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).