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).