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.