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.