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 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 (Northing ),
elevation (DEM ), number of days of frost annually
(Daysfrost ), number of days with an average
temperature below freezing annually
(Daysfreezing ), and number of days outside of the
growing season annually (Daysgrow ). 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 km2 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 (Northing ) and/or elevation (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 (<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 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 glmmfieldspackage (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.