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Fig. S1. Environmental coverage of predictor variables: (a) envelope uncertainty map (EUM) for extrapolating the best snow depth model beyond the parameter space used in model calibration and (b) non-weighted proportional distance map from slopes associated with the calibration sites used in model development across Idaho, USA, 1982–2003. The EUM is a contribution-weighted average of distance maps associated with each model parameter. This method estimates prediction uncertainty by calculating the proportional distance of each grid cell across a study region from the calibration envelope with respect to each covariate in a model, and uses the average of these distance maps, weighted according to the relative contribution of covariates in the model (drop in explained deviance with covariate removed; Platts et  al. 2008). Dormann (2007) recommends that model predictions should not be extrapolated beyond 1/10th of the parameter range; therefore, caution is advised for regions where the EUM >0·1 since this indicates that ≥1 predictors was extrapolated beyond the 1/10th-level (Platts et  al. 2008).

Fig. S2. Annual estimates of total area containing snow conditions that potentially benefit wolverine Gulo gulo winter habitat area (snow depths ≥1 m on February 28) in Idaho, USA from 1982 to 2003.

Fig. S3. Population growth of mule deer in Idaho Department of Fish and Game Game Management Unit 72 from 1982 to 2003 predicted by a Ricker model (Ricker 1954) with an additive affect of snow depth. Population size was estimated from aerial sightability surveys (Unsworth et  al. 1994) and corrected for harvest; harvest data were obtained from IDFG reports available at https://research.idfg.idaho.gov/wildlife/Wildlife%20Technical%20Reports/Forms/Show%20All%20Reports.aspx. Instantaneous rates vary from −¥ to ¥, with 0·0 representing a stable population, and the maximum value (rmax) occurring when a population increases at the maximum possible rate. Graph depicts the ranges of population size and snow depth present during the study.

Fig. S4. Estimated energy costs for mule deer Odocoileus hemionus on February 28 of year in the Idaho, USA from 1982 to 2003. Energy costs (%) are relative to traveling on bare ground based on Parker, Robbins, & Hanley (1984) energy cost model (= [0·71 + 2·6 × ( ρ − 0·2)] × RSD × e [0·019 + 0·016 × (ρ − 0·2)] × RSD), where = relative increase in energy costs for travel in snow (%), ρ = snow density (g cm−3), and RSD = relative sinking depth [(sinking depth brisket height−1) × 100]. We used mean snow density (0·35 g cm−3) for ρ (Parker, Robbins, & Hanley 1984) because snow densities were unavailable. Sinking depth is a function of snow depth, density, and hardness (Parker, Robbins, & Hanley 1984), and the depth an ungulate sinks into snow is the most appropriate measure of ‘effective’ snow depth (Parker, Robbins, & Hanley 1984). However, no such values are published for mule deer in the Columbia River Basin. Following Parker, Robbins, & Hanley (1984), who found that deer sank to the ground during controlled experiments in Oregon and Wyoming (i.e., sinking depth equaled snow depth), we assumed that sinking depth was equal to snow depth (e.g., Turner, Wallace, & Brenkert 1994), and used mean brisket height of mule deer (58 cm; Parker, Robbins, & Hanley 1984) to compute RSD in the corresponding 1-km2 cell. The relative increase in net cost of locomotion therefore increased exponentially as a function of relative sinking depth. Vertical bars are ±SD.

Table S1. Topographic conditions and data summary associated with Snow Course stations used for snow depth model calibration and validation for winter months in years <2003 in the Idaho portion of the Interior Columbia River Basin. Numbers in parentheses are averages.

Table S2. Frequency of wolverine Gulo gulo locations (n = 43) and available area according to inter-annual persistence of potential suitable wolverine winter habitat on February 28 across Idaho, USA from 1982 to 2003.

Appendix S1. Supplemental analyses of mule deer density datasets.

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