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Federal Register / Vol. 86, No. 148 / Thursday, August 5, 2021 / Rules and Regulations
Relative Den Density
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Polenlial OM Habilat
For each simulated den, we assigned dates of key denning events; den entrance, birth of cubs, when cubs reached 60 days of age, den emergence, and departure from the den site after emergence. These represent the chronology of each den under undisturbed conditions. We selected the entrance date for each den from a normal distribution parameterized by entrance dates of radio-collared bears in the Southern Beaufort subpopulation that denned on land included in Rode et al. 2018 and published in USGS
2018; n = 52, mean = 11 November, SD
= 18 days. These data were restricted to those dens with both an entrance and emergence data identified and where a bear was in the den for greater than or equal to 60 days to reduce the chances of including non-maternal bears using shelter dens. Sixty days represents the minimum age of cubs before they have a chance of survival outside of the den.
Thus, periods less than 60 days in the den have a higher chance of being shelter dens.
We truncated this distribution to ensure that all simulated dates occurred within the range of observed values i.e., 12 September to 22 December identified in USGS 2018 to ensure that entrance dates were not simulated during biologically unreasonable periods given that the normal distribution allows some probability
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albeit small of dates being substantially outside a biologically reasonable range. We selected a date of birth for each litter from a normal distribution with the mean set to ordinal date 348 i.e., 15 December and standard deviation of 10, which allowed the 95 percent CI to approximate the range of birth dates i.e., December 1 to January 15 identified in the peerreviewed literature Messier et al. 1994, Van de Velde et al. 2003. We ensured that simulated birth dates occurred after simulated den entrance dates. We selected the emergence date as a random draw from an asymmetric Laplace distribution with parameters m = 81.0, s = 4.79, and p = 0.79 estimated from the empirical emergence dates in Rode et al.
2018 and published in USGS 2018, n = 52 of radio-collared bears in the Southern Beaufort Sea stock that denned on land using the mleALD
function from package ald Galarzar and Lachos 2018 in program R R Core Development Team 2021. We constrained simulated emergence dates to occur within the range of observed emergence dates January 9 to April 9, again to constrain dates to be biologically realistic and to not occur until after cubs were 60 days old.
Finally, we assigned the number of days each family group spent at the den site post-emergence based on values reported in four behavioral studies,
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Smith et al. 2007, 2010, 2013 and Robinson 2014, which monitored dens near immediately after emergence n =
25 dens. Specifically, we used the mean 8.0 and SD 5.5 of the dens monitored in these studies to parameterize a gamma distribution using the method of moments Hobbs and Hooten 2015 with a shape parameter equal to 8.02/5.52 and a rate parameter equal to 8.0/5.52; we selected a post-emergence, pre-departure time for each den from this distribution. We restricted time at the den post emergence to occur within the range of times observed in Smith et al. 2007, 2010, 2013 and Robinson 2014 i.e., 223 days, again to ensure biologically realistic times spent at the den site were simulated. Additionally, we assigned each den a litter size by drawing the number of cubs from a multinomial distribution with probabilities derived from litter sizes n = 25 litters reported in Smith et al. 2007, 2010, 2013 and Robinson 2014.
Because there is some probability that a female naturally emerges with 0 cubs, we also wanted to ensure this scenario was captured. It is difficult to parameterize the probability of litter size equal to 0 because it is rarely observed. We, therefore, assumed that dens in the USGS 2018 dataset that had denning durations less than the shortest den duration where a female
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Figure 6-Depiction of the proposed project area with the underlying relative density of polar bear dens and potential polar bear den habitat as identified by Durner et al. 2006, 2013 and Blank 2013.