Northern Prairie Wildlife Research Center
During 1974-77, 56 captured bears were equipped with radiocollars and located daily by triangulation when they were within radio range of roads (~5 km). When collared bears moved farther from roads, they were relocated from aircraft within 1 week.
We used captures of bears ≥2 years of age that occurred during annual capture periods of May 1-September 30 for mark-recapture analyses. For these analyses, we used only captures accomplished with snares and culvert traps because other methods sometimes targeted specific individuals.
We used Jolly-Seber (J-S) open-population models (Pollock et al. 1990) to estimate numbers of female bears using the CLSA during 1969-76. By limiting this portion of our analysis to females, we eliminated bias resulting from sex-related differences in capture probabilities. To investigate possible effects of age-related differences in capture probabilities, we compared results for all females with a second set based only on adult females. Finally, to guard against spurious increases in estimates that might result from the temporary departure of marked bears from the CLSA, we computed a third set of estimates from capture histories truncated in 1974. To facilitate visual comparisons of trends resulting from these analyses, which were based on different-sized groups of bears, we plotted standardized deviates of estimates (Sokal and Rohlf 1981) instead of estimates themselves.
We could not estimate numbers of males by mark-recapture methods because the experimental removal of males resulted in the marking, release, and recapture of too few. Thus, we used indirect methods to determine whether numbers of subadult males captured annually on the CLSA indicated numbers residing in the area. We inferred trends in numbers of subadult males that were present at least temporarily from numbers of individuals captured and mark-recapture estimates of capture probabilities. We then estimated settling rates of subadult males (probabilities of surviving from 1 capture period to the next while continuing to use the CLSA) from generalized mark-recapture models (Lebreton et al. 1992). Finally, we considered trends in numbers of subadults and settling rates concurrently to determine whether numbers of subadults captured reflected numbers that used the study area on a continuing basis.
We depicted capture histories of individual bears as vectors of 0's and 1's, with 1's indicating capture. Our models represented probabilities of possible capture histories as combinations of settling and recapture probabilities (e.g., Lebreton et al. 1992:71). Settling rates were represented by Φi,k and recapture parameters by Pi,k, where subscript i denoted the capture period and k indexed age class (sa = subadults, ad = adults). Thus, Φi,k was the probability a bear in age class k would survive from capture period i to i+1 and still be using the CLSA during capture period i+1. Pi,k was the probability a bear in age class k would be captured during period i if it was using the CLSA.
Our full model was constrained by 4 sets of equalities:
Φ1968, k = Φ1969, k = Φ1970, k = Φ1971, k = Φ1976, k = Φpre, k ;
Φ1972, k = Φ1973, k = Φ1974, k = Φ1975, k = Φpost, k ;
P1969, k = P1970, k = P1971, k = P1976, k = P1977, k = Ppre, k ;
P1972, k = P1973, k = P1974, k = P1975, k = Ppost, k .
Constraints divided the study into 2 periods dictated by the volume of data available, which precluded separate estimation of every Φi,k and Pj,k. Periods corresponded with the pre-removal (1968-71) and post-removal (1972-75) periods described by Young and Ruff (1982), except that we placed previously unpublished data for 1976-77, when relatively few subadult males were captured, in the pre-removal period. We used nested models and likelihood ratio tests to test for significant differences between parameters of our full model. We used SURGE 4.2 computer software to compute maximum-likelihood estimates of model parameters and likelihood ratio tests (Lebreton et al. 1992).
We used the staggered-entry Kaplan-Meier (K-M) estimator (Pollock et al. 1989) to estimate survival rates of radiomarked bears and ratios of age- and sex-specific survival rates. For known or suspected mortalities, we used the date of last radio contact as the date of death. Records for bears with unknown fates were terminated (right censored) at the date of last radio contact. A log-rank test, stratified by year and age class, was used to compare rates for males and females. Age classes were compared after stratifying by year and sex. We used 1-tailed tests because we anticipated higher mortality rates for males and subadults than for females and adults. We used SAS PROC PHREG (Allison 1995), for survival analyses.