2.4 Estimating population energy density and storage energy
Total population energy density and storage energy were calculated based on population structure, abundance estimates, and individual body measurements. Capture records from 1985 to 2018 were used to estimate population structure; however, variation in yearly sample sizes (e.g., low numbers of bears caught from certain age classes in certain years) necessitated the use of bootstrapping over a five-year moving window to estimate yearly percentages of each age/sex class. Therefore, step one of the population energy estimation process involved calculating the mean percentage of each class in the five-year window around the year of interest from 2000 bootstrap iterations (sampling with replacement) using the boot package in R (Canty & Ripley 2019) to represent yearly population structure.
Abundance estimates were calculated in the program MARK using the POPAN formulation (Schwarz & Arnason 1996; Appendix S1). To account for uncertainty in MARK estimates, step two involved drawing a random value from a normal distribution (based on the MARK values) to estimate the annual abundance. The numbers of bears of each class were then calculated in step three by multiplying the bootstrapped age/sex class structure by the estimated annual abundance.
In step four, the yearly mean energy density and storage energy per class were calculated from 2000 bootstrap iterations (sampling with replacement) using the boot package in R (Canty & Ripley 2019). Step five involved calculating the yearly total energy density and storage energy for each class by multiplying the number of bears in that class by the mean energy of that class.
In step six, the yearly total population energy density and storage energy were calculated by summing the energy values across classes. To account for uncertainty in this process, steps 1-6 were conducted 10,000 times and the resulting mean and SE were used as the total population energy density and storage energy estimates in further analyses.

2.5 Temporal dynamics of population energy and environmental analyses

We examined temporal trends (1985-2018) in total population energy density, storage energy, and temporal dynamics of sea ice variables using linear regression models. We used multiple linear regression analysis to examine the relationship between total population energy values and environmental variables (Table S1). Model selection was conducted using AIC and the top model was used to make predictions about population energy given potential future environmental conditions (i.e., 180 day fasting period; Molnár et al. 2010, 2014; Pilfold et al. 2016). All statistical analyses were conducted in R v.3.6.1 (R Core Team 2019).