ABSTRACT. MARINE MAMMAL SCIENCE, 29(3): (July 2013) 2012 by the Society for Marine Mammalogy

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1 MARINE MAMMAL SCIENCE, 29(3): (July 2013) 2012 by the Society for Marine Mammalogy Published This article is a US Government work and is in the public domain in the USA. DOI: /j x Investigating the potential use of aerial line transect surveys for estimating polar bear abundance in sea ice habitats: A case study for the Chukchi Sea RYAN M. NIELSON, 1 Western EcoSystems Technology, Inc., 200 S. Second Street, Suite B, Laramie, Wyoming 82070, U.S.A., THOMAS J. EVANS, United States Fish and Wildlife Service, Marine Mammals Management, 1011 East Tudor Road, MS 341, Anchorage, Alaska 99503, U.S.A., MICHELLE BOURASSA STAHL, Western EcoSystems Technology, Inc., 200 S. Second Street, Suite B, Laramie, Wyoming 82070, U.S.A. ABSTRACT The expense of traditional capture-recapture methods, interest in less invasive survey methods, and the circumpolar decline of polar bear (Ursus maritimus) habitat require evaluation of alternative methods for monitoring polar bear populations. Aerial line transect distance sampling (DS) surveys are thought to be a promising monitoring tool. However, low densities and few observations during a survey can result in low precision, and logistical constraints such as heavy ice and fuel and safety limitations may restrict survey coverage. We used simulations to investigate the accuracy and precision of, DS for estimating polar bear abundance in sea ice habitats, using the Chukchi Sea subpopulation as an example. Simulation parameters were informed from a recent pilot survey. Predictions from a resource selection model were used for stratification, and we compared two ratio estimators to account for areas that cannot be sampled. The ratio estimator using predictions of resource selection by polar bears allowed for extrapolation beyond sampled areas and provided results with low bias and CVs ranging from 21% to 36% when abundance was >1,000. These techniques could be applied to other DS surveys to allocate effort and potentially extrapolate estimates to include portions of the landscape that are logistically impossible to survey. Key words: Chukchi Sea, distance sampling, line transect, polar bear, Ursus maritimus, population size, resource selection, sea ice, stratification. To date, there are few reliable abundance estimates for many of the polar bear (Ursus maritimus) subpopulations currently recognized by the International Union for the Conservation of Nature and Natural Resources (IUCN) Polar Bear Specialist Group (PBSG; Aars et al. 2006), including the subpopulation occupying the Chukchi Sea. The Chukchi Sea polar bear subpopulation occurs primarily in the Chukchi Sea and Bering Sea, and management is shared between the United States (Alaska) and Russia. The majority of the Chukchi Sea polar bear subpopulation remains on the ice 1 Corresponding author ( rnielson@west-inc.com). 389

2 390 MARINE MAMMAL SCIENCE, VOL. 29, NO. 3, 2013 year-round and inhabit large remote oceanic areas that are not accessible to land-based helicopters. The Chukchi Sea subpopulation also overlaps with the Southern Beaufort Sea subpopulation in northwestern Alaska. The Agreement between the United States of America and the Russian Federation on the Conservation and Management of the Alaska-Chukotka Polar Bear Population (Bilateral Agreement) became law in 2006 and was established in part to develop an effective unified management system between the two countries. Monitoring abundance of the Chukchi Sea subpopulation is necessary due to the intense interest in polar bear management following the listing of polar bears as threatened under the Endangered Species Act (ESA) on 15 May 2008 (U.S. Federal Register 73 FR 28212), concerns over overharvest, and the potential effects of global climate change on polar bear sea ice habitat (Durner et al. 2009). Due to the invasiveness, high cost and sample size requirements of a capture recapture study, aerial line transect distance sampling (DS; Buckland et al. 2001) methodology may provide a promising alternative for estimating polar bear abundance (Wiig and Derocher 1999, Aars et al. 2009). The main advantages of DS surveys are that they are less invasive and can be completed in a much shorter period of time. However, in addition to the relatively low density of polar bears in the region, there are many logistical constraints such as limited access to remote areas far offshore, the limited range of helicopters, and dynamic sea ice conditions that could complicate obtaining a reliable polar bear abundance estimate using DS for the Chukchi Sea subpopulation. It has been estimated that each autumn polar bears from the Chukchi Sea subpopulation come on land on Wrangel Island (Ovsyanikov and Menyushina 2010) and an additional 20 or more bears come on land on the Chukotkan coast (Kochnev 2005). Regular surveys along the US coast have not been conducted, but it is believed that few bears occur on land in the United States during the autumn. This study focuses on methodology to estimate the abundance of the polar bears in sea ice habitats as part of a larger, multisurvey effort of land and sea ice habitats that would be needed to estimate the size of the Chukchi Sea subpopulation. In August of 2000, the US Fish and Wildlife Service (FWS) conducted a pilot study in the eastern Chukchi and western Beaufort seas to assess the logistical feasibility of using ship-based aerial line transect DS surveys to estimate polar bear abundance in sea ice habitats (Evans et al. 2003). Although results from the pilot study were encouraging, precision was lower than desired (coefficient of variation [CV] = 38%). The greatest source of variation (53.2%) in the abundance estimate was the encounter rate. Only 25 groups were detected along 8,257 km of transect. In addition, the pilot study had restricted coverage (Fig. 1). Areas of heavy ice were avoided, and the helicopters were limited to a 185 km range from the ship and restricted from flying over open water due to fuel limitations and safety concerns. The high cost of conducting an expanded survey covering a larger portion of the Chukchi Sea prompted an investigation into methods for improving efficiency and potentially accounting for polar bears occupying sea ice habitats outside of the region reachable by ship-based surveys. The first phase of this investigation was to create a resource (habitat) selection function (RSF; Manly et al. 2002) to predict the autumn distribution of polar bears in sea ice habitats in the Chukchi Sea (Durner et al. 2006). Durner et al. (2006) developed a RSF for polar bears using sea ice habitats in the Chukchi Sea during autumn months using location data (n = 1,198) from 124 adult female polar bears equipped with platform transmitter terminal (PTT) radio collars during The RSF developed by Durner et al. (2006) predicted the relative probability of polar bear ice habitat selection as a function of the distance

3 NIELSON ET AL.: ESTIMATING POLAR BEAR ABUNDANCE 391 Figure 1. Study area, flight lines, and polar bear observations in the eastern Chukchi Sea and western Beaufort Sea off northern Alaska during August 2000 (pilot study; fig. 1 in Evans et al. 2003). (km) from the 50% ice contour (polygon of pack ice with 50% ice concentration, buffered by 50 km), bathymetry (m), and total ice concentration. Predictions of ice habitat selection from the RSF indicated that polar bears selected sea ice locations close to the 50% ice contour but north of the 50% ice edge, and closer to shallow waters (Fig. 2; Durner et al. 2006). Here, we address the objective of the second phase of this investigation by conducting a computer simulation to investigate the accuracy and precision of different approaches for using DS methods to estimate polar bear abundance in sea ice habitats. It can be difficult to obtain reliable population estimates for marine mammal populations that have high spatial and temporal variability, and occur in relatively low densities in remote areas that are difficult to access (Aars et al. 2009, Speckman et al. 2011). Thus, it is important to determine the feasibility of obtaining accurate and precise population estimates prior to undertaking what could be an expensive and logistically complicated survey. A principal component of our effort was to develop methods to account for polar bears in sea ice habitats that cannot be sampled during ship-based aerial surveys. In addition, we attempted to identify a minimum level of survey effort that might be required to obtain an unbiased estimate of polar bear abundance with a relatively low variance (CV) and appropriate confidence interval (CI) coverage (e.g., a 90% CI containing the true abundance 90% of the time). We simulated a DS survey for polar bears in sea ice habitats using two or more helicopters with two observers each, assuming observers would sit on each side of the aircraft

4 392 MARINE MAMMAL SCIENCE, VOL. 29, NO. 3, 2013 Figure 2. Resource selection function (RSF) distribution map for 15 October 1990, with locations of GPS collared polar bears. RSF intervals represent 5% of the landscape. RSF interval 1 represents the areas with the lowest relative probability of polar bear habitat selection, and interval 20 represents the 5% of the landscape with the highest relative probability of selection. The white polygon represents Wrangel Island, Russia. in the rear seats. We also assumed that future surveys would follow survey protocol described by Evans et al. (2003). Study Area METHODS The area for our simulation study, and the potential future study area for DS surveys of polar bears on sea ice habitats was identified as the region ranging from 156 W to 170 E and Nto80 N (Fig. 3). These boundaries represent the extent of historical ( ) movements of polar bears on the Chukchi Sea ice during

5 NIELSON ET AL.: ESTIMATING POLAR BEAR ABUNDANCE 393 Figure 3. Boundary of the full Chukchi Sea study area used in the simulation. 15 September to 14 November, based on relocations of radio-tagged individuals (Durner et al. 2006). Polar bears from the Chukchi Sea subpopulation typically follow the movement of the ice as it increases during the winter months and recedes during the summer (Garner et al. 1990, 1994). During the late summer and early fall, the recession of the Arctic sea ice reaches its maximum. The autumn survey period was chosen because minimal sea ice extent occurs at that time throughout the Arctic, and bears that remain on the ice are typically concentrated near the receding ice edge. Overview of Simulations Our simulations were designed to mimic historic sea ice conditions, practical survey protocols, and logistical constraints similar to the pilot study (Evans et al. 2003). We considered 4, 6, and 8 week-long survey periods in the simulations, and subpopulation sizes of 500, 1,000, 2,000, 2,500, and 3,000 polar bears occupying the sea ice within the study area. To ensure that we accounted for changing sea ice conditions in our simulations, we used daily passive microwave sea ice data to model ship movement, where DS could occur each day, and hypothetical polar bear locations. Step 1. Randomly select a survey year and start time For each replication in a simulation, a year from 1985 to 1994 was selected at random, along with a random starting date for DS survey that allowed for completion of the survey by 14 November. These dates represent the time period used by Durner et al. (2006) to develop the RSF in the first phase of this investigation. On the first day of each simulated survey, the ship was randomly placed in a 5 5 km cell within 8 km of the western ice edge in

6 394 MARINE MAMMAL SCIENCE, VOL. 29, NO. 3, 2013 the study region (Russian waters), and as close to the 50% ice contour as possible. The daily passive microwave sea ice data from subsequent dates in that year were then used to represent ice conditions in the simulation in order to mimic realistic changes over the course of a survey. Step 2. Simulate daily survey area The daily survey area was restricted by two factors. First, the sea ice data used in this investigation was based on passive microwave imagery (SSMR, SSM/I; National Snow and Ice Data Center [NSIDC], Boulder, CO). These data were originally in raster format with a pixel size of km, but resampled at a 5 5 km resolution. Because passive microwave data are not reliable along shorelines (Cavalieri et al. 1999), we excluded pixels that were within 25 km of land. A rasterized land mask (1:10 scale Digital Chart of the World; Defense Mapping Agency 1992) with a 25 km buffer effectively removed most of the coastal pixels. Second, the area sampled in the simulations was allowed to vary by day according to sea ice characteristics. Ship-based aerial surveys would be limited by the extent and concentration of sea ice, with daily variation due to the effects of wind and current. Icebreakers available for such a survey cannot efficiently travel through ice dominated waters, and areas of heavy ice are usually avoided (Evans et al. 2003). In addition, helicopter surveys sponsored by the FWS are not permitted over open water and have a limited range. We defined the southern boundary of the daily survey area as the southern extent of sea ice on that day. The resolution of the passive microwave satellite imagery meant that some pixels classified as open water may have contained undetected sea ice. To account for this lack of precision, we buffered areas of pack ice recorded with 15% ice concentration by 50 km. We then retained the single, very large polygon of pack ice within this area (Durner et al. 2006). This polygon contained the 50% ice edge described above. Consequently, any small parcels (islands) of sea ice south of the main pack were not included in the daily survey area. The periphery of the single large polygon was considered the edge of the main ice pack, and is hereafter termed the 15% ice contour. Step 3. Simulate polar bear locations The RSF was applied to the daily ice conditions to estimate daily RSF intervals (e.g., 0% 10% relative probability of use, 11% 20%, etc.). Hypothetical polar bear groups were placed within the study area on each survey day. This was done by sampling 5 5 km cells in the study area, with replacement, using a non-equal probability sampling scheme. Sampling weights were based on the proportion of historical polar bear locations (n = 1,862) in each RSF interval (Durner et al. 2006; e.g., Fig. 2). Thus, 5 5 km cells containing polar bears were clumped and not uniformly distributed across the sea ice. However, the exact location of polar bear groups within each 5 5 km cell was random. This method of modeling polar bear locations is based on empirical data and should mimic reality if the RSF developed by Durner et al. (2006) accurately predicts where polar bears will be in the future under changing sea ice conditions. A number (45) of the simulated locations were randomly designated as polar bears equipped with GPS radio telemetry collars. We believed it would be reasonable to capture 20 adult female polar bears on a yearly basis prior to a DS survey, and if telemetry collars were designed for a 2 yr deployment, we could expect approximately 45 collared bears to be present during the survey. The locations of these bears were used in the analysis to account for individuals outside of the area reachable by a ship-based aerial survey (see Step 9). Step 4. Simulate polar bear group sizes Polar bear group sizes were generated by adding 1.0 to a random value from a Poisson distribution with a mean of = 0.16.

7 NIELSON ET AL.: ESTIMATING POLAR BEAR ABUNDANCE 395 Figure 4. Example of a sampled region with icebreaker locations and transects for one simulated 3 d survey period. Transects surveyed from a given icebreaker location are those that start at the same latitude as the icebreaker. Under this scenario, mean group size was 1.16 bears (SD = 0.374); the same as that observed in the pilot study (Evans et al. 2003). The algorithm for assigning group sizes and locations to groups was developed so that the exact number of polar bears in the entire study area equaled the desired abundance for simulation. Step 5. Simulate sampling of transects A sample of transects near the ship s location was drawn by randomly sampling (two or four) transects from all available transects with southern endpoints 16 km from the ship (Fig. 4) to ensure the helicopter was never substantially >200 km away from the ship. The length of transect pairs was determined by randomly sampling from transect lengths completed during the pilot study (mean = 81.8 km; SD = 41.4 km). Although 100 km was the targeted transect length during the pilot study, weather, logistical and mechanical constraints resulted in shorter transects being surveyed. Transect lengths were selected in pairs to better mimic actual survey conditions where transects sampled out and back would have the same length. Limiting transect starting locations to be 16 km from the ship ensured that the helicopter was always <185 km away from the ship a safety requirement for the survey. Transects were spaced a minimum of 2 km apart to avoid double-counting polar bear groups. An average of three transects were flown each day. Two transects were flown on odd days, and four transects were flown on even days. This mimicked what two helicopters completed, on average, during the pilot study (Evans et al. 2003).

8 396 MARINE MAMMAL SCIENCE, VOL. 29, NO. 3, 2013 Figure 5. Detection function fit to the pilot study survey data. Step 6. Simulate DS All but one polar bear group detected during the pilot study was 675 m from a transect line. The furthest polar bear group detected during the pilot study was 980 m away, but treated as an outlier in this investigation. In the simulations, polar bear density was calculated using standard DS methods (Eq. 1 in Appendix S1), and probability of detecting a polar bear group with a perpendicular distance 675 m was based on the kernel-estimated detection function (Eq. 2 in Appendix S1) fit to the pilot study data (Fig. 5). For example, a polar bear group 200 m east or west of a transect was "observed" in the simulation based on a random draw from a binomial distribution with probability equal to the probability of detection at 200 m (i.e., P = 0.61 in this situation). Polar bear group sizes detected by Evans et al. (2003) were not correlated with distance from the transect line (r = 0.12; 95% confidence interval from 0.49 to 0.25), so probability of detection was considered independent of group size in this investigation. Step 7. Simulate ship movement Sea ice data from the NSIDC is updated every 24 h. We anticipated being able to determine the ship s movement on a daily basis in preparation for the next day s survey. In our simulation, the ship followed the 50% ice contour in a general west to east direction. During the 2000 survey from the U.S. Coast Guard icebreaker, Polar Star, the captain was reluctant to take the ship into heavy ice. However, because the highest RSF values usually occurred near the 50% ice contour, the simulated ship did not need to move into heavy ice to allow the DS to target areas with higher expected polar bear density. The distance the ship traveled each 24 h period was based on the distance from the ship s current position to the eastern-most cell along the 50% ice contour within the

9 NIELSON ET AL.: ESTIMATING POLAR BEAR ABUNDANCE 397 study region and the number of remaining survey days. For example, if the distance from the ship to the eastern-most cell containing the 50% ice contour was 1,000 km, and there were 19 d left in the survey, the ship was moved 1,000/(19 + 1) = 50 km to the east and as close to the 50% ice contour as possible in preparation for the next day s survey. The maximum distance the ship was allowed to travel in any one day was capped at 80 km, which was the maximum distanced traveled during the pilot study (Evans et al. 2003). This algorithm moved the ship at a somewhat consistent pace, allowed complete west to east coverage of the study area, and prevented the survey from reaching the eastern edge of the study area before the survey period elapsed. Step 8. Repeat steps 2 7 Steps 2 through 7 were repeated until the end of the survey period. Based on an average of 3 transects surveyed each day, this amounted to 84, 126, and 168 transects surveyed during the 4,6, and 8 wk simulated survey periods, respectively. Step 9. Estimate abundance based on simulated data Two issues related to conducting DS over sea ice complicate standard analyses. First, standard DS analyses assume the density of objects is constant during the study period (Buckland et al. 2001). However, even if the number of polar bears in the study area is constant during a survey period, polar bear density is expected to decrease over time due to expansion the area of available sea ice, i.e., as the sea ice surface extent increases polar bear density on the ice surface decreases. For example, the extent of ice in the Chukchi Sea nearly doubled (92% increase) from 15 September to 14 November in 1993 (Durner et al. 2006) while the number of bears in the area remained essentially constant. Second, we cannot expect to obtain a spatially representative sample of transects throughout the study area due to limitations of ship-based aerial surveys (Evans et al. 2003). This presents a major hurdle in estimation of polar bear abundance in the sea ice habitats, because polar bear density is not expected to be homogeneous (Durner et al. 2006, 2009). To overcome the issue of an increasing sea ice extent and the resulting decrease in polar bear density we divided the survey into 3 d segments, or survey periods (i.e., days 1 3, days 4 6, etc.), and estimated the polar bear abundance in the study area during each 3 d period. After estimating the total number of polar bears on the sea ice within the study region for each 3 d period, we averaged the 3 d period estimates for our final estimate of total abundance. We used all observations among survey periods to estimate a detection function and the average group size, but the total number of detected polar bear groups (n) and total length of transect lines flown during a 3 d period were used to obtain an estimate of the density of polar bears in the area searched during those three days (see Appendix S1). We then estimated the total number of polar bears occupying the sampled region during the 3 d period by connecting the northern and southern endpoints of each transect surveyed (Fig. 6). This polygon constituted the region sampled during the 3 d period, and total abundance was estimated for this polygon. To account for polar bears outside of the region sampled (polygon) during each 3 d period, we considered two extrapolation methods. The first method used the ratio of collared bears to the estimated total abundance in the study region (Eq. 3 in Appendix S1). The second method involved the ratio of areas under the RSF surface (Eq. 4 in Appendix S1). Use of both ratio estimators required assuming that the sea ice and distribution of polar bears was constant within each survey period. Thus, we felt three days was the maximum length of time that could be used for each survey period. In addition, we did not use a shorter survey period because of the likelihood

10 398 MARINE MAMMAL SCIENCE, VOL. 29, NO. 3, 2013 Figure 6. Example images of the 50% ice contour with simulated icebreaker locations, transects and sampled region (3 d survey period polygon) for an 8 wk survey. Note that the survey appears to deviate from the 50% ice contour in the last two images. This is due to the change in the sea ice over time. The underlying surface for each image is for the middle date of the current 3 d survey period (sampled region). The white polygon represents Wrangel Island, Russia, which was not included in the simulations. of seeing zero polar bears within only one or two days of surveys. The assumptions of standard DS analyses and how future surveys over sea ice might be conducted are described in the Appendix S1. Step 10. Bootstrap Bootstrapping (Manly 2005) was used to estimate standard errors for the abundance estimates. The 3 d periods were sampled, with replacement,

11 NIELSON ET AL.: ESTIMATING POLAR BEAR ABUNDANCE 399 for each of 200 bootstrap samples. Each bootstrap sample contained the original number of 3 d periods in the simulated survey. New estimates of polar bear abundance were calculated for each bootstrap sample. The standard error for total abundance was estimated as the standard deviation of the 200 bootstrap estimates, and 90% CIs were calculated using ˆN ± SE[ ˆN]. The primary sample units in our analysis are the 3 d survey periods (Step 9), so when calculating CIs, it is conservative (CIs are wider) to bootstrap the 3 d period estimates of abundance rather than the individual transects. This method does not account for the variability in the RSF surface, which we expect to be of minor significance. Step 11. Repeat steps 1 10 Steps 1 through 10 were repeated 500 times for each combination of abundance and survey period length. Step 12. Compute summary statistics based on simulation results We calculated the %CV, and the percent coverage of a 90% CI for each combination of abundance and survey period length. Overall, the objectives are to minimize the %CV and have a 90% CI contain the true abundance approximately 90% of the time. All simulation steps were conducted in R (R Development Core Team 2008). Survey Costs We evaluated the relative cost of DS compared to capture-recapture studies. The costs for capture-recapture efforts in Alaska and Russia were based on ongoing capture-recapture studies in Alaska and draft research proposals for conducting ground-based studies in Chukotka, Russia. Typically, most capture-recapture efforts have taken place from land-based logistic centers, and although ice-breakers could be used for capture-recapture efforts we did not consider this option when evaluating the relative costs. In addition, the use of genetic samples collected through biopsy darting and hair snares, which are alternative capture-recapture methods for estimating abundance, were not considered in this evaluation. We assumed that sampling would have to occur in at least one location in each country and that a 5 yr time frame would be sufficient for obtaining a population estimate from a capture-recapture study. Line transect survey cost estimates were based the cost of a U.S. Coast Guard icebreaker with the ability to support two helicopters during the DS survey. Cost estimates for concurrent aerial surveys along the coastline of Alaska and Chukotka, Russia, were based on previous surveys and cost estimates provided by our Russian colleagues. RESULTS In simulations where surveys lasted eight weeks, the ship moved between 11 and 79 km each day (median = 25.0). During the course of 6 wk surveys, the ship moved between 20.0 and 79.1 km each day (median = 32.0). For 4 wk surveys, the ship moved between 30.4 and 79.1 km each day (median = 47.2). Simulation results of primary interest (population estimates) are presented in Table 1. In general, the abundance estimator based on the area under the RSF surface (RSF estimator; Eq. 4 in Appendix S1) had a CV < 36% when abundance was >1,000, and 90% CI coverage was 86% for abundances 1,000. The average relative size of a 90% CI was plus/minus 66%, 41%, 37%, and 34% when abundance was 1,000, 2,000, 2,500, and 3,000, respectively. Bias for this estimator was generally <10% when the abundance was 2,000, but became larger as abundance decreased. The

12 400 MARINE MAMMAL SCIENCE, VOL. 29, NO. 3, 2013 Table 1. Average estimate of the number of polar bears in the Chukchi Sea, percent coverage of a 90% confidence interval (CI), and the average coefficient of variation (CV = SE/estimate) for two estimators of abundance, for each hypothetical subpopulation size and number of survey weeks considered in the simulations. Simulations had 45 bears equipped with radio telemetry collars, and flew an average of three transects per day. A 90% confidence interval should contain the true population size 90% of the time (i.e., CI Coverage = 90%). The average size of the 90% CIs could be approximated for each simulation using ±1.645 CV. Abundance Survey weeks Ratio of collared bears RSF surface N CI coverage CV N CI coverage CV 3, ,958 38% 28% 3,118 91% 21% 6 2,161 54% 30% 3,009 87% 23% 4 2,719 73% 35% 3,195 86% 29% 2, ,592 36% 29% 2,583 91% 23% 6 1,857 56% 32% 2,618 89% 24% 4 2,218 72% 39% 2,753 87% 34% 2, ,405 54% 32% 2,271 91% 25% 6 1,550 64% 35% 2,184 90% 28% 4 1,744 72% 40% 2,229 87% 36% 1, % 46% 1,397 91% 40% % 46% 1,381 89% 42% 4 1,246 80% 48% 1,526 86% 45% % 46% 1,098 59% 43% % 36% 1,066 44% 33% % 29% 1,201 34% 27% 8 wk simulation with 3,000 bears had the best performance with a CV of 21% and a 90% CI coverage of 91%. Decreasing the length of the survey, and thus number of transects flown, resulted in a small increase in the CV and a slight decrease in the 90% CI coverage. Similarly, decreasing the number of bears on the sea ice resulted in poorer performance as indicated by an increase in the CV and a decrease in CI coverage. Performance of the estimator using the ratio of collared bears in the surveyed region (Eq. 3 in Appendix S1) was poor under all conditions simulated (Table 1). This estimator was usually biased low (by 11% 30%) when the abundance was 2,000. However, the estimator was biased high for an abundance of 500. Coverage of the 90% CI based on the collared bear ratio was very low (38% 80%), regardless of the number of weeks surveyed when abundance was 1,000. Table 2 highlights additional simulation results. The mean number of polar bears observed in the simulation decreased with decreasing abundance and survey length. An average of 84 polar bears were observed under an abundance of 3,000 during an 8 wk survey period, resulting in an average of 0.5 polar bears observed on each transect, and an average of 1.49 polar bears observed each day. An average of 15 polar bears were observed under an abundance of 500 during an 8 wk survey period, resulting in an average of 0.08 polar bears observed on each transect, and an average of 0.25 polar bears observed each day. The estimated cost for a DS survey conducted using two ship-based helicopters over an 8 wk period is approximately 2.8 million US dollars (Table 3). With the additional costs of concurrent shoreline surveys over the coasts of Alaska and Chukotka, Russia,

13 NIELSON ET AL.: ESTIMATING POLAR BEAR ABUNDANCE 401 Table 2. Mean number of bears observed per survey, per transect and per day across all simulation repetitions for eight, six, and four week surveys. Survey weeks Mean number of bears observed Abundance Per simulation Per transect Per day 3, , , , Table 3. Estimated costs of aerial line transect surveys over the Chukchi sea ice and along the Alaskan and Russian shorelines, along with estimated costs of conducting a capture-recapture study to estimate abundance for the same region. Survey component Survey Survey Ice breaker and Alaska Chukotka duration and two helicopters shoreline shoreline Total cost Distance sampling 4 wk $1,400,000 $60,000 $98,000 $1,558,000 6 $2,100,000 $60,000 $98,000 $2,258,000 8 $2,800,000 $60,000 $98,000 $2,958,000 Wrangel Island Alaska Chukotka Total cost Capture-recapture 5 yr $650,000 $2,250,000 $330,000 $3,480,000 to account for bears on land, the total cost could be around 3 million dollars. In comparison, we estimated a cost of approximately 3.5 million dollars for 5 yr of capture-recapture surveys based from Wrangel Island and Chukotka, Russia, and the coast of Alaska, needed to produce abundance estimates for the region. We expect that a 5 yr capture-recapture study could involve a net total of observations of polar bears (some being recaptures). Abundance Estimation DISCUSSION The RSF estimator performed well overall with average CVs between 21 and 36%, and was nearly unbiased when the number of bears on the sea ice was 2,000, regardless of the number of weeks spent surveying. The RSF estimator became positively biased as the number of bears on the sea ice or survey length decreased. However,

14 402 MARINE MAMMAL SCIENCE, VOL. 29, NO. 3, 2013 confidence interval coverage was usually close to target. DS estimates deteriorated with very low densities ( 1,000), which suggest that with small populations and low encounter rates, the ability to detect trend will be greatly reduced, and density estimates may be misleading. As a general rule, the variability in encounter rates across transects is much larger for lower density populations compared to the variability in mean group size or the estimated detection function (Buckland et al. 2001). The poor performance of the collared bear estimator was likely due to its reliance on two small ratios: the ratio of collared to uncollared bears in the study area and the ratio of collared bears inside any given 3 d survey area.the small proportion of collared bears in the study area meant that in many 3 d survey periods there were no collared bears observed and an abundance estimate could not be calculated. We rarely obtained an abundance estimate for every 3 d survey period (i.e., 10 for 4 wk, 14 for 6 wk, and 19 for 8 wk) in every simulated survey, and often only had from one to three 3 d period estimates from which to calculate the total abundance. The collared bear estimator appears to improve as the sample size decreases (number of survey weeks). This is due to an increase in the size of the sampled region and an increase in the proportion of bears in that region which were equipped with telemetry collars. During surveys of shorter duration (e.g.,4 vs. 8 wk) the ship moved more quickly to cover the entire area and thus transects were further apart, and each 3 d period covered a larger area. This resulted in more 3 d survey periods with observations of collared bears, which stabilized the estimates during the simulation. This suggests that a higher number of collared bears in the study region may improve estimates of abundance under this method. Simulation Methods There are several advantages to using computer simulation to investigate problems and evaluate potential solutions. However, we must keep in mind that a simulation is a caricature of reality rather than reality itself, and the utility of a simulation usually depends on the validity of the assumptions made during its construction (Bromaghin et al. 2011). We attempted to design our simulation using real-world conditions, such as realistic sea ice conditions and changes in the sea ice over time. Movement of the icebreaker in the simulations and helicopter coverage of the study area were based on what was accomplished in the pilot study (Evans et al. 2003). Polar bear locations were based on empirical data (Durner et al. 2006) and group sizes matched those seen during the pilot study (Evans et al. 2003). In addition, probability of detecting polar bear groups in the simulations was based on detection rates from the pilot study (Evans et al. 2003). Our simulation did not consider polar bears occupying land or areas within 25 km of the shoreline. The methodology we employed necessarily omitted the nearshore coastal zone owing to the coarse resolution of the sea ice concentration data. However, a considerable proportion of the Chukchi Sea polar bear subpopulation is known to utilize coastal areas during autumn. Durner et al. (2006) estimated that 13.2% of the polar bear locations during 15 September to 14 November in were within 25 km of shore and up to 5 km inland. In more recent years, the number of bears from the Chukchi Sea subpopulation on land in the autumn appears to have increased and is currently estimated to range between 250 and 600 (Kochnev 2005, Ovsyanikov and Menyushina 2010). Because bears can stay on land throughout the autumn period, a population estimate would require surveys on

15 NIELSON ET AL.: ESTIMATING POLAR BEAR ABUNDANCE 403 the Alaskan and Chukotkan coast and Wrangel and Herald Islands in addition to the ice-based survey outlined in this study. A similar land and ice-based survey approach was recently applied successfully in the Barents Sea (Aars et al. 2009). However, because a population estimate would require an icebreaker and multiple land-based surveys, the relative confidence interval size and coefficient of variation may be larger than those reported for the ice-only based abundance estimates reported here. We did not consider polar bears occupying open water due to safety regulations enforced on the helicopter flights. Polar bears cannot forage effectively in open water, and individuals swimming in large expanses of open water are likely traveling to icecovered areas or land. Durner et al. (2006) found only a small portion ( 1%) of bear locations offshore and >50 km south of the 15% ice concentration contour during 15 September to 14 November in However, as the sea ice decreases bears may spend more time in open water (Durner et al. 2011). Based on analysis of the time spent in the water from satellite collars that are recovered with GPS positions (Durner et al. 2011), it would be possible to develop a correction factor if needed. Mauritzen et al. (2003) suggested that polar bears select habitat with sea ice concentrations that are optimal for hunting seals, provide safety from ocean storms, and prevent them from becoming separated from the main pack ice. Although polar bears are most often found where sea ice concentrations exceed 50% (Durner et al. 2004, 2006, 2009), they will use lower sea ice concentrations if this is the only ice that is available over the shallower, more productive waters near the continental shelf. This was evident during the late-summer to early-fall open-water period in August and September of During this time, most of the ice in the Beaufort Sea had receded beyond the edge of the continental shelf, except for a narrow tongue of sparse ice that extended over shelf waters in the eastern Beaufort Sea. Polar bears were documented using this marginal sea ice habitat with sea ice concentrations between 15% and 30%. Our simulation incorporated historical sea ice conditions and an RSF developed from polar bear locations in Sea ice extent, concentrations of multi-year ice, and sea ice stability have drastically declined since 1994 and are expected to further decrease into the 21st century (Derocher et al. 2004, Durner et al. 2004, Stirling and Parkinson 2006, Amstrup et al. 2008, Durner et al. 2009). Potential future changes in the quantity and quality of available sea ice habitat for polar bears in the Chukchi Sea warrant further investigation to determine if resource selection habits of polar bears can be expected to change before a DS survey can be conducted in the region. For these reasons, we recommend validating the RSF developed by Durner et al. (2006) using contemporary radio telemetry locations of polar bears in the Chukchi Sea. Results from this simulation suggest that DS has the potential to be a useful and, potentially, more economical method for estimating the abundance of polar bears in the Chukchi Sea polar region compared to capture recapture methods. The main advantages of DS surveys are that they are less invasive than methods that require capturing individual animals, can be completed in one season, and can theoretically be applied to widely distributed populations such as the Chukchi Sea polar bear subpopulation. DS surveys of the kind explored here also have the advantage of requiring less international and geographic coordination than would a capture-recapture study covering the same geographic area. This simulation supports the expectation that detection rates would increase at higher densities, but that at abundances below 1,000, DS may be of limited use. In contrast, capture-recapture methods allow for

16 404 MARINE MAMMAL SCIENCE, VOL. 29, NO. 3, 2013 collection of data on vital rates (survival and reproduction), movements and habitat use (if bears are fit with satellite tags), body condition, growth rates, sex and age composition, and spatial and temporal variability of polar bear distributions. In addition, we believe that a capture-recapture study would require a minimum of five years of field data collection before reliable abundance estimates would be available. Conclusions and Management Implications The two abundance estimators considered in the simulation can both be viewed as estimators for a stratified survey area. The estimator based on the ratio of collared bears is akin to dividing the study area into two strata surveyed and not surveyed. The estimator based on the volume under the RSF surface is akin to dividing the study area into a large number of strata one for each 5 5 km cell in the GIS. Our simulations indicate that DS surveys could be successfully used to estimate polar bear abundance on the sea ice, and survey costs are estimated to be lower for DS surveys compared to capture-recapture methodology. Although simulation results indicate that a longer survey period is preferable, the resulting sample size (number of transects flown) in the simulation was a function of the number of transects flown per day. Flying more transects can increase the number of transects flown during a shorter period. An additional simulation (not shown in Table 1) was run with an average of three sorties per day (six transects) over a 4 wk period with a subpopulation size of 2,000 polar bears to emulate a doubling of sampling intensity within the shortest survey period. The results for both ratio estimators from this simulation were similar to that for an 8 wk survey with an average of 1.5 sorties per day (i.e., 90% CI Coverage = 87%, CV = 26%). We expect that a 4 wk survey flying an average of six transects per day would result in estimates similar to those obtained using only three transects per day during an 8 wk survey. However, Evans et al. (2003) had two helicopters available but only managed to survey an average of three transects per day due to weather conditions, mechanical issues, and other constraints. Given the apparent advantages multiple aircraft provide, resolving obstacles to their use will be an important part of any survey implementation plan. Given the performance of the estimator based on the ratio of RSF predictions, we expect power to detect trends in the number of bears on the sea ice to be acceptable ( 80%) if DS surveys were repeated on an annual, biennial, or semiannual basis (e.g., every 3 5 yr) over a long period of time (20+ yr). Power to detect trends depends more on the accuracy of the methods used rather than the precision of the resulting estimates. However, precision in the abundance estimates from the simulations were acceptable, and gains in precision could be realized as the number of survey years increase if data are pooled across years for estimating probability of detection (Eq. 2 in Appendix S1), which can be justified when survey protocol is consistent (Nielson et al. 2011). To gain further insight into the statistical power of a long-term monitoring program for estimating trends, we recommend conducting a power analysis following additional surveys. In general, we recommend conducting simulations based on pilot study data to investigate the performance of estimators when conditions complicate standard DS analyses, such as when population densities are low and logistical constraints may limit spatial coverage. Inclusion of RSF predictions appears to be a viable method for survey stratification, which was intended to increase the number of polar bear observations available for analysis and improve precision of the final abundance

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