Drivers of tree-level 3-D density and abundance
Among subplot-level models,
the
most parsimonious predictors of tree-level 3-D density were (i) the
total abundance within the subplot; (ii) proportion of trees occupied
within the subplot; and (iii) the density of trees within the subplot
(Table 1).
Density
of trees had a large and highly significant positive effect on
tree-level 3-D density (regression coefficient: 9.664 ± 1.492, p
<0.0001), as did the proportion of trees occupied (regression
coefficient: 1.067 ± 0.301, p <0.0001) (Table 2).
Subplot-level abundance was only a significant contributor when
interacting with the proportion of trees occupied, but the effect was
small (0.001 ± 0.001, p=0.0492) (Table 2).
Results were comparable when modelled with tree-level abundance, for all
variables except density of trees (Table 2).
Density
of trees had a substantial and significant negative impact on the
abundance of bats per tree (regression coefficient: -5.053 ± 0.105, p
<0.0001) (Table 2),
suggesting
that abundance per tree is higher when fewer trees are available for
bats to roost in. Bats occupy more of the tree’s vertical space when
more bats are present (a pattern consistent across tree crown classes,
Appendix S2). The difference between tree-level 3-D density and
tree-level abundance indicates that bats change the height range they
occupy as total tree abundance increases.
At the roost level, density of
trees was a relatively poor predictor of tree-level 3-D density and
abundance and was not in the top-ranking model sets (Table 1). All fixed
terms in the roost-level model had negligible effects on tree-level 3-D
density (roost abundance: -0.084 ± 0.06, p=0.159; roost area:
<0.0001, p=0.014; and the interaction term: <0.0001,
p=0.021) and tree-level abundance (roost abundance: 0.447 ± 0.005,
p=<0.0001; roost area: <0.0001, p<0.0001;
and the interaction term: <0.0001, p<0.0001).
Roost-level predictors explained minimal variation in tree-level 3-D
density, with the overall most parsimonious GAM only explaining 3.8% of
variation (Table 1). Models with subplot-level and tree-level predictors
explained slightly more variation (subplot-level: 11.7% of variation;
tree-level: 13.6% of variation). The explanatory power of roost-level
models with tree-level 3-D density was comparable when species were
modelled separately (Appendix S3 in the Supporting Information).
Explanatory power and rankings were comparable for models with
tree-level abundance as the response variable (7.8% - 11.6% between
top ranking models) (Appendix S4 in the Supporting Information).
Neither estimated tree-level 3-D density, nor model outputs, varied
substantially under different values realistic for eucalyptus species
(Appendix S5). Full model outputs for both response variables are given
in Appendix S3 and Appendix S4 in the Supporting Information.
Discussion
We evaluated animal abundance and density at multiple scales to
determine what information is relevant for understanding transmission.
We used an extensive empirical
dataset of roosting Pteropus spp. collected over 13 months and
including 2,522 spatially referenced trees across eight roost sites.
Measures most commonly used to parameterise models of bat-pathogen
interactions (roost-level abundance and area) did not reflect the
density of bats at scales where transmission is likely to take place
(the abundance or density of bats within trees). Roost-level models
explained a little of the variation in these tree-level measures.
Density of trees was a better predictor of the likely conditions for
transmission than was the population size of bats at the roost, where
roosts with low tree density typically had a higher abundance but lower
density of bats per individual tree. These results have implications for
the structuring of infectious disease models for these species,
particularly for pathogens transmitted over small local scales (e.g.
within roosting trees), as discussed below.
An important consideration for bat-pathogen interactions should be
whether local abundance or density is the more pertinent measure for
transmission-relevant contact structure. In subplot-level models the
best predictor of tree-level
measures (abundance and density) was density of trees within roosts, and
this had opposing effects on tree-level bat abundance and tree-level 3-D
bat density. Roosts with a lower density of trees typically had more
bats per tree, but a lower 3-D density of bats within these trees. This
suggests that,
while
abundance per tree is higher when fewer trees are available for bats to
roost in, bats are able to decrease their local density by expanding
their occupied tree area (i.e. by spacing themselves out across the
tree). Roosts with a sparse tree structure may have larger crown areas
or have more foliage height available for roosting. For pathogens
transmitted by direct contact, density is likely to be the relevant
measure (as per standard mass action principles). If pathogens are
transmitted indirectly through contact with liquid urine falling
downward, or via contact with aerosolised urine particles, then total
abundance within trees may be the more pertinent measure. To help
illustrate this point, we provide a visual in Appendix S6 in the
Supporting Information. Distinction between these measures will be key
to framing ecologically relevant contact structures.
At the roost level, the associations between tree density, and bat
density and abundance were diminished, as density of trees was a
relatively poor predictor of tree-level abundance and 3-D density. This
is likely an artefact of scale, and heterogeneity of tree density across
larger areas (see similar issues of spatial heterogeneity and scale
originally discussed in Krebs (1999)).
Individual roosts in our dataset
varied substantially in their density of trees across space. As a
result, the mean density of trees (as used in these roost-level models)
may not be a meaningful measure of density in roosts with a heterogenous
tree structure. In other words, the variation in tree density is
important at localised scales (i.e. patches within the roost), but not
if averaged over the roost.
Measures of density also varied greatly by scale. This reflects the
highly aggregative nature of bat distribution which is captured to
different extents across the scales. Estimated mean density ofPteropus at the roost level was 13-fold lower than the
subplot-level mean estimate that accounted for heterogenous
distributions of bats (0.38 bats/m2 with an
interquartile range of 0.21-0.47, vs 5.13 bats/m2 with
an interquartile range of 2.71-6.09). At the roost-level, the total
roost area can encapsulate substantial unoccupied space, if trees are
sparsely distributed or not occupied, as the perimeter of the roost
boundary captures the maximum extent of inhabited roosting habitat, but
not trees that are occupied and unoccupied within this boundary. This
contrasts with other scales of density estimate in this study, like
subplot-level kernel density, which more effectively delineate
unoccupied and occupied space, and so generate higher estimates of
density. The latter estimates were more consistent with previous
estimates of Pteropus density, which have ranged between 0-8.7
bats/m2 (average 2.1 bats/m2) for
tree-level visual approximations (Welbergen 2005). The finding that
spatial distributions are a function of scale is not new (e.g. see
discussions of spatial distribution and scale in Krebs (1999)), but
highlights the need to consider which scale (or scales) are ecologically
relevant when considering the nature of density-transmission scaling in
host-pathogen interactions.
Mean estimated tree-level 3-D density was 0.34 bats/m3(0.03-0.32). The low level of variation explained by roost-level and
subplot-level models (minimum 3.8% and maximum 13.6% of variation
across top ranking models) likely reflects the highly heterogenous
spatial structuring of Pteropus bats, and indicates that neither
roost-level measures nor subplot-level measures adequately capture
heterogeneity in these finer, tree-level estimates. In Pteropusbats, ecological processes operate in complex ways to influence animal
density across different scales - at the roost level, a population can
expand in area in response to increasing total abundance (and so remain
constant in density), or remain stable in area occupied (and increase in
density). If a roost does not expand its roost area in response to
increasing total abundance (e.g. due to restrictions on space), bats may
either fill more trees within the perimeter of the roost (and increase
the density of bats at an intermediate subplot level by increasing the
proportion of trees occupied but not the density within individual
trees), or fill already occupied trees (and so increase both
intermediate subplot density and local tree-level abundance). Whether
tree-level 3-D density increases will be determined by how much bats
increase their utilisation of tree space, which will be driven by the
height and crown area available for roosting. The implication is that
the relationship between total roost abundance and density at any scale
may be unpredictable, and critically, that roost and subplot measures
may not provide adequate approximations for population density at scales
relevant for transmission. Tree density within roosts may provide a
better standard of comparison across roosts when reflecting the
conditions for transmission, but only when considered in local scales,
and in context of whether local abundance or density is the more
pertinent measure for transmission-relevant contact structure.
We would note here that our estimates of tree-level 3-D density and 2-D
density were based on overall estimated crown area, not occupied crown
area, and so may be underestimates of true density. This is an
acknowledged limitation of our approximation of crown area by
Dirichlet-Voronoi tessellation. True estimates of tree-level density
would require empirical estimation of occupied crown area in the field.
However, crown area can be difficult to measure accurately (Vermaet al. 2014) and measurement of occupied area may not be
practical. Our Dirichlet-Voronoi tessellation approach allowed us to
estimate crown area for a large number of trees which would not have
been feasible with field methods. While this approach could be
influenced by the choice of maximum crown area set for edge trees and
trees in open areas, we show that neither estimated tree-level 3-D
density, nor model outputs, varied substantially under different values
realistic for eucalyptus species (Verma et al. 2014) (Appendix
S5).