Multitype Analyses
Using this information to determine trends in the spatial correlation between points can reveal spatial point-processes that are obscured when examining unmarked points. Typical investigations of multitype point-patterns begin with assessments of differences in the intensity of types of points (Baddeley et al. 2015). However, the sampling locations in the Midwestern dataset intentionally focused on redcedar-dominated stands, so comparing the intensity (~ density) of redcedar and other species was not considered. In the Oklahoma dataset, the dominant tree species were Juniperus virginiana and varieties of Quercus (primarily Quercus stellata with intermittent Q. marilandica and Quercus muehlenbergii ). In addition, in both datasets, there were occurrences of a variety of small, deciduous understory trees included in the point-pattern data.
Each point-pattern (including select subsets of those patterns) in the Midwestern and Oklahoma datasets were tested against the null hypothesis of complete spatial randomness (CSR) using simulated K-function envelopes and Diggle-Cressie-Loosmore-Ford (DCLF) tests. For each dataset, a series of analyses were conducted. First, K-function and DCLF tests were conducted on all living and dead trees (all treesdataset) irrespective of marks. Next, dead trees were removed (living trees dataset) and the analyses were performed again. Performing the K-function procedures outlined above on datasets with and without dead trees and comparing the results allowed inference into ecological processes that occur over time. Then, the all treesand living trees datasets were further reduced by removing instances of deciduous trees and repeating the analyses. These small, understory trees may be masking an underlying point-process that influenced the distribution of the larger redcedar (in the Midwest dataset) or redcedar and Quercus (in the Oklahoma dataset). K-function tests were conducted on reduced datasets where non-Quercus deciduous trees were removed. Furthermore, the pattern of redcedar alone was of interest, so K-function tests were run on a dataset comprised of only redcedar in the Oklahoma dataset.
The size of trees could have a large effect on their proximity to neighbors. For the Midwestern and Oklahoma datasets, a K-function test weighted by tree diameter was conducted to determine if there were dependencies between trees based on their diameters. These tests followed the previously outlined procedure of visually comparing the empirical K-function with simulated acceptance envelopes and quantitatively assessing the model using the DCLF test. Trees under 1.4 m in height were assigned a DBH of 0.1 cm so they could remain in the analysis. Simulation envelopes and the DCLF test are conservative and the outputs of the two tests do not always align (Baddeley et al.2015). In cases where K-function tests provide strong evidence of departure from CSR, p-values of up to ~ 0.11 from the DCLF output are reported as marginally significant.
Examining nearest-neighbor distances between different species of trees can determine whether there is segregation between types (Pielou 1961). In the Midwestern dataset, contingency tables of nearest-neighbor distances were used to test for segregation between redcedar and deciduous species (Dixon 2002). In the Oklahoma dataset, Dixon contingency table tests of segregation were conducted between redcedar,Quercus , or other deciduous trees. Segregation based on tree size was another feature of interest. In both datasets, trees were grouped into ‘Small’ (DBH < 2.5 cm) and ‘Large’ (DBH > 2.5 cm) categories and tested for segregation between tree sizes as outlined above. For each dataset and contrast type (size or species) an independent test of overall segregation was conducted using thesegregation.test function in spatstat (Baddeley et al. 2015). This test uses a Monte Carlo kernel-smoothing approach to evaluate patterns in multitype point-pattern data (Diggle et al., 2005; Kelsall & Diggle, 1995).