Whitebark Pine, Population Density, and Home-Range Size of Grizzly Bears in the Greater Yellowstone Ecosystem

Changes in life history traits of species can be an important indicator of potential factors influencing populations. For grizzly bears (Ursus arctos) in the Greater Yellowstone Ecosystem (GYE), recent decline of whitebark pine (WBP; Pinus albicaulis), an important fall food resource, has been paired with a slowing of population growth following two decades of robust population increase. These observations have raised questions whether resource decline or density-dependent processes may be associated with changes in population growth. Distinguishing these effects based on changes in demographic rates can be difficult. However, unlike the parallel demographic responses expected from both decreasing food availability and increasing population density, we hypothesized opposing behavioral responses of grizzly bears with regard to changes in home-range size. We used the dynamic changes in food resources and population density of grizzly bears as a natural experiment to examine hypotheses regarding these potentially competing influences on grizzly bear home-range size. We found that home-range size did not increase during the period of whitebark pine decline and was not related to proportion of whitebark pine in home ranges. However, female home-range size was negatively associated with an index of population density. Our data indicate that home-range size of grizzly bears in the GYE is not associated with availability of WBP, and, for female grizzly bears, increasing population density may constrain home-range size.


INTRODUCTION
Although monitoring protocols for grizzly bears in the Greater Yellowstone Ecosystem (GYE) were not designed for density estimation, efforts to capture and radio-monitor individuals for research and management purposes began in 2975 and have been intensive and consistent since the early 1980s, involving over 1,800 captures of 870 individual bears, with capture effort distributed throughout the GYE. Estimating actual population density is unnecessary for most ecological questions concerning processes sensitive to the number of individuals involved and in most cases a reliable index is suitable for exploration of the importance of density dependence [1]. Accordingly, we developed a density index for grizzly bears in the GYE using a combination of very high frequency (VHF) telemetry data and histories (i.e., dates of capture, annual reproduction, cast transmitters, and known mortalities) of individual bears from 1983 through 2012. Using an annual time step and a coarse spatial scale (14 km × 14 km) approximating the average female grizzly bear activity range, we constructed a spatio-temporally explicit index of grizzly bear densities allowing exploration of the relative contribution of grizzly bear density in relation to variation in appropriate response variables (e.g., home-range size, survival, and movement parameters).

METHODS
The long-lived nature of grizzly bears, coupled with the substantial and sustained research efforts over time in the GYE has resulted in an accumulation of longitudinal data that present a unique opportunity to quantify the presence of individuals over time in discrete spatial units. Spatially, our approach was based on using locational data (VHF and capture locations) to reconstruct individual bears' extent of use, which we represent with a single, lifetime activity range. Temporally, we extruded these 2-dimensonal ranges through time from the age of independence (≥2 years of age) through the known or estimated year of death. We restricted telemetry data to known-aged individuals captured for research or management purposes during

Lifetime Activity Ranges
Spatial component.--We selected a circular activity range as the spatial metric for grizzly bear ranges. We generated lifetime activity ranges for all individuals assuming they were similar among cohorts within sexes. We used a sex-specific mean activity radius ( sex ) and individuals' lifetime center of activity to define the lifetime activity range. We used the harmonic mean of all VHF locations as our estimate of an individual's center of activity . For individuals located only once in their lifetime (i.e., captured once), we used the capture location to estimate the center of activity. We calculated the activity radius as follows:  To reduce bias in calculating the sex-specific activity radii we restricted data to bearyears containing ≥5 unique months of data during May-December, in which at least 1 VHF location was recorded for each unique month. For bears that were transported during their lifetime, we included VHF locations up to the time of first transport. For individuals that were transported, we evaluated if the transport was successful or if the bear returned to its natal range.
For bears that established new ranges, we created a second (temporally non-overlapping) activity range. To avoid overestimating bear ranges, we used the 80 th percentile of distances between locations from the center of activity, from which we calculated the mean lifetime activity radius for each bear. The sex-specific, mean radii were  male = 24.3 km  female = 12.8 km ( Figure S1). Missoula, Montana, USA) from which we estimated the birth year. We did not include cub and yearling contributions to density. Accordingly, activity ranges were hind-cast from the year of capture to the year the bear was age 2. For bears with known mortality, we forecasted activity ranges through the year of mortality, discretizing the lifetime activity range into annual ranges.
This can be visualized as a cylinder where the base is the spatial extent of the lifetime activity range and the height represents time from age of independence (≥2 years old) to death ( Figure   S2A). For bears whose fates were unknown, we used sex-specific survival probabilities (S F = 0.950, S M = 0.925; [2,3]) to forecast the annual probability they remained in the population. We thus reduced the contribution of their annual ranges to the density index according to annual survival rates. For these bears with unknown fates we limited their lifetime contribution to a maximum age of 30 years ( Figure S2B).

Density Index Calculation
The spatial resolution of our density index was based on 196-km 2  within BOAs (r = 0.725, P < 0.001, n = 28; Figure S6).

DISCUSSION
A valid population level density index is one that is directly related to density in such a way that it tracks temporal and spatial changes in density [1]. Our approach leveraged multiple datasets (capture, life history, and VHF telemetry) on 870 bears to reconstruct the spatial and temporal variability of bear occupancy at a coarse, yet meaningful, spatial scale to grizzly bear space use.   Once the age at capture is determined, the lifetime activity area is created by hindcasting to age 2 and forecasting until death (A) or age 30 (B). Figure S3. Calculation of annual grizzly bear density index. Visual representation of how the density index is calculated for a given year. Each grid cell is evaluated for occupancy by an activity range (grey circles in A and B) and a value corresponding to the amount of overlap is generated for each cell (B). For cells with more than one activity range (C) the value is the sum of proportional ranges within that cell (D).

Figure S4. Correlation coefficients between grizzly bear density index and trapping effort.
Distribution of correlation coefficients between the first derivatives of the grizzly bear density and trapping indices (n = 250). The red line represents a kernel density estimate.