Grizzly Bear Population and Density Estimates for the 2005 Alberta (Proposed) Unit 4 Management Area Inventory

Transcription

1 Grizzly Bear Population and Density Estimates for the 2005 Alberta (Proposed) Unit 4 Management Area Inventory Report Prepared for Alberta Sustainable Resource Development, Fish and Wildlife Division, December 2005 John Boulanger 1, Gordon Stenhouse 2, Grant MacHutchon 3, Michael Proctor 4, Stefan Himmer 5, David Paetkau 6, and Jerome Cranston 2. 1 Integrated Ecological Research, Nelson, BC V1L 5T2, boulange@ecological.bc.ca 2 Sustainable Resource Development, Fish and Wildlife Division, Box 6330, Hinton, AB T7V 1X6, Gordon.Stenhouse@gov.ab.ca Curtis Road, Comox, BC V9M 3W1, machutch@mars.ark.com 4 Dept. of Biological Sciences, University of Alberta, Edmonton, Alberta T6G 2E9, mproctor@netidea.com 5 Arctos Wildlife Services, Site 10, Comp. 7, R.R. 1,Crescent Valley, BC V0G 1H0, shimmer@netidea.com 6 Wildlife Genetics International, Nelson BC V1L 5P9, dpaetkau@wildlifegenetics.ca

2 Alberta Unit 4 Grizzly Bear Inventory Project 2 1. Abstract This report provides grizzly bear population and density estimates for a study area that includes the Alberta Provincial grizzly bear management area 4 (proposed) and a small eastern portion of Banff National Park. This area encompassed the current Alberta Bear Management Areas 4C, and portions of 3B, 7, 13 and 15. In 2005, a DNA hair capture grid (8477 km 2 ) was sampled. One hundred and seventy three 7x7 km grid cells were sampled with 1 hair capture bait site for 4 sampling sessions. Thirteen 7x7 cells were located wholly within Banff Park to meet the assumption of population closure. In addition, 11 transect cells were sampled in plains areas to detect occupancy of bears in these areas (but were not used in the mark-recapture analysis). Each bait site was moved between sessions to ensure adequate coverage of cell areas for cells within the main sampling grid. Forty one individual bears were captured in bait sites on the main sampling grid, and 1 other bear was captured in the transect grid cells. The distribution of bears was clumped along the west side of the study area. Data-based tests and GPS collared bears showed that closure violation was minimally violated with 95% of GPS collared bears locations occurring on the sampling grid. The estimate of the superpopulation of bears (including dependent offspring) in the grid and surrounding area was 47 (SE=3.99, CI=44 to 60). The average number of bears on the sampling grid was estimated by multiplying the superpopulation number by the proportion of GPS bear locations on the sampling grid (0.95) to estimate an average number of bears on the sampling grid at any one time of (SE=3.96 CI=41 to 52). The average number of bears at any one time was divided by the sampling grid area (8477 km 2 ) to derive a density estimate of 5.25 bears per 1000 km 2 (SE=0.47 CI=4.87 to 6.09) on the sampling grid. The capture probabilities (an index of sampling efficiency) for this project were the highest recorded for any DNA mark-recapture project in British Columbia or Alberta, since this technique was introduced in As a result, the precision of estimates was very high despite the lower population size of bears in the sampling area. 2. Introduction This report provides a population estimate for the grizzly bear DNA mark-recapture inventory project that occurred in 2005 on a study area containing Alberta grizzly bear management area 4 (proposed) and a small eastern portion of Banff National Park (BNP). The actual inventory area contained sections of the current provincial Bear Management Areas (BMA) 4C, 3B, 7, 13, and 15 as well as a small section of BNP. However, the majority of the sampled area was within BMA 4C (Appendix 1). Grizzly bear management area 4 resulted from a province wide genetic analysis of grizzly bears that indicated several partial genetic breaks, or discontinuities, that corresponded to major east-west highways (Proctor and Paetkau 2004). The resulting units depict areas where interbreeding between bears is clustered, and represent an improvement in the criteria to delineate biologically-based management units. We refer to this unit as BMA 4 for the remainder of this report although as of the time of report preparation this regulatory

3 Alberta Unit 4 Grizzly Bear Inventory Project 3 change has not yet occurred. From an inventory perspective, the study area attempts to contain most of this biological unit (between Highways 1 and 11) which will minimize violation of population closure, while surveying an entire biologically-based management unit. 3. Methods 3.1. Field methods A systematic DNA sampling grid with 173, 49 km 2 grid cells was placed in an area of approximately 8477 km 2 within the project study area boundary. Because population closure is an important assumption of our population estimators, we designed the study area to minimize the movement of bears across the boundaries. Our study area encompassed most of grizzly bear management area 4 which was bounded by Highways 1 and 11 providing relative closure to the south and north respectively. To the east, the area extended into land (minimally occupied or) unoccupied by grizzly bears. Here we additionally sampled 11 transect cells to determine bear occurrence in these areas. One potential issue with sampling the western border of bear management area 4 is that it was not topographically closed to bear movement with BNP. Using GPS radio collar data from the Foothills Model Forest Grizzly Bear Research Project, Resource Selection Function (RSF) models (Nielsen et al. 2002, Nielsen 2004), and local topography, we adjusted the western border of the grid to sample approximately 13 cells wholly within BNP. An additional 3 cells had 1 or 2 of 4 sites within Banff. The new grid boundary was determined by likely breaks in bear movement therefore accommodating the assumption of population closure. The actual strip of cells within BNP was approximately 10 km wide so it is very likely that these bear traversed within the 4C management area and therefore could be considered part of the 4C population. Extending the border provided insurance against detrimental effects of closure violation (reduced estimate precision and potential bias) with minimal addition of extra cells. One hair capture bait site was placed in each grid cell for 4, 14 day sampling sessions in the spring and early summer of Site selection was done prior to fieldwork and was based upon grizzly bear RSF models, GPS collar locations, remote sensing-based habitat mapping, aerial photographs, and expert opinion of bear biologists. Each bait site was moved after each session to ensure equal coverage of each cell. One strand of barbed wire at each site was used for sampling bear hair. Previous research as part of the 2004 Alberta 3B4B Inventory project (Boulanger et al. 2005b) suggested that a design with sites moved and one strand of barbed wire was optimal for mark-recapture sampling (Boulanger et al. 2005a). At each bait site, a strand of barb wire approximately 50 cm off the ground was attached around 3 to 6 trees to catch the hair of bears investigating the site. A scent lure mixture of 2 litres of rancid cow blood and 1 litre of rancid fish liquid was poured on top of a pile

4 Alberta Unit 4 Grizzly Bear Inventory Project 4 of wood debris and moss in the middle of the barb wire enclosure to attract bears but did not give them any food reward. Grizzly bear hair was collected from each bait site using methods documented in Woods et al. (1999). Applicable samples were then genotyped using methods documented in Paetkau (2003). Figure 1: DNA sampling grid layout for the Alberta 2005 DNA mark-recapture population inventory project. Each cell was 49 km 2. Main sampling grid cells had 1 bait site that was moved for each of 4 sampling sessions. Transect cells, on the east side of the grid area only had 1 bait site that was not moved during each of the sampling sessions Data summary Data was summarized in terms of overall frequencies of captures for individuals. For traditional mark-recapture analysis, multiple captures of an individual within one session are pooled into one capture per session. Summary statistics were generated for the pooled data set. See Appendix 2 for background information on mark-recapture population estimation.

5 Alberta Unit 4 Grizzly Bear Inventory Project Assessment of closure violation In review, closure violation is caused by bears moving in and out of the study areas during sampling (White et al. 1982). If closure violation is occurring, mark-recapture population estimates will pertain to the superpopulation of bears in the sampling grid and surrounding area during the time that sampling was conducted (White 1996, Kendall 1999). For estimation of density and comparison of different areas, the average number of bears on the sampling grid at any one time is most applicable. For this reason, we used data-based tests for closure violation (Boulanger and McLellan 2001), and used data from GPS collared bears to scale superpopulation estimates into average population size estimates (White and Shenk 2001) as discussed later. The Pradel (1996) model in program MARK (White and Burnham 1999) was used to assess the data set for closure violation as described by Boulanger and McLellan (2001). The main premise for this test is that, if closure violation was occurring, grizzly bears that were near the grid edge ("edge" grizzly bears) would have lower recapture rates due to a reduced trap encounter rate compared to grizzly bears farther from the edge ("core" grizzly bears). In addition, if grizzly bears moved from the grid for the entire sampling period, then edge grizzly bears would exhibit a lower apparent survival estimate than core grizzly bears. Also, grizzly bears, which immigrated into the grid area during sampling, would be more prone to be captured near the grid edge. The distance from edge of capture location was considered the shortest distance from the grid edge to the mean location of hair capture bait sites where a grizzly bear was identified during the entire project. The Pradel (1996) model estimates apparent survival (φ), recruitment (f) and recapture probability (p). The estimates for recapture rate are for the exact sampling period, whereas the estimates for the apparent survival rate (φ) and recruitment (f) correspond to the interval before the given sampling period. We assumed that the population of grizzly bears was demographically closed for this analysis. The duration of sampling was <2 months so this assumption was considered reasonable. Apparent survival equals true survival (S) (due to mortality) times the fidelity of grizzly bears (F) to the sampling grid (φ=sf). Because the population was demographically closed, we assumed that true survival equalled one (S=1) and therefore relative changes in φ reflect grizzly bear fidelity to the sampling grid rather than actual mortalities, i.e., (φ=f). The Pradel recruitment rate estimates the number of new individuals in the population at time j+1 per individual at time j. We assumed that the number of births during sampling was minimal and therefore measures of recruitment reflected permanent immigration or "additions" of grizzly bears into the sampling grid. For the sake of simplicity we will refer to φ as the rate of Fidelity and f as the rate of Additions in the rest of the report. As an initial appraisal of population closure we evaluated the goodness of fit of Pradel models constrained to only allow certain forms of closure violation as first proposed by Stanley and Burnham (1999). The exact models used in the test of Stanley and Burnham

6 Alberta Unit 4 Grizzly Bear Inventory Project 6 (1999) were the fully open Jolly Seber model (JS), a recruitment but not mortality model (NM), a mortality but not recruitment model (NR), and a closed model with no mortality or recruitment (M t ). We emulated the approach of Stanley and Burnham (1999) by fixing parameters to appropriately constrain the Pradel model as detailed in Boulanger and McLellan (2001). We then used continuous covariates to model the relationship of distance from edge for φ, f, or p as a logistic function. The potential shapes that the logistic curve, which is used to model covariates in MARK, could accommodate was restrictive, and therefore logistic equations with log transformed (+1) (Zar 1996) distance from edge and higher order polynomial (i.e. dfe 2 log (dfe) 2 +1) distance from edge terms were also considered. Covariates were standardized in program MARK by the mean and standard deviation of observed distances (White et al. 2002). A logit link was used for all analyses. In addition to covariates, both sex and time specific model formulations were considered in the building of mark-recapture models. The fit of models was evaluated using the Akaike Information Criterion (AIC) index of model fit. The model with the lowest AICc score was considered the most parsimonious, thus minimizing estimate bias and optimizing precision (Burnham and Anderson 1998). The difference in AICc values between the most supported model and other models ( AICc) was also used to evaluate the fit of models when their AICc scores were close. In general, any model with a AICc score of less than 2 was worthy of consideration. An assumption of the Pradel analysis was that capture, survival, and movements are independent. In addition, it is assumed that all individuals within a group have similar apparent survival rates and similar values of other model parameters. If individuals are not independent, the multinomial variances from the models become inflated or overdispersed, which causes underestimation of parameter variances and overfitting of models. Various goodness-of-fit tests are available to test and estimate the degree of overdispersion in the data set. Because lack of fit in the Pradel models can only be assessed for the recapture portion of the encounter history, the goodness-of-fit test in Program RELEASE (Burnham et al. 1987) was used to assess goodness-of-fit. If overdispersion was detected (as indicated by c ˆ > 1), we used QAICc instead of AIC c model selection criterion to select optimal models (Burnham and Anderson 1998, White et al. 2002). If a segment of core animals was identified by the Pradel analysis, then population estimates were calculated for this segment and extrapolated to the entire grid area (Boulanger and McLellan 2001). This extrapolation was based on the assumption that differences in population size estimates were due to closure rather than differences in densities of grizzly bear on the trapping grid. A test of uniform density (Otis et al. 1978) was therefore conducted to test whether density was reasonably uniform between core and extrapolated areas.

7 Alberta Unit 4 Grizzly Bear Inventory Project Closed population estimation model selection We primarily used the Huggins closed models (Huggins 1991) in program MARK for estimation model selection and population estimates. Sexes of grizzly bear were entered as groups in this analysis, testing whether sexes displayed differing forms of capture probability variation. Models with time, heterogeneity, and behaviour variation were considered in the analysis. Mean precipitation for each session was considered as a capture probability covariate to potentially explain temporal variation in capture probabilities. Mixture model heterogeneity estimators (Pledger 2000) as incorporated in program MARK (White and Burnham 1999) were used to model heterogeneity variation. This is modeled by letting capture probabilities come from more than one capture probability distribution. There are three parameters with the 2-distribution mixture model. The parameters are the probability that a given capture probability will come from the first distribution (π), the mean capture probability of the first distribution (θ 1 ), and the mean capture probability of the second distribution (θ 2 ). The probability that the capture probability comes from the second distribution is 1- π (Pledger 2000). As with the Pradel analysis, AICc model selection was used to assess parsimonious estimation models. In addition, tests for specific forms of capture probability variation in program CAPTURE (Otis et al. 1978) were used to assess capture probability variation and compared with MARK model selection results Population estimates Population estimates from the program MARK models and program CAPTURE models were considered. Estimates from all of the Huggins MARK models were modelaveraged, allowing population estimates that were influenced by all the estimation models considered in the analysis Simulation tests of estimators Two simulation methods were used to test estimation models. First, results from past projects, radio collared studies of grizzly bears, and expert opinion were used to devise simulation models of likely forms of capture probability variation in the bear population. These models were used to evaluate the precision of estimators across a range of sampling parameters. Second, direct estimates of capture probability variation obtained in program MARK were used to parameterize data-based simulations. As summarized in Table 1, each of these approaches has strengths and weaknesses. Simulation models based on data-based simulations are limited to detectable forms of capture probability variation in mark-recapture data sets. Because most data sets are sparse it is probable that certain forms of heterogeneity variation, such as low capture probabilities of cubs of the year, are not detected. Therefore, telemetry and expert based simulations are useful to allow exploration of non-detected forms of capture probability variation.

8 Alberta Unit 4 Grizzly Bear Inventory Project 8 Table 1: Methods used to estimate precision and evaluate estimator performance. Evaluation method Strengths Weaknesses 1) Simulations based on expert opinion and telemetry estimates of cub capture probability Incorporates biologicallybased forms of capture probability variation that may be difficult to detect in field Makes expert assumptions about main forms of capture probability variation in data that cannot be directly tested. data 2) Data-based simulations Uses direct estimates of variation from data with minimal expert-based assumptions May not include forms of capture probability variation not detected due to sparse data Each of these methodologies are explained in detail in Appendix 3. Estimators were evaluated in terms of bias, precision, and confidence interval coverage. Bias was defined by percent relative bias (Nˆ N) P.R.B. = where ˆN is the estimate population size from each model and N was N the true number of bears in the simulation. The optimal level of precision was indexed by the coefficient of variation (CV) which is ( ˆ CV ( Nˆ ) = SE N) ˆ X 100 N The CV is a convenient way to compare precision of different projects since it expresses standard error in percentage units of the estimate. The confidence interval width is approximately ± 1.96 (CV). So if a project has a CV of 10% then the confidence interval is roughly ± 20% of the estimated population size. Confidence intervals for markrecapture project are seldom symmetrical so this is a rough approximation. Confidence intervals can be conceptualized as a bell shaped curve with the most probable estimate being the point estimate and the least probable estimates being on either end of the confidence interval. Bias and precision were considered simultaneously by the mean squared error (M.S.E.), which is the absolute value of percent relative bias plus the coefficient of variation. An estimator with the lowest M.S.E. displays the best balance between bias and precision. In addition, confidence interval coverage was considered, which was the proportion of times the estimated population size bracketed the true population value Average population size on study area grid and density estimates We estimated average number of bears on the sampling grid using two methods. If assumptions were met we used the core-extrapolation method of Boulanger and McLellan

9 Alberta Unit 4 Grizzly Bear Inventory Project 9 (2001) as discussed previously. In addition, superpopulation estimates were multiplied by the proportion of sampling occasions that GPS collared bears were on the sampling grid (White and Shenk 2001) to obtain estimates of the average number of bears on the sampling grid. We estimated proportion of locations for GPS bears during the time of DNA sampling for 2003, 2004, and 2005 when a suitable spatial distribution of GPS bears were present on the sampling area. Bears were included if any of their locations traversed the grid during sampling in 2003, 2004, or Proportion for bears that occurred on the grid in was averaged to avoid psuedoreplication. This resulted in a sample size of 13 GPS bears for estimation of proportion of time on the sampling grid. Both the CAPTURE and MARK superpopulation estimate and the proportion of radio marked bears on the grid estimate have error. Therefore, we used the delta method (Seber 1982) to estimate combined variances under the assumption that correlation between population estimates and the proportion of time on the grid was zero. We calculated log-based confidence-intervals for the average number of bears on the sampling grid estimates using formulas presented in White et al. (2002). 4. Results 4.1. Data summary Forty-one bears (17 males and 24 females) were identified with the sampling grid hair capture bait sites. An additional female bear was identified in one of the outer transect cells. The distribution of captures was clumped in the western mountainous regions with few captures on the eastern plains area (Figure 2).

10 Alberta Unit 4 Grizzly Bear Inventory Project 10 Figure 2: Distribution of captures at bait sites for the Alberta Unit 4 inventory projects Sites are scaled by the number of unique bear captures that occurred at the site over the course of the project. Mean capture locations of DNA bears also suggest that most bears were found on the western edge of the study area (Figure 3). Sexes were intermixed fairly evenly with a slight tendency for males to be found in the plains and foothills of the DNA study area.

11 Alberta Unit 4 Grizzly Bear Inventory Project 11 Figure 3: Mean capture locations for individual bears in the Alberta Unit 4 inventory project. Summary statistics for mark-recapture modeling suggest that there was temporal variation in capture rates for bears as summarized by animals caught each session (Table 2). Most notably the number of captures for both males and females was lower in session 1. The number of newly caught (genotyped) individuals decreased with session for both sexes suggesting that sampling was effective in capturing the majority of bears in the area. Capture frequencies suggested higher recapture rates with more bears being captured 2 or more times than bears captured once.

12 Alberta Unit 4 Grizzly Bear Inventory Project 12 Table 2: Summary statistics for the DNA data set. Statistic Session total males Animals caught n(j) Total individuals caught M(j) Newly caught u(j) Frequencies f(j) females Animals caught n(j) Total individuals caught M(j) Newly caught u(j) Frequencies f(j) Pooled Animals caught n(j) Total individuals caught M(j) Newly caught u(j) Frequencies f(j) Tests for closure violation The Program RELEASE goodness-of-fit test for model φ[sex x time] p[sex x time] suggested minimal overdispersion of multinomial likelihoods or c ˆ = 1 (χ 2 = 3.96, df=7, p=0.78) and therefore AICc was used for model selection. Model selection results suggest minimal closure violation (Table 3). The most supported model assumed that there was no emigration from the sampling grid (φ fixed at 1) and no immigration into the sampling grid (f fixed at 0). Other models were substantially less supported with AICc values of greater than 2.

13 Alberta Unit 4 Grizzly Bear Inventory Project 13 Table 3: Pradel model selection. Akaike Information Criteria (AIC c ), the difference in AIC c values between the ith model and the model with the lowest AIC c value ( AIC c ), Akaike weights (w i ), and number of parameters (K) are presented Model AICc AICc w i K Deviance φ (1) A p(t1 B ) f(0) A φ (.) p(t1) f(.) φ (sexf@1) p(t) f(sexf@1) φ (sex) p(sex+t1) f(sex) φ (sex, + ld C ) p(sex+t1) f(sex, + ld) φ (sex F@1 M+ld) p(t1) f(sex) φ (sex, M + ld) p(sex+t1) f(sex, M + ld) φ (sex + d) p(sex+t1) f(sex +d) φ (sex) p(t) f(sex) φ (1) p(.) f(0) φ (1) p(.) f(.) φ (sex, M + ld, ld2) p(sex+t1) f(sex, M + ld,ld2) φ (.) p(.) f(.) φ (sex) p(sex) f(sex) A 1 or 0 denotes that φ or f was fixed at 1 or 0 (implying complete closure). B Capture probability was assumed to be different for session 1 but the same for other sessions. B ld denotes that the log of the distance of mean capture of bear from grid edge Model averaged estimates of demographic parameters suggested that apparent survival rates were close to 1 implying there was minimal emigration from the sampling grid. In addition, rates of addition were close to 0 implying that there was minimal immigration into the sampling grids (Table 4). Table 4: Model averaged estimates of Pradel model parameters Parm Sex Estimate SE LCI UCI φ (emigration) Male Female f (immigration) Male Female Results from the Pradel model and point estimates of apparent survival and rates of additions suggest minimal closure violation. These results were also corroborated by results of the program CAPTURE closure test that did not detect closure violation for the pooled sex or individual sex data sets (at α=0.05) (Pooled, Z=-0.86, p=0.19, male; Z=- 1.91, p=0.12, females: Z=0.25, p=0.59). Finally, as discussed later, GPS collar locations also suggested minimal movement of bears off the sampling grid with 95% of location contained within the sampling grid.

14 Alberta Unit 4 Grizzly Bear Inventory Project Population estimation model selection AICc model selection results suggested that models with time and heterogeneity variation were most supported by the data (Table 5). These models constrained per-session capture probabilities to be equal for all sessions except the 1st session. A model with undefined heterogeneity variation and lower capture probabilities in the first sample session was most supported. A model with capture probability varying as a function of distance from grid edge was also supported. However, increased support for the same model without the distance from edge covariate suggested that the relationship between capture probability and distance from edge was marginal. A model with equal capture probabilities but lower capture probabilities in the first sample session was also supported. Models with sex-specific capture probabilities, or behavioural response were less supported. Table 5: MARK Huggins closed model AICc model selection. Akaike Information Criteria (AIC c ), the difference in AIC c values between the ith model and the model with the lowest AIC c value ( AIC c ), Akaike weights (w i ), and number of parameters (K) are presented Model AICc AICc w i K Deviance M th2 pi(.) p1&2(.)+t1 A M th2 pi(.) p1&2(.)+t1+ ld B M t p (t1) M tbh2 pi(.) p1&2(.)+t1 c(.) M th2 pi(.) p1&2(.)+t1+ ld+ld M th p(sex) + t M th2 pi(sex) p1&2(sex) +t M t M th2 pi(.) p1&2(.)+t M th p(sex) + t1+ld M b M th p(sex) + t1 X ld M h2 pi(.) p1&2(.) M o (p(.)) M o (sex) A t1 denotes that capture probabilities were constrained to be different for session 1 but equal for other sessions B ld denotes that the log of the distance of mean capture of bear from grid edge One interesting attribute of this data set is the high capture probabilities of bears. Point estimates of capture probabilities from the most supported model in Table 5 are 0.37 (CV=0.54, CI= ) for session 1 and 0.61 (CV=0.36, CI ) for sessions 2-4. These estimates of capture probabilities are higher than estimates from the provincial B4B project (Boulanger et al. 2005) or any other grizzly bear DNA mark-recapture project. From a mark-recapture sampling perspective this is an interesting result given that capture probabilities from the 2004 AB 3B4B were higher than any other project

15 Alberta Unit 4 Grizzly Bear Inventory Project 15 conducted previously and provided good confidence limits around the population estimate. One potential reason for the high capture probabilities in 2005 is that the assumption of closure was better met than in That is, bears did not wander off the grid as much and as a result encountered more traps therefore increasing capture probabilities. This general hypothesis is supported by comparison of the average capture probability from the 2005 project (0.55) with the capture probabilities of the 2004 as a function of distance of mean capture from grid edge. Because closure was violated more often in 2004, capture probabilities were lower for bears that lived near the edge of the sampling grid. The highest capture probabilities were for core bears that lived near the center of the grid edge. It can be seen that capture probabilities for core bears in 2004 are equivalent to the mean capture probabilities of bears from the 2005 effort (Figure 4). In conclusion, the high capture probability levels of bears in 2005 can best be explained by the relatively higher grid closure compared to the 2004 project. From a mark-recapture sampling perspective this is an interesting result given that capture probabilities from the 2004 AB 3B4B were higher than any other project conducted previously. Capture probabilities Mean distance (km) of capture from grid edge Figure 4: Estimated capture probabilities of bears as a function of distance of mean capture from the grid edge for the B4B Inventory Project from Boulanger et al. (2005b). Standard errors of estimates are shown as error bars. These estimates are compared to the mean capture probability from the 2005 effort. This capture probability is roughly equal to that obtained for core bears in the 2004 effort.

16 Alberta Unit 4 Grizzly Bear Inventory Project Superpopulation and population estimates Superpopulation (the population of bears on the sampling grid and surrounding area) were estimated using program CAPTURE models and the Huggins MARK models (Table 6). In general the estimates from most models were similar. Estimates from nonheterogeneity estimators were slightly lower potentially due to heterogeneity variation of capture probabilities. The M th CAPTURE model displayed slightly higher estimates than other estimators. As discussed below, this could have been due to a positive bias with this estimator. The MARK model averaged estimates were potentially the most robust since they considered estimates of all models in Table 5. Table 6: Superpopulation estimates of grizzly bears for the Alberta grizzly bear management area 4 inventory project. Estimates correspond to bears in the sampling grid and surrounding area. MARK model ave. estimates correspond to model averaged population estimates from the models listed in Table 5. Estimator ˆN SE 95% CI CV Males and females MARK Model Ave % M th % M t (Chao) % M h (Chao) % M h (jackknife) % Females MARK Model Ave % M th % M t (Chao) % M h (Chao) % M h (jackknife) % Males MARK Model Ave % M th % M t (Chao) % M h (Chao) % M h (jackknife) % 4.5. Simulation tests of mark-recapture model estimators A key question was whether heterogeneity (M h ) model estimators were robust to the levels of time variation observed in the data set. In addition, the performance of heterogeneity estimators with higher capture probabilities observed in this project was also of interest. Results suggested that most estimators showed reasonable bias levels with the exception of the M t (Chao) estimator in the data-based simulations (Table 7). Of the CAPTURE estimators the M h (jackknife) estimator displayed the best performance

17 Alberta Unit 4 Grizzly Bear Inventory Project 17 with low mean squared error and reasonable confidence interval coverage. This general finding is corroborated by Otis et al. (1978) who comment that the jackknife estimator is the most robust estimator in capture if individuals are captured multiple times, a definite attribute of this data set. The M th (Chao) estimator displayed positive bias in both simulations and lower precision, a result corroborated by the simulations of Chao and Jeng (1992). The MARK model averaged estimates also displayed relatively low mean squared error estimates, however, confidence interval coverage was slightly lower. From these simulations we conclude the M h (jackknife) estimator or MARK Model averaged estimates are most applicable to this data set. Table 7: Simulation results from data and expert based simulations. Estimation model PRB CV MSE C.I. Coverage Data-based simulations M h (Chao) -7.1% M th 5.6% M h (jackknife) -6.4% M t (Chao) -10.3% MARK model ave -5.2% Expert based simulations M h (Chao) -3.7% M th 7.6% M h (jackknife) -0.5% M t (Chao) -7.4% MARK model ave -2.8% Estimation of average number of bears on the sampling grid and density The superpopulation estimates were used as the basis for estimates of density in the sampling grid area. Ninety four percent of GPS locations were on the sampling grid as averaged across individual bears that occurred on the sampling grid from Using this figure, superpopulation estimates were scaled to average population size on the sampling grid (Table 8). This resulted in average values of and for the MARK model average and M h (jackknife) estimates. Coefficients of variation for average number of bears on the sampling grid were well below 20% for the both estimators suggesting adequate precision of average ˆN estimates.

18 Alberta Unit 4 Grizzly Bear Inventory Project 18 Table 8: Superpopulation estimates, proportion of GPS collar locations on sampling grid and the estimated average population size of bears on the sampling grid. Superpopulation Proportion GPS bears Estimation model estimate on grid Average ˆN on sampling grid Estimator ˆN S.E. Estimate SE Ave ˆN SE 95% CI CV M h (jackknife) % 2.57% % MARK model ave % 2.57% % The average population size estimates were then divided by grid area (8477 km2) to obtain density estimates for the 2005 sampling grid area (Table 9). Table 9: Estimates of density ( ˆD )for the Alberta Unit 4 Inventory area. Density is expressed as bears per 1000km 2 Estimator ˆD SE 95% Conf. Interval M h (jackknife) MARK model ave Discussion Population density estimates from the grizzly bear management area 4 inventory in 2005 were slightly higher than density estimates from the 3B4B areas to the north ( ˆD =4.79, SE=0.84, CI=4.10 to 6.28) (Boulanger et al. 2005b). However, as with the 3B4B project, the actual number of bears on the sampling grid was below 50. Despite this, the levels of precision of population estimates from this project are the highest attained for any grizzly bear DNA mark-recapture project to date (Table 10). We used the Mh (Chao) estimate in Table 10 since this model was used for most other projects and therefore estimates from this model are most comparable. However, the higher frequencies of capture and higher capture probabilities made it possible to use the M h (jackknife) estimator. Using this estimator the actual CV of the superpopulation estimate of the project is even lower (8.5%). Superpopulation estimates were used to compare projects in Table 10 because closure corrected estimates have not been estimated for some of these projects. In addition, precision of superpopulation estimates best conveys the precision of the mark-recapture component of a project given that other factors (such as the method used to estimate average number of bears on the grid) will affect the ultimate estimates of density. However, we note that density or average numbers of bears on the sampling grid are the best ways to compare actual population numbers from different projects.

19 Alberta Unit 4 Grizzly Bear Inventory Project 19 Table 10: Superpopulation estimates from DNA mark-recapture project conducted in British Columbia and Alberta. Projects are ordered by the coefficient of variation of the superpopulation estimate. A lower CV indicates higher estimate precision. Project Model ˆN SE CV ˆp Cell Sites Size(km 2) moved? Sessions Reference 1 Alberta Unit 4 M h (Chao) % yes 4 Parsnip M th % yes 4 (Mowat et al. 2005) Alberta 3B4B M h (Chao) yes 4 (Boulanger et al % b) Jumbo M h (Chao) % no 4 (Strom et al. 1999) Prophet M th % yes 5 (Poole et al. 2001) UCR 97 M h (Chao) % no 5 (Boulanger et al. 2004a) Kingcome M h (Chao) % yes 5 (Boulanger and Himmer 2000) UCR 96 M h (Chao) % yes 4 (Boulanger et al 2004a) Flathead M h (Chao) % yes 4 (Boulanger 2001) UCR 98 M t (Chao) % no 5 (Boulanger et al. 2004a) Granby Kettle M t (Chao) % yes 5 (Boulanger 2000) 1 Further details on British Columbia projects can be found in Boulanger et al. (2002) Special care was taken to ensure the accuracy of the genetic results. Genetic assignments of individual identity can be compromised if match probabilities are high enough that some individuals will have identical genotypes. It has been demonstrated in several bear populations, using 6-locus marker systems with similar variability to that employed in the current study, that there are stepwise 10-fold decreases in the number of individuals that match at 3 of 6 markers, 4 of 6 markers, 5 of 6 markers,and all 6 markers (Paetkau 2003). We pre-tested the 6-markers that were used in the current study by analyzing 255 samples from hunter-killed bears spanning the north-south range of grizzly bears in Alberta. These 255genotypes fit the expected pattern with 2276, 255, 19 and 2 pairs of individuals matching at 2, 3, 4 and 5 markers, respectively. As expected from this trend, no pairs of individuals had genotypes that matched at all 6 markers. Given that the number of individuals captured in the current dataset is much smaller (n = 42), and given that we observed 21 and 2 pairs of genotypes in this dataset that matched at 3 and 4 markers, respectively, the probability that we captured even a single pair of individuals with identical genotypes, and thus underestimated the number of captured individuals, is remote. The best estimate of this probability is obtained by taking the number of pairs that match at 4 of 6 markers and dividing by 100 (Paetkau 2003), and is thus In other words, match probabilities were low enough to ensure that each sampled individual had a unique genotype.

20 Alberta Unit 4 Grizzly Bear Inventory Project 20 The second way that genetic assignments of individual identity can become inaccurate is if errors are incorporated into genotypes. thus causing different samples from the same individual to receive different individual assignments. We followed published recommendations (Paetkau 2003) to demonstrate the reproducibility of each pair of genotypes that were similar enough to have a realistic chance of having originated from genotyping error. Data images showing the replication of the relevant data points are available on request. One issue that has been raised is whether live capture of bears for radio collaring causes radio collared bears to be less likely to be captured due to the similarity of snare capture and DNA bait sites. In general, reduction of capture probabilities of GPS collared bears is not likely to be a large issue given that mark-recapture models allow bears to have unequal probabilities of capture and estimate the number of bears not captured during DNA sampling. In addition, Boulanger et al (2004b) modelled differences in capture probabilities between GPS bears and DNA-capture bears during the 1999 Foothills Model Forest DNA mark-recapture project. They found that GPS collared bears had similar capture probabilities to DNA captured bears in this study. Boulanger et al (2004a) also modelled difference between radio collared bears for the West Slopes Study in British Columbia. They found that radio collared bears displayed slightly lower capture probabilities, however, the reduction of radio collared bear capture probabilities was not large enough to cause a bias in estimates. In this project, nine previously live-captured bears with GPS collars or VHF collars were known to be on the DNA sampling grid during sampling. Of these 9 bears, all but 2 were captured using DNA hair snags. The low number of previously captured GPS/VHF collared bears precludes statistical analysis of this data, however, these results suggest that the majority of GPS collared bears known to be on the DNA grid were captured, and the 2 bears that were not captured could easily be contained within the mark-recapture estimate of population size. A previous DNA study was undertaken in Banff Park in 1996 (Proctor 1998). The study design for this effort was one bait site within a 10 X 10 km cell. Each bait site was sampled then moved for 3 sessions. The estimate from this effort was very imprecise and capture probabilities were approximately 0.22 potentially due to the larger cell size and low number of sample session conducted. In addition, it is likely that bait types, and sampling methods were not as well developed at this time given that it was the first year that DNA sampling for grizzly bears in British Columbia was attempted. The difference in results from the 1996 effort and the current study illustrate the large influence that study design and field implementation have on the results of DNA mark-recapture projects. As with the 2004 effort, we speculate several factors helped in obtaining this higher level of precision. First, the relatively small grid cell size relative to average home range size maximized the probability of encountering a hair trap. Second, we used an a-priori siteselection protocol that integrated a combination of expert bear biologist opinion enhanced by a suite of supporting information including, quality RSF models of the area, GPS

21 Alberta Unit 4 Grizzly Bear Inventory Project 21 locations for radio-collared bears, remote sensing-based habitat maps, and ortho photos of the study area. In addition, the 2005 study design was effective at minimizing population closure therefore increasing capture probabilities and further enhancing estimate precision. Precision of estimates from both the 2004 and 2005 efforts have been the highest obtained for DNA mark-recapture projects despite the relatively small sample sizes of bears. In terms of management of bears, the estimate of average number of bears on the grid at any one time is most applicable since it directly pertains to the management area. Because the grid was relatively closed the superpopulation and average number of bears on the sampling grid at any one time are similar (47 vs. 44). The high degree of closure is most likely due to careful delineation of study area boundaries. To minimize closure we chose to sample the entire genetically determined management unit (4) that is bordered to the north and south by major highways, The eastern boundary is minimally occupied by grizzly bears, and a strip of Banff National Park was included along the western boundary (Figure 1) to optimize topographical limits to bear movement in and out of the study area during the time of sampling. The actual area sampled in BNP was relatively narrow therefore it is very likely that bears in this area spend some time within Alberta management area 4 and are part of the biological population of the area. In other words, it is possible we would have captured these bears if only the area east of the BNP boundary was used for DNA sampling. However, the bears probably would have wandered across the boundary during sampling, which would have caused closure violation and reduced estimate precision. Therefore, from a sampling perspective, sampling within BNP was one of the reasons for the higher precision of population estimates during this project. Estimates of population size for Alberta management area 4 assume that the sampling grid sampled all of the bears in the study area. Transect sites to the east only captured 1 bear so it is reasonable to assume that the population size of bears east of the sampling grid was negligible. The success of this grizzly bear population inventory project was in large part due to the data sets collected for the study area through the Foothills Model Forest Grizzly Bear Research Project over the past 6 years. Having remote sensing based habitat maps, RSF models, and GPS bear movement data proved invaluable in the design and analysis of this DNA population inventory. This highlights the need to have these types of data available before embarking on inventory efforts in other bear management units in Alberta. 6. Acknowledgements We thank the field crew for collection of DNA data: Jocelyn Akin, Nicole Heim, Audrey Lorincz, Michelle McLellan, James Minifie, Kirk Safford, Robin Steenweg, Chelsey Whenham, and Kellie Wodchyc. John Saunders (Peregrine Helicopters), Paul Tigchelaar (Glacier Helicopters), and Bob Skinner (Thebacha Helicopters) provided expert and safe

22 Alberta Unit 4 Grizzly Bear Inventory Project 22 access to remote DNA bait sites. Alberta Sustainable Resource Development, Fish and Wildlife Division, and Forestry provided logistical support. Tobi Anaka and Paul Sylvestre of Wildlife Genetics International conducted genetic analysis of DNA samples. Alberta Sustainable Development, Fish and Wildlife Division provided funding for this project. Administrative and logistic support was provided by the Foothills Model Forest in Hinton. 7. Literature cited Boulanger, J Granby-Kettle/Boundary Forest District 1997grizzly bear DNA mark-recapture inventory project: Statistical analysis and population estimates. Kamloops: Ministry of Environment, Lands, and Parks. Boulanger, J Analysis of the 1997 Elk Valley and Flathead valley DNA markrecapture grizzly bear inventory projects. Cranbrook, BC: Ministry of Environment, Lands, and Parks. Boulanger, J., and S. Himmer Kingcome (1997) DNA mark-recapture grizzly bear inventory project final report. Naniamo: Ministry of Environment, Lands, and Parks. Boulanger, J., and B. McLellan Closure violation in DNA-based mark-recapture estimation of grizzly bear populations. Canadian Journal of Zoology 79: Boulanger, J., B. N. McLellan, J. G. Woods, M. F. Proctor, and C. Strobeck. 2004a. Sampling design and bias in DNA-based capture-mark-recapture population and density estimates of grizzly bears. Journal of Wildlife Management 68(3): Boulanger, J., G. Stenhouse, and R. Munro. 2004b. Sources of heterogeneity bias when DNA mark-recapture sampling methods are applied to grizzly bear (Ursus arctos) populations. Journal of Mammalogy 85: Boulanger, J., M. Proctor, S. Himmer, G. Stenhouse, and D. Paetkau. 2005a. An empirical test of DNA mark-recapture sampling strategies for grizzly bears. Ursus submitted. Boulanger, J., G. Stenhouse, M. Proctor, S. Himmer, D. Paetkau, and J. Cranston. 2005b population inventory and density estimates for the Alberta 3B and 4B Grizzly Bear Management Area. Hinton, Alberta: Alberta Sustainable Resource Development.

23 Alberta Unit 4 Grizzly Bear Inventory Project 23 Boulanger, J., G. C. White, B. N. McLellan, J. G. Woods, M. F. Proctor, and S. Himmer A meta-analysis of grizzly bear DNA mark-recapture projects in British Columbia. Ursus 13: Burnham, K. P., and D. R. Anderson Model selection and inference: A practical information theoretic approach. New York: Springer. 353 p. Chao, A. L., and S. L. Jeng Estimating population size for capture-recapture data when capture probabilities vary by time and individual animal. Biometrics 48: Huggins, R. M Some practical aspects of a conditional likelihood approach to capture experiments. Biometrics 47: Kendall, W. L Robustness of closed capture-recapture methods to violations of the closure assumption. Ecology 80(8): Mowat, G., D. C. Heard, D. R. Seip, K. G. Poole, G. Stenhouse, and D. Paetkau Grizzly Ursus Arctos and black bear U. americanus densities in the interior mountains of North America. Wildife Biology 11: Nielsen, S. E Habitat and grizzly bear density estimates for the 2004 DNA census of grizzly bear management areas 3B & 4B, west-central Alberta, Canada. Edmonton: University of Alberta. Nielsen, S. E., M. S. Boyce, G. B. Stenhouse, and R.H.M.Munro Modeling grizzly bear habitats in the Yellowhead ecosystem of Alberta: Taking autocorrelation seriously. Ursus 13: Otis, D. L., K. P. Burnham, G. C. White, and D. R. Anderson Statistical inference from capture data on closed animal populations. Wildlife Monographs 62: Paetkau, D Genetical error in DNA-based inventories: insight from reference data and recent projects. Molecular Ecology 12: Pledger, S Unified maximum likelihood estimates for closed models using mixtures. Biometrics 56: Poole, K. G., G. Mowat, and D. A. Fear DNA-based population estimate for grizzly bears Ursus Arctos in northeastern British Columbia, Canada. Wildlife Biology 7: Proctor, M Eastern Slopes Grizzly Bear population estimate. In: Gibeau ML, Herrero S, editors. Eastern Slopes Grizzly Bear Project: a progress report for Calgary, AB: University of Calgary. p