Drone laser scanning data acquisition and preprocessing

In 2017, DLS data were acquired in April for the RH site. A Vapor-35 platform was used (AeroVironment, Simi Valley, CA, USA) carrying a YellowScan Surveyor Core LiDAR unit (Monfeerier-sur-Lez, France). This unit consisted of a Velodyne VLP-16 laser scanner (Velodyne, San Jose, CA, USA) and a GNSS-inertial Trimble APPLANIX APX-15 (Trimble, Richmond Hill, ON, Canada). The specifications are summarized in Table ​Table1.1. Preprocessing and strip adjustment were conducted before DLS data processing in the YellowScan CloudStation software. Ground control used a real-time kinematic geographic positioning system (RTKGPS; Topcon GR-3) with precision ≤10 cm and positional accuracy ≤5 cm.

In 2021, the RH site was reflown with a different DLS system, during July. The DJI M600 hexacopter platform (DJI Technology Co. Ltd., Shenzhen, China) provided the platform. The sensor was a Riegl MiniVux1 LiDAR scanner (RIEGL Laser Measurement Systems GmbH). This also incorporated an APPLANIX APX20 GNSS-inertial measurement unit (Trimble, Richmond Hill, ON, Canada). The specifications are summarized in Table ​Table1.1. Preprocessing and strip adjustment were conducted before DLS data processing in the RiPROCESS software (RIEGL Laser Measurement System GmbH, Horn, Austria). Ground control was provided by a RTKGPS (Spectra SP80) with a post-processed positional accuracy ≤0.3 cm.

All preprocessing and analyses were conducted in the R software (version 4.3.1.) ([63]). Table ​Table22 summarizes all packages used in the analysis. We preprocessed the DLS data by initially classifying and removing potential noise points, using the isolated voxel filter ([64,65]). We used the following settings, which were determined visually after several permutations. This method functions by creating a 3D matrix encompassing the extent of the point cloud, where voxels were cubic with a side length of 1 m. Returns were classified as noise if only one return was detected within a 3 × 3 × 3 m search kernel. The cloth simulation filter [66] method was used to classify ground returns. Aboveground return heights were calculated by first creating a surface from ground-classified returns, using a triangular irregular network; this height was then subtracted from all non-ground classified returns.

Individual tree crown processing

We implemented 2 ITC delineation approaches, summarized below. The results of each will be compared to field data with regard to commission/omission error and crown horizontal diameter estimate accuracy. Only the approach that provided the most accurate results, in terms of crown horizontal size, would be used for further analysis.

We implemented the ITC delineation method as described by Sumnall et al. [38]. The ITC delineation process was conducted for each of the DLS acquisitions (in 2017 and 2021). No changes to the method were made with regard to the datasets from either acquisition. In summary, initial ITC center coordinate markers were located using a local maximum search of a raster layer representing a 2D vertical occupancy index from vertically aggregated 0.2 × 0.2 × 0.2 m voxels. ITC horizontal extents were established using the marker-based approach defined by Silva et al. [67] using a 0.1 × 0.1 m canopy height model (CHM). The non-ground classified returns were reclassified into ITC objects using this layer. All returns, below 1-m height aboveground, were considered as understory vegetation and removed.

A second ITC delineation method was applied to both datasets using the PTrees method [68] to classify the point cloud directly, as implemented in lidRplugins [69]. This approach was implemented to ensure that segmentation boundaries would not potentially be influenced by the CHM pixel size. The method uses multi-scale and dynamic segmentation approaches based upon k-nearest neighbors and convex hulls. We initially tested a number of k-nearest neighbors to use for a 10% subset of the dataset (both years). Given the high-point density for our DLS datasets, k-nearest neighbors to use were set to 1,000; all points below 2 m were excluded and could not form apices or increase convex-hull sizes.

The DLS point cloud was subset by the ITC classification, and metrics related to the ITCs location size were calculated. We assessed each ITC separately. Total or top height was defined as the tallest return height associated with the ITC classification. The mean average of ITC horizontal (X and Y) coordinates of returns in the top 50% of height was considered as the center position of the crown.

We paired ITCs using these central coordinates, from the 2 acquisition dates, with their closest horizontal neighbor. Duplications of ITC unique identifiers were not permitted. If the distances between pairs of center coordinates were more than 2 m, ITCs could not be paired. This process was repeated to link paired ITC geometric centers to planting GPS locations. Examples of the differences in individual tree point clouds (for classified and paired ITCs) for 2017 and 2021 are illustrated in Fig. ​Fig.2,2, in addition to visible variation in laser penetration to lower portions of the crown.

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Fig. 2.

Individual tree crown point clouds classified from the DLS data and spatially matched for 2017 and 2021. (A and B) Tree number 53 from plots 1 to 3 (block 1; genotype 3—narrow crown) for data acquired in 2017 and 2021, respectively. (C and D) Tree number 42 from plots 3 and 4 (block 3; genotype 4 —wide crown) for data acquired in 2017 and 2021, respectively. (E and F) Tree number 48 from plots 4 and 5 (block 4; genotype 5—control pollinated) for data acquired in 2017 and 2021, respectively.

For the purposes of defining a reference location for crown horizontal growth, it was necessary to estimate the stem location. We expected that the stem would be most identifiable in the bottom half of total tree height. We assumed the stem to be straight and vertical. In order to best estimate crown horizontal projection, it was necessary to classify those ITC returns most likely to be from the tree stem; thus, returns below 50% of the total height of the ITC returns were subset. A Gaussian mixture model-based clustering approach was applied to this 3D point-cloud subset (X, Y, and Z coordinates) where the optimum number of clusters was determined automatically using the entropy method documented by Baudry et al. [70], as implemented in the mclust package (an example is provided in Fig. ​Fig.3A).3A). Any cluster containing less than 5 returns was ignored. If all of the clusters were too small, the mean average of horizontal (X and Y) coordinates of canopy points (all returns above 50% of top height) was assumed to be tree center horizontal coordinates.

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Fig. 3.

All plots represent a point cloud for a portion of a single tree (lowest 50% of total height with heights below 1 m removed). Model-based clustering (A) is applied to the data, where clusters are colored randomly. Weights are applied, and a likely stem cluster is classified in 3D space (here, cluster 7). Returns likely belonging to the stem are illustrated in (B) (highlighted in blue or dashed gray line). Two overlaid point clouds (C) and overlaid 3D alphashape shapes (D) for a single tree in 2017 and 2021. The red 3D point cloud (C) and shape (D) represent the tree crown scanned in 2017 and, likewise, in blue for 2021. The yellow lines represent the estimated stem location, and the ball represents tree top height. An example of estimating crown projection directions and distance from the stem center. A cross section is identified on the ITC alphashapes 3D mesh around the point cloud (E) via a plane (F), in this example at a height of 6 m. The green spheres in (E) represent the outline of the plane shown in (B). The resulting cross-section is converted into a standard 2D polygon (F), and from the estimated stem location, the projected distance to the polygon edge is calculated every 10°.

Four metrics were computed to characterize the size of each potential stem cluster identified in the previous step: (a) the cluster center (mean X and Y coordinates) horizontal distance to crown geometric center, (b) the difference in height value range (maximum-minimum), and (c) horizontal convex hull area. The fourth variable was calculated as a sequence of 1-m tall height bins from 1 m to 50% of the total tree height, where, if one or more returns were incident within each height bin, a value of one was recorded, and zero for no returns. A sum of these values divided by the total number of bins comprised the fourth variable: (d) the proportion of vertical occupancy. Each of these metrics were rescaled, with respect to all of the clusters, to be between a value of 0 and 1 using the following:

where p_var is the rescaled cluster metric and x is the individual cluster metric value. The notation x_max and x_min represent the maximum and minimum value of all clusters for that metric, respectively. The aforementioned metrics 1 and 3 were inverted (i.e., p = 1 − p) to prioritize clusters closest to the center and smaller horizontal areas, respectively.

We expected branches and foliage beneath the height to the live crown to be projected horizontally (e.g., [71]) and to have small vertical extents. Therefore, we assumed a stem cluster to occupy a larger height range than that of other clusters and to return consistently across this vertical range. We then developed the following weighting equation based on a 10% sample of classified clusters across our 2017 and 2021 DLS datasets. Each of the clusters was then assigned a weight value (W) using the following equation:

where p₁ … p₄ represent the 4 cluster metrics. Those clusters with the largest weight value represented the cluster containing returns from the stems (illustrated in Fig. ​Fig.3B).3B). A mean average of the stem cluster return X and Y coordinates were then used to represent the stem location, rather than the ITC return geometric center. For the paired ITCs, the coordinates of the stem cluster with the largest number of returns for either year were given priority; otherwise, the coordinates were averaged (mean). The accuracy of stem estimated locations was assessed against field GPS coordinates.

In order to approximate the visual outline of the tree crowns, an alphashape 3D mesh was calculated for each complete ITC point cloud, separately for both dates, using the ashape3d function within the alphashape3d package [72,73]. The same α value, which was set as 1 m (or α = 1), was used for all ITCs. The α value can be defined such that an edge of a sphere, with a radius of 1/α, can be drawn between any 2 diametrically opposed edge members of a set of points and still contain all the points within the sphere. An example of alphashapes created for both 2017 and 2021 acquisitions for a single tree is provided in Fig. ​Fig.3C3C and D. Alphashape volume and surface area were calculated.

Alphashape crown metric calculation

Calculating 3D crown volumes in different azimuths

To evaluate crown volume changes in any potential direction between 2017 and 2021, we calculated the following for each of the ITC 3D alphashapes: A 3D voxel grid was created, where each cell was sized 0.1 × 0.1 m horizontally and 0.5 m vertically (0.1 × 0.1 × 0.5 m). We intersected this grid with the 3D mesh. Cells that did not intersect within the 3D mesh were removed. We created search areas, 3D wedges, originating from the tree stem. Each of these wedges covered a horizontal 45° span (i.e., 0° to 45°, 45° to 90° … 315 to 360°), resulting in 8 wedges per tree crown (Fig. ​(Fig.4).4). We then classified all voxels (via centroid coordinates) that intersected within each of the search wedges’ azimuth angles and summed their incident voxel volumes.

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Fig. 4.

Wedge calculation example. The 3D mesh is subdivided into 45° segments horizontally around the stem center location. Each of the red lines represents a dividing plane. The gray stacked polygons represent horizontal cross-sections at different heights.

We also tested if there were any specific differences between the DLS-derived alphashape crown volume for the north- and south-facing crown segments per crown. We summed the volume of 2 wedges for north (315° to 0° and 0° to 45°) and 2 wedges for south (135° to 180° and 180° to 225°) and calculated the 3D mesh volume. This was computed for all crowns for 2017 and 2021.

Circular analysis of potential crown foraging direction

We evaluated the largest cumulative horizontal projection direction for all trees, which are summarized in Table ​Table5.5. The results indicated a similarity in mean azimuth for 2017 and 2021 (152° and 160°, respectively, or ±8°). The Rayleigh test of uniformity was significant (P < 0.05), suggesting that individuals are larger in a preferred direction and not at random. The Watson’s 2-sample test of homogeneity of largest mean azimuth of 2017 against 2021 was not significant (P > 0.05), suggesting that the 2 groups have the same preferred direction. The Rayleigh test also indicated that there was a significant directionality to the azimuth of the LL (mean of 10.2°).

When stratifying the results by genotype, summarized in Table ​Table6,6, the circular mean for 2017 varied from 101 to 188° between genotypes, whereas in 2021 the circular mean varied from 150 to 173° between genotypes. There was a difference between the mean largest azimuths in 2017 and 2021 for each genotype. The largest difference was observed for genotype 2 (46°). Circular variance and standard deviation of the largest projection azimuth could vary by ±16.1° and ±49.5° (Table ​(Table6),6), respectively. When evaluated with the Rayleigh test, with the exception of genotypes 2 and 6, all data from 2017 were significant, indicating non-random directionality to growth. All Rayleigh test results from 2021 were significant. The Watson’s 2-sample test was significant only for genotypes 2 and 6, indicating different preferred directions between the 2 dates.

To reiterate, the following LG, LL, and AC metrics were computed for the overlapping portions of the ITC alphashape meshes. The mean LG azimuth varied between genotypes. For genotypes 4 and 5, this was 302° and 2°, respectively; for genotypes 1 to 3, this was 125° to 186°; and finally genotype 3 was 252°. Except for genotype 2, the Rayleigh test was insignificant, meaning that the LG for all trees was mostly random. Mean LL was generally in the opposite direction to LG, apart from genotype 5. LL ranged from 340° to 341° for genotypes 1 and 6, and 10° to 64° for genotypes 2 and 3. For genotype 4, LL was 168°, and for genotype 5, LL was 257°. Except for genotypes 2 and 3, the Rayleigh tests were insignificant. The AC was very similar to LG for genotypes 2 to 4 (<10° difference). The Rayleigh tests were insignificant for AC, with the exception of genotype 2.

When stratifying the results by treatment block to investigate if differences in row-direction influences crown growth—summarized in Table ​Table7—the7—the circular means of largest projection for 2017 and 2021 for block 4 were noticeably different than the others (±67° and ±38°, respectively). All Rayleigh test data from 2017 and 2021 largest projections azimuths were significant, implying a preferred direction. The Watson test, comparing 2017 to 2021 largest projection azimuth, was significant for blocks 1 to 3. Among all tests, crown projection tended to be greater in a southerly direction and projection losses tended to be in a non-southerly direction. Specifically, 2021 mean largest projection azimuth varied from −16° to −34° from true south (i.e., |x − 180|) for blocks 1 to 3, and +5° for block 4. The LL varied from 85° to 176° for blocks 1 to 3, relative to true south, and 84° for block 4. The analysis by block indicates that while growth still tends to be southerly, the crowns will grow where space is available in a southerly direction.

Evaluating differences in row direction on tree size

For field-measured stem volume and DBH, from both 2017 and 2021, as the dependent variables in mixed-effects analysis, block, genotype, and the interaction between the 2 were not significant. The post hoc pairwise comparison indicated that trees in block 4 (spaced widest along a 45° azimuth) were smaller than trees in the other 3 blocks (spaced widest along a 135° azimuth).

For both dates (2017 and 2021), block and genotype were significant as main effects (P = 0.01) in predicting crown volume. For crown volume change, both block and genotype were, again, significant (P < 0.01). The interaction between block and genotype was not significant in all models. Post hoc tests indicated that trees in 2017 block 4 (spaced widest along a 45° azimuth) had crown volumes that were typically smaller than trees in the other 3 blocks (spaced widest along a 135° azimuth), but the opposite was true in 2021. Crown volume change between 2017 and 2021 was smaller in blocks 1 to 3. Crown volume change in block 1 to 3 was 59.8 m³ tree⁻¹ [±1.35, 99% confidence interval (CI) = 55.7:63.9 m³ tree⁻¹]. Crown volume change in block 4 was 71.9 m³ tree⁻¹ (±2.33, 99% CI = 64.9:79.0 m³ tree⁻¹).

Tree crown complexity and volume mixed model analysis

Assessment of crown variables and stem volume change

Each of the models presented in Table ​Table88 had significant interactions when predicting stem volume change (P < 0.05). The highest marginal R² values were observed for models using crown volume and OPCR (R² = 0.24:0.34). The 2 respective best-performing models, in terms of pseudo-R² value, are illustrated in the scatterplots of Fig. ​Fig.5,5, where larger crown volume, and complexity, correlated with higher stem volume change; however, difference in genotypes was present.

Table 8.

Summary of significant (P < 0.05) only mixed-effects models predicting stem volume change between 2017 and 2021 using crown metrics and genotype. Marginal ($R_m^2$) and conditional ($R_c^2$) pseudo-R² metrics are reported and represent the variance explained by the fixed effects and the entire model, respectively. The terms are defined as follows: SVC is the change in stem volume from 2017 and 2021, OPCR_yr is the orientation patch count rotated index ([56–58]), and CVol_yr denotes crown volume, where yr can represent data from the year 2017 or 2021. Random effects included the unique plot identifier (PlotID).

Variable	Significant mixed-effects model equation	$R_m^2$	$R_c^2$
OPCR	SVC = OPCR2017 × Gen + (1|PlotID)	0.24	0.31
OPCR	SVC = OPCR2021 × Gen + (1|PlotID)	0.24	0.29
OPCR	SVC = (OPCR2021 − OPCR2017) × Gen + (1|PlotID)	0.24	0.29
CVol	SVC = CVol2017 × Gen + (1|PlotID)	0.34	0.40
CVol	SVC = CVol2021 × Gen + (1|PlotID)	0.34	0.41
CVol	SVC = (CVol2021 − CVol2017) × Gen + (1|PlotID)	0.34	0.41

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Fig. 5.

Scatterplots generated from the mixed-effects model generated for 2017 to 2021 stem volume change against either (A) 2021 alphashape crown volume or (B) 2021 alphashape orientation patch count rotated (OPCR) index and loblolly pine genotype (1 to 6).

In contrast to stem volume change, more of the complexity indices were significantly related to DBH change (P < 0.05; Table ​Table9).9). The highest marginal R² values were observed for models using crown volume (Table ​(Table99).

Table 9.

Summary of significant (P < 0.05) only mixed-effects models predicting diameter at breast height (DBH) change between 2017 and 2021 using crown metrics and genotype. Marginal ($R_m^2$) and conditional ($R_c^2$) pseudo-R² metrics are reported and represent the variance explained by the fixed effects and the entire model, respectively. The terms are defined as follows: DBH_change is the change in DBH from 2017 and 2021, OPCR_yr is the orientation patch count rotated index [56–58], and CVol_yr denotes crown volume, where yr can represent data from the year 2017 or 2021. The unique plot identifier (PlotID) is the random effect.

Variable	Significant mixed-effects model equation	$R_m^2$	$R_c^2$
OPCR	DBHchange = OPCR2017 × Gen + (1|PlotID)	0.17	0.34
CVol	DBHchange = CVol2017 × Gen + (1|PlotID)	0.19	0.33
CVol	DBHchange = CVol2021 × Gen + (1|PlotID)	0.28	0.37
CVol	DBHchange = (CVol2021 − CVol2017) × Gen + (1|PlotID)	0.28	0.37

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We further explored those variables that significantly predicted stem volume or DBH change, and which maximized pseudo-R², by generating linear model coefficients and assessing if there were differences between genotypes. These models included OPCR and crown volume as covariates (in Table ​Table10).10). Each of the linear model coefficients were similar or identical (<0.02) for each of the 6 genotypes. For stem volume change, intercept values varied from −0.08 to 0.03 and −0.13 to 0.01 for CVol₂₀₁₇ and OPCR₂₀₁₇, respectively, across the genotypes. For DBH change, intercept values varied from 0.22 to 1.77 for the CVol₂₀₂₁ metric for each genotype.

Table 10.

Summary of linear models generated from a subset of mixed-effects models that were significant (P < 0.05) and that maximized pseudo-R². Linear model intercepts generated for the crown complexity/volume metric for each of the genotype factors included. OPCR_yr [56–58] is the orientation patch count rotated index and CVol_yr denotes crown volume, where yr can represent data from the year 2017 or 2021.

Dependent variable	Independent variable		Genotype
			G1	G2	G3	G4	G5	G6
Vchange	CVol 2017	Intercept	−0.03	−0.01	−0.09	−0.09	−0.00	0.03
		Coefficient	0.01	0.00	0.01	0.00	0.00	0.00
		R 2	0.37	0.23	0.41	0.36	0.24	0.24
Vchange	OPCR 2017	Intercept	−0.13	0.01	−0.08	−0.09	−0.12	0.02
		Coefficient	0.02	0.01	0.01	0.01	0.01	0.01
		R 2	0.24	0.09	0.22	0.21	0.21	0.13
DBHchange	CVol 2021	Intercept	1.40	1.22	0.22	0.84	1.29	1.77
		Coefficient	0.01	0.01	0.02	0.01	0.01	0.01
		R 2	0.25	0.15	0.39	0.30	0.22	0.14

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Assessment of crown horizontal foraging direction

Trees consistently grew in a more southerly direction, and the southerly crown was more efficient at converting crown volume to stem volume. The ability to allocate crown volume also differed among the genotypes.

With the exception of the ITCs from genotypes 2 and 6 in 2017, all Rayleigh tests were significant (P < 0.05), suggesting that the ITCs have a preferred direction of growth across all genotypes and blocks. The overall average azimuth was 152° for 2017 and 160° for 2021. The majority of the direct radiation is from southern directions in this geographical region [33], which aligned with the largest volume of crown facing south.

There were differences between 2017 and 2021 directions for each of the genotypes, ranging between 6° and 55° when comparing means. When compared using the Watson test, genotypes 2 and 6 exhibited statistically significant different directions between the 2 acquisitions’ ITC populations. This suggests a potential for change in crown shape over time.

We calculated the change in direction for overlapping vertical regions of the 3D alphashapes. We should note that, within our study, the vertical overlap between the 2 times, 3D alphashapes for our matched ITCs was often limited, accounting for only small portions of the total crown. This could explain the increased variability when assessing azimuth of crown growth, loss, and absolute change. Genotypes 2 and 4 exhibited a significant azimuth for growth. Genotypes 2 and 3 exhibited a significant azimuth for loss. Only genotype 5 (control pollinated) had a significant absolute change. Genotype 6 (open-pollinated) met our expectation as being the most variable in terms of shape (as in [81]). The results relating to genotype 2 imply that it may have a tighter control over its growth directionality in contrast to the other genotypes tested.

The results reported here are supported by Chmura et al. [71], which evaluated 2 genotypes of loblolly pine, which each exhibited different crown and needle traits, and biomass partitioning patterns. Uria-Diez and Pommerening [82] assessed how Scots pine (Pinus sylvestris) individuals responded to the presence of neighbors and stated that trees were able to make an efficient use of the canopy space by shifting their crowns to reduce the inter-tree competition. As indicated in our results, crown shape changes over time. Uria-Diez and Pommerening [82] went on to state that young stands did not show crown displacements as much as mature stands. The results presented in Table ​Table66 and Fig. ​Fig.77 imply that crown asymmetry would increase with time for genotypes 2 and 6. Repeated DLS acquisitions may therefore allow us to monitor such changes through time.

There were differences observed in tree sizes between block 4 (spaced widest along a 45° azimuth) and the other 3 blocks (1 to 3; spaced widest along a 135° azimuth). The row spacing was 4.4 m within row and 3.7 m between rows; therefore, there was greater available space in the direction of the row. The different row orientation present in block 4 would also account for the different observed mean projection azimuth there. These row orientations would likely account for the difference between our observed mean values and true south. We assume that the only site differences were row orientation as the plots were equally intensively managed as a research trail. Block 4 crown volume was typically smaller than those of the other blocks in 2017 and larger in 2021. This may reflect that available crown growing space diminished for the more rapidly growing trees in blocks 1 to 3 by 2021, but crown growing space had yet to be fully occupied in block 4. This finding suggests that thinning may need to be conducted later in stands orientated at 45° and earlier in 135° as they occupy growing space faster and experience a reduced stem growth rate once horizontal crown growing space is fully utilized. Thus, for the former, growth is slowing down from 2017 to 2021.

These results contrast those of Amateis et al. [29], who stated that row azimuth had no significant impact on either basal area or height growth (over 20 years of observations). While there are few studies investigating the effects of row orientation on pine plantation productivity, there are several studies that have evaluated row orientation on crop or vineyard development. Hunter et al. [26] and Buesa et al. [27] noted differences in canopy light interception, photosynthesis, and water-use efficiency for disparate row orientations, but this did not significantly affect carbon assimilation. Others have found that row orientation can suppress weed growth and increase crop yield [83]. Our results suggest that orientation can impact earlier development, but these differences can potentially reduce over time, especially if stands are not thinned in a timely manner once canopy growing space has diminished.

Assessment of tree crown complexity indices and volume

We evaluated the ability of ITC 3D shape complexity and 3D alphashape volume to predict stem size and stem size changes. When OPCR and crown volume model coefficients were calculated per genotype, there were noticeable differences observed among values, implying differences in crown shape, size, and growth efficiency among genotypes, as was also found by Chmura et al. [71,84].

There were differences between the 2017 and 2021 dataset for both the OPCR complexity index and the alphashape volume, reflective of the growth of the crowns over time. We would expect crown shape to change as the tree grows. For example, Baldwin and Peterson [85] modeled the change from conical juvenile loblolly crowns to more ellipsoidal shapes as the tree matured.

It follows that a larger crown object may result in a more complex shape. This reasoning was supported by our results, where 3D alphashape crown volume and OPCR were correlated in linear models and exhibited significant interactions in mixed effects. When compared, OPCR and crown volume did not exhibit multicollinearity when predicting stem size and stem volume change, indicating that these variables were describing different features of the crown, size, and shape. Linear models (Table ​(Table11)11) containing only crown volume metrics generally had higher R² and lower AIC values when estimating either stem volume or DBH change. Models that included both OCPR and crown volume metrics again generally outperformed models containing OCPR metrics alone. This implies that DLS-derived crown volume is more strongly related to stem size within this study. We divided a tree’s crown volume by its shape complexity index value to create a new metric (complexity per unit of volume), which was significantly related to stem volume and DBH change; however, it was only weakly correlated. This provides only a weak implication that complexity in crown shape adds much to the predictive power of this when relating crown metrics to stem growth.

Tree crown volume in different azimuths

The 6 different genotypes exhibited statistically significant differences in crown volume for each of the 8 azimuths tested, with 2 exceptions. Two pairs of genotypes (1 and 5, and 2 and 6) were similar (P > 0.05) in crown volume across all tested azimuths. When plotted (Figs. ​(Figs.66 and ​and7),7), all genotypes appeared to have the largest proportion of crown volume change facing south–southeast. Over time, genotypes 2 and 6 comparatively had relatively little crown volume change/increase facing north. Genotypes 1, 3, and 5 generally had more uniform crown volume change, with a small tendency toward the south. Genotype 4, however, did not appear to alter its relative crown volume over time and was generally uniform among azimuths.

We also evaluated crown volume and crown volume change in the northern and southern directions and their potential effects on stem growth. Increases in the southern-crown segment volume generally represented more positive stem volume change per unit of crown volume change than the northern-crown segment. Both north- and south-crown segment volumes were significantly related to stem growth. Genotype did not significantly impact crown change in either direction. While there appears to be variation in crown size change by direction for each genotype (Fig. ​(Fig.7),7), these results would imply that there may be too much variability within each genotype to discern an affect. Note that wedge size was increased from 45° to 90° for this part of the study that may also increase the variability of volumes observed. Crown volume change and segment direction were significant when modeled against stem volume change. Within the context of the current study, these results imply that crown growth direction will influence stem growth, and suggest that growth in the southern-crown volume has a higher stem volume growth efficiency. Previous studies have implied that crown metrics (e.g., crown volume, crown length, and leaf area index) correlate with stem size (e.g., [38,86,87]). Thus, larger tree crowns will result in greater stem growth.

Rouvinen and Kuuluvainen [34] and Pretzsch [9] observed similar growth behavior in terms of crown asymmetry and plasticity with regard to the prevalent directionality of solar radiation in order to increase light interception. The presence of competing vegetation and the availability of gaps (caused by mortality or thinning operations) has also been linked to the causes of crown asymmetry (e.g., [9,34,82,88]). The prevailing row direction in the majority of our study site (75% were south-east) may explain the differences in volume in directions that are not purely to the south (i.e., the direction of maximum solar radiation exposure). The effects of the terrain’s slope on crown asymmetry has also been demonstrated [19] but assumed to be of little effect in our study. Given ALS ability to provide digital terrain models, future work could evaluate if this information would be of benefit.

Our results suggest that the 6 loblolly pine genotypes present at our study site exhibited differences in crown plasticity. Chmura et al. [71,84] noted that genotypes could exhibit differences in crown shape. High pulse density DLS allows us the potential to evaluate changes at scales within the ITC, and over large spatial extents, such as complete stands.

Funding: This work was primarily funded by the Forest Productivity Cooperative. This work was also supported by the Virginia Agricultural Experiment Station (Critz, VA) and the USDA National Institute of Food and Agriculture, U.S. Department of Agriculture (Washington, DC, USA).

Author contributions: Conceptualization: M.J.S. and D.R.C. Methodology: M.J.S. and D.R.C. Visualization: M.J.S. Software: M.J.S. Investigation: M.J.S. Validation: M.J.S. and T.J.A. Writing: M.J.S. Review and editing: All the authors.

Competing interests: The authors declare that they have no competing interests.