The authors have declared that no competing interests exist.
Conceived and designed the experiments: GM DCH. Performed the experiments: GM. Analyzed the data: CJS GM. Contributed reagents/materials/analysis tools: GM DCH CJS. Wrote the paper: GM DCH CJS.
Conservation of grizzly bears (
Grizzly bear hunting is controversial because of peoples' conflicting values and interests. Sarewitz
In the last 15 years, improvements in aerial survey
Three approaches for predicting grizzly bear density have been proposed where field-based estimates are unavailable. 1. Measures of grizzly bear abundance can be generated by assigning densities based on expert opinion regarding the value of landcover attributes, supported by, or in conjunction with, field estimates derived in similar ecosystems
2. Resource selection function models can be used to predict the absolute or relative probability of occurrence
3. Trend data can be used to predict density from areas with known abundance
For the greatest general application, predictive abundance models must be underpinned by an understanding of the functional processes affecting density, use direct measures of resource abundance, and apply to all environments and life history strategies
We considered both bottom–up (food supply) and top-down (competition and predation) influences on grizzly bear abundance. Grizzly bears are omnivores and their reliance on animal protein varies greatly across their range
Competition may limit grizzly bear density where they are sympatric with black bears (Ursus americanus)
Grizzly bears have no significant predators
Humans limit grizzly numbers by direct mortality, habitat loss, and displacement due to disturbance. Mortality obviously reduces density temporarily, but the relationship between mortality rate and density is complex due to the effects of age ratios and density dependence on vital rates. Habitat loss, and environmental change that completely precludes occupancy by grizzly bears, obviously reduces density. Disturbance has been shown to reduce grizzly bear density at fine scales (e.g., along road corridors and near developments
In this paper we modeled the relationship between existing grizzly bear density estimates and potential limiting factors. We then use those relationships to predict grizzly bear density across a large and varied portion of their Canadian range and demonstrate how the use of these predictions for setting hunting quotas and evaluating past levels of human-caused mortality can support the process of developing grizzly bear conservation policy.
Based on previous research we felt that the following factors may functionally influence grizzly bear density at the population scale: plant productivity, vegetation type, fish and meat availability, scramble competition with black bears, human disturbance, and human-caused mortality. Based on this functional model, we began by assembling and deriving indices for these factors while attempting to choose measures that were not highly correlated with other factors to avoid collinearity (
Plant productivity | Vegetation type |
Diet | Competition with black bears | Human disturbance | Human-caused mortality |
annual precipitation | tree10 | salmon presence | tree10 | tree10 | human density |
annual temperature | tree25 | %salmon in diet | tree25 | tree25 | human+livestock density |
annualized NDVI | herb50 | %terrestrial meat in diet | black bear presence | livestock density | human+livestock density within 10 km |
evapotranspiration | herb75 | human density | human+livestock density within 50 km |
||
ruggedness | herb100 | human+livestock density | mean recorded human-caused mortality in past 10 years | ||
human+livestock density within 10 km |
|||||
human+livestock density within 50 km |
= the proportion of the study with pixels rated as >50% herb/shrub.1 This is the sum of all pixels with >the stated percentage of described cover. For example, herb50
2 This is the mean human and livestock (sheep and cattle) density (summed) for the area within 10 or 50 km of the study area boundary.
The only mortality factor we considered was direct killing by people. Although it has been mandatory to report all human-caused deaths in all jurisdictions in North America since the 1970's, a substantial proportion of that mortality goes unreported
We critically reviewed estimates of grizzly bear population size or density in the published and unpublished literature. We were interested in estimates for landscapes large enough to represent a grizzly bear population affected largely by births and deaths rather than immigration and emigration, so we only used data where study area size was >800 km2 (range 789–22,875 km2) or approximately 10 female home ranges, and contained at least 15 resident bears (
We selected 16 study areas in places that were historically occupied by grizzly bears, but were currently not occupied. These areas were all adjacent to occupied areas and there was no known barrier to dispersal. We chose these areas to represent the range of contemporary forces that work to exclude grizzly bears from parts of their range. We selected areas of similar size to other studies in those ecosystems and derived measures for independent variables as for occupied study areas. Though the density estimate was zero, based on local knowledge, we assigned upper CLs based on trapping results, non-hunter kills and the recent record of bear sightings in the study area.
We revised all grizzly bear density estimates by removing the area of water, rock, and bare ground, because we considered these unsuitable to bears.
We derived average annual precipitation, average annual temperature, NDVI, and evapotranspiration to index plant productivity from freely available spatial databases (Table S1 in
Landcover had been previously assigned into 3 structural classes at 500 m resolution: herbaceous (which includes shrubs <2 m in height), trees >2 m tall, and barren (
We used the fraction of salmon and animal tissue in the diet of bear populations as surrogates for salmon and terrestrial meat availability. Diet fractions may not be linearly related to resource availability, but deriving measures of salmon and meat availability across large areas was not feasible. Salmon and terrestrial meat components of the diet were predicted using isotope analysis of grizzly bear hair collected from each study area
Human and livestock density was used to index human displacement, disturbance, and unreported bear mortality. We tested log transformations of these variables, because the influence was expected to be nonlinear
Human-caused mortality necessarily reduced bear density and was entered directly and as a squared term to account for the non-linear influence of recent mortality on the standing population. We estimated the number of bears killed by people from government databases or published accounts. Counts of all legally killed bears have been recorded since at least the mid 1970s for all the jurisdictions in this study and represent a minimum number of bears killed by people. We calculated the annual kill rate (number bears killed/bear population estimate) over the 10 years previous to each density estimate. Unoccupied areas were assigned mean kill rates so these records did not bias the fitting of this variable. Raw data are available in
We used Principal Components Analysis (PCA;
Ordinary least squares regression cannot be used directly to fit these models, because of the inclusion of study areas where no grizzly bears were located. For these points, the assumption of normally distributed errors about the regression line is violated. Consequently, Tobit regression
However, only the max(0, Y *) can be observed, i.e. it is impossible to observe negative densities.
Maximum likelihood was used to fit the Tobit model (Proc QLIM, SAS 9.2). Models were fit where every study area was given equal weight and where study areas were weighted by the inverse of the relative CLs to downweight study areas with less precise estimates of density.
We constructed an a-priori suite of models based on expert judgment, including variables thought to affect grizzly bear densities. Additional models were added to the initial model set where potential predictors were dropped or transformed.
Potential models included transformed values for human and livestock density to approximate the known form of the relationship, based on previous research as described earlier. We also included indicator variables that controlled for 3 cases we considered outliers, based on initial screening of the data. Two study areas had high and presumably unsustainable mortality rates, and one unoccupied area had very high human density. We used the small-sample corrected AICc to compare model fit, ranked models using AIC weights
We used a leave-one-out jackknife procedure to estimate the increase in prediction error that might occur when the model was used to predict densities outside of the set used to build the model. Each individual study area was sequentially dropped from the analysis, the remaining data were used to fit the model being examined, and this fitted model with sample size
We derived 118 estimates of density including 16 for areas currently unoccupied by grizzly bears (
Areas currently unoccupied are filled with hatching. The presence of black bears throughout the study area is denoted by a black outline, partial presence of black bears by a gray outline and a hatched gray or no outline means black bears did not occur on the study area. Areas without salmon are not colour filled, those with abundant salmon are filled in red, and those where salmon were present but not abundant in rose. The black bear distribution in North America is shown in tan
Variable | Occupied areas | Unoccupied areas | ||||||||
SD | Min | Max | SD | Min | Max | |||||
Population size | 92 | 96 | 15 | 765 | 76 | 0 | 0 | 0 | 0 | 14 |
Study area size (km2) | 5110 | 4297 | 789 | 22875 | 76 | 6358 | 1629 | 3913 | 8959 | 14 |
Barren (% of study area) | 6.7 | 8.6 | 0.0 | 34.6 | 76 | 1.7 | 2.1 | 0.1 | 6.7 | 14 |
Density (barren area removed) | 23.0 | 15.1 | 2.5 | 64.6 | 76 | 0.0 | 0.0 | 0.0 | 0.0 | 14 |
CL relative (% of density) | 1.0 | 0.5 | 0.1 | 1.9 | 76 | 0.8 | 0.3 | 0.5 | 1.0 | 14 |
Human-caused mortality (%) | 3.7 | 3.9 | 0.0 | 20.1 | 76 | 0 |
0.0 | 0 | 0 | 14 |
Annual precipitation (cm) | 84 | 40 | 16 | 199 | 76 | 52 | 7 | 43 | 68 | 14 |
NDVI | 116 | 15 | 77 | 137 | 76 | 129 | 5 | 115 | 136 | 14 |
AET | 296 | 104 | 97 | 443 | 76 | 342 | 60 | 228 | 440 | 14 |
Average annual temperature | −4.0 | 5.0 | −17 | 3.7 | 76 | 0.9 | 3.1 | −5.0 | 4.7 | 14 |
Ruggedness | 3.9 | 1.4 | 1.0 | 6.0 | 76 | 2.2 | 1.3 | 1.0 | 4.2 | 14 |
Trees (>25% per pixel) | 48.1 | 34.7 | 0.0 | 99.5 | 76 | 69.7 | 30.0 | 8.4 | 99.7 | 14 |
Herb-shrub (>50% per pixel) | 57.6 | 28.1 | 3.1 | 99.1 | 76 | 50.6 | 28.4 | 6.8 | 94.0 | 14 |
Salmon (% of diet) | 1.0 | 3.0 | 0.0 | 14.0 | 76 | 1.5 | 3.6 | 0.0 | 10.2 | 14 |
Kokanee (% of diet) | 0.7 | 3.5 | 0.0 | 26.0 | 76 | 0.6 | 1.5 | 0.0 | 5.1 | 14 |
Meat (% of diet) | 25.1 | 15.5 | 0.0 | 58.2 | 76 | 29.3 | 13.9 | 12.5 | 48.1 | 14 |
Human density (humans/km2) | 0.9 | 1.7 | 0.0 | 8.4 | 76 | 4.3 | 5.6 | 0.0 | 21.4 | 14 |
Livestock density (animals/km2) | 1.7 | 5.5 | 0.0 | 39.4 | 76 | 11.5 | 16.9 | 0.0 | 53.2 | 14 |
1 The kill rate in unoccupied areas was zero, but we used the mean rate of 3.7 for occupied areas during analysis so that these areas did not bias the distribution for this variable.
Variable | Black bears present | Black bears absent | ||||||||
SD | Min | Max | SD | Min | Max | |||||
Population size | 81 | 88.6 | 0 | 352 | 17 | 619 | 450 | 102 | 1548 | 11 |
Study area size (km2) | 3743 | 2858 | 431 | 9854 | 17 | 2829 | 2463 | 228 | 9163 | 11 |
Barren (% of study area) | 16.0 | 10.4 | 0.7 | 43.4 | 17 | 9.6 | 10.0 | 1.1 | 35.7 | 11 |
Density (barren area removed) | 31.1 | 25.9 | 0 | 86.6 | 17 | 332 | 215 | 37 | 856 | 11 |
CL relative (% of density) | 1.1 | 0.5 | 0.1 | 2.0 | 17 | 0.6 | 0.5 | 0.2 | 1.5 | 11 |
Human-caused mortality (%) | 2.3 | 2.6 | 0.0 | 10 | 17 | 3.8 | 2.7 | 0 | 7.3 | 11 |
Annual precipitation (cm) | 275 | 111 | 115 | 473 | 17 | 160 | 57 | 101 | 255 | 11 |
NDVI | 109 | 16 | 75 | 130 | 17 | 104 | 12 | 79 | 115 | 11 |
AET | 370 | 58 | 263 | 474 | 17 | 321 | 30 | 239 | 351 | 11 |
Average annual temperature | 1.6 | 2.5 | −2.6 | 6.7 | 17 | 1.0 | 2.0 | −4.5 | 2.6 | 11 |
Ruggedness | 5.5 | 0.6 | 4.2 | 6.2 | 17 | 4.3 | 1.0 | 2.6 | 5.4 | 11 |
Trees (>25% per pixel) | 54.4 | 23.1 | 17.8 | 96.8 | 17 | 40 | 25 | 1 | 79 | 11 |
Herb-shrub (>50% per pixel) | 44.9 | 16.6 | 8.8 | 71.6 | 17 | 68 | 21 | 36 | 98 | 11 |
Salmon (% of diet) | 41 | 22 | 0 | 78 | 17 | 59 | 15 | 28 | 82 | 11 |
Kokanee (% of diet) | 0.4 | 0.8 | 0.0 | 3 | 17 | 0 | 0 | 0 | 0 | 11 |
Meat (% of diet) | 2.3 | 3.9 | 0.0 | 13.4 | 17 | 3 | 11 | 0 | 36 | 11 |
Human density (humans/km2) | 4.3 | 13.4 | 0.0 | 55.0 | 17 | 0.6 | 1.6 | 0.0 | 5.5 | 11 |
Livestock density (animals/km2) | 1.1 | 4.3 | 0.0 | 17.9 | 17 | 0.01 | 0.00 | 0.0 | 0.02 | 11 |
In coastal areas, where salmon were abundant (i.e., >27% of diet), grizzly bear density estimates were up to an order of magnitude higher than in interior areas (
Study areas where grizzly bears were allopatric are denoted by squares and where black and brown bears were sympatric by diamonds. Open symbols denote coastal study areas where salmon was a major component of the diet; filled symbols show study areas where salmon were few. Unoccupied areas and one coastal area where brown bears were allopatric and at very high density (856) are not shown.
In interior areas, density varied from 2.5 to 65 grizzly bears/1000 km2 and there was a broad range of values for most independent variables (
In interior areas, the first eigenvector of a PCA suggested all 5 vegetation productivity variables were correlated and that ruggedness and NDVI contrasted in the second eigenvector. These results suggested ruggedness and NDVI should be included in the multivariate analysis, but that any of the five productivity variables could substitute for one another. For this reason we decided to include all five variables in the analysis. A second PCA with the vegetation type variables also demonstrated strong correlation among 4 of the 5 variables, whereas the fifth variable, herb100, was nearly invariant across the data. These results suggested that any one of the vegetation type variables could be used to index vegetation cover. We chose herb50, because we felt it would index bear food with the most sensitivity. We also included tree25 in the global model to index black bear competition, which was supported by comparing black bear presence across vegetation cover. Although the vegetation cover variables were strongly correlated, the presence of black bears was most clearly separated across the tree25 variable (
These are 76 sites from across interior North America where salmon is a minor component of the diet. We compare this relationship between 2 variables, tree cover (a–b) and herb-shrub cover (c–d). We also present 2 levels of summary within each study area for each variable. For example, tree>10% means that we summed the pixels where tree cover was >10% and calculated the proportion of the study area where this occurred. Black bears appear to be absent from areas where grizzlies are present and trees cover < about 20% of the study area. The proportion of the study with >25% tree cover appears to best describe this process.
There was very little variation in salmon in diet (which included kokanee) in interior areas and so the composite of fish and terrestrial meat in the diet was dominated by the meat component. For this reason the food composite variable was not considered further in the analysis.
In coastal areas with black bears, a PCA for the vegetation productivity variables yielded similar results to the interior dataset and we considered all five variables for the same reasons as above. We also chose to include herb50 and tree25, because these two variables may contrast herbaceous food abundance with competition with black bears. Human density was the only human influence variable that had substantial variation across the dataset and was the only variable we included. Diet was dominated by salmon and this was the only diet variable considered (
Based on biological considerations and the above investigation of the data, we included the following variables in our global regression: precipitation, NDVI, AET temperature, ruggedness, herb50, tree25, salmon-in-diet or salmon-presence, meat-in-diet, human density, livestock density or human + livestock density, human-caused mortality, and (human-caused mortality)2. Log transformations were also compared for the human-influence variables. When we compared the effect of salmon-in-diet versus the salmon-presence variable, only the salmon-presence variable remained consistently in the top models and we therefore excluded the salmon-in-diet variable.
When we compared the prediction strength of ‘human and livestock density’ versus the single composite variable, the composite variable was not included in the top-competing models. A log transformation did not improve the fit of the composite variable. This suggests the form of the relationship between human density and bear density differed from that of livestock density and bear density, so we dropped the summed variable, ‘human plus livestock density’.
One unoccupied area had double the human density of the next lowest value and was considered an outlier. This study area (Thompson) and the two other study areas (Upper Susitna and Swan Hills), where the number of grizzly bears killed by people was very high, were modeled using indicator variables in order to test their influence on fit. No models that included these indicator variables were included in the top models, suggesting these cases did not unduly leverage the analysis (
Model number | Model description | AICc | ΔAICc | K | AICc weight |
2 | Prcp_NDVI_AET_H50_LHum_Live_Rug | 978.9 | 0.0 | 9 | 0.17 |
3 | Prcp_NDVI_AET_H50_T25_LHum_Live_Rug | 979.0 | 0.1 | 10 | 0.16 |
4 | Prcp_AET_H50_Meat_LHum_Live_Rug | 979.1 | 0.3 | 9 | 0.15 |
5 | Prcp_NDVI_AET_H50_T25_Meat_LHum_Live | 980.1 | 1.2 | 10 | 0.09 |
6 | Prcp_NDVI_AET_H50_T25_SP_Meat_LHum_Live_Rug | 980.2 | 1.4 | 12 | 0.08 |
7 | Prcp_NDVI_AET_H50_SP_Meat_LHum_Live_Rug | 980.5 | 1.6 | 11 | 0.07 |
8 | Prcp_AET_H50_SP_Meat_LHum_Live_Rug | 981.2 | 2.3 | 10 | 0.05 |
9 | Prcp_AET_H50_T25_Meat_LHum_Live_Rug | 981.5 | 2.6 | 10 | 0.05 |
10 | Prcp_NDVI_AET_H50_T25_SP_Meat_LHum_Live | 982.6 | 3.7 | 11 | 0.03 |
11 | Prcp_AET_H50_T25_SP_Meat_LHum_Live_Harv_Rug | 982.8 | 3.9 | 12 | 0.02 |
= precipitation, NDVI = normalized differential vegetation index, AET = actual evapotranspiration, H50 = herbaceous and shrub cover >50%, T25 = tree cover >25%, Meat = terrestrial meat in diet, SP = presence of salmon in diet, LHum = log human density, Live = livestock density, Harv = human-caused mortality, Rug = ruggedness. The top-ranked model was excluded from this list, because it contained 2 uninformative variables. Variables are: Prcp
The weighted Tobit models gave highest AIC weight (18%) to the global model, but this model had 9 variables, whereas the next model, that had only 7 variables, had similar weight (17%) and an AIC value that was only 0.3 higher than the global model. We chose to exclude the global model on the basis that it contained noise parameters and considered Model 2 to be our best model (
Residual plots, using Model 2, showed no evidence that the regression assumptions were not met
Data included 76 inventoried study areas and 14 unoccupied areas across the interior of western North America. Error bars are 95% confidence limits for observed data derived from the survey results or estimated subjectively, based on survey methods (see Methods for detailed description). The cases with the largest residuals often had the greatest error and were hence weighted lower in the regression.
The mean model error for all jackknife runs was compared to the mean error of the model with all data included. For the top 10 interior models, the mean squared prediction error was 9–13% greater using the jackknife procedure compared to the model fit using all of the data. Model 1, the global model, which we excluded, had 12% higher model error using the jackknife procedure compared to the model error based on all the data whereas Model 2, our preferred model, had 9% higher error (Table S2 in
Based on biological considerations and the above investigation of the data, we included the following 7 variables in our global regression: precipitation, NDVI, AET, temperature, ruggedness, herb50, tree25, salmon-in-diet, and human density or log human density. The top model in the weighted Tobit analysis had 7 variables and the second model had 6 variables (
Model number | Model description | AICc | ΔAICc | K | AICc weight |
3 | T25_salmon_Rug | 157.7 | 0.0 | 5 | 0.17 |
4 | Prcp_NDVI_AET_salmon_Hum_Rug | 157.8 | 0.1 | 8 | 0.16 |
5 | Prcp_NDVI_AET_salmon_LHum_Rug | 158.0 | 0.3 | 8 | 0.15 |
6 | Prcp_NDVI_Temp_H50_salmon_Hum_Rug | 158.8 | 1.2 | 9 | 0.10 |
7 | Prcp_NDVI_Temp_H50_salmon_LHum_Rug | 159.9 | 2.2 | 9 | 0.06 |
8 | Prcp_NDVI_Temp_H50_T25_salmon_Rug | 160.2 | 2.6 | 9 | 0.05 |
9 | Prcp_NDVI_Temp_T25_salmon_Hum | 160.7 | 3.1 | 8 | 0.04 |
10 | Prcp_NDVI_H50_T25_salmon_LHum_Rug | 160.9 | 3.3 | 9 | 0.03 |
11 | Prcp_NDVI_H50_T25_salmon_Hum_Rug | 161.2 | 3.5 | 9 | 0.03 |
12 | NDVI_T25_salmon_Rug | 161.2 | 3.5 | 6 | 0.03 |
The jackknife procedure was also used to compare among coastal models. The mean square prediction error from the jackknife models varied from 30–112% greater than that of the fitted model; it was 30% higher for Model 3, our preferred model (Table S3 in
Residual and leverage plots using Model 3 showed no evidence of lack of fit and no serious outliers. Plots of predicted versus observed densities showed a modest variation of residuals (
Data included 15 inventoried study areas and 2 unoccupied areas across the interior of western North America. Error bars are 95% confidence limits for observed data derived from the survey results or, estimated subjectively based on survey methods (see Methods for detailed description).
Our models can be used to predict grizzly bear density for any area for which data exist for the input variables. Population size can be derived from density and these can be added to derive a population prediction for a larger area. We could not compute estimates of the uncertainty in composite predictions (i.e. for the total over several prediction areas), because predictions for study areas that are geographically adjacent with similar covariate sets are unlikely to be independent. Combining the uncertainties of the individual predictions will underestimate the uncertainty of the total. Without further information about the spatial structure of predictions from neighboring geographical areas, it is unclear how to compute an appropriate measure of uncertainty for the total over multiple study areas.
We predicted grizzly bear densities for Canada by summing the individual predictions within wildlife management units (
Province | Current population projection | Predicted population size from this paper | Prediction units | Number in National Parks |
Alberta | 867 |
1250 | ecoregions | 396 |
British | 16,014 |
13,131 | WMU's | 126 |
Columbia | 13,974 | GBPU's | ||
14,101 | ecoregions | |||
Nunavut | 1000 |
8080 | ecoregions | 0 |
Northwest Territories | 5100 |
16,771 | ecoregions | 835 |
Yukon | 6300 |
10,404 | guide territories | 465 |
10,465 | ecoregions |
–5 WMUs), and territorial guide territory boundaries which were roughly similar to WMUs in size. We predicted density for small portions of each province using ecological unit mapping (ecoregions-the largest units used), provincial wildlife management units (WMUs), provincial grizzly bear population units (GBPUs, groups of 1
Predicted grizzly bear densities in the Northwest Territories and Nunavut varied from zero in southcentral NWT to >30 bears/1000 km2 in parts of the western arctic coast, densities decline to the east and were much lower east of the Mackenzie River. In Yukon, the model predicted densities that vary from 0–31 bears/1000 km2 (Table S5 in
Predicted densities for British Columbia varied from 0 to 58 bears/1000 km2. The highest coastal densities were in northern areas where salmon consumption was high and tree cover was low. Interior areas with high density occurred throughout the province, but were always rugged areas with high rainfall and few people. Many units in the province were predicted to have low density and, whereas this was often associated with high human density, predicted densities in flat areas with low rainfall and low herb-shrub cover were also low. The average rate of human-caused mortality was 2.9%/yr, with most mortality from hunter kills (mean = 295/yr), but problem bear kills, and road and rail collisions, (mean = 61/yr) comprised a greater proportion of deaths in units with low predicted bear populations or relatively high human density (Table S4 in
We lacked the data to systematically test our models independently, so our testing was confined to comparisons with other approaches and examining areas of known low density. Boyce and Waller
Mattson and Merrill
There were 14 study areas not known to support grizzly populations in the interior dataset. The predicted density was zero for 8 of these areas and >4 for the 6 other areas. Two areas had predicted density of >14 bears/km2. Grizzly bears do not occur in the southern boreal regions of NWT and Nunavut and northern Alberta and Saskatchewan
We also used our preferred models to predict equilibrium densities in known extirpated areas and zones with depressed populations that are designated as threatened or endangered in British Columbia and the lower 48 states (
Population unit | Current population estimate | Predicted population size |
Okanagan Valley, BC | 0 |
27 |
Thompson Valley, BC | 0 |
13 |
Caribou Plateau, BC | 0 |
0 |
Peace River agriculture zone, BC | <40 |
29 |
North Cascades, BC | 23 |
284 |
Garibaldi-Pitt, BC | 18 |
40 |
Squamish-Lilloet, BC | 56 |
180 |
Toba-Bute, BC | 75 |
211 |
Stein-Nahatlach, BC | 61 |
129 |
South Chilicotin Ranges, BC | 104 |
257 |
Blackwater West Chilicotin, BC | 193 |
24 |
Granby-Kettle, BC | 81 |
88 |
South Selkirks, BC | 58 |
85 |
Yahk, BC | 20 |
12 |
Bitteroot, ID and MT | 0 |
445 |
Cabinet-Yak, ID and MT | 44 |
130 |
North Cascades, WA | <5 |
874 |
Northern Continental Divide, MT | 765 |
641 |
South Selkirks, ID and WA | 30–40 |
64 |
Yellowstone, WY, MT, ID | 600 |
567 |
Current population estimates were taken from government sources in British Columbia and the US and predicted population sizes were derived using our top coastal or interior model.
C. Servheen, USFWS, Montana, pers. com.
Our interior model predicted grizzly densities between 19 and 35 bears/1000 km2 in the six recovery areas in the lower 48 United States. This resulted in population predictions between 64 and 874 per study area, which is many more bears than currently occurs in two of these 6 areas (
We compared prediction units of various size and the results did not alter total population predictions for British Columbia or Yukon greatly (
The models we developed, and the population sizes predicted from them, provide information to support the implementation of grizzly bear management policies. Population predictions were used to calculate human-caused mortality limits and predict habitat capability. Sustained yield management involves the trade-off between conservation risk and benefits to society. Conservation risk can be minimized by policy, such as reducing the maximum harvest rate, or by investment, such as by increasing inventory effort. In 1978 the Government of British Columbia began to move from seasonal hunting restrictions to a quota system to manage grizzly bear hunter kill. This change was effected in order to reduce conservation risk and indeed there is evidence some grizzly bear populations increased following to this policy change (
Our study demonstrates the uncertainty in extrapolating animal densities, even for species for which there is considerable inventory data and a good understanding of the population biology. Many areas were predicted to be unoccupied, or nearly so, when clearly this was not the case based on local knowledge or kill data, and vice-versa. This presents 3 problems for wildlife managers; 1) they will be forced to decide between those conflicting data (i.e., whether to allow hunting), 2) if they allow hunting then they will have to assign a density to the area either subjectively or using some other method, and 3) the credibility of the modeling process will be reduced, because it will be clearly evident that the model is ‘wrong’. These nuances and decisions are regularly confronted by wildlife managers and our example highlights the fact that removing subjectivity from the decision making process is impossible, even for very well studied species. Our study demonstrates the benefit of local knowledge, even for this highly data-driven management system. For example, 15% of our data were from extirpated areas where the population estimates and precision were based on local knowledge.
The population predictions were higher than current estimates for all Canadian provinces and territories except British Columbia
Both our models predict more variable densities than other modeling efforts in British Columbia
Evaluation data required | Evaluation reasoning | Evaluation outcome |
Anecdotal data including the locations where bears were sighted | If the distribution or number of bears people see is increasing this suggests an increasing population | Sightings of sows with cubs suggest the unit is occupied; distributional changes suggest corresponding changes in bear numbers; increased sightings suggest an increasing population |
Locations where bears were killed or conflicted with people | The distribution of conflict or kill locations over time may suggest expanding, static or contracting bear distribution | Conflicts with sows and cubs suggest the unit is occupied; distributional changes suggest corresponding changes in bear numbers; increased conflicts suggest the population is increasing |
Absolute ages of dead bears (from all human caused mortality) | Females older than 7 years are likely residents because they are unlikely to emigrate from their home range | Presence of resident bears suggests the unit is occupied; older median age at mortality of males suggests a lower kill rate |
Age by sex of bears in the hunter kill | Trend in median age suggests a population trend | Decreasing age of males or increasing age of females may signal a declining population |
Hunter success rates | Trend in success suggests a population trend | Higher success rates may indicate an increasing population |
Proportion of females in the hunter kill | Trend in female proportion suggest a population trend | Increasing proportion of females suggests a declining male population |
These criteria can be used to confirm residency, to identify suspect predictions, evaluate a predicted level of harvest, or help decide what level of harvest to allow.
We demonstrate that grizzly bear density is related to general indices of resources in the environment. Our results suggest that ultimate factors, such as vegetation biomass and productivity, vegetation structure, and protein abundance and availability, influence grizzly bear density across its North American range. We further show the degree to which density can be reduced by human influences, other than hunting, although the limiting effect of competition on density was equivocal. Other research has demonstrated the link between forage abundance and population growth in black bear
Our results suggest the plant portion of the bear diet is indexed by precipitation and NDVI. Precipitation likely indexes plant productivity whereas NDVI is thought to index plant biomass
In coastal areas density increased as the amount of salmon in the diet increased
Mattson and Merrill
Reported human-caused mortality explained relatively little of the variation in density when other factors were accounted for. Our data did not suggest a non-linear relationship between density and kill rate, as would be expected based on current theories of population growth
Our approach to predicting density differs from most previous attempts that have usually been based on bear distribution or movement data and applied a use-versus-availability analysis approach
In contrast we followed a more functional approach using measures of grizzly bear density at the landscape scale as the dependent variable rather the presence or abundance of individuals at a site. Density combines all the factors that influence population dynamics in a single measure and should be independent of factors such as individual behaviour which influence the outcome of finer scale analyses. Our analysis was unaffected by the relative abundance or availability of different resources within a study area that can limit predictions of an RSF model
Perhaps the largest weakness of our coastal model are the salmon diet data. This was a key variable, but it was extracted from a diet surface constructed from 81 diet measures across northwest North America, and many fewer along the coast. We augmented extracted data with local diet data where they were available, but this was sporadic. Perhaps the most important influence of the diet data on outcome was in deciding whether prediction areas were coastal or interior. The main information we used for this was the salmon diet data and when these were not available we used local knowledge though this was incomplete. Finer scale diet measures should improve the models and their application.
The variables driving our model were largely static. A dynamic model would require annual databases for each variable, such that every variable would be an appropriate multiannual mean pre-dating each survey. This would require vastly more digital data and the elimination of much early bear density data, because most databases begin in the 1980's or later. An effort of this level should also attempt to document human use of the landscape via a dynamic measure of road abundance and distribution; this too would require annual road layers for the past and the future. For its current application, it is crucial that local practitioners of the model understand its limitations so they understand where model predictions are least certain.
We were unable to index the availability of terrestrial meat and the correlation between precipitation and terrestrial meat in the diet (r = −0.63) undermined our ability to evaluate this factor using diet proportions. Also, the correlation of these two variables with tree cover (rprecip = 0.33, rmeat = −0.35) negated a controlled evaluation of the importance of competition with black bears (ignoring the question as to whether the tree cover variable was a reasonable index of competition). The availability of salmon was not correlated to other independent variables, but salmon was not a major contributor to diet in the interior. In the coastal model the salmon diet proportions were quite variable and appeared sensitive to changes in salmon availability
We were unable, at the scale we worked at, to index key vegetative foods like berries. Huckleberries (
Density estimates may vary with the size of the area over which they were measured
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We thank the many scientists who shared their data and advice, especially A. Hamilton, S. Miller, R. Sellers, E. Becker, R. Flynn, L. Van Daele, G. MacHutchon, C. Apps, A. Laliberte, C. Servheen and C. Carroll. T. Gaines and D. Pritchard skillfully did the GIS analysis. Thanks to B. McLellan, C. Johnson, and J. Swenson for reviewing drafts of the manuscript and B. Cadsand for help with formatting references. We dedicate this paper to Tom Gaines who worked tirelessly on earlier versions.