher dbh classes (
Figure 6 and
Figure 7). The tree species with the greatest density, European hornbeam, had high volume distributions in the smaller dbh classes. Due to the fact that volume is based on dbh and height, while there are more trees in the smaller diameter classes, larger amounts of per-hectare volume can be found in the larger diameter classes. From an analysis of the data, we determined that the average growth rate of the plots in the study area was about 4 m
3 ha
−1 yr
−1. Interestingly, neither the shape or magnitude diameter distribution nor the shape or magnitude of the volume distribution changed much between the measurement periods.
The results of regression modeling effort, using species richness as the dependent variable, are as follows (11):
where SR is the species richness, SH is Shannon Wiener index, EV is evenness, BA is the basal area (m
2/ha) in 2003, and WIND is the general speed of wind in the area of the plot. The coefficient of determination (
R2) of this modeled equation was 0.92, the RMSE was 0.55 m
2/ha, and the relative RMSE was 17.39%. As can be seen, species richness had a significant relationship only with species evenness and Shannon Wiener index, wind velocity, and basal area. In addition, as in the above relationship, the relationship of species richness with the evenness factor is negative. This suggests that, with increasing species richness, species evenness decreased. According to field data from permanent sampling plots, in these forests, the range of Shannon Wiener index and the Simpson index was 0.5 to 1.5. A good relationship was observed between actual and modeled species richness based on the conditions within each permanent plot.
The neural network structure consisted of a multi-input layer, a hidden multilayer, and an output layer, with a minimum of 6 and a maximum of 30 layers (
Table 3 and
Table 4). The independent variables of BA
2, BA, BAL, WIND, TWI, EV, AIRTEM, and ASOL were input layers, and the dependent variable (species richness) was the output layer. For each of the MLP- and RBF-based ANNs, five models were examined. MLP-based ANNs and RBF-based models for data collection and test data are shown with
R2 = 0.94 values in
Table 3 and
Table 4, indicating that a strong linear relationship existed between the actual measured species richness and the predicted species richness by the MLP.
Table 3 and
Table 4 show the statistics for the two models RBF and MLP and the ANN model for two stages training and evaluation, respectively. For each step, 10 models are used, and in these tables, the selected models are highlighted based on their low RMSE and bias values. With respect to model training and valuation, the multilayer perceptron (MLP 10-6-1 with
R2 = 0.94 and RMSE = 0.008) model was noted as being the most effective at predicting species richness.
The relationship between the actual and predicted species richness when the ANN model was used was strong (
Figure 8). However, the relationship between actual and predicted species richness from the two models (regression and ANN) suggests that the ANN model was more capable in predicting species richness. The influential factors in this method are the following variables: EV, BA
2, BA, TWI, AIRTEM, WIND, and ASOL.
With respect to the field plots, species diversity varied considerably across the landscape. The size of the points representing the locations of the field plots were scaled according to the Shannon Wiener index values of each plot (
Figure 9). Larger points represent higher index values, and smaller points represent lower index values. The range of the index was about 0.1 to 1.5.
The following relationship is the regression model developed to estimate productivity from the independent variables in the study area (12):
where
P is productivity, the 9-year net annual volume growth (m
3/ha); BA is the basal area (m
2/ha) in 2003; and WIND is the general speed of wind in the area of the plot. BA (
t = −3.90,
p = 0.00013), BA
2 (
t = 4.73,
p = 0.00000413), and WIND (
t = 2.32,
p = 0.021) were statistically significant components of the model. The net annual volume growth model using the regression method had an
R2 of 0.20, a RMSE of 0.41 m
3 ha
−1, a BIAS of 0.0035 m
3 ha
−1, a relative RMSE of 48.63%, and a relative BIAS of 0.55%. In summary, this method for estimating productivity based on biological and environmental variables was not very good.
Figure 10 shows the relationship between actual net annual volume growth (m
3 ha
−1 year
−1) and predicted net annual volume growth (m
3 ha
−1 year
−1). This suggests that predicting net annual growth from the actual growth of these forests is difficult using a regression model.
When using the ANN, a minimum of 4 layers and a maximum of 27 hidden layers were used. The results show that when 12 hidden layers were used, the highest accuracy can be estimated (
Table 5 and
Table 6). While the RMSE and bias were low, MLP-based ANNs and RBF-based models had moderately good coefficient of determination values (
R2 = 0.34 for the selected model), indicating that a fair linear relation existed between the actual measured net annual volume growth and the predicted net annual volume growth.
According to the sensitivity analysis, a species enrichment factor of 31% had the greatest effect on productivity and biotic and abiotic factors including square of plot basal area, plot basal area, wind velocity, air temperature, ASOl, and TWI, which had 15.9%, 13.3%, 10.3%, 9.8%, 9.8%, and 10% effects, respectively. Therefore, it can be said that, in total, species richness (31%), total biotic factors (about 29%), and total abiotic factors (about 40%) described the variation of productivity.
Table 7 shows the results of the sensitivity analysis for the best model to illustrate the effect of biotic, abiotic factors, and species richness on productivity.
5. Discussion
In this study, the results suggest that there is a positive and significant relationship between species richness and forest productivity in the study area. Productivity estimates based on the ANN and regression models illustrated the role of species richness as an influential factor in estimating productivity. However, this relationship was stronger and more meaningful in the results from the ANN model. Based on the modeling results, forest productivity in the study area was largely dependent on nonbiological factors such as wind velocity and TWI. The results of this study are consistent with other studies that have concluded there is a significant relationship between productivity and forest biodiversity, ranging from regional to global scales [
2,
58].
The predominant forest management system employed in this study area has been close-to-nature management of forests, and this has caused these forests to become uneven-aged over time. The use of this forest management system has resulted in mixed and heterogeneous stands of tree species. In such forests, there may be a higher resistance to change caused by biotic and abiotic factors and events such as insects, disease, droughts, or storms [
59,
60,
61,
62]. In mixed stands, different tree species occupy different niches. These types of forests can be more resistant to change because they possess different tolerances against environmental disturbances. Among the important factors affecting species richness in the study area were wind velocity and topographic wetness index. Wind velocity, alone, explained much of the richness of species. This result is consistent with the findings of Bourque and Bayat [
22] in the Kheyroud forest, which examined changes in the landscape on biodiversity. In that study, wind velocity, surface reflection of blue light, height of land above the nearest drainage point, and TWI had the greatest effects on the species richness. Wind speed has also been shown to provide favorable conditions for the growth of beech species [
23]. For example, wind speed can exert either a positive or a negative physiological and biomechanical effect on plants. In a low wind velocity environment, the transfer of carbon dioxide to plants can be hindered due to the large boundary layer resistances that exist, and this can result in decreased growth rates for the plants that are affected [
35]. In addition, in a high wind velocity environment, permanent deformation of plants can occur, as wind can distort growing patterns through application of constant bending pressures. Further, it may be observed that an increase in the transfer of water vapor from plants to the atmosphere has occurred in this type of environment, causing the closure of leaf stomata to help prevent desiccation. In this latter case, uptake of CO
2 may be reduced, negatively affecting plant growth. As a result, the optimal growing conditions based on wind velocity occur somewhere in between these extremes [
22,
23].
In terms of productivity prediction models, species richness was one of the important factors and had a stronger presence in the ANN model. However, according to sensitivity analysis, the most important and influential factor in this regard was the BA, while abiotic factors such as TWI, wind speed, and solar radiation were also important in later stages. This result is in line with the findings of Bayat et al. [
32], who studied factors affecting the growth of beech diameter in the forests of northern Iran. However, the regression analysis produced a nonlinear model that was better able to predict growth based solely on basal area. The relationship between species richness and productivity in the study area can be explained by, among other things, the dominant species in an area being the most fertile species. This is the effect of natural selection. More importantly, the richness of the species leads to the division of niches between the six species, which creates a wide range of functional strategies between species. As a result, this can be the main and important process in the relationship between species richness and productivity in a forest [
63,
64]. Another important factor that can justify this relationship is that higher species diversity has led to higher structural complexity that indirectly affects biomass, and, as it has been proven, forests with higher carbon storage potential also have higher biodiversity potential [
65]. It is also important to note that the relationship between productivity and biodiversity can change with spatial scale and climate. As various studies have shown, this relationship has been stronger in boreal forests and less or even meaningless in temperate forests [
8,
20].
Huang et al. [
19]; Paquette and Messier [
8]; and Rita and Borghetti [
20], in their studies in Chinese, Canadian, and Italian forests, concluded that the richness of the species has a strong effect on forest productivity, and in these diverse environments, coexisting species can have different niches and competitiveness. Biodiversity and its various effects have also been reported to be much stronger in boreal biomes than in temperate regions [
63]. In boreal environments where environmental conditions are more extreme, disturbances are more intense, and tensions are higher, the interactions between species may be more important and decisive Paquette and Messier [
8]. Therefore, these reasons can justify the relative low effect of biodiversity on productivity in the study area.
In this study, it was observed that ANN models, based on criteria for evaluating models such as RMSE and coefficient of determination, were more accurate than regression models and showed better relationships between productivity and biodiversity in the studied forest. As the results showed, they are in line with the findings of other research [
32,
66,
67]. The ANN of the multilayer perceptron (MLP) type had good ability in prediction and estimation of productivity in our forests. With respect to species richness, Model 4, which had 10 inputs, 6 hidden layers, and 1 output, had the highest R
2 (0.94) and the lowest RMSE (0.75) and was selected as the best SR predictor model. With respect to forest productivity, MLP Model 2 with 10 inputs, 12 hidden layers, and 1 output, had R
2 and RMSE of 0.34 and 0.42, respectively, representing the best model. Both of these used a logistic function.
Therefore, it can be said that the nonlinear and complex nature of the relationship between biodiversity and forest productivity may be better described using neural network models. However, each modeling method has its own set of strengths and weaknesses. In regression models, the relationship between variables is simple, yet assumptions such as normality of data, independence of variables, and many other conditions are limitations on the use of these models [
32]. Bayat, Bettinger, Heidari, Henareh Khalyani, Jourgholami, and Hamidi [
67] used comparative regression and artificial intelligence methods to conclude that artificial intelligence methods such as neural networks have a higher ability and accuracy in determining height in these forests. Artificial intelligence-based models such as neural networks do not have the same limitations as regression models and have the ability to work with qualitative variables. The results of various studies show that they can have a relatively high accuracy in predicting different conditions of a forest [
68].