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Federal Register / Vol. 86, No. 148 / Thursday, August 5, 2021 / Rules and Regulations
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denning bears Durner et al. 2020. To approximate the distribution of dens, we used an adaptive kernel density estimator Terrell and Scott 1992
applied to n observed den location, which took the form 8

Il
fs oc -;;- Li k
S-Si hs

where the adaptive bandwidth hs = b0
+ b1Isi MIs Mb2 for the location of the ith den and each location s in the study area. The indicator functions allowed the bandwidth to vary abruptly between the mainland M and barrier islands. The kernel k was the Gaussian kernel, and the parameters q, b0, b1, b2
were chosen based on visual assessment so that the density estimate approximated the observed density of dens and our understanding of likely den locations in areas with low sampling effort.
The kernel density map we used for this analysis differs slightly from the version used in previous analyses, specifically our differentiation of barrier islands from mainland habitat. We used this modified version because previous analyses did not require us to consider denning habitat in the CC region, which has a significant amount of denning that occurs on barrier islands compared to the other two regions. If barrier islands were not differentiated for the kernel density estimate, density from the barrier island dens would spill over onto the mainland, which was deemed to be biologically unrealistic given the clear differences in den density between the barrier islands and the mainland in the region. For each grid cell in the kernel density map within the CC
region, we then determined the
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minimum distance to roads and pads that had occupancy 0.50 identified by AOGA during October through December i.e., the core period when bears were establishing their dens. We restricted the distance to infrastructure component to only the CC region because it is the region that contains the vast majority of oil and gas infrastructure and has had some form of permanent industrial infrastructure present for more than 50 years. Thus, denning polar bears have had a substantial amount of time to modify their selection of where to den related to the presence of human activity.
To simulate dens on the landscape, we first sampled in which kernel grid cell a den would occur based on the underlying relative probability Figure 6 within a given region using a multinomial distribution. Once a cell was selected, the simulated den was randomly placed on the denning habitat Blank 2013, Durner et al. 2006, 2013
located within that grid cell. For dens being simulated on mainland in the CC
region, an additional step was required.
We first assigned a simulated den a distance bin using a multinomial distribution of probabilities of being located in a given distance bin based on the discretized distribution of distances described above. Based on the distance to infrastructure bin assigned to a simulated den, we subset the kernel density grid cells that occurred in the same distance bin and then selected a grid cell from that subset based on their underlying probabilities using a multinomial distribution. Then, similar to other locations, a den was randomly placed on denning habitat within that grid cell.

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in the region with denning habitat identified Durner et al. 2013.
To account for the potential influence of industrial activities and infrastructure on the distribution of polar bear selection of den sites, we again relied on the subset of dens from the den catalogue Durner et al. 2020 discussed above. We further restricted the dens to only those occurring on the mainland because no permanent infrastructure occurred on barrier islands with identified denning habitat Durner et al.
2006. We then determined the minimum distance to permanent infrastructure that was present when the den was identified. This led to an estimate of a mean minimum distance of dens to infrastructure being 21.59 km SD = 16.82. From these values, we then parameterized a gamma distribution: Gamma21.592/16.822, 21.59/16.822. We then obtained 100,000 samples from this distribution and created a discretized distribution of distances between dens and infrastructure. We created 2.5-km intervals between 0 and 45 km, and one bin for areas >45 km from infrastructure and determined the number of samples that occurred within each distance bin.
We then divided the number of samples in each bin by the total number of samples to determine the probability of a simulated den occurring in a given distance bin. The choice of 2.5 km for distance bins was based on a need to ensure that kernel density grid cells occurred in each distance bin.
To inform where dens are most likely to occur on the landscape, we developed a kernel density map by using known den locations in northern Alaska identified either by GPS-collared bears or through systematic surveys for
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