Field research was conducted at the Randolph-Macon College Martin Marietta Field Station in Doswell, Virginia. The site is 55 ha in size, with approximately half covered by mature, naturally regenerated, deciduous forest that originated at least 70 years prior to data collection. The canopy is dominated by American beech, yellow poplar (Liriodendron tulipifera), and several oak (Quercus) and hickory (Carya) species. The subcanopy layer is dominated by American holly (Ilex opaca) and abundant small stems of American beech, and also includes flowering dogwood (Cornus florida), eastern redbud (Cercis canadensis), and American hornbeam (Carpinus caroliniana). The terrain is gently rolling, with slopes rarely exceeding 20%, and the elevation is approximately 70 m above sea level. The site lies near the eastern edge of the Piedmont geologic region, which is characterized by deep weathering and high geological complexity (Dietrich 1988). The local climate is humid subtropical (Köppen climate classification), with hot summers (mean July high = 31.1 °C) and relatively mild winters (mean January low = –2.1 °C), and very consistent precipitation throughout the year (average annual total = 1108 mm) (NOAA National Climatic Data Center).
Data collection occurred in eight plots randomly located in areas of upland, mature, naturally regenerated, deciduous forest that exhibited no evidence of natural or anthropogenic disturbance (Additional file 1: Figure S1). In the summer of 2014, we surveyed tree regeneration in 3-x-1 m subplots, with four subplots per plot (see Additional file 1: Figure S2 for detailed layout). Within each subplot, we identified all tree seedlings, which we defined as individuals that belonged to species capable of reaching at least 10 m in height and that were: a) woody at ground level (i.e. extremely small and delicate individuals were ignored, primarily because most of these individuals could not be identified), b) < 3 cm diameter at breast height (DBH) and c) not of basal or root sprout origin. All tree seedlings were tallied and inspected for evidence of browse damage (e.g. by white-tailed deer; Odocoileus virginianus). In the summer of 2015, we mapped trees ≥ 3 cm DBH in these same plots (circular plots with a radius of 23 m; 1/6 hectare). Species not capable of reaching canopy height (e.g. flowering dogwood, eastern redbud) were omitted from our measurements. All trees were identified to species and inspected to determine seed vs. sucker origin (following the methods in Beaudet and Messier (2008)); in the latter case, clumps of vegetatively linked individuals were recorded. Across the eight plots, we measured and mapped a total of 1622 trees.
All analyses focused on American beech, as no other species in our study area were sufficiently abundant across plots and size classes for meaningful assessment of CNDD. However, for comparative purposes, we also conducted some analyses with “all other canopy species” (pooled into a single category) and smaller size classes of American holly (individually). Small stems of American holly were examined individually because of their high densities, which enabled robust statistical analysis, and the similar shade tolerances of American holly and American beech (Stutz and Frey 1980; Grelen 1990; Tubbs and Houston 1990), which allowed for a useful comparison presented in the Discussion.
First, to assess dispersal limitation in American beech, we analyzed seedling density as a function of adult conspecific abundance. We examined these patterns at two spatial scales: a) subplot-level seedling counts as a function of conspecific basal area (BA) within 10 m of each subplot, and b) plot-level seedling counts (mean across all four subplots) as a function of the conspecific BA in the entire 23 m radius plot. For comparison, and to account for any general inhibitive effects of mature American beech on seedling establishment, we also examined relationships between American beech BA and seedling densities of both American holly and all other canopy species. In all cases, to capture early establishment only, we excluded seedlings > 30 cm in height (matching Johnson et al. 2014). Second, we conducted similar analyses relating plot-level densities of “saplings” (trees 3–10 cm DBH) to plot-level American beech BA. Saplings were mapped throughout the entire plot, but unlike the analyses described below, this initial assessment was non-spatial.
Third, we conducted bivariate point pattern analyses to examine fine-scale spatial relationships between different species and size classes. We individually analyzed American beech and American holly, and once again pooled all other canopy species into a single category (due to low numbers for each individually). With regard to size classes, stems were divided into saplings and “large trees” (trees ≥ 20 cm DBH). Trees in between these two size classes (10–20 cm DBH) were excluded from our spatial analyses to ensure that large trees have the potential to disproportionately affect saplings (and not vice versa). In other words, it would make little sense to assume that a 10.1 cm DBH tree has a qualitatively different effect on its local neighborhood than a 9.9 cm DBH tree. American holly was abundant only in the sapling size class, and thus our analysis of American holly saplings is done for comparison with American beech saplings, not for investigating CNDD in American holly.
We used bivariate pair correlation functions (Illian et al. 2008; Law et al. 2009), with associated confidence envelopes, to quantify the spatial positioning of sets of points (two sets at a time), relative to each other. For instance, an analysis of American beech saplings and American beech large trees reveals the extent to which saplings are clustered, randomly arranged, or over-dispersed around large conspecifics. For comparative purposes, we conducted all of the following bivariate point pattern analyses: a) American beech saplings with respect to American beech large trees, b) American beech saplings with respect to large trees of all other canopy species, c) American holly saplings with respect to American beech large trees, d) American holly saplings with respect to large trees of all other canopy species, e) saplings of all other canopy species with respect to American beech large trees, and f) saplings of all other canopy species with respect to large trees of all other canopy species. All point pattern analyses were done separately within each plot.
While visually comparing the results of these bivariate pair correlation functions is illuminating, we also formally assessed the significance of the difference between the results of several different analyses. Specifically, for each sapling group (American beech, American holly, and other canopy species), we determined if the clustering around large American beech trees differed significantly from the clustering around large trees of all other canopy species. To determine the significance of the difference, we used an approach similar to Larson et al. (2015) and Janik et al. (2014), including a comparable null model (“random labeling”). We repeated the following steps 1000 times to generate null distributions for our bivariate pair correlation functions: 1) shuffle labels across large trees (American beech vs. all other canopy trees), 2) calculate both bivariate pair correlation functions (sapling clustering around American beech and sapling clustering around all other canopy trees), and 3) subtract one set of resulting values from the other. Next, we calculated a 95% confidence envelope for the simulated differences between groups (2.5th through 97.5th percentile), and determined the distance bands for which the actual difference between groups departed from the confidence envelope.
Analyses were conducted with the statistical software R and the supplemental package spatstat, which is specifically designed for spatial analysis. In our bivariate pair correlation functions, we analyzed successive distances from 1 to 10 m, with the bandwidth (the width of the concentric ring analyzed) consistently set to 2 m; for instance, at a distance of 5 m and a bandwidth of 2, all saplings between 4 and 6 m are analyzed. For all pair correlation functions, we used Ripley’s isotropic edge correction. Secondary stems (all stems other than the largest within a multi-stemmed clump) were excluded from point pattern analyses because these stems are likely subsidized by larger ramets, and thereby effectively function as lower branches. As such, basal sprouts within the sapling size class were ignored and spatial patterns of saplings are specifically for seed origin saplings (although this is an inconsequential detail given that analyses with basal sprouts included yielded qualitatively identical results). While American beech sprouts are common in more northern regions, on steep slopes, in areas where roots have been disturbed, and in stands affected by beech bark disease (Held 1983; Cleavitt et al. 2008), basal and root sprouts were rare at our study site, which is beyond the current range of beech bark disease (Virginia Department of Forestry 2014).