Guiding Questions: How do distances between trees differ depending on tree height? How does the spatial pattern of tall trees relate to the spatial pattern of slope and elevation?

Methods: I used a combination of ArcMap, QGIS and R to perform analyses and view results. I used the results of my previous distance analysis within the HJ Andrews Forest, which grouped individual trees into ten height classes and calculated the mean distance between trees within the same height class, to correlate tree spacing with other spatial phenomena. I wanted to know if hot spots in within class tree spacing correlated with hot spots in tree height, so I examined hot spots and cold spots of tree distances within each height class and compared them to tree heights, slope and elevation. Height class 1 is the shortest class of trees and height class 10 is the tallest class of trees.

I used the Hot Spot Analysis Tool in the Arc Toolbox > Spatial Statistics Tools > Mapping Clusters > Hot Spot Analysis (Getis-Ord Gi*) to perform a Hot Spot Analysis on each of the ten height classes by mean distance to the 30 closest trees of the same height class. In the context of this analysis, the interpretation of a hot spot is that it is a region of greater than expected distances between trees of the same height class. For example, in the shortest height class, 1, hot spots are regions of greater than expected mean distance between a short tree and the 30 closest short trees. Cold spots would then be regions of closer than expected mean distance between short trees.

The Hot Spot Analysis in ArcMap used a self-generated distance band of 113m for my original hot spot analysis of the global dataset (not broken up by height class), so I decided to use a distance band of 100m for each subsequent hot spot analysis. Each height class has a different number of total trees in it, so by holding the distance band constant, I hoped to avoid influence from any differences in total number of trees between height classes.

After viewing the hot spot results, I plotted the z-scores of heights for each height class against the z-scores of the distances between trees to visually examine their relationship. If both heights and distances between trees were perfectly normally distributed, one would expect a circular distribution on the density plots with a slope of zero.

I then compared the mean slopes, elevations, and standard deviation of slopes and elevation within height classes across the entire forest. Since HJA is a research forest with many different management areas, including harvested patches and research plots, I limited the next part of the analysis to only within control areas of the forest. I downloaded the most recent (2014) land use designations from the HJA data repository (http://andlter.forestry.oregonstate.edu/data/abstract.aspx?dbcode=GI008). For this analysis, I used Entity Title 3: Reserved areas (controls) within the Andrews Experimental Forest. I compared slopes and elevations within the control plots only by height class, to see if there were differences between the global dataset and the control regions of the forest.

Results:

The density plots of height z-score versus distance z-score revealed a different pattern between smaller height classes of trees and tree spacing than the relationship between larger height classes of trees and tree spacing. As we go from shorter height classes of trees to taller height classes, the density plot distributions change (Figures 1-10). There is strong evidence of positive correlation between hot spots of short trees and hot spots of distance between short trees, but from height class 6-10, there is little to no evidence of a relationship between hot spots of trees and distance between them. Tall trees are more or less distributed randomly throughout the forest.

 

 

 

 

 

 

 

 

 

There is clearly some structure to the density plots (especially in height classes 1-5), so we can assume that the trees are not randomly distributed and that there is a relationship between height and distance between trees. I compared mean and standard deviation of slope, as well as mean and standard deviation of elevation for each height class of trees (Table 1). Mean slopes do not significantly differ between height classes, so slope is likely not a main driver of tree height. However, there is some evidence that tree heights differ at lower and higher elevations, with the shortest height class of trees at a mean elevation of 1014 m, and the tallest height class at a lower mean elevation of 831 m. It’s important to note that mean elevations have large standard deviations, so the trend may not be as strong as it first appears. I wanted to know if there was more evidence for this pattern, so I calculated the same statistics for subsets of the hotspot analyses constrained to only the control areas of the forest (Table 2) to get an idea of how management may or may not influence the relationship between tree height and tree spacing throughout the forest. Mean slopes and elevations, accounting for standard deviation from the mean, do not differ significantly between the global and control datasets, meaning that the control regions are reasonable representations of the rest of the forest. To examine this further, I examined the same data for the entire forest excluding the control areas (Table 3). The same pattern holds between the three datasets; class 10 is the only class that is consistently at lower elevations across the forest. I made two density plots to display this relationship. Figure 11 shows the distribution of elevation for the shortest height class (class 1) of trees (green) versus the global dataset of all trees (red). The short trees follow the same distribution as the rest of the dataset, meaning that they are dispersed more or less evenly across elevations. Figure 12 shows the distribution of the tallest height class of trees (class 10; light blue) by elevation versus the global dataset of trees by elevation (red). This clearly shows that tall trees are not distributed at higher elevations.

 

Table 1: Global dataset

Height Class	Mean Slope	SD Slope	Mean Elevation (m)	SD Elevation
1	23	11.7	1014	294
2	23	11.6	1008	291
3	25	11.6	990	295
4	25	11.5	948	291
5	25	11.3	931	293
6	26	10.9	972	291
7	27	10.5	982	250
8	26	10.6	959	221
9	25	10.7	926	207
10	23	11.2	831	197

 

Table 2: Subset of control regions

Height Class	Mean Slope	SD Slope	Mean Elevation (m)	SD Elevation
1	27	11.9	1104	317
2	27	11.5	1136	328
3	28	11	1157	329
4	28	10.8	1143	311
5	28	10.2	1133	285
6	28	10	1071	262
7	28	10	992	228
8	27	10.6	955	193
9	26	10.8	935	187
10	24	11	869	189

 

Table 3: Global dataset excluding control regions

Height Class	Mean Slope	SD Slope	Mean Elevation (m)	SD Elevation
1	22	11.4	991	284
2	22	11.4	979	273
3	24	11.6	952	272
4	24	11.5	902	266
5	24	11.5	867	265
6	25	11.3	908	290
7	26	10.7	973	267
8	25	10.5	964	242
9	23	10.4	919	221
10	22	11.2	793	198

 

Critique of the method:

A criticism of hot spot analysis is that it’s basically a smoothing function that places a focal around an area but does not account for the distribution of values within that area. So, the tallest tree in the dataset could be in cold spot (region of shorter than expected trees) and the hot spot analysis would give you no indication of that, so one may miss out on potentially useful/interesting information.

This is only a cursory look at the data and a next step is to more closely examine how slope, elevation and aspect influence distribution and height of trees, particularly within the control areas of the forest.