Neighborhood density
For each tree, we located every other tree < 20 m away. This
can be done efficiently in a large plot by first assigning every tree a
cell number within a grid of 20 x 20 m. Then, inter-tree distances were
calculated only for trees within the same cell or neighboring cells.
That locates every tree within 20 m but reduces enormously the number of
distances calculated. The identity of all neighbors alive during any
given year and within 20 m of every tree was calculated and saved.
Neighbor density was defined as the basal area of all those neighbors
that were alive in any one census. Neighbor density was divided into
species groups. For every individual of Q. macrocarpa , the
neighboring basal area was considered in two categories: conspecific,
meaning all basal area of neighboring Q. macrocarpa , and
heterospecific, that of all other species. Likewise, neighboring basal
area of every Q. ellipsoidalis was divided into the same two
groups, conspecific (other Q. ellipsoidalis ) vs. heterospecific
(all species except Q. ellipsoidalis ). The two oak species so
thoroughly dominate the study site that heterospecific basal area is
nearly all due to the opposite oak. (In 1995, the two oak species
represented more than 92% of the basal area in the study grid, which
had increased to 95% by 2005 and 97% by 2020 (Davis 2021).)
We further subdivided neighbors by distance, 0-5, 5-10, and 10-20 m away
from a focal tree, dividing basal area by surface area of each ring. In
preliminary analyses, we found no difference in the impact of neighbors
within 5 m and at 5-10 m, so we combined those categories. This left
four measures of neighbor density, two taxonomic (heterospecific vs.
conspecific) and two distance categories.
Because neighbor density was limited to a fairly small range, no
transformation was necessary, matching other analyses of local density
(Condit et al. 1994, Comita et al. 2010). We chose to measure
neighborhood density in m2. ha-1,
units we will refer to as condits . Specifically, we chose a
magnitude of 10 condits as the density measurement because this
was close to two standard-deviations (SD ) of both conspecific and
heterospecific density, in both distance categories, for the two
abundant species. For example, the SD of neighbor density
around Q. ellipsoidalis individuals in the four categories was
between 3.5 and 8.9 condits (across all five censuses); in Q.
macrocarpa , it was 3.1-7.7 condits. This means that varying neighbor
density by one condit indicated an increase that covered most of the
range of density.