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\begin{document}

\title{What is winter? Modelling spatial variation in bat host traits and
hibernation and their implications for overwintering energetics}



\author[1]{C. Hranac}%
\author[2]{Catherine Haase}%
\author[3]{Nathan Fuller}%
\author[4]{Meredith McClure}%
\author[1]{Jonathan Marshall}%
\author[5]{Cori Lausen}%
\author[6]{Liam McGuire}%
\author[7]{Sarah Olson}%
\author[1]{David Hayman}%
\affil[1]{Massey University}%
\affil[2]{Montana State University System}%
\affil[3]{Texas Tech University}%
\affil[4]{Conservation Science Partners}%
\affil[5]{Wildlife Conservation Society Canada}%
\affil[6]{University of Waterloo}%
\affil[7]{Wildlife Conservation Society}%


\vspace{-1em}



  
  \date{May 27, 2024}


\begingroup
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\selectlanguage{english}
\begin{abstract}
White-nose syndrome (WNS) has decimated hibernating bat populations
across eastern and central North America for over a decade. Disease
severity is driven by the interaction between bat characteristics, the
cold-loving fungal agent, and the hibernation environment. While we
further improve hibernation energetics models, we have yet to examine
how spatial heterogeneity in host traits is linked to survival in this
disease system. Here we develop predictive spatial models of body mass
for the little brown myotis (Myotis lucifugus) and reassess previous
definitions of the duration of hibernation of this species. Using data
from published literature, public databases, local experts, and our own
fieldwork, we fit a series of generalized linear models with
hypothesized abiotic drivers to create distribution-wide predictions of
pre-hibernation body fat and hibernation duration. Our results provide
improved estimations of hibernation duration and identify a scaling
relationship between body mass and body fat; this relationship allows
for the first continuous estimates of pre-hibernation body mass and fat
across the species' distribution. We used these results to inform a
hibernation energetic model to create spatially-varying fat use
estimates for M. lucifugus. These results predict that WNS mortality of
newly and soon-to-be infected M. lucifugus populations in western North
America may be comparable to the substantial die-off observed in eastern
and central populations.%
\end{abstract}%



\sloppy


\textbf{What is winter? Modelling spatial variation in bat host traits
and hibernation and their implications for overwintering energetics}

C. Reed Hranac\selectlanguage{ngerman}\textsuperscript{1¥}, Catherine G.
Haase\textsuperscript{2+}, Nathan W. Fuller\textsuperscript{3\$},
Meredith L. McClure\textsuperscript{4}, Jonathan C.
Marshall\textsuperscript{5}, Cori L. Lausen\textsuperscript{6}, Liam P.
McGuire\textsuperscript{3\^{}}, Sarah H. Olson\textsuperscript{7}, David
T. S. Hayman\textsuperscript{1}

\textsuperscript{1} Molecular Epidemiology and Public Health Laboratory,
Hopkirk Research Institute, Massey University, Palmerston North, New
Zealand

\textsuperscript{2} Department of Microbiology and Immunology, Montana
State University, Bozeman, USA.

\textsuperscript{3} Department of Biological Sciences, Texas Tech
University, Lubbock, USA

\textsuperscript{4} Conservation Science Partners, Truckee, USA

\textsuperscript{5} Institute of Fundamental Sciences, Massey
University, Palmerston North, New Zealand

\textsuperscript{6} Wildlife Conservation Society Canada, Toronto,
Canada

\textsuperscript{7} Wildlife Conservation Society, Health Program,
Bronx, USA

*\emph{Corresponding author:}crh244@gmail.com

\textsuperscript{¥}Current affiliation: Colorado Department of Public
Health and Environment, Healthcare Associated Infections and
Antimicrobial Resistance Program, Denver, USA

\textsuperscript{+}Current affiliation: Department of Biology, Austin
Peay State University, Clarksville, USA

\textsuperscript{\$}Current affiliation: Texas Parks and Wildlife
Department, Nongame and Rare Species Program, Austin, USA

Waterloo, Ontario, Canada

\textbf{Abstract}

White-nose syndrome (WNS) has decimated hibernating bat populations
across eastern and central North America for over a decade. Disease
severity is driven by the interaction between bat characteristics, the
cold-loving fungal agent, and the hibernation environment. While we
further improve hibernation energetics models, we have yet to examine
how spatial heterogeneity in host traits is linked to survival in this
disease system. Here we develop predictive spatial models of body mass
for the little brown myotis (\emph{Myotis lucifugus} ) and reassess
previous definitions of the duration of hibernation of this species.
Using data from published literature, public databases, local experts,
and our own fieldwork, we fit a series of generalized linear models with
hypothesized abiotic drivers to create distribution-wide predictions of
pre-hibernation body fat and hibernation duration. Our results provide
improved estimations of hibernation duration and identify a scaling
relationship between body mass and body fat; this relationship allows
for the first continuous estimates of pre-hibernation body mass and fat
across the species' distribution. We used these results to inform a
hibernation energetic model to create spatially-varying fat use
estimates for \emph{M. lucifugus.} These results predict that WNS
mortality of newly and soon-to-be infected \emph{M.
lucifugus}populations in western North America may be comparable to the
substantial die-off observed in eastern and central populations.

\textbf{Keywords}

Hibernation energetics, \emph{Myotis lucifugus} , \emph{Pseudogymnoascus
destructans,} white-nose syndrome, winter duration

\textbf{INTRODUCTION}

In temperate zones of North America, hibernating animals,
including\emph{Myotis lucifugus} (little brown myotis), bridge resource
poor winters through energetic budgeting and behavioural changes (Hock
1951, Wang 1978, Speakman and Rowland 1999, Ruf and Geiser 2015).
Survival over winter hibernation depends upon three main facets: 1) the
amount of energy stored, primarily in body fat, 2) energetic expenditure
(rate of metabolic consumption), and 3) the duration of hibernation
(Humphries et al. 2002). Hibernation is composed of bouts of torpor,
during which body temperature drops to near ambient temperature to limit
heat loss and results in reduced metabolism to restrict the consumption
of finite metabolic resources. Torpor is periodically interrupted by
energy intensive periods of arousal during which hibernators return to
euthermic body temperature (Hayman et al. 2010). Hibernators arouse for
a variety of proposed reasons (for a review see Carey {[}2019{]} and
citations within), including the need to eliminate metabolic waste,
regain water balance, or mate. While arousals represent a small fraction
of the total time spent in hibernation, they account for the majority of
energy consumed, with a single arousal costing as much as 5\% of total
overwinter energetic costs (Thomas et al. 1990).

Microclimate selection is critical for hibernators (Boyles et al. 2007).
By allowing body temperature to drop during torpor, \emph{M.
lucifugus}consumes roughly 80-fold less energy per unit time due to the
relationship between metabolic rate and temperature (Hock 1951, Speakman
and Thomas 2003). To maximize the utility of these metabolic reductions,
bats seek out caves, mines, scree slopes, or other locations generally
referred to as ''hibernacula'' where they can overwinter (Speakman and
Thomas 2003). Relative to the surface landscape, subterranean locations
can provide suitable low temperature (i.e., 0 --10 \selectlanguage{english}@C) habitats for
hibernators (Thomas and Cloutier 1992). Microclimate selection will vary
greatly based on species-specific preferences (Haase et al. 2021), and
roost selection within the larger hibernaculum critically affects both
the frequency of arousals and efficiency of torpor (Humphries et al.
2002, Czenze et al. 2013, Haase et al. 2019). Species such as \emph{M.
lucifugus} appear to choose roost locations with stable, nearly
saturated environments and low temperatures to ameliorate their
relatively high rates of evaporative water loss, while other bat species
are capable of using more arid, and less thermally-stable, roosts as
hibernacula (Kl\selectlanguage{ngerman}üg-Baerwald and Brigham 2017, Klüg-Baerwald et al. 2017).
Even so, within a cave or mine system, roost conditions may not remain
stationary throughout the duration of hibernation and some bats will
relocate within the hibernaculum to seek specific microclimate
conditions as their body condition changes (Hayman et al. 2010).

The duration of winter hibernation is another critical determinant to
the survival of hibernators. The stimuli that drive immergence
(entrance) to and emergence (exit) from hibernation, and their
geographic variation, are under-described (Norquay and Willis in press,
Lane et al. 2012, Czenze et al. 2013). The duration of winter
hibernation presents a strong selective pressure, as longer winters
result in shorter growing seasons and less time available for
pre-hibernation fattening (Kunz et al. 1998). While animals that
hibernate at more southern latitudes may be able to capitalize on breaks
in the winter weather to opportunistically feed (Thomas et al. 1990),
this is not always an option for other latitudes. Entrances to
hibernacula may be blocked by snow, preventing foraging even if breaks
in the weather did allow for the re-emergence of prey species
(CLL,\emph{unpublished data} ). Because North American hibernating bats
feed on insects, researchers have estimated effective hibernation
duration based upon the number of freezing days, with the assumption
that freezing temperatures prevent insect availability until spring
(Humphries et al. 2002, Hayman et al. 2016). However, some populations
of bats may emerge from hibernation while freezing temperatures are
still present, suggesting that there may be more complex determinants of
emergence times (Johnson et al. 2017). Additionally, site-level
differences, such as slope aspect, foliage cover, and proximity to water
may influence the density of prey insects and their ability to persist
on the landscape.

Beyond the normal challenges of hibernation, the epizootic white-nose
syndrome (WNS), caused by the psychrophilic fungus\emph{Pseudogymnoascus
destructans} , has increased energetic demands for hibernating bats
(Blehert et al. 2009). The fungal pathogen responsible for the disease
has spread rapidly through North America since 2006 and has killed
millions of hibernating bats (Frick et al. 2015). Bats can be exposed to
the fungus during the swarming period or over hibernation in the
hibernacula. Once infected, the fungus grows during hibernation when bat
skin temperatures are reduced and immune function is suppressed (Verant
et al. 2012, Langwig et al. 2015, 2016). While there is still discuss
the ultimate cause of mortality in WNS-impacted bats, it has been linked
to the increased frequency of arousals in infected bats, ultimately
resulting in the depletion of fat stores prior to the end of the
hibernation period and subsequent starvation (Warnecke et al. 2012,
Lilley et al. 2016).

There has been much research on energy consumption over hibernation in
multiple bat species (Thomas et al. 1990, Cryan and Wolf 2003, Willis et
al. 2006, Jonasson and Willis 2012, McGuire et al. 2014, Haase et al.
2019) and across the distribution of single bat species (Humphries et
al. 2002, Hayman et al. 2016), but we have yet to determine how the
spatial variation in the other two critical parameters governs
overwinter survival for hibernators: duration of winter hibernation and
amount of fat stores taken into hibernation. Previous models (Hayman et
al. 2016) allowed for spatial variation in winter duration; however, the
definition of winter duration was made \emph{a priori} and based solely
upon the number of nights with an average temperature below 0°C
(Humphries et al. 2002). Similarly, the amount of body fat has generally
been fixed as 25-30 \% of total body mass in most studies (Humphries et
al. 2002, Hayman et al. 2016, Haase et al. 2021). Fat resources are a
major determinant of survival (Haase et al. 2019) and thus this
assumption of proportion of body fat warrants review. Here we used
generalized linear and linear models to: 1) estimate hibernation
duration, 2) relate body mass to pre-hibernation fat stores, and 3)
predict pre-hibernation body mass and fat across the distribution
of\emph{M. lucifugus} . We focused on \emph{M. lucifugus} due to the
high impact of WNS on \emph{M. lucifugus} populations, its widespread
distribution, and the availability of published data. We predicted that
spatial variation in overwinter duration would drive variation of body
mass and fat to account for different energy requirements leading to
spatial variation in WNS disease outcomes. Finally, we used a
mechanistic model of hibernation energetics (Haase et al. 2019) to
estimate the total metabolic costs of hibernation with and without the
impacts of WNS across the species' distribution of \emph{M. lucifugus} .

\textbf{METHODS}

\textbf{Hibernation duration data}

We compiled hibernation duration data from literature, publicly
available datasets, and our own field data. We also solicited data-based
estimates of hibernation duration from local bat researchers across
North America where few records were available from other sources (Table
S1, Figure S1). We restricted the study region for this analysis to
temperate North America (above the Tropic of Cancer and below the Arctic
Circle), although the published range of \emph{M. lucifugus} extends
into the Arctic (Fenton and Barclay 1980). Spatially explicit records of
immergence and emergence collected from the literature generally
reported the average day of entrance or emergence, although some data
were presented only as the duration of hibernation. Where sex-specific
dates were given for a location, dates were averaged as insufficient
data existed to complete a sex-specific analysis.

Acoustic bat recorders (Songmeter SM2+BAT; Wildlife Acoustics, MA, USA)
were deployed by Wildlife Conservation Society Canada (WCS-C) to record
bat activity across western Canada between 2008 and 2016. Microphones
(either SMX-US or SMX-U1) were placed on 12-18-foot-tall telescoping
poles above likely hibernation or commuting areas (e.g. riverbanks,
cliff ridge tops) starting as early as mid-August. Acoustic activity was
typically recorded throughout the duration of the winter and data were
retrieved between mid-March and mid-May. Recordings were manually
analysed using AnalookW software (Titley Scientific, Inc.) and
customized noise-filters were used to pull files containing bat pulses.
The occurrence of at least 2 bat echolocation pulses in a file was
required to identify the recording as a `bat pass', and the number of
passes were summed nightly. The start of the hibernation period was
defined by the last 3-night window between August 15 and December 31, in
which \selectlanguage{english}[?]10 passes were identified, while the end of the hibernation
period was defined by the first 3-night window between March 1 and May
15 in which \selectlanguage{english}[?]10 passes were recorded (Lausen and Barclay 2006). In
locations where bat activity was consistently low throughout the year
(spring and fall nightly activity often failing to exceed 10 passes),
hibernation start and end points were defined by date of the last and
first bat recordings, respectively. For sites with multiple years of
data, we took the mean immergence and emergence dates.

\textbf{Pre-hibernation fat and body mass data}

The data required to directly assess the spatial variation in body fat
for \emph{M. lucifugus} prior to hibernation do not exist, so we relied
upon scaling fat mass with spatially-varying body mass. We used body
composition datasets obtained by quantitative magnetic resonance (QMR;
McGuire and Guglielmo 2010) measurements that provided both
pre-hibernation fat mass and body mass information from multiple\emph{M.
lucifugus} populations, including New York, Vermont (McGuire et al.
2018) and Montana (Haase et al. 2019). We tested for differences in fat
among locations using a linear model with fat as a response variable.
Given that there was no significant difference among locations, we then
fit a linear model with fat as the response and body mass as the
predictor variable to predict fat mass from body mass (French 1985).
This fitted relationship then allowed us to predict fat mass at
locations where we only had body mass measurements. We gathered
additional body mass data from the literature and VertNet (vertnet.org),
in which records were filtered to include only those with geographic
location, body mass, and recorded between September and December (Table
S2, Figure S1).

\textbf{Prediction of spatially-varying hibernation duration and fat
mass}

Rather than photoperiod-based metrics, we used the availability of food
resources to predict the onset of hibernation, including climatic
variables due to the correlation between ambient temperature and insect
activity (Mellanby 1939). The first (herein \emph{Original} model)
definition of hibernation duration (Humphries et al. 2002) was the
number of days per year where mean nightly temperature from 12 a.m. to 6
a.m. was below freezing. The alternative spatial covariate layers we
assumed to be related to the duration of winter were: degrees latitude
North (\emph{Northing} ), elevation (\emph{DEM} ), number of days of
frost annually (\emph{Days\textsubscript{frost}} ), number of days with
an average temperature below freezing annually
(\emph{Days\textsubscript{freezing}} ), and number of days outside of
the growing season annually (\emph{Days\textsubscript{grow}} ). Climate
data were generated with the ClimateNA v5.10 software package based on
methodology described by Wang et al. (2016). All spatial data were
re-projected to the same 1 km\textsuperscript{2} resolution, cropped,
and masked to the study extent (Frick and Hijmans 2017).

All covariates were regressed against the estimated duration of
hibernation in univariate models and in multivariate models adjusting
for latitude (\emph{Northing} ) and/or elevation (\emph{DEM).} Models
were assessed through a two-step process: initial linear models were
cross-validated using Holm's method (Holm 1979) to identify outliers and
generalized linear models were then fit to the modified data set. From
initial model fits, externally studentized residuals were converted to
p-values and adjusted for multiple testing using Holm's method.
Observations with adjusted p-values (\textless{}0.5) across multiple
models were excluded, and subsequent models refitted using reduced data.
Generalized linear models were then fit with the modified data set and
model selection was assessed by Akaike information criterion (AIC;
(Burnham and Anderson 2002).

To predict hibernation duration over the study region using the best
model selected by AIC, we first assessed model residuals for spatial
auto-correlation using Moran's I from the \emph{spdep} R package (Bivand
and Wong 2018). When no autocorrelation was identified, the top model by
AIC was predicted across the study extent using the spatial layers to
create a continuous estimate of hibernation duration across the species'
distribution. If autocorrelation was detected, a spatially-weighted
generalized linear model was generated using the
\emph{glmmfields}package (Anderson and Ward 2019) for the top model by
AIC and then hibernation duration was projected across the species'
distribution.

Since these proposed spatial covariates defined the annual inactive
period, we also assume that they were likely to drive spatial variation
in body mass as bats would need increased metabolic resources to survive
longer durations of hibernation. We repeated the above model fitting and
selection methods of the same independent variables against the response
variable of pre-hibernation body mass across all data collection
locations. We then assessed the top model for spatial autocorrelation
and predicted body mass across the species' distribution. Finally, we
predicted spatially-varying pre-hibernation fat mass across the species'
distribution using the scaling equation fit above.

\textbf{Prediction of spatially-varying hibernation survival}

We used a mechanistic hibernation energetics model to estimate the total
cost of hibernation (in grams of fat) for a hibernating \emph{M.
lucifugus} across its distribution (see Haase et al. (2019) for complete
model documentation). The model is dynamic and species-specific, using
metabolic and morphometric parameters to estimate the amount of fat used
during hibernation. We used published parameter values for \emph{M.
lucifugus} (Haase et al. 2019) with the exception of arousal duration,
which was set to 2.2 h (CLL, \emph{unpublished data} ).

These energetic functions are dependent on temperature and relative
humidity of the roost to provide estimates of energy expenditure across
a wide range of potential conditions. The temperature and humidity
dependent growth of \emph{P. destructans} can be included in the model
to estimate the metabolic impact of infection on energy consumption as
the fungal load increases. We modelled the total energetic costs of
hibernation with and without the impacts of \emph{P. destructans} across
two hibernaculum microclimate scenarios. First, we used fixed
microclimate conditions that assumed a bat could access the preferred
optimal hibernaculum microclimate conditions across the species'
distribution. We used conditions of 4degC and 98\% relative humidity based
on observations reported in the literature (Table S3). These
microclimatic conditions are thought to provide for the longest possible
hibernation duration, a hypothesis supported by recent findings (Haase
et al. 2019). Second, we used a spatially-explicit model of subterranean
temperature conditions to predict the best available (i.e., closest to
optimal) temperature at a given location. This approach assumes that
bats will select roosts within hibernacula that offer their preferred
temperature when possible but will likely tolerate warmer or cooler
temperatures when necessary, especially at the range margins.
Unfortunately, the not much information exists for relative humidity;
therefore, we used the optimal 98\% relative humidity for both the
optimal and best available temperature scenarios.

To estimate the closest available temperature to the optimal temperature
at any given location, we used a spatially explicit model of
subterranean winter temperatures (McClure et al. 2020). This model
estimates subterranean winter temperature should a potential
hibernaculum exist based on mean annual surface temperature, site type
(cave or mine), distance from the site entrance, and several less
influential predictors representing topography, land cover, and presence
of water. The model predicts an increase in subterranean temperature
with increasing mean annual surface temperature and distance from the
site entrance and higher temperatures in mines than in caves. For each 1
km\textsuperscript{2} cell we estimated minimum and maximum roosting
temperatures likely to be present within a hibernaculum using methods
described in McClure et al. 2020. We then assigned each raster cell the
best available temperature; either the preferred temperature if that
temperature was predicted to be available given the minimum and maximum
temperature estimations, or the closest temperature available to the
preferred roost temperature.

Finally, we estimated the amount of fat required to survive hibernation
for each of our 1 km\textsuperscript{2} cells for both healthy and
WNS-impacted bats by using the dynamic hibernation energetics model and
our spatially-varying predictions of hibernation duration and fat. We
determined if an average bat could survive hibernation for each cell by
subtracting the predicted fat required to survive the hibernation
duration from the fat available prior to hibernation. Positive values
indicate a bat's ability to survive hibernation with excess fat, while
negative values indicate the depletion of fat stores prior to the end of
the hibernation period. We compared the predicted amount of fat required
by healthy bats against the fat required by infected bats to estimate
the relative increase of energetic costs of \emph{P. destructans}
on\emph{M. lucifugus} as a percentage (the difference between resources
required to survive hibernation when infected and when healthy in grams
of fat, divided by grams of fat required to survive hibernation as
healthy bat, multiplied by 100)\emph{.} We also translated the amount of
fat ``leftover'' after the conclusion of hibernation into days post
hibernation, i.e., how long the bat could continue hibernating, for both
healthy and infected bats.

All analyses were performed in R (R Development Core Team 2009), with
spatial handling tools from \emph{raster} (Hijmans 2016) and
\emph{sp}packages (Pebesma and Bivand 2005).

\textbf{RESULTS}

\textbf{Hibernation duration}

Latitude (\selectlanguage{greek}\emph{Northing; β = -}\selectlanguage{english} 0.22\emph{, p-value =} 0.85), elevation
(\selectlanguage{greek}\emph{DEM; β =}\selectlanguage{english} -0.03\emph{, p-value =} 0.04), and the number of days
in frost (\selectlanguage{greek}\emph{Days\textsubscript{frost}; β =}\selectlanguage{english} 0.83\emph{,
p-value}\textless{} 0.001) best predicted hibernation duration across
the study area (\emph{AICc} = 489.29; Table S4). There was no spatial
correlation of these predictions (\emph{Moran's I} = -0.0036,
\emph{p-value =}0.354) and thus no spatial corrections were needed. The
selected model outperformed the original \emph{a priori} estimate of the
duration of winter (\emph{Original,} [?]AIC 19.06).

Given the best model, median predicted hibernation duration was
\textasciitilde{} 179 days (\emph{mean} = 169.16, \emph{sd =} 45.36).
Maximum hibernation duration across the study extent was estimated at
\textasciitilde{}289 days in the upper portions of Manitoba, Ontario,
and Quebec, 45 days longer than the longest observation in the training
data (from Manitoba, Canada, 19; Figure 2). Despite this, 95\% of all
cells had a predicted hibernation duration below 225 days, and only 5\%
were below 80 days (Table S5).

\textbf{Body mass}

Pre-hibernation fat stores were strongly related to body mass (\selectlanguage{greek}\emph{β}\selectlanguage{english}=
0.597, \emph{F\textsubscript{1,171}} = 826.7, \emph{p} =
\textless{}0.001, adjusted R\textsuperscript{2} = 0.8276; Figure 2).
Latitude (\selectlanguage{greek}\emph{Northing; β =}\selectlanguage{english} -0.08\emph{, p-value =} 0.07) and the
number of days below freezing (\selectlanguage{greek}\emph{Days\textsubscript{freeze}; β
=}\selectlanguage{english}0.04\emph{, p-value} \textless{} 0.001) best predicted fat mass across
the species' distribution (\emph{AICc} = 162.57; Table S4). However, the
model including latitude, number of annual days below freezing, and
elevation performed similarly (\selectlanguage{greek}\emph{ΔAICc}\selectlanguage{english} \textless{} 2; Table S4).

Given the best model, the median predicted pre-hibernation body mass
across the species' distribution of \emph{M. lucifugus} was 8.65 g
(\emph{mean} = 9.14 g, \emph{sd =} 1.84 g) and 95\% of the cells
predicted values between 7.04 g and12.52 g. Median pre-hibernation fat
stores were predicted at 2.32g (\emph{mean} = 2.61 g, \emph{sd =} 1.10
g) with 95\% of cells predicting available fat available ranging between
1.36 g and 4.63 g.

\textbf{Overwinter hibernation survival}

Overall, our energetic model predicted nearly ubiquitous survival of
uninfected bats throughout the range of \emph{M. lucifugus} with
\textless{} 0.0001\% of cells falling below the threshold for
survival\emph{.} Our results found that 95\% of all uninfected bats
roosting at \(4\)@\selectlanguage{english}C and 98\% relative humidity during
hibernation would only require 0.21 g--0.60 g of fat to survive the
duration of hibernation (\emph{median} = 0.48 g, \emph{mean} = 0.45 g,
\emph{sd} = 0.12 g, Figure S2). When considering the amount of fat bats
had pre-hibernation, the median bat emerged with 1.85 g of body fat
remaining (\emph{mean} = 2.16 g, \emph{sd} = 1.01 g) and the heaviest
95\textsuperscript{th} percentile of bats had up to 4.05 g of fat
remaining. Considering these residual fat values in the terms of days
spent in hibernation, the median bat would have sufficient fat resources
to survive an additional 181 days (\emph{mean} = 190.83 days, \emph{sd}=
45.35 days) and those bats with \textless{} 4 g of fat remaining could
be capable of surviving another 280 days in those optimal roosting
conditions.

When \emph{P. destructans} infection was included into the optimal
roosting conditions, the median value of fat required to survive
hibernation was increased by 0.7 g to 1.21 g (\emph{mean} = 1.16
g,\emph{sd} = 0.45) and the residual fat values dropped to a median of
1.22 g (\emph{mean} = 1.45 g, \emph{sd} = 0.76). In total, 95\% of bats
were predicted to emerge with between 0.61 g and 2.93 g of fat remaining
after the hibernation. Translating the fat values into days, the median
value was reduced \textasciitilde{} 135 days to 45.63 days (\emph{mean}=
55.41 days, \emph{sd} = 45.35 days). Mortality of bats prior to the end
of the hibernation period was predicted in 4.82 \% of the cells where
the survival of hibernating bats fell \textless{} 0, visible in the
northeastern provinces of Canada (Figure S2).

Most of the predicted best available subterranean hibernacula were
expected to have available temperatures at or above 4\selectlanguage{ngerman}°C. Despite this,
32.64\% of cells fell below that temperature and 6.44\% of cells fell
below the lower critical temperature of 2°C that \emph{M.
lucifugus}defends during hibernation (Figure S3). Despite these lower
than optimal temperatures, \emph{M. lucifugus} was predicted to survive
across most of its distribution, with only 0.5\% of cells predicted to
fall below the survival threshold---primarily around Denali National
Park in Alaska. Median fat required to survive hibernation as an
uninfected bat dropped 0.71 g to 1.11 g (\emph{mean} = 1.41 g, \emph{sd}
= 0.93) with a nearly identical 95\% interior range. When including
infection with\emph{P. destructans,} the hibernation energetics model
predicted the median fat required for hibernation increased 0.72 g to
1.21g, (\emph{mean} = 1.20 g, \emph{sd} = 0.40g). Like optimal roosting
conditions, infection resulted in 4.74\% of cells falling below the
survival threshold.

While neither of the considered hibernation conditions predict large
areas to result in mortality, the increased percent of fat needed to
hibernate with \emph{P. destructans} highlights the metabolic
consequences of infection (Figure S4). At \(4\)\selectlanguage{english}@C and 98\%
relative humidity, bats were predicted to expend a median of 154\% more
body fat resources to hibernate while infected for the same winter
duration (Table S4). Overall, 95\% of infected bats are predicted to
increase their metabolic expenditure between\textasciitilde{}66\% and
195\% compared to their healthy counterparts. Hibernating at the
predicted best available temperature suggested similar increases in the
energy expended; however, the geographic distribution of where the
greatest increases occurred were different than those observed under
static preferred conditions.

\textbf{DISCUSSION}

Here we examined the spatial variation in hibernation duration and
estimated pre-hibernation fat stores across North America and applied
these estimates to an updated model of hibernation energetics (Haase et
al. 2019) to estimate the overwinter fat necessary for \emph{M.
lucifugus} to survive the hibernation. By comparing the required fat and
the fat available, we predicted survival of \emph{M. lucifugus} across
its distribution for two different ecological situations: one in which
bats roost within their most preferred conditions and one in which they
roost in the best conditions predicted to be available. Finally, we
modelled the possible impact of \emph{P. destructans} infection to
understand the implications for \emph{M. lucifugus} populations where
bats have yet to be impacted by WNS.

Winter hibernation duration is a key determinant of the overwintering
survival for any hibernating species. While local variation in winter
onset due to unique landscape features may create refugia where bats may
persist later than or emerge from hibernation earlier than average, the
lack of any previous broad-scale estimates for this critical variable
highlights the need for this study. Prior work (Humphries et al. 2002,
Hayman et al. 2016) had defined the hibernation period \emph{a priori}as
the yearly number of nights with a mean nightly temperature below
freezing. Our results suggest that substantial improvements in the
estimation of hibernation duration can be made by including elevation,
latitude, and the number of days with frost. The number of days of
frost, rather than the number of days below freezing, and the
counter-intuitive negative coefficients for both \emph{Northing} (-0.45)
and \emph{DEM} (-0.04) in the model suggest that there is more nuance to
the relationship between bats and low temperatures than currently
understood. Our model is potentially biased in part by the
over-representation of Canadian data, low elevation sites, and the
collinearity of elevation and latitude with other explanatory variables.
Notably, however, when included in univariate models, the coefficient
signs regress as expected with the coefficients increasing with latitude
and elevation; yet the univariate models do not predict hibernation
duration as well and had higher AIC scores. Because we were interested
in prediction, we kept the best model by AIC; however, clearly more work
is required to understand what predicts overwinter duration in bats.
Also, there were few estimates of hibernation duration from the
western-most US states and the more southern latitudes within the
species' distribution. These factors likely impacted model results in
unpredictable ways and highlights the need for additional data
collection.

Species such as \emph{M. lucifugus} may not hibernate across their
broadest summer distribution, but likely seek out locations with more
favourable conditions to overwinter. The maximum winter hibernation
duration predicted within the distribution of \emph{M. lucifugus} was a
month and a half longer than the longest observation within our dataset,
and this did not consider the portion of the species' distribution that
extended into the Arctic Circle. In all probability, bats likely do not
overwinter within these regions for multiple reasons. First, while our
survival models predict that an uninfected bat could survive the longest
predicted winter hibernation, the necessary roosting microclimate
conditions may not exist on the landscape (Perry 2013, McClure et al.
2020). A series of complex interactions between surface features
(\emph{e.g.,} slope, aspect, elevation, suitable crevices) or cave
features (\emph{e.g.,} number of entrances, air flow, depth) ultimately
define when and where suitable hibernacula conditions exist (Perry 2013,
McClure et al. 2020). These site level determinants of microclimate
conditions make it difficult to define a relationship between
landscape-level features and the available subterranean conditions and
create challenges in attempting to predict where suitable hibernacula
conditions exist (McClure et al. 2020). Despite this, our use of
modelled subterranean temperatures offers an improvement over assuming
either static optimal conditions or mean annual surface temperature used
in Hayman \emph{et al.} 2016. Second, and perhaps more importantly,
regions where extended winters reduce the summer active period to
\textless{}100 days likely create significant challenges to reproductive
success. With a gestation period of \textasciitilde{}60 days (O'Farrrell
and Studier 1973, Kurta et al. 1989), a female bat would be hard pressed
to gestate, nurse, and wean young, while still allowing the young of the
year time to fatten sufficiently to survive such an extended hibernation
period. These results highlight the fact that only a subset of summer
distributions may be suitable for overwinter survival, an idea rarely
considered in the definition of bat species' distributions.

Localized clines in body size and body mass of \emph{M. lucifugus} have
previously been recorded (Lausen et al. 2008, Lacki et al. 2015). When
we compare more detailed metrics of body composition (lean mass and body
fat content), however, these clines are better understood: the lean mass
of bats generally stays consistent, while the difference in body mass is
due to increases in fat. Our model selection suggests that variation in
the duration of winter hibernation may in part drive variation in both
body mass and fat stores across the range of the species. The
relationships between mass (and thus fat) and latitude and days below
freezing also suggest stronger selection pressure for heavier bats in
more extreme conditions. While still useful, the relationship between
the selected abiotic variables and body mass of bats showed strong
spatial autocorrelations among residuals, and there may be additional
continental-scale drivers or local determinants not investigated in this
study.

The scaling relationship identified between pre-hibernation fat stores
and body mass is a departure from the fixed 30\% value used in previous
energetic modelling studies (Humphries et al. 2002, Hayman et al. 2016)
and is supported by contemporary findings (Cheng et al. 2019). More
localized body mass--body fat relationships may exist, yet without
increased data resolution drivers of the true relationship will remain
difficult to assess. Here we assumed bats did not forage during
hibernation, but some bats (primarily from southern hibernacula) have
been known to forage over winter (Bernard and McCracken 2017). Without
data, we were required to assume bats relied exclusively on
pre-hibernation fat stores.

For our modelled roost conditions, virtually all uninfected \emph{M.
lucifugus} could survive the estimated duration of winter. Observed
rates of survival among uninfected overwintering bats is high (Boyles
and Brack 2009) and bats are likely capable of overwintering across most
of their summer distribution where suitable hibernacula exist. These
results are an improvement over previous models which did not predict
survival where hibernation duration \textgreater{} 6 months (Hayman et
al. 2016) despite our prediction that some 51\% of the study extent may
experience winters longer than that. In previous models, roosting
microclimatic space was derived exclusively from surface metrics (i.e.,
mean annual surface temperature and relative humidity). Our use of a
static, optimal roosting scenario served as a baseline for a best
available temperature scenario and provided a more biologically relevant
conditions for \emph{M. lucifugus,} as bats are known to preferentially
roost in these conditions when available (Thomas and Cloutier 1992,
Haase et al. 2019). In areas where WNS has devastated hibernating
colonies of \emph{M. lucifugus} , available microclimates are often
warmer with temperatures reaching 10\selectlanguage{ngerman}\textsuperscript{°}C (Perry 2013).
This warmer microclimate has a significant impact on energy expenditure
during hibernation (Figure S4). Despite this, our predictions for
overwinter survival using estimates of the best roosting temperatures
available suggest that survival may still be possible, if bats use the
coldest areas within the cave or mine system. In a rare ray of hope, all
of the hibernation temperatures that we recorded in the West were well
below the 10\textsuperscript{°}C mark, with hibernating \emph{M.
lucifugus} in northeastern Alberta and Northwest Territories roosting at
about 2\selectlanguage{english}@C and 100\% relative humidity (CLL, \emph{unpublished data} ).
While the high relative humidity is generally beneficial to the growth
of \emph{P. destructans} (and thereby a promoter of WNS pathology), the
cooler temperatures may slow fungal growth in comparison to the warmer
roosts of the Eastern United States.

Our model predicted uninfected bats to emerge from hibernation with
remaining fat quantities far greater than the amount of fat thought to
be needed to hibernate for the entire duration of winter. Some of this
may be an artifact of our modelling, as we may be missing additional
energetic costs such as flight during the arousal periods or sex-related
differences, and we did not model deviance from the most optimal arousal
patterns that can result from arousals of individuals sharing the
hibernacula (neighbour-initiated arousals; Hayman et al. 2010, Jonasson
and Willis 2012, Turner et al. 2015, Czenze et al. 2017). Alternatively,
remaining fat stores may be retained as a buffer against adverse abiotic
conditions experienced after emergence, especially among females that
undergo pregnancy immediately upon exit from hibernation (Johnson et al.
2017, Czenze et al. 2017) and whose reproductive success stands to
benefit from a longer growing season. Early emergence would provide a
selective advantage to the young of the year, as even one or two extra
weeks foraging on the landscape could increase fat stores, making them
more prepared for hibernation (Reynolds and Kunz in press). Currently,
little is known about the energetic demands of the emergent bats as they
return to the landscape, and accurate parameterization of this factor
could significantly change our definition of survival capacity and
increase our estimates of WNS-related mortality.

Modelled hibernation survival predictions of bats infected with \emph{P.
destructans} at either \(4\)@\selectlanguage{english}C and 98\% relative humidity
or using the best available temperature do not match observations from
the Eastern United States where mass mortality events have occurred due
to WNS (Blehert et al. 2009, Frick et al. 2010, 2015) (23,24,54). While
our analysis did demonstrate infection with \emph{P.
destructans}dramatically increases the amount of energy expended during
hibernation, nearly 95\% of all cells analysed predicted survival
despite infection. Interestingly, however, the areas with the greatest
increase in hibernation energy expenditure using the best available
temperature were much more in line with regions where bat populations
have experienced the greatest mortality.

Irrespective of the absolute values for survival predicted within this
work, our modelling predicts that \emph{M. lucifugus} populations where
WNS is currently absent, especially those along the Rocky Mountains,
Alberta, British Columbia, and Alaska will require similar increases in
energetic expenditure as populations currently impacted by WNS. Thereby,
if the increase in energy expenditure results in the same pattern of
mortality, \emph{M. lucifugus} populations in western North America may
be expected to suffer mortality events similar to those experienced in
the eastern and central populations (Frick et al. 2010, 2015). The long
duration winters, especially in northern British Columbia, northern
Alberta, Alaska, Yukon, Northwest Territories, and portions of the Rocky
Mountains, may result in severe WNS-associated pathology and disruption
to hibernation physiology, although use of cool available hibernacula
microclimates in some of these areas may slow fungal growth (Reeder et
al. 2012, Verant et al. 2014). Identifying and describing roosting
microclimates in these areas will allow for better predictive models at
a regional scale. Some northern hibernacula may provide a refugia
for\emph{M. lucifugus} infected with WNS; however, this cannot be
defined until the availability of microclimates and spring energy
requirements are quantified. For example, if gleaning of arthropod prey
in spring is typically required for successful reproduction in northern
latitude\emph{M. lucifugus} (Talerico 2008, Kaupas and Barclay 2017),
then the extra energy expenditure associated with gleaning (Norberg et
al. 1987) may require additional fat stores and WNS-related mortality
rate may in fact be higher than predicted. Additionally, even if WNS
related mortality is not directly observed, reproductive success may
decline resulting in more long-term population decline.

The outputs of the energetic model that we applied are sensitive to a
number of parameters and assumptions (Haase et al. 2019). The
hibernation energetic model is largely derived from first principles and
deviations in parameters, especially those defining the frequency or
duration of arousal (cluster-based arousal, partial arousals,
disturbances, etc. 8) or increasing these costs (e.g. increased number
of mid-winter flights or disease pathophysiology), have the potential to
alter the amount of resources required to survive hibernation. Roost
microclimates are important to survival predictions and impact bat
energetic and fungal growth dynamics (Marroquin et al. 2017), and
further study is required to understand how relative humidity may vary
across the landscape and within hibernacula.

Overall, this work represents an effort to iteratively refine both
individual and landscape models of bat hibernation physiology and the
impacts of WNS on bat populations. By specifically addressing the
spatial heterogeneity of both abiotic phenomena and host traits, we
offer some of the most detailed predictions for the potential impacts of
WNS on \emph{M. lucifugus} as \emph{P. destructans} continues to spread
through western North America.

\textbf{Ethics Statement}

All procedures were approved by the Texas Tech University Institutional
Animal Care and Use Committee (protocol 16031-05) and permits from the
Montana Department of Fish, Wildlife \& Parks (permits 2016-104,
2017-018, and 2018-008).

\textbf{Funding}

This project has been funded in part with Federal funds from the
Department of Defence Environmental Research and Development Program
(SERDP), under Contract Number W912HQ-16-C-0015 to Wildlife Conservation
Society; U.S. Fish and Wildlife Service grant F17AP00593 to Wildlife
Conservation Society Canada; Alberta Conservation Association grant
030-00-90-272 to Wildlife Conservation Society Canada; Royal Society Te
Aparangi, grant number MAU1701 to DTSH; and funding from Texas Tech
University to LPM.

\textbf{Acknowledgements}

For contributing additional data, we thank: Karen Blejwas (Alaska
Department of Fish and Game), Tom Jung (Yukon Department of
Environment), Joanna Wilson (Northwest Territories Environment and
Natural Resources), Sharon Irwin (Wood Buffalo National Park), and
Wildlife Conservation Society Canada's BatCaver program (analyst Jason
Rae); for assistance in the field, Chuck Priestley, Cory Olson, Dave
Critchley, Dave Hobson, Erin Low, Greg Horne, Heather Gates, Lisa
Wilkinson, Mike Kelly, David Bobbit, Lauri Hanauska-Brown and many
others. Any opinions, findings, and conclusions or recommendations
expressed in this publication are those of the author(s) and do not
necessarily reflect the views of the Government.

\textbf{Data availability}

All data pertaining to the work are available publicly, included as
supplementary materials with this publication or available by request.
All custom code for this project is available at
github.com/cReedHranac/winTor and the energetic model code is available
from github.com/cReedHranac/batwintor.

\textbf{Author Contributions}

CRH, DTSH, LPM, SHO, and CLL conceptualized the study, CGH and NWF
collected field data for the project and LPM and CLL provided additional
data and liaised with external research groups. CRH lead the data
analysis with assistance from CGH, DTSH, and JCM. MLC created the
hibernacula temperature model. All authors provided critical review and
editing to the manuscript.

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\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image1/image1}

\end{center}
\end{figure}

\textbf{Figure 1. Predicted hibernation duration, fat and body mass
for\emph{Myotis lucifugus}.} Top left: Predicted hibernation duration
(days) across temperate North America for \emph{Myotis lucifugus} . Top
right: Linear relationship between body fat and body mass. Each point
represents an individual bat and colours indicate the state of each
record (Montana = red, New York = green, Vermont = blue). Bottom left:
Predicted pre-hibernation body mass of \emph{M. lucifugus} (g) across
the species' distribution. Bottom right: Predicted pre-hibernation fat
resources (g) from the linear relationship between fat mass and body
mass. Numbers define changes in contours.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image2/image2}

\end{center}
\end{figure}

\textbf{Figure 2.} Top row: Predicted survival (days) for healthy (top
left) and infected (top right) \emph{Myotis} \emph{lucifugus}hibernating
at the best available temperatures (\selectlanguage{ngerman}°C) in caves or mines and 98\%
relative humidity. Survival was calculated by subtracting the maximum
days in hibernation that an individual can tolerate based upon
pre-hibernation fat stores from the predicted duration of hibernation.
Positive values (purple) suggest bats will likely survive the duration
of hibernation under those conditions while values below 0 imply that
the fat stores were insufficient for survival. Bottom: Relative increase
(\%) in fat stores used over predicted hibernation duration when
infected with \emph{Pseudogymnoascus destructans} compared with healthy
bats when hibernating at the best available temperature predicted to
occur within caves and mines at 98\% relative humidity.

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