The provision of ecosystem functions and services in forests is closely linked to the presence of complex structures. One such service is the ability to store carbon. It has recently become possible to quantify both structural complexity and biomass of forests (as proxy of carbon storage) using light detection and ranging (LiDAR). The objective of this study was to analyze how the communitylevel complexity of a forest stand relates to structural characteristics, and biomass in particular, of the trees comprising the stand. To do so, we virtually assembled 30 forests (3D models), all representing different versions of a beechpine forest in Germany, based on real world 3D LiDAR scan data of all trees in the forest. At the individual tree level, various structural characteristics, including wood volume and biomass were derived using both voxel models and quantitative structure models (QSM). Basal area and biomass, as well as to a lower degree also the mean height of maximum crown projection area, significantly affected the structural complexity at stand level. Among the different forest models, the variation in complexity could best be described using a combination of basal area, mean height of the maximum crown projection area, and the coefficient of variation of total tree height. Biomass alone explained 54% of the variation in standlevel complexity, while the multivariate model based on measures addressing the amount and vertical distribution of plant material explained 86% of the variability in complexity. Using a laserbased and holistic approach of assessing the structural complexity, namely the boxdimension, allowed identifying key structural attributes that promote aboveground structural complexity of the forest studied here.
In the context of increasing sociopolitical demands on forest ecosystems, the challenge for forest management is to ensure that ecosystem services are provided and ecosystem multifunctionality is maintained (
Structural complexity can be defined as the sum of all dimensional, architectural and distributional characteristics of all plant individuals in a given space and at a given point in time (
Similarly, from laser scanning data it is today possible to automatically reconstruct accurate 3D models of trees to estimate aboveground biomass (
Structural complexity and biomass are two forest characteristics that are seemingly interlinked, but a forest rich in biomass is not necessarily highly complex in structure as well. Most biomass is stored in the tree trunks, while structural complexity is largely driven by overall space occupation (
The objective of this case study was to identify key structural parameters for promotion of structural complexity and to analyze the relationship between biomass and structural complexity in particular. For this purpose, 3D data of a mixed pinebeech forest in the leafless state (winter) were obtained from mobile laser scanning and thirty virtual 3D forest models were created by combining the segmented individual trees of the real forest. The resulting stand models varied according to various structural parameters.
We hypothesized that (i) structural characteristics of the trees comprising a stand can explain the community complexity of a stand. We also hypothesized that (ii) stand biomass, if all wooden aboveground plant organs (stem, branches and twigs) are considered, is positively related to the complexity of a stand.
The forest studied here is involved in a longterm study program within the International Cooperative Program on Integration Monitoring (ICP IM) to investigate the effects of air pollution on ecosystems. It is located at the site “Neuglobsow” in the catchment area of the Lake Stechlin in the State of Brandenburg, NorthEast Germany (53° 08′ N, 13° 02′ E 
The forest stand was surveyed using a GeoSLAM ZEB® Horizon (GeoSLAM Ltd., Nottingham, UK) handheld mobile 3D laser scanner. During scanning, a maximum distance of 100 m can be measured between the laser scanner and the objects to be measured with a positional accuracy of around 3 cm. The LiDAR sensor of the device, a Velodyne VLP16® (Velodyne Lidar, San Josém, CA, USA), measures distances using the timeoflight method. A total of 300.000 points can be captured per second (
For data collection, the study area was first circled with the laser scanner and later crossed several times without a fixed pattern, simply to ensure good coverage of the site. The duration of the recording was approx. 20 minutes and the stand was recorded in winter 2020 to 2021 (leafoff state). The scan was processed using GeoSlam Hub v. 6.1 (GeoSlam Ltd.) and exported as xyzfile (point cloud) for further postprocessing. Slope correction of the point cloud was performed using LIDAR360 (Greenvalley International, CA, USA). To reduce noise in the 3D point cloud, subsampling (0.01 m) and noise filtering (spherical: 0.1 m) were applied in CloudCompare (version 2.12 beta  http://www.danielgm.net/). To address the individual trees, they were segmented manually from the point cloud for maximum quality. All trees located with their stem base inside the fence and with at least 4 m in height were considered in our study (n = 100 trees).
At the individual tree level, a series of structural parameters were derived using the methods introduced in the literature (
Wooden tree volume (WTV) was determined using the CompuTree software with the SimpleForest plugin (
To determine the aboveground biomass (AGB), WTV was multiplied by the speciesspecific functions for the conversion of volume to dry wood substance. A density of 558 kg m^{3} was assumed for beech and 431 kg m^{3} for pine (
For the analysis of the biomasscomplexity relationship, thirty virtual models of the forest stand were “assembled” in CloudCompare using the trees identified and segmented from the real stand (
The current stand situation in the real world was represented as model 1. The additional models varied in different aspects, such as tree species mixture (pure stands of
In model 10, random representatives of each diameter class (one individual per class) were combined to form a forest stand and in model 1113 the trees were assigned to their developmental stages (immature, intermediate, mature). In model 14, the trees with the largest diameter (10% of the highest DBH) were removed from the stand. In model 1524 different architectural parameters like crown volume (CrVo), crown surface area (CSA), height of the greatest crown projection area (H_{Maxarea}), and the maximum crown projection area (Max_{Area}) were varied, selecting the trees with the highest and medium expressions of these parameters, respectively. In addition, model 2224 contained trees with only low, medium, and high individual tree complexity (D_{b}), respectively.
In model 25 to 30 tree positions were not based on the realworld location anymore. Instead, plantationlike forests were created in which identical, randomly selected individual trees of
For each 3D forest, the structural complexity was determined based on the boxdimension of the final model. The boxdimension (D_{b}) is a holistic measure of structural complexity that can be obtained from laser scanning in an efficient manner for single trees (
For each forest model, the mean and coefficient of variation of the parameters of the individual trees were determined. The relationship between this data and the complexity (D_{b}) of the whole 3D forest model (study stand) was tested using simple linear regression. The best multiple linear regression model explaining standlevel structural complexity was selected using stepwise variable selection (stepAIC). The independent variables in the model were also tested for multicollinearity using variance inflation factor (VIF) values. Analysis of residuals of the statistical model was then carried out to check for validity. All statistical analyses, models and graphs were performed with RStudio Desktop v. 2022.07.2+576 (
A total of 100 individual trees were segmented from the original point cloud, of which 63 trees were in the upper stand layer (dominant) and 37 in the lower and intermediate stand (codominant or suppressed). In the dominant stand layer, 47 (75%) European beech and 16 (25%) Scots pine trees were recorded. In the understory, mainly individuals of
In the realworld condition (model 1, the reference), the investigated forest stand reached a D_{b} value of 2.17. If the beech and pine percentages (model 4) were set equal, the D_{b} value decreased slightly (2.11) and if only the pines were represented (model 3), the lowest complexity (D_{b}: 1.18) was achieved. When the tallest trees in the study stand (model 7) were presented together, here resulting in a higher proportion of pines being present, structural complexity decreased. In contrast, the stand created in model 8, in which medium tree heights were present, reached a relatively high complexity (D_{b}: 2.07). In the subsequent models, the highest D_{b} was achieved when the trees with the highest DBH (10%; model 14) were not included. Moreover, the scenario that contained of mature trees had a low complexity of only 1.4 units in D_{b}.
Model 21 referred to the upper half of the trees with a high Max_{Area} and resulted in a rather high D_{b} value (D_{b}: 2.03). In the plantationlike stands, model 25 (pure beech stand) showed an identical D_{b} value as the reference stand, while the simulated pure pine stand (model 26) had a lower D_{b} value (2.03). The tree by tree mixture in model 28 achieved a D_{b} value of 2.16. An overview on the structural complexity of all modelled forests is given in
For a visual comparison of the complexity of the forests created in the different model groups (
From stepwise variable selection, the best regression model explaining structural complexity was identified using AIC comparison. It contained stand basal area, mean H_{Maxarea} and the coefficient of variation of TTH as combined predictors of D_{b}. Multicollinearity of the independent variables could be excluded (VIF < 10). The respective regression coefficients of the variables (
Among all tested bivariate relationships between complexity at standlevel and statistical measures describing the structural characteristics of the trees in the stand, the D_{b}biomass relationship had the highest coefficient of determination (R^{2} = 0.54 
We investigated thirty different 3D forest models created from realworld trees in terms of their structural complexity to gain a deeper understanding of the geometric drivers of complexity at stand level.
As we used the boxdimension as a holistic measure of complexity (
If only the tallest trees were selected for building a forest model, the structural complexity was comparatively low. In contrast, models that mainly included the dominated trees in addition to the less dominant ones showed a higher structural complexity. Models 8 and 9 additionally differed in the height of the understory trees added to the scene, which had a rather small influence on structural complexity. The predominant singlelayered structure of the studied stand in its natural form (model 1) can be seen in the regression coefficient of the multiple regression model (
As we found three of the tested structural characteristics of the individual trees to relate significantly to the standlevel complexity, namely the sum of the trees’ biomass, the basal area, and the mean height of maximum crown projection area (
Our data also support hypothesis (ii), stating that the D_{b} is sensitive to the amount of biomass in a forest. It is important to mention here, that this relationship has been shown before on the treelevel scale, but not on stand scale. The strong explanatory power of biomass in our study (R^{2} = 0.54 
Finally, the mean height of the maximum crown projection area was significantly but weakly related to D_{b}. The negative direction of the correlation seems plausible, as a lower mean height of maximum crown projection area basically indicates the presence of trees with deeper crowns, greater vertical layering and overall increased space filling, all factors associated with greater forest complexity (
Despite overall confirmation of hypothesis (ii), the identified significant relationship between biomass and complexity also shows quite some unexplained variation (46%). For example, the initial stand (model 1) had a lower biomass than the forest stand built by model 25, but these two stands possessed the same structural complexity. Increasing biomass therefore not necessarily results in an increased complexity. The quantitative structure models here used for biomass quantification are considered the most reliable nondestructive method available (
In this case study, the variation of structural complexity (D_{b}) as a function of stand structural parameters was investigated in thirty different 3D forest models of a mixed European beech and Scots pine stand using realworld structural information from hand mobile laser scanning. The D_{b} of the stands in the individual forest models was most appropriately described (R²_{adj} = 0.86) by a combination of stand basal area, mean height of the greatest crown projection area and the coefficient of height variation. Among the tested single structural variables, biomass of the stand was most closely related to the stands’ complexity but with a much lower explained variation (R² = 0.54).
As predicted by the theoretical derivation of the boxdimension, biomass alone is unlikely to explain structural complexity observed in a forest to a level where it could be justified using biomass alone as a solid proxy. The threedimensional character of structural complexity is better reflected if additional measures addressing the vertical distribution of plant material are used in addition.
The authors declare no conflict of interest.
This work was funded through grant SE2383/81 provided by the German Research Foundation (DFG).
General map of the study site at the station “Neuglobsow“ with a 3D representation of the mixed beechpine stand (3D point cloud from laser scanning) on the left.
Boxplots showing the variation of D_{b} in the respective silvicultural models depending on the grouping variables mixture, tree height (TTH, m), diameter at breast height (DBH, cm), crown structure, structural complexity (D_{b}) and plantation. The individual tree parameters were varied in their expression (high, medium, low) and the modelled stands were compiled accordingly. Model assignment to the groups was according to
3D forest models. Representation of the point clouds of the thirty forest models with their respective characteristic values of structural complexity (D_{b}). The assignment of each model to the different model groups is reported in
Scatterplots showing the relationship between D_{b} and the mean and coefficient of variation of height (TTH), diameter at breast height (DBH), height of maximum crown projection area (H_{maxarea}, m), Maximum crown projection area (m^{2}), crown surface area (CSA), crown volume (CrVo), as well as basal area, biomass and the structural complexity (D_{b}) on single tree level. R^{2} is the coefficient of determination of the linear regression models and the dashed lines indicate the confidence interval at 95% for significant relationships.
Structural attributes determined at single tree level.
Parameter  Abbrev.  Type  Reference 

Total tree height (m)  TTH  cloudbased 

Diameter at breast height (cm)  DBH  cloudbased 

Maximum crown projection area (m^{2})  Max_{Area}  cloudbased 

Height of maximum crown projection area (m)  H_{Maxarea}  cloudbased 

Crown volume (m^{3})  CrVo  cloudbased 

Crown surface area (m^{2})  CSA  cloudbased 

Boxdimension  D_{b}  cloudbased 

Wooden tree volume  WTV  QSMbased  Hackenberg et al. ( 
Overview of the varied structural parameters within the 30 forest models.
No.  Description  Group  No. trees 

1  Current stand situation  Original  100 
2  pure beech stand (all pine trees removed, without understory)  Mixture  47 
3  pure pine stand (all beech trees removed, without understory)  Mixture  16 
4  50% beech, 50% pine (no understory, randomly selected trees)  Mixture  32 
5  80% beech, 20% pine (no understory, randomly selected trees)  Mixture  59 
6  70% pine, 30% beech (no understory, randomly selected trees)  Mixture  23 
7  20% of the tallest trees with respect to TTH (both species)  TTH  21 
8  60% symmetrically distributed around mean TTH (both species)  TTH  59 
9  20% of the tallest trees removed  TTH  79 
10  All diameters represented once (classes of 1 cm)  DBH  43 
11  developmental stage: immature timber (15 cm to 37 cm DBH)  DBH  29 
12  developmental stage: intermediate timber (38 cm to 50 cm DBH)  DBH  21 
13  developmental stage: mature timber (> 50 cm DBH)  DBH  12 
14  trees with the highest DBH removed (upper 10%)  DBH  90 
15  trees with highest crown volume (upper 10%)  Crown structure  10 
16  30% symmetrically distributed around the mean of CrVo  Crown structure  30 
17  of trees with greatest CSA (upper 20%)  Crown structure  20 
18  60% symmetrically distributed around the mean of CSA  Crown structure  60 
19  trees with highest H_{Maxarea }(upper 40%)  Crown structure  40 
20  trees with lowest H_{Maxarea }(lowest 60%)  Crown structure  60 
21  trees with highest Max_{area }(upper 50%)  Crown structure  50 
22  least complex trees (lower 35%)  Complexity  35 
23  30% symmetrical distributed around the mean of D_{b}  Complexity  30 
24  most complex trees (upper 35%)  Complexity  35 
25  pure beech stand, evenly distributed, without understory (copies of an identical, randomly selected single tree)  Plantation  49 
26  pure pine stand, evenly distributed, without understory (copies of an identical, randomly selected single tree)  Plantation  25 
27  rowwise mixture of beech and pine, without understory (two identical, randomly selected individuals of each tree species)  Plantation  52 
28  stand with single tree mixture of two trees with the highest D_{b} of the respective tree species  Plantation  47 
29  stand with stripwise mixture of two randomly selected trees from the upper and lower layer  Plantation  78 
30  stand with troop mixture of randomly selected trees from all stand layers  Plantation  187 
Statistical measures of the structural parameters of the individual trees (n = 100) in the studied forest. (SD): standard deviation.
Parameter  Min  Max  Mean ± SD 

TTH (m)  4.04  33.83  20.83 ± 11.49 
DBH (cm)  2.4  73.26  27.11 ± 20.00 
H_{Maxarea} (m)  1.6  30  16.18 ± 10.67 
Max_{area} (m)  0.66  99.56  24.83 ± 22.83 
CrVo (m^{3})  0.95  961.28  150.40 ± 19.07 
CSA (m^{2})  12.43  952.28  257.91 ± 222.44 
D_{b}  1.45  2.03  1.76 ± 0.10 
AGB (t)  0.01  10.65  1.19 ± 1.58 
Coefficients of the “best” multiple linear regression model for estimating D_{b} as a result of stepAIC. The model goodness of fit is R^{2}_{adj} = 0.86. All coefficients are significant (significance level: *** = p < 0.001).
Parameter  Estimate  Pr(>t) 

Intercept  3.036  2.50e14 *** 
Basal area  0.024  4.97e12 *** 
Mean of H_{Maxarea}  0.068  6.98e09 *** 
CV of TTH  0.01  2.34e06 *** 