Keywords: Contact rate; density-dependent transmission;
frequency-dependent transmission; heterogeneity; mass action;
nonlinearities; pseudo-mass action
Introduction
A central aim of disease ecology is to understand how pathogens spread
within host populations (Brandell et al. 2020). Implicit to this
is the elucidation of a pathogen’s transmission dynamics (Smith et
al. 2009). For directly transmitted pathogens, transmission is
effectively the product of the contact rate between hosts, the
proportion of contacts that are between susceptible and infectious
hosts, and the proportion of effective contacts that result in infection
(McCallum, Barlow & Hone 2001). In models of infectious diseases,
transmission mechanisms are typically combined into a single term, the
transmission coefficient (β), and modelled with one of two simplified
functions that describe how infectious contacts scale with population
size: that scaling is linear
(‘density-dependent’)
or independent (‘frequency-dependent’) (McCallum, Barlow & Hone 2001;
Begon et al. 2002; McCallum et al. 2017). Selecting a
function that provides a useful approximation for modelling transmission
has been debated extensively (e.g. McCallum, Barlow & Hone 2001; Begonet al. 2002; Lloyd-Smith et al. 2005; Cross et al.2013), although in practice, the model is often based on the
transmission route of the pathogen: density-dependent for direct
transmission, and frequency-dependent for vector-borne or sexual
transmission. While this approach may accurately reflect transmission at
the local scale where contacts happen (though see Ryder et al.2005), there is growing evidence to suggest this may not scale correctly
to describe transmission in the population as a whole (the ‘global’
scale) (Smith et al. 2009; Ferrari et al. 2011; Cross,
Caillaud & Heisey 2013). For example, transmission may be
density-dependent at the local scale, but appear more consistent with
frequency-dependent transmission at the global scale (Ferrari et
al. 2011; Cross, Caillaud & Heisey 2013). Two interrelated questions
arising from this paradox need to be answered to more thoroughly
consider the nature of transmission in wildlife populations: how should
density in natural populations be defined and measured, and what spatial
scales are appropriate for understanding transmission in particular host
pathogen systems (De Jong 1995; McCallum, Barlow & Hone 2001; De Jong
2002). Understanding how
transmission scales with density is especially important for wildlife
populations, in comparison with human infections, where population size
may change by orders of magnitude over relatively short periods.
Quantifying animal density can be complex, however. Animal behaviour and
heterogeneity in the environment can create aggregate distributions of
animals that are not adequately represented in estimates when divided by
total inhabited area (Krebs 1999). Defining and measuring density is
additionally complicated if animals are distributed in three dimensions
(i.e. across horizontal and vertical space). Finally, aggregative
distributions of animals may also deviate from the random-mixing
assumption that underlies density-dependent and frequency-dependent
transmission models, if contacts between neighbours are more frequent
than contacts between distantly spread animals (McCallum, Barlow & Hone
2001). An imperative question, therefore, lies in determining the
appropriate ‘local’ scale at which transmission occurs, and where
contacts may be more homogenous (McCallum, Barlow & Hone 2001). In
addition, for highly aggregative species, where local groups form within
the global population, processes that drive transmission within groups
may not match processes that drive transmission between groups. In such
species, transmission within groups may be driven by local group size,
while transmission between groups by the structure of the population and
the connectivity between local groups (Jong, Diekmann & Heesterbeek
1995; Ferrari et al. 2011).
These issues are prevalent across most wildlife disease systems. Indeed,
it has been suggested that seal colonies are one of the few natural
situations where transmission can be adequately modelled with population
abundance rather than animal density (possibly owing to uniform
distancing between individuals) (De Koeijer, Diekmann & Reijnders 1998;
McCallum et al. 2017). Issues surrounding the definition and
estimation of density are particularly problematic in models of zoonotic
pathogens that have bat reservoirs. Bats are among the most gregarious
of all mammals – a high proportion of species are social, with some
forming the largest aggregations of resting mammals known (Kerth 2008).
Bats typically gather together during inactive periods of the diurnal
cycle, either in natural habitat
(e.g. tree foliage, tree hollows and caves) or anthropogenic
structures
(e.g buildings, mines and bat boxes) (Kerth 2008). Some species switch
roosts frequently (e.g. Rhodes 2007) while others regularly return to
the same roost space, or even to specific locations within the roost
(Nelson 1965; Lewis 1995; Markus & Blackshaw 2002). This can also be
variable among individuals within species (e.g. Welbergen 2005;
Welbergen et al. 2020). Spatio-temporal changes to roost
structure and organisation are often observed in response to ecological
factors like season, mating and gestation, food availability,
thermoregulation, parasite accumulation, or site disturbance (Lewis
1995; Kerth 2008). By altering rates of contact, spatial and temporal
changes in bat aggregations can contribute to spatio-temporal dynamics
of transmission, infection, and risk of disease spillover (Altizeret al. 2006). Framing transmission in ecologically relevant
contexts will therefore be important for accurate infection modelling in
these species, where population size often changes dramatically.
In models of bat viral transmission where contact rate is assumed to be
density-dependent, and where pathogen transmission occurs within the
roost (generally the case if individuals forage independently), the
transmission coefficient is often parameterised with total roost
abundance (George et al. 2011; Plowright et al. 2011; Wanget al. 2013; Hayman 2015; Jeong et al. 2017; Colombiet al. 2019; Epstein et al. 2020). Likewise in statistical
models, population size is often fit with total abundance (Serra-Coboet al. 2013; Giles et al. 2016; Páez et al. 2017).
If the population size is modelled to be constant (e.g., Plowrightet al. 2011; Wang et al. 2013) it is irrelevant how
transmission scales with population size. If population size is variable
however, parameterisation with total abundance implicitly assumes that
the area occupied remains constant with increasing population size (so
that roost abundance scales linearly with bat density), and that this is
consistent across scales. Whether this occurs in reality is not
routinely evaluated. Indeed, changes to density may be multifaceted and
hard to predict. In tree-roosting Pteropus , for example, new
individuals arriving into the roost could be accommodated by an
expansion of the total roost area, by increasing the number of trees
occupied within the roost perimeter, or by crowding more animals into
occupied individual trees. These processes may all occur simultaneously.
Over what spatial scale transmission can reasonably be expected to occur
within roosts is also a critical question, and one that will define the
scale at which density is ecologically relevant to infection dynamics.
This is likely to depend on: (i) the mode of pathogen transmission, (ii)
animal behaviour and (iii) the structural heterogeneity in the roost
environment. First, the mode of transmission will determine the distance
over which transmission can occur and will frame the scale relevant for
population measures – transmission via aerosols or droplets, or
indirect contact with infectious excretions has a greater potential for
spread over large distances compared with transmission via direct
contact, meaning that a larger scale of density estimation may be
warranted. Second, animal behaviour, specifically range of movement,
site fidelity, and tendency to aggregate, will influence the spatial
extent of contact throughout populations, and so also the scale relevant
for population measures. Animals that constantly move through their
environment will be likely to contact other animals over a greater area
than animals that are more sedentary, for example. Finally,
environmental heterogeneity can influence the probability and rate of
movement between groups in highly aggregative populations, and so
influence the rate and extent of spread over space. Currently, there is
little empirical evidence available to understand how viral transmission
depends on density in bat populations, or the spatial scale on which
density might be relevant. Moreover, there is little empirical support
for traditional density-dependent viral transmission in bats, which may
reflect complexity in transmission underpinned by ecological processes
across different scales (Plowright et al. 2015; McCallum et
al. 2017).
Here, we investigate the roosting characteristics of AustralianPteropus bats. Australian Pteropodid bats are the reservoir hosts
for Hendra virus (HeV), an emerged paramyxovirus in the genusHenipavirus that causes lethal disease in horses and humans in
eastern Australia (Plowright et al. 2015). We present a 13-month
dataset of roosting Pteropus spp. from 2,522 spatially referenced
trees across eight roost sites, to compare estimates of density across
scales (roost-level, subplot-level, and tree-level). We focus on
tree-level measures of abundance and density to then evaluate whether
roost features at the different scales relate to these local dynamics.
We focus our analyses on tree-level measures of abundance and density,
as this is the scale at which the majority of contacts are likely to
occur, given the nature of viral transmission between bats, and aspects
of bat behaviour – i.e. while vertical transmission of Hendra virus has
been documented (Halpin et al. 2000), transmission between bats
is assumed to be primarily horizontal through contact with infectious
urine, either through close contacts with individuals, contacts through
the vertical tree column (e.g. with excretion from bats roosting above),
or exposure to clouds of aerosolised urine over small distances (Fieldet al. 2001; Plowright et al. 2015). In addition,
flying-fox activity within roosts is limited - bats rarely move from
their roosting position after they return at dawn, and diurnal
activities primarily consist of roosting, sleeping and grooming (Markus
& Blackshaw 2002). Moreover the roosting positions of individuals can
be highly consistent, with animals often returning to the same branch of
a tree over many weeks or months (Markus 2002; Welbergen 2005).
Considered together, it is plausible that tree-level measures of
abundance or density will be the most relevant for understanding
transmission in these species. Through these analyses we aim to provide
data on ecologically relevant estimates of density for these species and
highlight predictors of the local density most important for
transmission of Hendra virus. Understanding gained on the nature of
animal density will be important to give more realistic predictions of
pathogen invasion and persistence within bat populations. To this end,
we also propose a framework to help guide incorporation of heterogenous
contact structures into bat infectious disease models more generally.
Methods
Data collection
We collected data on roosting structure of three species (black
flying-fox: P. alecto ,
grey-headed flying-fox: P.
poliocephalus and little red flying-fox:P. scapulatus ) from eight
roost sites in south-east Queensland and north-east New South Wales,
Australia (Fig. 1).P.
alecto are believed to be the primary reservoir for Hendra virus in
this study region (Goldspink et al. 2015), however a
newly-identified Hendra virus variant has been detected in P.
poliocephalus and P. scapulatus tissues (Veterinary
Practitioners Board of New South Wales 2021). All sites were previously
documented as having continuous occupation by at least one species of
flying-fox (National Flying-Fox Monitoring Program 2017). Roosting
surveys were repeated once a month for 13 months (August 2018 - August
2019).
Methodological details are described in Lunn et al. (2021).
Briefly, we mapped the spatial arrangement of all overstory, canopy and
midstory trees in a grid network of 10 stratified random subplots (20 x
20 meters each) using an ultrasound distance instrument (Vertex
Hypsometer, Haglöf Sweden). Trees were mapped and tagged using tree
survey methods described in the “Ausplots Forest Monitoring Network,
Large Tree Survey Protocol” (Wood et al. 2015). This approach
allowed for precise spatial mapping of trees, with locations of trees
within subplots accurate to 10-30 cm. Tagged trees were revisited
monthly, and the number of bats per tree was visually estimated and
recorded per species using a quasi-logarithmic index: 0: no bats, 1: 1-5
bats, 2: 6-10 bats, 3: 11-20 bats, 4: 21-50 bats, 5: 51-100 bats,
6:101-199 bats and 7: 200+ bats. In total 2,522 trees were mapped across
the eight sites. For a subset of trees (60 per site, consistent through
time) absolute counts, minimum roosting height, and maximum roosting
height of each species were recorded. The roost perimeter boundary
(defined as the outermost perimeter delimitating occupied space, as per
Clancy and Einoder (2004)) was mapped with GPS (accurate to 10 meters)
immediately after the tree survey by walking directly underneath
roosting flying-foxes. This track
was used to calculate perimeter length and occupied roost area (QGIS
3.1). Total abundance at each roost was estimated with a census count of
bats where feasible (i.e. where total abundance was predicted to be
<5,000 individuals), or by counting bats as they emerge in the
evening from their roosts (“fly-out”), as per Westcott et al.(2011). If these counts could not be conducted, population counts from
local councils (conducted within ~a week of the bat
surveys) were used, as total abundance of roosts are generally stable
over short timeframes (Nelson 1965). Because roost estimates become more
unreliable with increasing abundance, we converted the total estimated
abundance into an index estimate, as per values used by the National
Flying-Fox Monitoring Program (2017). Index categories were as follows:
1: 1-499 bats; 2: 500-2,499 bats; 3: 2,500-4,999 bats; 4: 5,000-9,999
bats; 5: 10,000-15,999 bats; 6: 16,000-49,999 bats; and 7: 50,000+ bats.
All observations were made from a distance to minimise potential
disturbance to bats during the survey. In general, bats showed minimal
response to the
observers
during the surveys, providing observers remained quiet, did not move
quickly, and kept an appropriate distance, consistent with other studies
on flying-foxes (Markus & Blackshaw 2002; Klose et al. 2009).