1. Introduction
Tree growth is influenced by several factors, including climate patterns, site conditions, and competition processes [
1,
2,
3,
4] Among them, tree competition measures are the main predictors of individual trees’ growth [
5]. Competition among trees is defined as the negative effects that neighboring trees have on a subject tree. These negative effects depend on the interactions between trees in acquiring limited resources, such as light, water, and nutrients [
6,
7]. Quantifying the competitive effect of neighboring trees is difficult due to the co-occurring effects of various environmental factors on trees.
Many indices have been developed in numerous studies in order to quantify the level of competition that individual trees experience, and to assess how competition affects growth rates (e.g., [
8,
9,
10,
11,
12]). Competition models, based on competition indices of single trees, can be classified into two main groups: distance-independent and distance-dependent models [
13,
14,
15,
16]. Distance-independent models use only non-spatial competition indices. These indices are based on the size distribution of competitor trees within a given area, without considering their spatial distribution. Differently, distance-dependent models are based on spatial competition indices that incorporate both the size and the spatial distribution of competitors [
17]. Distance-dependent indices may offer more reliable forecasts of the growth of single trees [
18,
19], as tree size, species composition, and stand structure vary within a stand and, consequently, the availability of resources [
20]. In forests with a spatially inhomogeneous distribution of trees, and in particular in unmanaged mountainous areas, there is usually stronger growth competition between neighboring trees and thus biomass growth can be more easily influenced by the available light intensity and site quality.
Several studies (e.g., [
16,
21]) found that the canopy neighborhood plays a key role in understanding tree competition. Therefore, the availability of light is probably a determining factor for the growth of individual trees [
22,
23,
24,
25]. However, species-specific differences in crown characteristics may influence light capture differently in different canopy classes [
26]. Yet, the co-occurrence of species that differ in their root architecture may improve the uptake of nutrients and water [
27,
28]. Below-ground competition does not only consider the interactions between dominant and/or subdominant trees with the subject tree but also those trees whose roots occupy the root distribution area of the subject tree [
29]. These differences in functional traits for the capture and assimilation of resources (such as light, water, and nutrients) may lead to changes in biomass partitioning and, therefore, change the productivity of forests. According to Fox et al. [
30], the productive potential of forest stands can be greatly increased by competition. Competition is linked to the acquisition of environmental resources by species in close spatial proximity, so changes in biomass partitioning may affect the productivity of forests [
31,
32]. Many studies (e.g., [
33,
34]) have investigated the relationship between biomass partitioning and plant competition. For example, Lin et al. [
34] showed that the allocation of biomass can vary due to different types of competition, above and below ground. Increased competition among trees due to the limitation of underground resources can lead to changes in roots’ biomass [
35]. Furthermore, according to Petersen et al. [
36], removal of the effects of competition in a controlled environment led to an increase in the above ground biomass of Douglas fir. These studies suggest that competition is closely related to biomass partitioning, and biomass distribution directly affects forest productivity. Furthermore, according to Zhou et al. [
33], biomass distribution directly affects forest productivity, and productivity is closely related to forest competition.
Obtaining information regarding the spatial distribution of individual trees, and their height, diameter, crown projection, and biomass requires methods based on field measurements. Although these conventional techniques provide reasonably accurate estimates, they often require labor-intensive and time-consuming measurements and inspections. Moreover, the measurements are always limited to small areas while in many cases, it is necessary to have measurements over large areas. Therefore, the use of remote sensing, in particular of light detection and ranging (lidar) remote sensing technology, partially overcomes these limitations. Several methods have been developed using airborne lidar metrics (e.g., [
37,
38,
39]) for the estimation of forest biomass and volume (e.g., [
40]), and other forest characteristics (e.g., [
41]). The majority of the studies in the literature have focused on the prediction of volume and biomass, many on forest structure, and few on competition. As an example, Lo et al. [
42] predicted volume, DBH, and a height-based competition index using lidar metrics at the individual tree level. Relating volume and DBH to the competition index, they showed that they are negatively related. Similarly, Lin et al. [
43] showed that by using a lidar-based height competition index it is possible to predict the aboveground carbon density of individual trees. Ma et al. [
44] predicted tree growth in terms of an increase in height crown area and crown volume using bi-temporal airborne lidar data and they related this to some competition indices.
The objective of this study was to use lidar metrics to predict competition indices and to show how they relate with tree aboveground biomass (AGB). In particular, we focused on two competition indices, one related to height and one to the diameter at breast height (DBH). To the best of our knowledge, no study has explored the possibility of predicting DBH and height competition indices for individual trees detected on lidar data, using lidar metrics extracted both at the plot and ITC level.
4. Discussion
In this study, we demonstrated that it is possible to predict DBH and height competition indices using lidar metrics. We also showed how competition affects the AGB of individual trees. The results showed that no real improvement is gained in using a species-specific model with respect to a general model. It is worth noting that for the species-specific models, we had quite a low number of samples (especially for Norway spruce) and this could have influenced the results. In terms of overfitting, all models showed reasonable values of
R2
R and
SSR; in particular, only the model for
of Norway spruce showed values much above 1.1, which was suggested by Lipovetsky [
60] as a desirable limit in order to not have overfitting.
Analysis of the five ITC metrics selected indicated that they are all related to the competition indices. Some of them are clearly related, like the and indices computed using the ITCs (CI_DBH_ITC, and CI_H_ITC), while the others are representative of a part of the competition index equations (DBHsumITC, and CAmeanITC) and of the density of the forest (DsdITC), which is related to competition. Regarding the plot metrics, it was slightly harder to find a direct relation to the competition indices. Metrics based on the distribution of Z are likely related to competition even if not directly. The Zq20_F, Zq95_L, Zpcum1_F, Zpcum2_F, and Zpcum2_L metrics describe the vertical distribution of the lidar points, and the vertical distribution of the points is related to the forest structure and density, which are related to competition. In contrast, the intensity metrics could be related to the species. As an example, Imean_F has a quite different distribution of values for the two species: It has a mean value of 23.47 (standard deviation of 3.63) for silver fir compared to 20.15 (standard deviation of 3.82) for Norway spruce.
The effectiveness of lidar metrics in predicting both AGB and competition indices was also found in the study conducted by Lin et al. [
43]. In particular, Lin et al. [
43] showed that the height competition index estimated by lidar, especially when combined with other lidar metrics (crown radius and height) of the trees, is capable of effectively estimating above-ground carbon (AGC) at both the stand and tree level. In our case, the competition indices were used to assess the influence that high or low competition values have on biomass. The results showed that high competition values led to a decrease in biomass. Therefore, the competitive pressure of neighboring trees is probably an important factor influencing tree growth and biomass partitioning, especially for small trees. Indeed, according to Litton et al. [
61] and Poorter et al. [
62], biomass partitioning may vary with soil resource availability and with the ability of plants to withstand competition for light. Furthermore, according to the theory of biomass allocation, high competition may increase or reduce biomass allocation in plants [
63,
64]. Zhou et al. [
33] found that the biomass ratio of roots and stems decreased with increasing intensity of competition from neighboring trees, while biomass at the level of branches and leaves increased.
Few previous studies were found in the literature that combined lidar and competition indices. Among the ones present in the literature, the ones of Lo et al. [
42], Lin et al. [
43], and Ma et al. [
44] are the only ones slightly related to this work. In all these studies, competition indices were computed using ITCs automatically delineated on lidar data, in a similar way to our computation of the lidar metrics
CI_DBH_ITC and
CI_H_ITC. None of these studies analyzed the accuracy of the prediction of competition indices using lidar metrics or validated the predictions using field data. In contrast to the present study, these studies used lidar-predicted competition indices as metrics to predict trees attributes, such as DBH, volume, and carbon density.
Several studies have shown the relationship between radial growth and height growth of trees [
65,
66] and that the crown:height ratio may quantify competition among trees [
67,
68]. Therefore, the diameter and height of a tree are not only closely linked to light capture but also to the effects of water, nutrients, and soil conditions [
33]. Moreover, according to the results of Zhou et al. [
33], during growth, plants change how they are affected by the competition of neighboring plants, and their competitive effect on other plants. This suggests a close relationship between individual competition and tree growth.
In the workflow proposed in this study, some parameters were fixed in a way that could have influenced the final results. The main one was the search radius used to compute the competition indices. Many studies in the literature focusing just on the computation of indices using field data used a different radius for each area analyzed. This is possible if all the tree crowns are measured on the ground; however, that was not our case. Moreover, as we wanted to relate the indices to the lidar data in order to have the possibility of also predicting competition indices in areas not covered by field data, we needed to have a fixed value of the search radius. We chose 10 m as it was used before in other studies investigating forests with similar characteristics [
53]. It is worth noting that we also carried out the same analyses using other values, computed in other ways, but the used radius was quite close to 10 m and the final results were very similar or the same.
The ITCs delineation could also have had an effect on the final results. Indeed, the higher the accuracy of the delineation, the more valuable ITC metrics are, and the more trees can be considered as subject trees in the area. The algorithm selected is a simple method when compared with the many algorithms in the literature [
69], and has been used successfully in many other studies on forests with similar characteristics (e.g., [
47,
55]). It was effective for different forest scenarios in a previous study conducted on various forest sites in the Alps [
70].
Despite the high potential of lidar technology for the estimation of vegetation parameters, it must be considered that lidar also has limitations. According to Rosette et al. [
71], the ability to estimate vegetation parameters (tree height and DTM) decreases in the presence of high terrain slopes and high canopy coverage. Moreover, in very dense forests, it is only able to identify dominant trees, as in our study. Values of competition indices calculated using metrics derived from lidar can be biased due to the fact that small trees are not detected.