Aerial Survey for Moose in the Range of the Narraway Caribou Herd Using Distance Sampling March 15th March 22nd 2010

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1 Aerial Survey for Moose in the Range of the Narraway Caribou Herd Using Distance Sampling March 15th March 22nd 2010 Prepared by: Wibke Peters (M.S. Student) and Dr. Mark Hebblewhite Wildlife Biology Program College of Forestry and Conservation University of Montana Missoula, MT, USA and Conrad Thiessen Wildlife Biologist Ministry of Environment th Avenue Fort St. John, BC V1J 6M7, Canada

2 Introduction Despite their key role in provincial harvests of British Columbia (BC) and Alberta (AB), knowledge of moose (Alces alces) density is also important for caribou (Rangifer tarandus) conservation and recovery planning if caribou declines are a result of apparent competition with moose. Modeling studies by Weclaw and Hudson (2004), Lessard et al. (2005) and Courtois and Quellet (2007) showed that wolf (Canis lupus) reduction without concurrent reduction of moose populations will fail to recover caribou. For example, the woodland caribou recovery plan for Alberta recommend active management of predators in combination with controlling moose densities in caribou ranges (Alberta Woodland Caribou Recovery Team 2005). Population assessment is viewed as one of the primary components of moose management (Ward et al. 2000) and is a baseline requirement to simultaneously consider the aforementioned conflicting goals. However, little is known about moose population abundance throughout many caribou ranges in west-central AB and east-central British Columbia. Monitoring efforts by managers are often impeded in the presence of limited financial resources. In North America, moose populations are commonly estimated using the Gasaway-method (Gasaway et al. 1986), a stratified random block (SRB) sampling design, or modifications of this method (e.g. Lynch 1997). Due to high time and cost requirements (Ward et al. 2000), the Gasaway method is appropriate for dense moose populations in small survey areas (Buckland et al. 2001, Nielson et al. 2006). Contrary to the SRB survey design, where essentially the probability of detecting an animal is assumed to be constant for all distances within a fixed transect width (Shorrocks et al. 2008), Distance Sampling uses the perpendicular distances to derive a relative measure of detection probability as a function of distance (Buckland et al. 2001). The most critical assumption to Distance Sampling is that all moose are detected with certainty on the transect line (g(0)) or that an unbiased correction factor can be estimated (Buckland et al. 2001). Distance Sampling is more cost- and time efficient in larger study areas with sparsely distributed animal populations (Buckland et al. 2001, Nielson et al. 2006). We aimed to estimate the relative abundance of moose in portions of two Management Units (MUs) using Distance Sampling data corrected for decreased sightability on the transect line in Management Unit (MU) 7-19 in east-central BC and Wildlife Management Unit (herein also MU) 445 in west-central AB, Canada. 1

3 Study Area Our survey area ranged from the south-eastern portion of MU 7-19 in British Columbia to the south-eastern portion of MU 455 in Alberta. Its eastern border was defined by the Narraway River and the AB/BC border further north and its western extend reached the Red-Willow River and the mountain/foothill edge down towards Sherman meadows in AB. The south-western portions of the survey area are characterized by dense pine stands and rugged terrain, which give way to rolling boreal foothills in the north-eastern parts, where pine stands and mixed-wood stands can be found. Also, human landscape use is higher at lower elevations in the north-eastern portions and thus, a mosaic of clear cuts and seismic lines often characterizes the landscape. Oil and gas well site development is considered moderate in this region (Alberta Woodland Caribou Recovery Team 2005). Our survey area represents parts of the northern most extend of the Narraway woodland caribou home range. This caribou herd is currently considered as declining (AB data summarized in Hebblewhite et al. 2010) Figure 1: Map of the transboundary survey area for moose (Alces alces) in Management Units (MUs) 7-19 (British Columbia; BC) and 445 (Alberta; AB) with east-west running transect lines. Start and end points of transects can be found in Appendix 3. Also displayed is the annual 95% Kernel home range of the Narraway caribou (Rangifer tarandus) herd. 2

4 Methods Following a Distance Sampling survey in AB in 2009 under similar conditions, we initially evaluated whether the four main assumptions to Distance Sampling, 1) transect lines are placed randomly, 2) objects on the line are always detected, 3) objects are detected at their initial location prior to movement in response to observers, and 4) distances are measured accurately, could be met in this survey area. We established a systematic grid of equally spaced transects running from east to west along Universal Transverse Mercator (UTM) zone 11(Nad 83) along the full extent of the survey area from which we selected a random start. We spaced transects every 4km. The survey was flown with a Bell 206 Jet Ranger helicopter, equipped with bubble windows. The pilot used a global positioning system (GPS, Garmin GPS60; Garmin International, Olathe, Kansas) following previously uploaded transects and tried to keep lines as straight as possible by references to GPS, within certain limits imposed by wind. The altitude above the ground level (AGL) and survey speed varied slightly overall between 70m and 100m AGL and 80 km/hr and 140 km/hr, but were kept approximately consistent for different habitat types. The helicopter was staffed with four observers with the pilot being the front right observer. The observer next to the pilot was responsible for detecting moose at closer distances through the foot-window of the helicopter and also assisted with navigation and determined height and speed of search. The rear-right observer behind the pilot had a separate GPS unit to record location data of moose to measure perpendicular distance from the transect line following Marques et al. (2006). Every time a moose was detected a point was marked on the transect line and then a second location was obtained by flying off transect to where the moose had initially been detected or the center of the moose cluster (Marques et al. 2006). These GPS data were downloaded to a computer post survey and the perpendicular distances were calculated from the first to the second waypoint in ArcGIS software (Environmental Systems Research Institute, Inc., Redlands, Calif.). A moose cluster was defined as moose that were socially or behaviorally associated, such as cow-calf pairs or moose that were spatially closely aggregated (i.e. approximately <50m apart). Besides cluster size we also recorded covariates known to influence detection probability, including moose activity, topography and snow cover (e.g. Drummer and Aho 1998, Quayle et al. 2001; Appendix 1). The age of spotted moose was categorized as calf or adult and females were identified from males based on the presence of the vulval patch and absence of antler scars. Age classification of male moose based 3

5 on their antler architecture was not possible as surveys were conducted in mid March and antlers were not present. Distance Sampling data were analyzed in program DISTANCE v (Thomas et al. 2010). We initially conducted exploratory analysis to determine a suitable truncation distance to improve model fit of the detection functions (Buckland et al. 2001). Modeling the detection function in program DISTANCE followed a two-stage modeling approach, where first a key function is selected and then a series expansion (adjustment term) is added to improve the fit of the model to the distance data (Buckland et al. 2001, Southwell 2006). We considered robust combinations of key functions, up to three adjustment terms and also included covariates in our detection function modeling process (Buckland et al. 2001). Our a-priori candidate models were a half-normal key function with the option of hermite adjustment terms, a uniform key function with the option of cosine or polynomial adjustments and a hazard-rate key function with cosine adjustments. We considered the covariates snow cover, canopy closure, cluster size or activity to influence moose sightability. The best detection function was determined using Akaike s Information Criterion with small sample size correction (AICc; Buckland et al. 2001, Burnham and Anderson 2002). We examined results from Goodness-of-fit tests (χ2 GOF) and Qq-plots, especially at distances near zero, to detect potential violations to the assumptions of Distance Sampling (Buckland et al. 2001). To avoid size bias in the estimate of moose clusters at further distances, we used a size-bias regression estimator in program DISTANCE, where the log of moose cluster size is regressed against the estimated detection probability at distance x (Buckland et al. 2001). This method estimates the expected cluster size on the transect line, where size bias should be largely negligible. We estimated density separate for the BC and AB portion of our survey area, but also calculated the pooled estimate. Finally, we used a correction factor for sightability bias on the transect line (transect line was defined as distances 0-25m) derived from a sightability model (Appendix 4) as a multiplier in program DISTANCE to re-scale the detection function (Buckland et al. 2004) for each survey unit and for the pooled estimate. The standard error of the predicted probability of detection on the transect line was estimated with the Delta method (Seber 1982). The variance of the density estimate was calculated analytically at a 90% confidence interval (CI) by combining the individual variance of the model components in program DISTANCE (Buckland et al. 2001). 4

6 Results Distance Sampling surveys in MUs 7-19 and 445 were flown on four days between March 15 th and March 20 th The total transect length was 597km, with 141 km flown in AB and 456km flown in BC (Table 1). We detected a total of 34 moose in 22 clusters (11 individuals in nine clusters in AB and 23 individuals in 13 clusters in BC). Moose clusters consisted of 11 females, five males and two unknowns in BC and five females, four males and two unknowns in AB. We did not detect any calves. Low numbers of detections of moose made fitting the detection function difficult. To overcome some of the uncertainty with modeling detection probability given the small sample sizes, we considered pooling data of this transboundary survey area with data collected in winter 2008/2009 in MU 440 in west-central Alberta (Figure 2). A pooled detection function can increase precision and we explored the validity of pooling data across surveys conducted under similar conditions by comparing AICc values of different strata versus AICc values of pooled data. The sum of AICc values for data from individual data sets was found to be lower than the AICc value from the pooled data (ΔAICc =1.3), indicating that detection function did not differ for strata and pooling data is justified to increase precision of the Figure 2: Aerial Distance Sampling surveys were conducted for moose (Alces alces) in winters 2008/2009 (within Management Unit (MU) 440, blue) and in 2009/2010 (within MUs 7-19 and 445, red). detection function (Buckland et al 2001). This increased our sample size for estimating detection probability to 53 samplers (transect lines) and 47 observations (moose clusters). Following the outlined model selection process we modeled moose density using a halfnormal model with no adjustment terms and snow cover as a covariate term (see Appendix 2 for candidate models). The pooled detection function had an average probability of detection (not 5

7 corrected for sightability at g(0)) of 0.54 (CV=11.19) and the effective strip width was 142m. The average cluster size was 1.36 (CV=7.21) and the expected cluster size was 1.25 (CV=5.87). Applying this detection function and a sightability correction factor at g(0) (see Appendix 4 for details) we estimated moose density for the BC and AB portions and both survey units pooled (Table 1). The correction factors for g(0) differed between survey units and varied between detection probabilities of 0.37 (SE=0.135) in BC and 0.57 (SE=0.197) in AB. The probability of detection for the pooled transboundary study area was 0.43 (SE=0.153). Moose densities were lower in the BC portion of the survey area ( BC=0.34 versus AB=0.49) and its estimate was more variable (CV BC = 59.72% versus CV AB =52.56%, 90%CI). The density estimate for the pooled survey area was 0.38 with a CV of at a 90%CI. Table 1. Number of transect lines (# Samplers), total survey effort in kilometers, the number of moose clusters (groups) detected and the estimated detection probability on the transect line (g(0)) along with its standard error (SE) and the degrees of freedom (df) in two survey units, portions of Management Unit (MU) 7-19 in British Columbia and portions of MU 445 in Alberta, Canada, and both units pooled. Density estimates and their coefficients of variation (CV) were corrected for decreased detection probability on the transect line. Stratum # Samplers Effort # Clusters CV g(0), SE, df Density (km) Detected (90%CI) British Columbia , 0.135, Alberta , 0.197, Pooled , 0.153, Discussion We surveyed 597km of transect line and recorded a density of 0.38 moose/km 2 under challenging sightability conditions and a low overall sightability of ~0.43 during March 2010 in westcentral BC and east-central AB. Despite large variation of estimates, moose density appeared to be higher in MU 445 on the Alberta side of the border than in MU 7-19 in British Columbia by a density of 0.15 moose/km 2. The best supported Distance Sampling model indicated that decreased snow cover reduced sightability of moose. While low encounter rates of moose increased variation in our surveys, moose density estimates were close to moose densities observed in adjacent MUs, e.g. MU 355 ( =0.36, CV=16%; surveyed in 2005; M. Russel, AB Sustainable Resource Development, unpubl. data ) or MU 357 ( =0.38, CV=12%; surveyed in 2009; Stepnisky at al. 2009). Moose play a key role in BC and AB as they are a valued big game species to humans, but also 6

8 because of their importance for caribou conservation due to hypothesized apparent competition between moose, caribou and wolves (Lessard et al. 2005, Wittmer et al. 2007). The data collected during this survey provided important information on the role of moose in this ecosystem. Our density estimates had very high CVs and the low encounter rate (detected number of moose/km transect line) of moose clusters contributed the largest portion of the variance (e.g. 51% for the CV of the pooled density estimate). The total transect line length would have to be increased substantially to increase the number of moose cluster encounters, essentially decreasing variance of density estimates. However, we feel that the biggest problem during our 2009/2010 survey was not too little survey effort that lead to these rather large variances, but the unfavorable survey conditions. Distance Sampling generally accounts for variability in survey conditions through pooling robustness and the sightability correction factor that is inherent to the method (detection probability is function of distance; Buckland et al. 2001). Nonetheless, a sample size of at least 60 observations is recommended to generate population estimates with acceptable precision (Buckland et al. 2001). We were not able detect this number of moose observations, even after pooling data with survey data of comparable MU (MU440). Temperatures were highly variable during our survey and ranged from -15 C during one morning to 10 C during some days. While temperature has no direct effect on sightability of moose, it greatly effects other variables, such as canopy closure of preferred habitat and activity levels of moose (Quayle et al. 2001). Moose are easier to detect in colder temperatures as they seek more open habitats (Peek et al. 1976) and Crete et al. (1986) found that counts in March were only about half of those in January. Also, observer experience was very hard to control for during our surveys due to very limited availability of experienced personnel. The primary observer remained the same during all flights and was very experienced, however the level of experience of the remaining two observers in the back of the helicopter varied from high experience to very low. LeResche and Rausch (1974) found a significant difference between experienced and inexperienced observers and experienced observers spotted up to 20% more moose. Snow cover was very variable throughout our survey and in some spots we saw larger patches of ground, especially around the base of trees. During the Distance Sampling survey conducted in MU 440 snow conditions were a little bit better and in total (in MUs 7-19, 445 and 440 combined) 13 moose clusters were detected in poor snow conditions and 34 in good snow conditions. A model with snow cover as a covariate had the lowest AICc value and therefore was selected to predict detection probability for moose. While our sample 7

9 size is barely sufficient to model the effect of a covariate on detection probability, our results make sense biologically and the effective strip under poor snow conditions was about 100m less than under good snow conditions. Thus, we feel that we modeled the given data appropriately, even though a larger sample size would be much preferred. However, we strongly recommend conducting future survey flights under conditions that optimize sightability, i.e. following fresh snowfall, during periods of high moose activity (e.g. in the morning or evening), only with experienced observers and pilots and surveys should be conducted preferably earlier in winter (December January) before moose shift into denser habitats (Timmermann and Buss 2007), to increase the encounter rate of moose and thereby decrease variability of density estimates. Overall, we showed that Distance Sampling holds promise in effectively estimating moose densities, even in denser canopy closure and under survey conditions that were not ideal. Even though the variation of our density estimates was very high, this survey provided important density data in a survey region were moose populations estimates have not been assessed in the past. Acknowledgements We thank the BC Ministry of Environment for financial support and the AB Sustainable Resource Development for provision of fuel. We also greatly acknowledge assistance of volunteer observers, including Harry Prosser, Erin Fredlund, Lane Doucette and Randy Bedell. Helicopter charter was provided under contract by Qwest Helicopters Inc. of Ft Nelson and we especially thank Newman Subritzky for safe flying under difficult conditions. Literature Cited Alberta Woodland Caribou Recovery Team Alberta woodland caribou recovery plan 2004/ /14. Edmonton, AB. Buckland, S. T., D. R. Anderson, K. P. Burnham, J. L. Laake, D. L. Borchers, and L. Thomas Introduction to Distance Sampling, Estimating abundance of biological populations. Oxford University Press, New York. Courtois, R., and J. P. Ouellet Modeling the impact of moose and wolf management on persistence of woodland caribou. Alces 43: Drummer, T. D., and W. R. Aho A Sightability Model for Moose in Upper Michigan. Alces 34: Gasaway, W. C., S. D. DuBois, D. J. Reed, and S. J. Harbo Estimating moose population parameters from aerial surveys. Biological Papers of the University of Alaska, Fairbanks. Hebblewhite, M., M. Musiani, N. DeCesare, H. S., W. Peters, H. Robinson, and B. Weckworth Linear Features, Forestry and Wolf Predation of Caribou and Other Prey in West Central Alberta. Final report to the Petroleum Technology Alliance of Canada (PTAC). 8

10 LeResche, R. E., and R. A. Rausch Accuracy and precision of aerial moose censusing. Journal of Wildlife Management 38: Lessard, R. B., S. J. D. Martell, C. J. Walters, T. E. Essington, and J. F. Kitchell Should ecosystem management involve active control of species abundances? Ecology and Society 10. Lynch, G Nothern moose program, moose survey field manual. Unpublished report by Wildlife Management Consulting. Marques, T. A., M. Andersen, S. Christensen-Dalsgaard, S. Belikov, A. Boltunov, O. Wiig, S. T. Buckland, and J. Aars The use of Global Positioning Systems to record distances in a helicopter line-transect survey. Wildlife Society Bulletin 34: Nielson, R. M., L. L. McDonald, and S. D. Kovach Aerial line transect survey protocols and data analysis methods to monitor moose (Alces alces) abundance as applied on the Innoko National Wildlife Refuge, Alaska. Technical report prepared for US Fish and Wildlife Service Peek, J. M., D. L. Urich, and R. J. Mackie Moose habitat selection and relationships to forest management in northeastern Minnesota USA. Wildlife Monographs:1-61. Quayle, J. F., A. G. MacHutchon, and D. N. Jury Modelling moose sightability in southcentral Bristish-Columbia. Alces 37: Seber, G. A. F The estimation of animal abundance and related paramters. 2 edition. Chapman, London and Macmillan, New York. Shorrocks, B., B. Cristescu, and S. Magane Estimating density of Kirk's dik-dik (Madoqua kirkii Gunther), impala (Aepyceros melampus Lichtenstein) and common zebra (Equus burchelli Gray) at Mpala, Laikipia District, Kenya. African Journal of Ecology 46: Stepnisky, D., R. Stavne, and N. Webb WMU 357 Moose, White tailed Deer, and Elk. Pages In: N. Webb and R. Anderson. Delegated aerial ungulate survey program, survey season. Data Report, produced by the Alberta Conservation Association, Sherwood Park, Alberta, Canada. Timmermann, H. R., and M. E. Buss Population and Harvest Management. Pages in A. W. Franzmann, andc. C. Schwartz, editors. Ecology and Management of the North American Moose. University Press of Colorado, Boulder. Ward, M. P., W. C. Gasaway, and M. M. Dehn Precision of moose density estimates derived from stratification survey data. Alces 36: Weclaw, P., and R. J. Hudson Simulation of conservation and management of woodland caribou. Ecological Modeling 177: Wittmer, H. U., B. N. McLellan, R. Serrouya, and C. D. Apps Changes in landscape composition influence the decline of a threatened woodland caribou population. Journal of Animal Ecology 76:

11 Distance Appendix 1. Data sheet used for aerial Distance Sampling surveys for moose (Alces alces) in westcentral Alberta and east-central British-Columbia conducted in winters 2008/2009 and 2009/2010. Distance Survey Form Date: Weather: Temperature: Cloud Cover: Precipitation: Data recorder (FL): Pilot (FR): Back left observer (BL): Back right observer (BR): Line ID Moose number Canopy Closure seen by (FR, FL, Snow Estimated Light BR, BL) Cows Calves Bulls Activty Cover 10 m 50 m Terrain height ABL intensity Comments Activity: B= bedded,s= standing, M= moving Snow Cover: 1=poor (bare ground showing), 2= good (some low veg. showing), 3=excellent (complete snowcover, fresh or moderate) Canopy closure: Any vegetative cover that blocks view of the moose; based on % of ground not being visible in a 10 m diameter around the moose initially sighted in a group. L= low (open: 0-33%), M= medium (34-66%), H=high (67-100%) Terrain: F= flat, M= moderate, S= steep Light intensity: F= flat, B = bright 10

12 Appendix 2. Candidate models (consisting of key functions and potentially adjustment terms and covariates) for modeling moose (Alces alces) probability of detection during Distance Sampling in portions of Management Units (MUs) 7-19 in British Columbia, 445 and 440 in Alberta, Canada. Ranking of candidate models is based on the difference in Akaike s Information Criterion corrected for small sample sizes (ΔAICc). The χ² GOF is the p-value of the χ² goodness of fit test. Aerial surveys were flown in winters 2008/2009 in MU 440 and in 2009/2010 in MUs 7-19 and 445. Key Adjustment Terms Covariates # Key Parameters # Adjustment Terms AIC c Δ AIC c χ2 GOF Half-normal Snow Uniform Cosine Half-normal Cosine Snow Half-normal Cluster Size Half-normal Hazard-Rate Uniform Polynomial Half-normal Cosine Half-normal Cluster Size Half-normal Hermite Half-normal Canopy Half-normal Terrain Half-normal Canopy Hazard-Rate Cosine Hazard-Rate Activity Hazard-Rate Polynomial Hazard-Rate Snow Hazard-Rate Canopy Hazard-Rate Terrain Half-normal Hermite Hazard-Rate Cluster Size Half-normal Cosine Half-normal Terrain Half-normal Activity Half-normal Activity

13 Appendix 3: Details on transect lines for Distance Sampling. Survey area comprised of portions of Management Units 7-19 in British Columbia and 455 in Alberta, Canada. Aerial surveys were conducted in March 2010 to estimate population size of moose (Alces alces). 3a) Detailed survey area maps. The first map is the northern portion of the survey area and the second one represents the southern portion. 12

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15 3b) Start and end Universal Transverse Mercator (UTM; Zone 11, Nad 83) points. Lines are in order from north to south. Line ID Orientation UTME UTMN Comments 1 W E W E W E W W E W E W E W W E W E W Transboundary 10 E W Transboundary 11 W E Transboundary 12 W E Transboundary 13 W E Transboundary 14 W W Transboundary 15 E W Transboundary 16 E W Transboundary 17 E W Transboundary 18 W E W

16 20 E W E W W E W E W E

17 Appendix 4: Development and Results of Moose Sightability Model Background and Methods A moose sightability model was developed based on aerial survey trails (n=41) using radiocollared moose (Alces alces; University of Montana Animal Care and Use Protocol MHECS ) in winters 2008/2009 and 2009/2010. Sightability trials were flown in west-central Alberta and East-central British Columbia (Figure 1a). Sightability trials consisted of first locating radiocollared moose from a fixed-wing aircraft, and then conducting helicopter surveys using a strip width of 400m to determine detection probability for moose within those strips. For each observed or missed moose (missed moose were located via radio-collar signal), group size, canopy closure, terrain, light intensity, GPS waypoints to measure perpendicular distance following Marques et al. (2006) were recorded. Following univariate analysis, sightability data were analyzed using multiple logistic regression models (Hosmer and Lemeshow 2000). We screened all candidate variables for collinearity, excluding variables above the threshold of Pearson s correlations between variables of r >0.6 by calculating the Pearson s correlation between variables (Hosmer and Lemeshow 1989). We compared a priory defined models using Akaike s information criterion with a small sample size correction (ΔAICc) to select a top model (Manly et al. 1996, Burnham and Anderson 2002). We evaluated model fit using the Pseudo R 2, Hosmer-Lemeshow s C-statistic, classification tables, Likelihood ration χ2 goodness-of-fit statistics, the area under the receiver operating characteristic (ROC) curve (Hosmer and Lemeshow 2000). Data analysis was conducted using STATA v.10.1 (StataCorpLP, Tex.). Results Figure 1a. Capture locations of GPS- and VHF- collared moose (Alces alces) to conducts sightability trials in winters 2008/2009 and 2009/2010. During the 41 sightability trials, 20 moose (51%) were missed within the 200m strips on either side of the helicopter. Univariate analysis indicated that cluster size, canopy closure and terrain significantly affected sightability of moose. Building from these univariate relationships, the best fitting multiple logistic regression model from our candidate model set was a function of cluster size, topography, and canopy closure with all predictor covariates being significant at an alpha-level of The linear part of the top logistic regression top model is given by: 16

18 ŷ = Cluster Flat Canopy1. Thus, moose sightability decreased for single moose (Cluster1), increased in flat topography (Flat) and open canopy closure (0-33%, Canopy1). The categories Canopy2 (34-66% canopy closure) Canopy3 (67-100% canopy closure), Cluster2 (two moose), Cluster3 ( three moose) and uneven terrain (Uneven) were subsumed into the intercept. The model predicted moose sightability very well according to the Hosmer and Lemeshow χ2 statistic (χ2=0.85, df=7, P=0.97). Classification success was high (overall 85.4% at a cut-point probability of 0.5), with high classification of both detections (i.e., sensitivity = 90.5%) and missed (i.e., specificity = 80.0%). The model validated well showing ROC value of 0.93, demonstrating outstanding discrimination (Hosmer and Lemeshow 2000). Literature Cited Buckland, S. T., D. R. Anderson, K. P. Burnham, J. L. Laake, D. L. Borchers, and L. Thomas Introduction to Distance Sampling, Estimating abundance of biological populations. Oxford University Press, New York. Burnham, K. P., and C. R. Anderson Model selection and inference: A practical information theoretic approach Volume second edition.wiley. Gasaway, W. C., S. D. DuBois, D. J. Reed, and S. J. Harbo Estimating moose population parameters from aerial surveys. Biological Papers of the University of Alaska, Fairbanks. Hosmer, D. W., and S. Lemeshow, editors Applied Logistic Regression. John Wiley and Sons, New York. Manly, B. F. J., L. L. McDonald, and G. G. Garner Maximum likelihood estimation for the double-count method with independent observers. Journal of Agricultural, Biological, Environmental Statistics 1: Marques, T. A., M. Andersen, S. Christensen-Dalsgaard, S. Belikov, A. Boltunov, O. Wiig, S. T. Buckland, and J. Aars The use of Global Positioning Systems to record distances in a helicopter line-transect survey. Wildlife Society Bulletin 34: