Tests of CSR for Midwestern Dataset
The analyses of the Midwestern dataset including all trees(Figure S1) and those containing only living trees (Figure S2) revealed several sites that departed from CSR. Tests for homogeneity found four sites (Caesar Creek, Edge 2, Lakeside 2, and Rush Run) in theMidwest all trees dataset and three sites (Edge 2, Lakeside 2, and Rush Run) in the Midwest living trees dataset to be inhomogeneous and were evaluated using a K-function and DCLF test designed for inhomogeneous data. In the Midwest living trees andMidwest all trees datasets, visual inspection of the inhomogeneous K-function envelopes indicated three sites showed strong signs of regular-spacing with confirmation of this pattern using DCLF tests. These three sites were comprised of small trees (mean height > 1 m). In the Midwest all trees dataset, the K-function envelopes of four sites (Bernheim, Caesar Creek, Lakeside 1, and Tranquility) indicated clustering, with DCLF tests confirming the findings for Lakeside 1 (p = 0.049) and Tranquility (p = 0.004). The removal of dead trees did not alter signal of clustering and was confirmed in the sites Tranquility (p = 0.038), and Lakeside 1 (p = 0.071) in the Midwest living trees dataset (Figure S2). The tree height of potential clustered sites varied, with median heights for Bernheim, Caesar Creek, and Tranquility being similar (median height = 3.7-7.0 m) and Lakeside 1 being much shorter (median 0.7 m). The seven other sites showed no significant deviation from CSR when examining K-function envelopes and DCLF tests in the Midwest all trees orMidwest living trees datasets.
The sample sites in the Midwestern dataset contained a varying number of deciduous trees (0-60 deciduous trees per site). Deciduous trees were removed from the Midwest all trees and Midwest living trees datasets to examine the pattern of redcedars alone. There was only one deciduous tree among the three inhomogeneous sites, so they were omitted. The Midwest all redcedar and Midwest living redcedar point-patterns were re-checked for homogeneity. The site Edge 1 was found to be inhomogeneous in both datasets. Visual assessment of the inhomogeneous K-function envelopes and DCLF testing (Midwest all redcedar p = 0.007; Midwest living redcedar p = 0.019) provided strong evidence of overdispersion at the Edge 1 site. Visual and quantitative assessment of the remaining 11 sites in theMidwest all redcedar dataset indicated five sites (Bernheim (p = 0.106), Caesar Creek (p = 0.003), Gettysburg 1 (p = 0.044), Lakeside 1 (p = 0.22), and Tranquility (p = 0.012)) showed evidence of clustering (Figure S3). The clustered sites were similar in tree size (mean DBH ~ 23 cm) except for Lakeside 1, which consisted of mostly saplings. The omission of dead trees in the analysis of theMidwest living redcedar data removed all evidence of clustering.
The final examination of the Midwestern dataset ran simulated K-function and DCLF tests weighted by the tree diameter at each homogeneous site. Visual inspection of the weighted K-function envelopes revealed a shift towards overdispersion for many of the sites relative to the K-function plots of unmarked data (Figure 2). Interestingly, the DCLF tests weighted by diameter did not always reflect the observed trend, with only Edge 1 and Mammoth confirming a regularly-spaced pattern. The diameter-weighted analyses was performed on the Midwest living trees dataset (Figure S4) and had results that were similar to theMidwest all trees dataset, with only Edge 1 (p = 0.025) and Mammoth (p = 0.048) having enough evidence to definitively state they are overdispersed.