Vegetation Structural Complexity and Biodiversity Across Elevation Gradients in the Great Smoky Mountains Running Title: Structure, Biodiversity and Elevation

Questions: Elevation, biodiversity, and forest structure are commonly correlated, but their relationships near the positive extremes of biodiversity and elevation are unclear. We asked 1) How does forest structure vary with elevation in a high biodiversity, high topographic complexity region? 2) Does forest structure predict vascular plant biodiversity? 3) Is plant biodiversity more strongly related to elevation or to forest structure? Location: Great Smoky Mountains National Park, USAMethods: We used terrestrial LiDAR scanning (TLS) to characterize vegetation structure in 12 forest plots. We combined two new canopy structural complexity metrics with traditional TLS-derived forest structural metrics and vascular plant biodiversity data to investigate correlations among forest structure metrics, biodiversity, and elevation. Results: Forest structure varied widely across plots spanning the elevational range of GRSM. Our new measures of canopy density (Depth) and structural complexity (σDepth) were sensitive to structural variations and effectively summarized horizontal and vertical dimensions of structural complexity. Vascular plant biodiversity was negatively correlated with elevation, and more strongly positively correlated with vegetation structure variables. Conclusions: The strong correlations we observed between canopy structural complexity and biodiversity suggest that structural complexity metrics could be used to assay plant biodiversity over large areas in concert with airborne and spaceborne platforms.


Introduction
Habitat physical structure, biodiversity, and topography are interrelated elements controlling key ecosystem functional properties. Canopy structural complexity-the arrangement of wood and foliar elements in plant canopies-correlates positively with tree biodiversity  for complex, interrelated reasons. Different tree species may have different growth forms (Verbeeck et al. 2019). More diverse forests, it follows, may have more growth forms represented, and thus have more building blocks with which to construct structural complexity (Gough et al. accepted). A more structurally complex forest tends to have increased available niche space for other flora and fauna species, for example by creating microhabitats (Hansen et al. 1994;Hyde et al. 2006). In mountainous regions, air temperature, solar radiation, and atmospheric pressure all vary as a direct function of elevation (Körner 2007); but state variables such as light availability (i.e. photosynthetically available radiation, or PAR), soil moisture, soil temperature, and nutrient availability covary as a function of elevation and topographic heterogeneity (Alves et al. 2010). These processes are reflected in how elevation influences both plant biodiversity and forest structure. Plant biodiversity tends to decline with increasing elevation (Homeier et al. 2010;Toledo-Garibaldi & Williams-Linera 2014), while canopy height and structural complexity also tends to change with altitude (Homeier et al. 2010).
For example, along a 3300 m elevational gradient in South America extending from the Amazon lowlands to the tree line in the Peruvian Andes, changes in forest structure were manifested as decreases in canopy height and increases in canopy gap fraction (Asner et al. 2014). While it is clear that elevation, biodiversity, and forest structure are commonly related, it is unclear how they are interrelated near the positive extremes of both biodiversity and elevation.
In the southern Appalachians, complex topography creates steep ecological gradients that drive structural and compositional patterns (Whittaker 1956;Harmon et al. 1984) and produce high levels of biodiversity (Latham & Ricklefs 1993;Gough et al. 2019). Southern Appalachian forests, such as those of Great Smoky Mountains National Park (GRSM), are among the most diverse temperate forests in the world with over 100 woody plant species (Latham & Ricklefs 1993). As such, these forests have long been studied for insights into biodiversity (Whittaker 1956), and related topics including forest productivity (Whittaker 1966;Gough et al. 2019), disturbance (Harmon et al. 1984;Atkins et al. 2020), resource acquisition , habitat fragmentation (Ambrose & Bratton 1990), pollution (Mathias & Thomas 2018), and land cover change . Perhaps surprisingly, then, we are unaware of earlier studies relating biodiversity and forest structure in this high-diversity, topographically complex system. Advances in remote sensing, specifically light detection and ranging (LiDAR), have enabled mapping of forest structure and complexity with unprecedented precision, at plot-level to regional scales . Ecological applications of LiDAR have broadened our understanding of resource acquisition (Stark et al. 2015;Atkins et al. 2018), allocation strategies (Stovall et al. 2017;Stovall et al. 2018b;Stovall & Shugart 2018;Stovall et al. 2018a), use efficiencies (Hardiman et al. 2013), drought response (Atkins & Agee 2019;Smith et al. 2019;Stovall et al. 2019), productivity , and disturbance history (Fahey et al. 2015;Atkins et al. 2020). However, recent studies of forest structural complexity either focus on broad, landscape to continental scale patterns Atkins et al. 2018;Gough et al. 2019;Fahey et al. 2019), or are limited to characterizations of stand-scale phenomena Hickey et al. 2019), without fully considering how forest complexity varies at the stand to regional scale in response to ecological gradients.
Forest structure is most commonly characterized using two-dimensional indices that describe either vertical or horizontal space only, often ignoring canopy structural traits that describe internal canopy characteristics (Paynter et al. 2018;Fahey et al. 2019) or how forest structure varies simultaneously along both the vertical and horizontal axes. For instance, horizontal structural heterogeneity can be characterized via passive (optical) remote sensing as variation in canopy cover (Morton et al. 2014;Verrelst et al. 2015), while active (radar and LiDAR) remote sensing captures vertical heterogeneity as changes in canopy height (Camaretta et al. 2019). Both metrics of forest structural complexity focus on the outer canopy and ignore internal canopy characteristics (e.g. canopy structural traits such as layering or foliage density).
Internal canopy structure can be inferred using statistically derived metrics such as the 90th percentile or standard deviation of LiDAR measured heights above ground level. Statistical metrics derived directly from LiDAR point clouds can be effective and efficient for predictive models of species biodiversity (Goetz et al. 2007), but lack ecological meaning and may be unstable or non-transferrable across forest types. Recent developments of ecology-based structural metrics that effectively characterize internal canopy structural traits Fahey et al. 2019) describe two-dimensional structure over ground-based transects and are unable to fully capture three-dimensional complexity. Since biodiversity is often dependent on the interior of the forest canopy, new metrics need to be developed that synthesize the canopy structural traits such as layering, density, canopy height, and openness in three-dimensional space.
To understand relationships between forest structure, biodiversity, and elevation in a topographically complex, high-biodiversity region, we used three-dimensional terrestrial lidar scanning (TLS) to sample 12 forest plots in Great Smoky Mountains National Park that were previously inventoried by the National Ecological Observatory Network (NEON). We developed two new canopy structural complexity metrics and combined them with traditional TLS-derived forest structural metrics and vascular plant biodiversity data to address the following questions: 1) How does forest structure vary with elevation in a high biodiversity, high topographic complexity region? 2) Does forest structure predict vascular plant biodiversity? 3) Is plant biodiversity more strongly related to elevation or to forest structure?

Data Collection and Post-Processing
Terrestrial LiDAR, or terrestrial laser scanning (TLS), captures detailed 3D information of the forest, enabling the reconstruction and quantitative analysis of forest structure. We visited 12 National Ecological Observatory Network (NEON) distributed vegetation plots (Kao et al. 2012) located in GRSM ( Figure 1). Plots were chosen based on field accessibility and ancillary NEON data availability at time of analysis. Four TLS scans were acquired at plot center and three points around center in each of 12 plots between August 23 and 25, 2018 using two Faro Focus 1203D scanners (FARO, Lake Mary, FL, USA). Scans were taken at 1/5 resolution and 4x quality for a total of 28.2 million pulses per scan. All returns with intensity lower than 650 (maximum value = 2100) were removed. Filtering low intensity returns reduces noise and ensures gaps are correctly identified.
Filtered scans were used to estimate the vertical distribution of plant material or plant area vegetation density (PAVD) at the plot-level. We roughly follow the method described by PAVD. The one key difference in the current study is the adoption of a fully 3D digital elevation model to normalize topographic effects, as opposed to simple plane fitting. We found plane fitting was inappropriate in the complex topography of the GRSM national park, resulting in overestimates of total canopy height and a misrepresentation of the vegetation distribution.
Topographic normalization followed the following procedure: [i] estimate ground surface, [ii] remove spikes and anomalous points, and [iii] refit and normalize TLS data with 5 m surface model. The ground surface is first estimated as the 1st percentile of height from TLS points in a 5 m grid over a 200 m x 200 m area. The initial model is optimized to remove spikes by excluding all pixels greater than 40% slope. The remaining pixels are refit using a k-nearest neighbor inverse distance weighting (k = 21) and the resulting surface model is subtracted from the height measurements in the TLS data.
PAVD distributions are derived from a simple calculation of the vertically resolved gap probability (Pgap). Pgap is calculated as: where z is the height above ground and ̅ is the midpoint of the 5-degree zenith angle bin used to aggregate the LiDAR returns. The equation essentially calculates the cumulative number of returns per unit height divided by the total number of outgoing laser pulses. In essence, as more vegetation is intercepted, the probability of a laser pulse escaping the canopy decreases.
PAVD is accurately estimated at the hinge angle (a viewing zenith angle of 57.5 degrees) with Pgap. The hinge angle is used to estimate total VAI as this is the angle at which the G-Function is nearly invariable at 0.5 for all typical leaf angle distributions (MacArthur & Horn 1969;Jupp et al. 2008). A 5-degree zenith bin between 55 and 60 degrees is used to approximate the hinge angle region. Pgap is converted to the cumulative VAI distribution with respect to height aboveground ( ( )) using: ( ) ≈ −1.1 log( (57.5)).
Estimates of ( )at the top of the canopy approximate the total VAI for a particular sample location. Once cumulative VAI is estimated, Pgap is calculated at 5-degree zenith angle bins from 0-60 degrees and weighted by the sine of the zenith angle to sample the uppermost area of the hemisphere viewable by the laser scanner. Finally, the total VAI in each 1 m vertical bin is estimated as the 1st derivative of the ( )curve after weighting with respect to zenith angle.

Metrics
We derived a suite of structural metrics from TLS data to characterize the horizontal and vertical distribution of vegetation (Table 1). As described above, we derived the cumulative VAI, and subsequently, PAVD, for every scan location. Using the PAVD, we calculated foliage density dependent median height and 80th and 90th percentiles (i.e. the height at which 80% or 90% of foliage falls below). While these metrics summarize vertical structure, they are unable to quantitatively describe trends in horizontal structure. For this reason, we developed a new metric we call Depth, which describes percentiles of canopy penetration at the hinge angle. Depth percentiles are calculated as the distance from the laser scanner at which a certain percentage of the total number of returns are observed for 10-degree azimuth bins. A single scan produces 36 estimates of Depth from which a standard deviation can be calculated, which we denote σDepth.
For this work, we derived mean and standard deviation values from median Depth estimates for each azimuth angle bin; Other percentiles of depth can be calculated (e.g. 80 th , 90 th ), but were colinear with the median estimates, so we use median as the basis for all subsequent analyses.
The inherent benefit of using Depth percentiles and variability is that this information synthesizes vertical and horizontal structural complexity and allows for normalized comparisons among scans, regardless of canopy height.

Relationships between biodiversity, elevation, and forest structure
We used NEON vascular plant diversity data from 12 NEON plots coinciding with our TLS scans. Plant abundance of each 400 m 2 (20 m x 20 m) plot was sampled using a nested hierarchical protocol in which presence was observed in eight 1 m 2 subplots and eight 10 m 2 subplots distributed within four 100 m 2 subplots. Subplots were aggregated to plot level. We used plant abundance data from July and August 2017. We quantified plot biodiversity using species richness. Diversity indices that take into account abundance, such as Shannon's Index and Simpson's Index, were deemed inappropriate given the orders-of-magnitude sizes differences in the species included in NEON's dataset (all vascular plants, including trees).
Pearson correlation was used to quantify how plant species richness is correlated with elevation and TLS-derived forest structural metrics. We considered the forest structural metrics vegetation-area index (VAI), canopy height (90 th percentile of TLS returns), Depth, and σDepth.
To obtain forest structural metrics at the plot level, we averaged metrics for all scans taken at each plot (n = 3 to 5). Statistical analyses were conducted in R 3.6.2 (R Core Team 2020).

Forest Structure and Complexity
Forest structure varied widely across plots spanning the elevational range of GRSM. Forest structural metrics considered in this study were moderately to strongly correlated with each other (Figure 5). Lower stature canopies had higher VAI in GRSM (Figure 4). VAI was also moderately negatively correlated with both Depth and Depth, but taller canopies were consistently more structurally complex ( Figure 5). Total VAI was of less relative importance than canopy height in capturing changes in structural variability ( Figure 5). Depth and σDepth were strongly positively correlated with each other ( Figure 5).
Topographic gradients in the GRSM controlled forest structure and complexity ( Figure   6). Canopy height declined with increasing elevation. VAI was highest in the high-elevation plots, and lowest in the low elevation plots. Forest complexity, as measured by Depth and σDepth decreased from low to high elevation.
Although the strongest correlate of plant species richness was σDepth, the confidence interval on r included the estimates for canopy height and Depth.

Discussion
In this study, we developed two new forest structural complexity metrics suited to quantifying aspects of the 3D structure of forests (Depth and σDepth) and investigated how they correlate with elevation and biodiversity across a high-biodiversity, high-relief area in Great Smoky Mountains National Park. Statistically derived LiDAR structural metrics have been limited by either focusing solely on characterizing either horizontal structure (Fischer et al. 2019) or vertical structure (Fotis et al. 2018;Kamoske et al. 2019), or by a lack of true representation of how 3D structure varies with space (Stark et al. 2015;Atkins et al. 2018;Hardiman et al. 2018). Capturing the complex relationships between biodiversity and physical structure requires the summation of multiple dimensions of variability, including the biological and physical. The bounds of forest structural complexity are likely set by the species pool from which that forest draws. Depth and Depth metrics likely correlate strongly with measures of species richness since the greater the number of species, the more likely the species included will be architecturally dissimilar from others. These metrics capture canopy structural traits such as vegetation density and complexity, summarized in both vertical and horizontal dimensions. In doing so, these metrics describe the internal arrangement of the forest, characterizing where space is being filled by foliar elements.

Across the high-biodiversity, high-relief and topographically complex Great Smoky
Mountains, both forest structural complexity and vascular plant biodiversity tended to decline with elevation. One goal of this study was to examine whether elevation-biodiversity-complexity relationships persist in a regional biodiversity hotspot. In this case, we observed high among-plot variability in plot-level species richness (alpha-diversity), even as high regional species richness (gamma-diversity) was maintained by substantial species turnover among plots (beta-diversity).
The elevational gradient in GRSM seems to create a microcosm of latitudinal clines in biodiversity, where an increasingly inhospitable environment supports fewer species and constrains plant growth (Whittaker 1956;Hawkins et al. 2003;Gillman et al. 2015). However, inference here is limited, the main caveat being an approximately 1000 m gap in elevation between our low and high elevation plots. While many studies of elevation and diversity relationships show monotonic declines in species richness with elevation, there are as many studies showing a humped relationship, with species richness peaking at mid-elevations (Rahbek 1995;Grytnes & Vetaas 2002). It is important to note that "mid-elevation" is relative to the study system-different ranges for what mid-elevation is would exist when comparing the Appalachians to the Rockies, or either to the Himalayas.
It is unclear, despite plant biodiversity being more strongly correlated with forest structure than with elevation, whether structural complexity begets biodiversity, or vice-versa.
Indeed, neither direction of causality strictly excludes the other. Structural complexity could enhance biodiversity by creating niche space that can be filled by other species, or biodiversity could enhance structural complexity due to architectural diversity among species creating more ways to build complexity Verbeeck et al. 2019) at higher values of species richness. It may, in principle, be possible to disentangle these effects if a scenario with many plots featuring different subsets of an overlapping species pool. However, with a modest number of plots with high beta-diversity, this is not possible in our study.
The strong correlations we observed between canopy structural complexity and biodiversity suggest that structural complexity metrics could be used to assay plant biodiversity over large areas. The availability of LiDAR from airborne platforms is increasing due to programs such as NEON (Kao et al. 2012), and new satellite-borne sensors such as GEDI ) create opportunities for quantifying forest structural complexity at fine spatial resolutions over unprecedented geographic extents. Studies such as ours are important precursors, however, because they explicitly link biodiversity and forest structural complexity, but studies in other systems are needed to parameterize the forest structure-biodiversity relationship. The metric foliage height diversity (Tang et al. 2019;Burns et al. 2020), which is an established GEDI data product, captures similar canopy properties to our Depth and Depth metrics and is a likely candidate for inclusion in successful predictions of biodiversity from airborne and satellite-borne LiDAR sensors.        Correlation (r) is measured using Pearson correlation, and nominal p-values assume independent tests.