The temperature sensors deployed on collared adult female polar bears provided data at a frequency ranging from every twenty minutes to once every four to seven hour duty cycle. We used statistical process control methods (i.e., control charts) to identify maternal denning behavior in polar bears based on sensor temperature data. We quantified the routine variation in the temperatures of non-denning bears (n = 109) in order to identify extended periods of warmth indicative of denning animals. The expected mean and control limits were derived using a subset of temperature records spanning from 1 July to 30 June (i.e., “bear-winter”) in which denning statuses had previously been assigned qualitatively using a combination of activity, temperature and location data (Fischbach et al. 2007). We smoothed the daily averages of non-denning bear temperatures using a locally-weighted scatterplot smoothing (i.e., LOESS; span = 0.35) to create an expected seasonal mean for our control charts. Because individual temperature profiles varied substantially from this expected average, we adjusted the starting intercept of the expected seasonal mean for each bear-winter using the mean of the first five temperature observations in an individual bear’s temperature dataset. This altered the actual temperature but maintained the seasonal variation typical of non-denning bears. If the first recorded temperatures occurred during typical denning months (Oct–Apr), the mean of the final five observations was used rather than the first five observations to adjust the starting intercept for a bear-winter. We used an upper control limit of 1.8-sigma which provided a standard deviation of 9 °C for all bear-winters. Setting the control limit to 1.8-sigma provided the temperature limits that most accurately distinguished between denning and non-denning bear-winters (n = 418) as previously determined in Fischbach et al. (2007).
We based den status classifications on the number of days a bear’s temperature remained above the upper control limit. Bear temperatures were considered above or below control limits when >1 consecutive mean daily temperature rose above or below the upper control limit, respectively. We used temperatures from previously identified denning bears (Fischbach et al. 2007) to calculate a minimum number of days a bear’s temperature remained above the upper control limit to be classified as denning. In this subpopulation, data suggest that only pregnant females den, thus it was assumed that all dens were attempted maternity dens. Bear-winters that met the minimum duration of 34 days but had <6 mean daily temperature observations were considered to have insufficient data for classification. We also excluded bear-winters that had no observations during denning months (Oct–Apr), and those in which observations ended before January 1 unless denning status was identified before January 1. Bear deaths or shucking of collars were determined from location and activity sensor data and were excluded from the dataset.
We validated our classifications of denning behavior using direct observations of denning made via VHF radio tracking or of females with dependent cubs during annual spring capture efforts. We further compared our classifications to those made via qualitative classification informed by activity and temperature sensor data and location quality (Fischbach et al. 2007) although this was not an independent comparison since classifications from Fischbach et al. (2007) were used to develop our methodology. Denning substrate was determined using location data collected from radio collars. Before 2009, most radio collar locations were determined by the Argos system. These location data were filtered to remove implausible locations using the Douglas Argos-Filter algorithm, which retained all standard quality class locations (classes 3, 2, and 1), rejected all class Z locations, and retained auxiliary class locations (0, A, and B) if they were corroborated by a consecutive location within 10 km (maxredun = 10), or if movement rates were <10 km hr-1 (minrate = 10) and turning angles were not extremely acute such that bears were immediately returning to a location they had just been. Accuracy estimates for Argos locations were provided by Collecte Localisation Satellites, the operator of Argos (i.e., 3: <250 m, 2: 250-500 m, 1: 500-1500 m, 0:>1500 m
http://www.argos-system.org/manual/; accessed 8 Mar 2016). Because location accuracies were not provided for auxiliary location classes A or B, we prescribed conservative location accuracies of 5000 and 10,000 m, respectively. Some collars deployed 2004-2008 and all collars deployed 2009-2014 provided GPS-derived location data. We assigned locations obtained from GPS collars an accuracy of 30 m.
If at least one observed location at the start of, during, or at the end of the denning period identified via temperature data occurred on land and locations preceding or subsequent to denning demonstrated a trajectory to or from that location, it was assumed that the den occurred on land. Dens that occurred on landfast ice were included with land dens (n = 8 of 142 bear-years) for the analysis because we were interested in changes in broad patterns of geographic distribution of dens between pack ice and coastal regions; and because fast ice only occurs along a narrow band near shore in the southern Beaufort Sea.
Substrate use before denning was determined based on the number of days bears spent onshore during the months of August to October. Bears were classified as having summered on land if they spent ≥25 days onshore, a timespan intended to identify longer durations rather than shorter visits to shore. Because location data were collected at varying intervals and with varying location accuracies, we used the R statistical computing (R Development Core Team 2013) package ‘crawl’ to model polar bear locations at daily intervals that were then used to determine the number of days a bear spent onshore before denning. We projected the geographic coordinates to reduce geographic biases of the estimated locations on non-Cartesian coordinates near the pole. The ‘crawl’ model allows data to be fit into regular time scales by assuming that a predicted location is a linear interpolation of a bracketed set of modeled locations. A bear was classified as on land or fast ice if its predicted location was within 5 km of land as identified by the Global Self-consistent, Hierarchical, High-resolution, Geographic Database (GSHHG version 2.3.4;
http://www.soest.hawaii.edu/pwessel/gshhg/; accessed 8 Mar 2016), as described in Rode et al. (2015). Because transmissions cannot be propagated when a bear is in the water because the antenna is submerged, it is unlikely that locations received within 5 km on shore occurred in water. The 5 km buffer was used to account for low accuracy of some locations. Our 5 km buffer might have resulted in some bears that were on ice being classified as on land but this was less likely to occur during the August to October timeframe in which we analyzed land use because landfast ice is largely absent during this period and the pack ice has generally receded far north of the coast.