Abundance and density estimates
Information collected during the bat roosting surveys were used to
calculate measures of bat density and abundance at three scales:
roost-level, subplot-level and tree-level. For a visual summary of
metrics see Fig. 1.
Roost-level density was calculated as the total roost abundance divided
by the total roost area (Fig. 1A). Measures of subplot-level density
were estimated with two methods: either as a total count per subplot
divided by the total subplot area (“subplot-level density”, Fig. 1B),
or as the average of fixed-bandwidth weighted kernel estimates,
estimated using the spatstat package in R (Diggle 1985)
(“subplot-level kernel density”, Fig. 1C). Kernel values were
estimated using tree locations weighted by tree-level bat abundance with
Gaussian kernel smoothing and a smoothing bandwidth of 0.6 (Baddeley
2010). Bandwidth was selected by comparing projected kernel density
values to expected density values based on within tree abundance and
canopy area. Kernel averages were calculated per subplot, and averages
included only occupied pixels in the subplot (pixel size = 0.156 x 0.156
meters). This latter approach has the advantage of explicitly
incorporating the distribution of trees into the density estimate, as
well as the number of bats per tree, and can therefore distinguish
between degree of tree-level aggregation. Note that neither roost nor
subplot-based density measures consider the vertical distribution of
bats.
Measures of tree-level density were estimated in either two-dimension
(2-D; for comparison with other two-dimensional estimates) or
three-dimension (3-D). Tree-level 2-D density was estimated from within
tree abundance and canopy area (Fig. 1D). Tree-level 3-D density was
estimated for the tree subset, as the absolute count of bats divided by
the volume of tree space occupied (i.e. per cubic metre rather than
square metre, Fig. 1E). Volume of tree space was calculated from the
height range occupied (maximum height minus minimum height) and the
approximate crown area of trees. To estimate crown area of tagged trees
for both measures, we computed the area of Dirichlet-Voronoi
tessellations from tree distribution maps of canopy trees per subplot,
with the spatstat package in R (Baddeley 2010). To control for
edge effects we imposed a maximum crown area of 199 m2(radius ~8 m) based on mean values reported across
species of eucalypts in New South Wales (Verma et al. 2014).
Overstory trees and trees outside of the canopy were also assigned this
mean value. Crown area of midstory trees was assigned as the first
quartile of canopy tree crown area (5.8 m2), to
reflect observations that trees beneath the canopy were typically
smaller than trees within the canopy. Mean calculated crown area was
30.4 m2 (crown radius ~ 3.1 m). To
investigate whether the choice of maximum crown area impacted results,
we also repeated analyses for additional values of maximum crown area
(140 m2, 170 m2 and 230
m2) chosen to cover the range in smallest to largest
mean values reported for individual eucalypt species in Verma et
al. (2014).