Figure 4. K-function envelopes and Diggle-Cressie-Loosmore-Ford (DCLF) test p-values for select sites in the OK redcedar and oakdataset. Dashed red lines represent the theoretical Poisson distribution. Grey shaded sections are 95% acceptance envelopes. The black line illustrates the empirical K-function. Departure of the black line from the envelope signify a non-random distribution where points above indicate clustering and below indicate overdispersion.
Visual examination of the K-function acceptance envelopes weighted by tree diameter in the OK all redcedar and oak dataset found six sites with potential overdispersion with DCLF tests confirming the findings at sites 3, 8, 9, and 12 (Figure 5). The dataset was reduced to include only living trees and diameter-weighted K-function tests found probable overdispersion for eight sites with DCLF testing confirming overdispersion at site 3 (p = 0.059), site 8 (p = 0.07), site 9 (p = 0.051), and site 12 (p = 0.019).