Quantifying Understory Complexity in Unmanaged Forests Using TLS and Identifying Some of Its Major Drivers

: The structural complexity of the understory layer of forests or shrub layer vegetation in open shrublands affects many ecosystem functions and services provided by these ecosystems. We investigated how the basal area of the overstory layer, annual and seasonal precipitation, annual mean temperature, as well as light availability affect the structural complexity of the understory layer along a gradient from closed forests to open shrubland with only scattered trees. Using terrestrial laser scanning data and the understory complexity index (UCI), we measured the structural complexity of sites across a wide range of precipitation and temperature, also covering a gradient in light availability and basal area. We found signiﬁcant relationships between the UCI and tree basal area as well as canopy openness. Structural equation models (SEMs) conﬁrmed signiﬁcant direct effects of seasonal precipitation on the UCI without mediation through basal area or canopy openness. However, annual precipitation and temperature effects on the UCI are mediated through canopy openness and basal area, respectively. Understory complexity is, despite clear dependencies on the available light and overall stand density, signiﬁcantly and directly driven by climatic parameters, particularly the amount of precipitation during the driest month.


Introduction
The understory of a forest, as well as vegetation in shrublands without a distinct overstory, are important contributors to several ecosystem functions and services, including flora and fauna diversity [1][2][3]. Shrubby vegetation also affects nutrient cycling [4] and provides breeding and feeding grounds for large mammals [5]. In addition to these ecological functions, the understory layer determines the future species composition and structure of forests [6,7], which is of economic and ecological importance [8]. This is simply because juvenile trees-the so-called regeneration-are also part of the understory layer. In forests, the understory layer hence contains those trees that are potential future overstory trees through successional dynamics [9,10]. In shrublands with only scattered large trees, shrubby vegetation constitutes an important transitional habitat that results in high taxonomic and functional diversity [11].
Research on the development, composition, and structure of the understory layer in forests was largely motivated by the question of what conditions enabled the successful establishment of regeneration trees [10,12,13]. Forest managers require this knowledge to establish the regeneration of the forests with the desired tree species in order to control that the UCI was responsive to the presence of established regeneration trees (the more trees the higher the UCI) and the existence of skid-trails in European beech forests, with skid trails reducing the understory complexity significantly [42].
Here, we aimed at using this new index to investigate the structural complexity of vegetation between 0.8 and 1.8 m above ground across a climatic gradient in old-growth forests and a shrubland in Chile. It is worth mentioning that it was not our intention to depict the different elements that create complexity in this vegetation layer (herbs, shrubs, regeneration trees, overstory stems) but to quantify the general level of structural complexity in an objective and holistic way, and to investigate how it relates to the presence of overstory trees, to the available light, and to climatic parameters, namely precipitation and temperature.
We hypothesized that (i) the understory complexity index (UCI) is negatively related to the basal area at a site, as a higher basal area will result in greater competition for growing space and hence less favorable conditions for plant growth in the understory layer. We also hypothesized that (ii) an increase in canopy openness results in greater understory layer complexity due to increased light availability. Furthermore, we hypothesized (iii) that water availability is a key top-down driver of the complexity of the understory layer and hence UCI increases with mean annual precipitation and precipitation during the driest month. Finally, we hypothesized (iv) that the complexity of the understory layer increases with mean annual temperature.

Study Sites
Between February and March 2019, we measured the complexity of vegetation between 0.8 and 1.8 m above ground across a gradient ranging from understory layers of temperate old-growth forests to the open conditions of a Mediterranean shrubland (see Figure 1). Our sites covered different overstory densities (basal area), light availabilities (canopy openness), a large gradient in precipitation and a notable range in mean annual temperature (Table 1). At five sites located in northern, central and southern Chile, we selected sampling areas that were undisturbed (unaffected by roads, hiking trails, nearby settlements) and without any signs of harvesting (e.g., stumps) to avoid anthropogenic influences (see Figure 1). Despite the effort, in the case of one site (Parque Nacional la Campana; from here on: La Campana), we observed some signs of livestock (cow dung) in some of the investigated patches. The soil moisture regime at two sites, La Campana and the Reserve las Chinchillas (from here on: Las Chinchillas), was xeric. All other sites were characterized by an udic soil moisture regime [43].

Sampling Scheme and Scan Settings
At each site, we placed between three and nine sample plots, each consisting of five measurement positions for scanning with a spatial arrangement resembling a five on a dice (quadratic layout with an additional central position, see Figure 2) as introduced in [40] for a similar task. Avoiding hiking trails, as well as topographical issues such as canyons, steep slopes, or rivers, we selected the location of the plots by beginning at a random starting point without such issues in the area of interest and defined it as the center of the first plot. Since some of the investigated sites were rather small with regard to the available undisturbed areas (without nearby hiking trails or adjacent managed forest areas), the next plots were then selected randomly by proceeding to walk in one direction. Thereby, the minimum distance between two plots' edges was 60 m to avoid larger overlap in the scanned scenes (only 15 m around each scan are used during analysis, but see chapter 2.3 for details). Plots were then randomly located in terms of azimuth directions (random rotation around center point of the five-on-a-dice scheme). This sampling scheme, with 123 sample points, resulted in 27 plots, with only very few plots consisting of less than five sample points (Table 1). This was due to general inaccessibility of the plots, e.g., sample point in a river gorge. At each sample point, we estimated the basal area (m 2 /ha) using the angle count approach [44] facilitated through a Dendrometer II device [45]. Table 1 provides an overview on the main characteristics of the sites.  Table 1, due to varying sizes of the investigated forest patches and accessibility.
On every sample point, we conducted a terrestrial laser scan using a Faro Focus M70 laser scanner (Faro Technologies, Lake Marry, USA) mounted and leveled on a standard tripod at breast height (1.3 m). The scanner was set to capture 300 • and 360 • in the vertical and horizontal direction, respectively. The angular step-width (scan resolution) was set to be 0.035 degrees and the maximum distance at which objects can be captured by the instrument was 70 m.

Calculation of Understory Layer Complexity and Canopy Openness from Laser Scans
All scans were individually treated as single scans in this study. First, using Faro Scene software (Faro Technologies, Lake Marry, Fl., USA), we filtered each scan for erroneous scan points applying the standard filters for isolated points, split laser beams, and low reflectivity. Then, each scan was exported as an xyz-file. Based on these files, we calculated the understory complexity index (UCI) as introduced by [42] using Mathematica software (Vers. 12, Wolfram Research, Champaign, IL, USA). To determine the UCI, first, the single scan point clouds were limited to all data within 15 m horizontal distance to the scanner. Then, this circular patch of the xyz-data of the scanned scene was corrected for slope or undulation in the scanned area using normalized heights. These normalized heights are needed in order to address specific horizontal layers in a scene parallel to the ground. Normalized heights were based on a correction of each laser hits' vertical position (z-value of xyz-data) with the height of the underlying terrain derived from the scan through the interpolation of ground-hits [42]. From the normalized point cloud (ground-parallel data), a horizontal layer ranging from 0.8 to 1.8 m was extracted as presented in [42]. Due to the technical limitations of a single perspective of the scanner mounted on the tripod at 1.3 m height above ground, it is not recommended to consider a larger vertical layer. The layer or "slice" through the scenes, consisting of tree stems of adult trees, regeneration trees, shrubs and all other plant material reaching into this layer, was then considered the understory layer and characterized for its complexity. To do so, a polygon is created by connecting all hits based on their position (azimuth angle and distance to the scanner) after sorting them clockwise according to the azimuth angles. This polygon is more complex in shape when distances to hits of consecutive azimuth angles differ strongly when compared to distances that are fairly equal (cf. [42]). The degree of complexity of the shape of the polygon was finally determined using a modified version of the circumference-to-area ratio, the so-called fractal dimension index, introduced by [60], and originally designed for the analysis of the shape of landscape elements. The UCI cannot be strictly compared to conventional approaches that focus on specific objects, e.g., an inventory of regeneration trees or understory layer presence, a biomass assessment or an inventory of understory cover, as it does not distinguish different objects. It addresses the complexity of all vegetation present in this layer at once and summarizes it in a single number. Therefore, the UCI can be considered a holistic approach to complexity. For a more in-depth introduction of the UCI, the interested reader is referred to [42]. A graphical illustration of the procedure is depicted in Figure 4. In the following, canopy openness was derived from each scan following the approach presented in [61,62]. First, all points scanned at the respective scanning position were projected to the hemisphere described by the maximum scan distance (point distance was set to 70 m). Then, a stereographic projection was applied to create a circular image of the forest canopy similar to a hemispherical photograph. From this image, only the central area describing a 60 • opening angle directly above the scanner was used for the calculation of canopy openness, defined as the area in the image uncovered by plant material and hence considered open sky (white pixels in the image) expressed as ratio (0 = no sky visible; to 1 = no plant material visible (100% sky)). The reduced field of view (60 • opening angle) is used to ensure that no areas are considered for the image that are out of reach of the scanner (range = 70 m). We conducted the procedure also in the shrubland site with only scattered trees, expecting canopy openness to reach as much as 100% in these cases.

Climate Data
We used the publicly available database WorldClim Version2 [54] to obtain the following climatic variables (averages for the years 1970-2000) from the 1 km-resolution dataset provided at the URL: https://www.worldclim.org/ (accessed on 20 August 2020). In this study, we used the mean annual precipitation, mean precipitation of the driest month and mean annual temperature to address precipitation effects, seasonality effects as well as effects of the temperature. All of these were shown to be of relevance for overall forest structural complexity in a recent study including some of our sites [41] and were therefore considered interesting climate attributes in our present study. Using the free software QGIS (Vers. 2.18 Las Palmas) and the "point sampling tool" plugin, we automatically collected the climate data for our sampling points based on the GPS location of every scan obtained during field work using a Garmin GPS-Map64 GPS device (Garmin AG, Schaffhausen, Switzerland).

Statistical Analysis
All data were aggregated to the plot level by taking the mean of all measures of all scans (usually five) per plot. This was carried out since reliable estimates of plot level understory structure should not be obtained from single-scan positions but from a sampling approach, as shown earlier [33,34,41]. The relationships among all explanatory variables for the UCI, namely the basal area, canopy openness and the climatic variables were first tested using Spearman's correlation analysis. Significant differences among means of the UCI across sites was tested using the ANOVA and Tukey post hoc test.
Relationships between the explanatory variables and the UCI were evaluated using non-linear generalized additive modeling (GAM) techniques [63]. This allowed one to not need to predefine the relationship between the response and explanatory variable, which results in an unbiased detection of the trends in the data themselves [64]. The effective degrees of freedom (EDF) were limited to a maximum of 3 (number of knots = 4), to avoid over-fitting of the data, with the amount of smoothing to be chosen automatically through generalized cross-validation [65]. EDF values around 1 point towards the linearity of the data; larger than 1 towards non-linear trends in the data. The data family was set to Gaussian type as the identity-link function [63]. In order to disentangle direct and mediated effects of climatic variables on the UCI, we used structural equation models (SEMs) as facilitated in the software Onyx [66]. We used a latent variable for the unknown error contribution to changes in the UCI and modelled the effect of mean annual precipitation, mean annual temperature, and precipitation in the driest month on the UCI. Thereby we modeled the direct effect of the variables on the UCI and the indirect effect through the basal area and canopy openness as mediators. We then evaluated the model performance (maximum likelihood models) based on the Akaike information criterion (AIC) and chi-quadrat statistics. The same was performed to investigate whether the interaction between the precipitation variables and mean annual temperature yield a significantly better prediction of the UCI than models considering only direct effects of the individual climatic variables. The significance level was p < 0.05 for all tests. All the statistical analyses were conducted using R (3.4.4, R Development Core Team). The used methods are visualized in the flow-chart shown in Figure 5.

Results
We observed several relationships among the explanatory variables based on Spearman's correlation analysis (Table 2 and Figure 6). Mean annual temperature had a significant negative effect on the basal area, while precipitation during the driest month or mean annual precipitation showed no correlation with the basal area. Both precipitation measures (annual and during driest month) affected the canopy openness negatively. The basal area and canopy openness were also significantly negatively correlated.
Overall, mean understory layer complexity (UCI) was highest in Tantauco, followed by San P. d. Tregua, Villarica and La Campana (no significant differences among these three) and lowest in the shrubland at Las Chinchillas with scattered trees only. Despite strong differences in the mean values, Tantauco and La Campana as well as Villarica and the Las Chinchillas were not significantly different from one another (Figure 7). Table 2. Relationships among all explanatory variables accessed via Spearman's rho and the according p-values. A visualization of some of the relationships is also provided in Figure 6.  Table 1.
The analysis based on generalized additive models revealed a significant humpshaped relationship between the complexity of the understory layer, here described using the UCI, and the basal area present at a site ( Figure 8).
With 66.5% explained deviance, the model showed a steep increase in the UCI from the shrubland site at Las Chinchillas, where only scattered trees were present (basal area between 1 and 2.5 m 2 ha −1 ) towards the oasis-like forest of the La Campana with a basal area between 25 and 32 m 2 ha −1 . A further increase in basal area to 40 m 2 ha −1 , as observed in the dense forest of the Tantauco site, resulted in a maximized complexity of the understory layer. With further increase in basal area towards 70 m 2 ha −1 , the understory layer complexity decreased to 50% of the maximum and less. Furthermore, canopy openness affected the mean UCI significantly (deviation explained: 48.4%; see Figure 9). With increasing openness, the UCI successively dropped, reaching a minimum of just over one at 100% canopy openness. This relationship was, according to the GAM, not linear. We also found significant relationships between the tested climatic variables and the understory complexity index (Figure 10). A positive exponential relationship (deviation explained 48.4%) was detected between the mean annual precipitation and UCI ( Figure  10A) and an even stronger (deviation explained 55.7%) but linear relationship between the mean precipitation of the driest month of the year and UCI ( Figure 10B). For mean annual temperature, we discovered a significant hump-shaped relationship with UCI ( Figure 10C), however admitting a rather large gap in our data between 9.3 • C and 14 • C. The analysis of direct vs. mediated effects through structural equation modelling revealed significant direct effects of precipitation on the UCI without mediation through the basal area, but only mediated effects of temperature on the UCI (mediated through the basal area). Furthermore, SEMs indicated a direct effect of precipitation during the driest month on the UCI without mediation of canopy openness, but not so for the annual precipitation. The UCI was not significantly better predicted using an SEM including the direct effects of mean annual precipitation when compared to one without the direct effect, modelling only the mediated effect through canopy openness. Finally, we found that the combined effect of the climatic variables yielded a significantly better prediction of UCI than models that considered only the direct effect of each variable individually and without interaction (see Table 3). Table 3. Summary of the major properties of the compared structural equation models. Note: in every model we also used a latent variable for the error (soil differences, etc.) not shown in the first column. Brackets in the first column indicate that two variables were considered with their combined effect. The " "-symbol indicates "effect of x on y". MAT = mean annual temperature; BA = basal area; UCI = understory complexity index; MMP = mean precipitation during driest month; CO = canopy openness; AIC = Akaike information criterion.

Structural Equation Models
Compared

Discussion
In this study, we aimed for a better understanding of the drivers of understory layer complexity in the absence of management activities. In contrast to our hypothesis of a negative relationship between the basal area and the UCI (hypothesis (i)), we discovered a hump-shaped relationship. On the lower end of the gradient in the basal area, particularly in the Mediterranean shrubland at Las Chinchillas, the UCI was extremely low despite the low basal area (Figure 8). We argue that the sites low in basal area were, despite the available growing space, too dry to enable the development of a complex shrub layer or an actual understory layer. This argument is supported by the results of the structural equation modelling, clearly indicating that precipitation had a significant direct effect on the UCI if modelled in addition to the mediated effect through the basal area (Table 3). Unfortunately, a gap exists in the basal area gradient in our data set, since we had no sites with basal areas between 3 and 26 m 2 ha −1 . This means our findings should be treated with caution, despite the GAMs and SEMs being significant. On the other end of the covered basal area gradient, on those sites with high basal area (Villarica and San P. d. Tregua), which are characterized by a few but tall trees forming a closed overstory layer, conditions were also not favorable for shrub layer complexity. Here, the negative effect of tall trees on the shrub layer development are clearly visible despite sufficient precipitation (Figure 8). Increased basal area resulted in reduced canopy openness ( Table 2) which in turn resulted in reduced light availability on the forest floor (lower canopy openness) which consequently hampered understory layer development and complexity (cf. Figure 9). The results from [42], investigating humid beech forests in Europe, provide additional evidence for this argument, showing that the UCI was greatest when only very few overstory trees remained on the sites (low basal area, high canopy openness). This is also in line with earlier findings on the basal area-canopy openness relationship [67] or studies showing that even overstory tree height in a temperate forest is negatively related to understory layer density [68]. The negative effect of reduced light availability in the understory with high basal area on tree regeneration is well documented in the literature for various forest types [16,[69][70][71]. However, at intermediate basal area (25-40 m 2 /ha), our sites not only showed a large variation in understory layer complexity but also the highest values in general (optimum curve). A large variation in the UCI at a given basal area is not surprising and in fact should be expected. It has already been documented that there is a large heterogeneity in the understory of these old-growth forests [9,72]. The high understory layer complexity at the Tantauco site with intermediate basal areas can be explained through the favorable conditions for tree regeneration caused by natural tree death and single tree fall gaps, as well as beneficial climatic conditions in general (i.e., the moistest site). Additionally, in this forest, the regeneration of tree species is mostly from seeds and in elevated microsites over dead logs [73]. As mentioned earlier, the SEM approach also confirmed the strong direct effect of precipitation on the UCI even without mediation through the basal area (Table 3). Summarizing this, we can say that the basal area has a direct and negative effect on the UCI, even if precipitation is sufficient. Low basal areas, in contrast, do not have a direct causal contribution to the observed low UCIs, but rather did precipitation. This means that sites low in UCI are low in basal area because it is simply too dry for the development of a complex understory layer, or because overstory trees limit the resources available (high basal area) for understory layer development.
Surprisingly, and contrary to our expectation, we also have to reject hypothesis (ii) stating that an increase in canopy openness results in greater understory layer complexity. While there is a large literature presenting canopy openness (or other surrogates of light availability) as strong driver of understory layer growth and development [74][75][76] we found the opposite effect. We argue that in addition to different successional stages of dynamics not addressed here, the gradient of canopy openness covered in our data was determined by the large differences in climatic conditions at the sites rather than overstory disturbance per se. This is supported by the SEM approach, showing that models predicting the UCI from precipitation during the driest month or annual temperature performed significantly better if the direct effect of the climatic variables is included instead of using only the mediated effect through canopy openness (Table 3). Interestingly, this was not the case for mean annual precipitation. Here, we saw no significant improvement in model quality if the direct effect of mean annual precipitation on the UCI was explicitly modelled in addition to the mediated effect through canopy openness. This means, canopy openness may be a crucial driver of UCI if climatic conditions are comparable, but it is rather a mediating agent for mean annual precipitation if looked at across biome borders, as carried out here (forest to shrubland transition). If precipitation is too low throughout the year, closed canopies are no longer possible and scattered trees will dominate (woodlands and shrublands). In our data, the driest site, Las Chinchillas, is also the most open site, with some plots having a canopy openness of as much as 100% (sky pixel fraction of 1) for the viewing angle considered here (60 • ). Hence, we have to reject our hypothesis (ii), as the positive effect of canopy openness on understory layer vegetation observed in many earlier studies [77] is in our case overruled by the climatic differences between the sites.
Considering the above, the plots at the La Campana had remarkably low openness values and high understory layer complexity given the low precipitation. For this site, we argue that a closed canopy is due to the presence of the characteristic Chilean Palm (Jubaea Chilensis (Molina) Baill.) on all plots scanned at La Campana, resulting in a higher than usual overstory density and lower canopy openness in the National Park (oasis character) when compared to the surrounding shrublands. In the shade of the palm trees, understory layer vegetation developed well despite low precipitation rates. In that way, spatial patterns show that trees of J. chilensis have a positive effect on the regeneration of other tree species, indicating a facilitation mechanism by producing semi-shade conditions, milding the air temperature and increasing the soil water availability [52]. This produces significant heterogeneity in the stands with clumped palm trees nested with understory trees, enhancing the understory layer complexity in this arid environment. This is supported by the large range of UCI at this site visible in Figure 7. However, our canopy openness data indicate that we missed a significant part of the gradient, not covering sites with an openness between 40% and 85%. Hence, caution is advised when trying to generalize these findings.
We confirmed our hypothesis (iii) by identifying relationships between the UCI and all tested climatic variables ( Figure 10A-C). The positive effect of water availability (in general) on forest structure was reported earlier for forests in Patagonia [78][79][80]. The SSCI (stand structural complexity index), a holistic measure of structural complexity of the entire forest that is also based on single scans, was recently shown to be mostly driven by precipitation in primary forests around the world [41]. Other, more conventional measures related to forest structure, such as the normalized difference vegetation index (NDVI) were also shown to be related to the annual precipitation [81]. Overall, the relationship between precipitation and forest structure is of such strong manifestation that it is a key element in Holdridge's concept of life zones [82] and other global classifications of biomes [83]. We provide supporting evidence from our Chilean sites that a similar pattern exists for vegetation in the understory layer, with precipitation being clearly beneficial to the development of complex structures. For annual precipitation, the GAM approach even indicated that the relationship is exponential ( Figure 10A). Furthermore, an even stronger (though linear) relationship between the UCI and precipitation during the driest month indicates that dry periods can be particularly threatening to the understory layer complexity ( Figure 10B). Earlier studies already showed that seasonal precipitation is a stronger predictor of community productivity in forests than annual precipitation [84]. [41] provided strong evidence for precipitation seasonality also being crucial for stand structural complexity across biomes. We can extend this by stating that seasonal precipitation is also a strong predictor of understory layer complexity ( Figure 10A vs. Figure 10B). Vegetation is known to be sensitive to the timing and magnitude of droughts and this was particularly shown for water-limited regions [85], also represented by our driest site with the lowest understory layer complexity (Las Chinchillas). Furthermore, we could show that the effect of precipitation on the UCI is a direct one (Table 3), and not only mediated through a lower basal area and hence reduced competition for water.
Finally, we could show that the temperature-understory layer complexity relationship in Chile does not follow a linear scheme, but is better described by an optimum-curve (rejection of hypothesis (iv)). Beyond a certain point (~11 • C mean annual temperature), temperature appeared to be not beneficial anymore to the development of a complex understory layer at the investigated sites. However, it is likely that the negative effect of temperature beyond an optimum was directly associated with the fact that the two warmest sites investigated were also the driest, with precipitation dropping to as little as 185 mm to 343 mm per year (cf. Table 1 for Las Chinchillas and La Campana). Therefore, it is rather the limited water supply than the temperature per se that limited the development of a complex understory layer. This is further supported by the better performance of models that predict the UCI from combined effects of temperature and precipitation ( Table 3). In that regard, future studies in tropical sites may help to understand the understory layer complexity-temperature relationship for conditions with high temperatures in combination with sufficient precipitation.

Conclusions
We conclude that understory layer complexity, as determined by the understory complexity index, in unmanaged Chilean landscapes is strongly driven by climatic variables (temperature and precipitation). While there are known close relationships between stand density (basal area) as well as light availability (canopy openness) and understory layer development, we could show that there are also direct effects of the climate on the understory layer complexity. We observed a similar pattern for the understory layer as those depicted for entire forests in the concepts of global life zones or biomes. The concept of life zones of Holdridge [82], Whittaker [83], and others created theoretical models that related temperature, precipitation (and in the case of Holdridge also to evapotranspiration) to typical biomes or life zones characterized by typical vegetation types. These vegetation types were not described using species identities, but by using typical formations, e.g., "rainforest". We argue that these characterizations, though not based on quantitative data, were based on typical vegetation structures. The qualitative description of these structures, e.g., by [83], indicated a greater vegetation complexity in humid and warm climates. Only a few studies have attempted to provide empirical evidence for these patterns [41,86]. Here, we provide evidence from sites in Chile situated along a large climatic gradient. Understory layer complexity is strongly driven by precipitation and temperature, particularly by precipitation during the driest month. This holds implications for climate change scenarios, with extended droughts threatening the complexity of the understory layer and hence related ecosystem functions and services.