ESTIMATING MOOSE ABUNDANCE IN LINEAR SUBARCTIC HABITATS IN LOW SNOW CONDITIONS WITH DISTANCE SAMPLING AND A KERNEL ESTIMATOR
Eric J. Wald1,3,4 and Ryan M. Nielson2
1US Fish and Wildlife Service, Yukon Delta NWR, PO Box 346, Bethel, Alaska 99559; 2Western EcoSystems Technology, Inc, 415 W. 17th St., Suite 200, Cheyenne, Wyoming 82001; 3University of Wyoming, Department of Ecosystem Science and Management, Dept. 3354, 1000 E. University Ave., Laramie, Wyoming 82071-3354
ABSTRACT: Moose (Alces alces) are colonizing previously unoccupied habitat along the tributaries of the lower Kuskokwim River within the Yukon Delta National Wildlife Refuge (YDNWR) of wes- tern Alaska. We delineated a new survey area to encompass these narrow (0.7–4.3 km) riparian corri- dors that are bounded by open tundra and routinely experience winter conditions that limit snow cover and depth necessary for traditional moose surveys. We tested a line-transect distance sampling approach as an alternative to estimate moose abundance in this region. Additionally, we compared standard semi-parametric detection functions available in the program Distance to a nonparametric kernel-based estimator not previously used for moose distance data. A double-observer technique was used to verify that the probability of detection at the minimum sighting distance was 1.0 (standard assumption). Average moose group size was 2.03 and not correlated with distance from the transect line. The top semi-parametric model in the program Distance was a hazard-rate key function with no expansion terms. This model estimated average probability of detection as 0.70 with an estimated abundance of 352 moose (95% CI = 237–540). The CV for the semi-parametric model was 20% and had an estimated bias of 1.4%. The nonparametric kernel-based model had an average probability of detection of 0.73 and an estimated abundance of 340 (95% CI = 238–472) moose. The CV for the kernel method was 18% and the estimated bias was <0.001%. Line-transect distance sampling with a helicopter worked well in the narrow riparian corridors with low snow conditions, and survey costs were similar to traditional surveys with fixed-wing aircraft. The kernel estimator also per- formed well compared to the standard semi-parametric models used in program Distance. Our technique provides a viable approach for surveying moose in similar areas that have restrictive conditions for standard aerial surveys.
ALCES VOL. 50: 133–158 (2014)
Key Words: Alaska, Alces alces gigas, distance sampling, kernel, line-transect, moose, population estimate, survey, Y-K Delta
The Yukon Delta National Wildlife 2008), which is the preferred method Refuge (YDNWR) is divided into 4 primary adopted by the Alaska Department of Fish moose (Alces alces) survey units along the and Game (ADFG) and several other federal Yukon and Kuskokwim Rivers. Surveys in agencies including other National Wildlife these units are typically conducted using Refuges in Alaska. Only one survey unit is the GeoSpatial Population Estimator on the lower Kuskokwim River within (GSPE) technique (Ver Hoef 2002, DeLong YDNWR, and encompasses nearly 2250 2006, Kellie and DeLong 2006, Ver Hoef km2 of contiguous habitat along the
4Present address: Arctic National Wildlife Refuge, 101 12th Ave, Rm# 236, Fairbanks, Alaska 99701 133 ESTIMATING MOOSE ABUNDANCE – WALD AND NIELSON ALCES VOL. 50, 2014 relatively wide riparian corridor. The GSPE Wildlife Refuge; Aderman and Woolington technique overlays a grid of sample blocks 2006). The Kuskokwim tributary survey unit on the study area where each block is strati- was first proposed, designed, and partially fied into high or low moose density based surveyed in the winters of 2009 and 2010 on a previous stratification flight. A random using the GSPE technique; weather and lack selection of survey blocks in each strata are of snow cover prevented completion of both surveyed using a fixed-wing aircraft to com- surveys. pletely search each selected block. The ana- Environmental conditions such as snow lysis uses the block’s spatial correlation to cover are among the most influential vari- increase the estimate’s precision based on ables that affect survey quality (LeResche finite population block kriging (Ver Hoef and Rausch 1974, Gasaway et al. 1986, 2002). Complete and adequate depth of Quayle et al. 2001, Oehlers et al. 2012). snow cover is essential for this type of survey. The GSPE technique recommends that sur- Ideally surveys are conducted approximately veys occur after fresh or moderately fresh every 3–5 years to monitor trends in moose snow with complete ground coverage (Gas- abundance. However, the Yukon-Kuskokwim away et al. 1986, Kellie and DeLong 2006), Delta and other coastal areas of western typically ≥20 cm in this area. Retrospec- Alaska experience moderating climatic effects tively, we questioned the suitability of the from the Bering Sea and have frequent thaw- GSPE technique for these tributaries because refreeze events (1–9 events/winter; Wilson of the time and cost required to conduct et al. 2013). As a result, weather and snow the survey given the unreliable weather and conditions may preclude survey initiation or snow conditions. In addition, we sought completion, extending the typical period to evaluate whether this technique is ideal between surveys. for use in the narrow linear habitats given Despite adequate habitat to sustain a that large portions of many survey blocks higher moose population, the lower Kuskok- (∼3.7 km 4.5 km) included non-moose wim River has historically had a low moose habitat (i.e., open tundra). The stratified ran- density (0.03 moose/km2 in 2004; Perry dom block design of the GSPE is better sui- 2010) because of extensive hunting pressure ted for larger and more contiguous blocks (Coady 1980). Therefore, a moratorium was of similar habitat (Kellie and DeLong 2006). implemented on the lower Kuskokwim A minimum count (termed complete River watershed between 2004 and 2009 count, a non-sampling approach) survey is when the population increased substantially used in adjacent areas (Aderman 2008) with (0.23 moose/km2 in 2008; Perry 2010) and a fixed-wing aircraft flown throughout the expanded into previously unoccupied, or entire area, counting all moose observed; occasionally occupied habitat making it the count is the population estimate (Lancia necessary to create an expanded survey et al. 2005). This method requires more fly- unit. The new survey unit was developed to ing time to search all areas completely and include the major tributaries of the lower the minimum count has neither an estimate Kuskokwim River within the YDNWR, of precision (i.e., confidence interval) nor which are narrow riparian corridors that ori- typically a sightability correction factor ginate from the adjacent mountains (Fig. 1). (Gasaway and DuBois 1987). Simple aerial These tributaries can support a substantial strip-transect surveys require less flying population and are important wildlife corri- than minimum counts and incorporate an dors to other parts of YDNWR and neighbor- estimate of precision (Timmermann 1974, ing conservation units (i.e., Togiak National Timmermann and Buss 2007, Jung et al.
134 ALCES VOL. 50, 2014 WALD AND NIELSON – ESTIMATING MOOSE ABUNDANCE
Fig. 1. The Yukon Delta National Wildlife Refuge encompasses the Yukon-Kuskokwim Delta in western Alaska. Bethel is the main community along the Kuskokwim River. The four main tributaries of the lower Kuskokwim River include the Tuluksak, Kisaralik, Kwethluk, and Eek Rivers which form the study area. These rivers are characterized by narrow riparian corridors bounded by open tundra.
2009); however, this method assumes equal Anderson 1984). Typically there is no esti- detection of animals from the centerline out mate of sightability with strip transect sam- to the designated strip width (Burnham and pling (Evans et al. 1966, Timmermann
135 ESTIMATING MOOSE ABUNDANCE – WALD AND NIELSON ALCES VOL. 50, 2014
1993), although sightability could be esti- (Nielson et al. 2006). Although distance mated with marked animals (Anderson and sampling has been used successfully to esti- Lindsey 1996), or more intensive flying at mate moose abundance in relatively large an increased cost (Gasaway et al. 1986, Gas- contiguous blocks of boreal forest habitat away and DuBois 1987). with adequate snow conditions, no study has We determined that a viable survey demonstrated that this technique works in method was line-transect distance sampling subarctic tundra along small, narrow riparian (Burnham et al. 1985, Buckland et al. corridors. 2001) using a helicopter for several reasons: Distance sampling analyses typically 1) the area tends to have marginal snow involve estimation of semi-parametric detec- cover each year making it difficult to com- tion functions (Buckland et al. 2001, Thomas plete a GSPE, 2) a helicopter can fly lower et al. 2010). During early development and more slowly with better visibility than and analyses of line-transect distance data, a fixed-wing aircraft, helping to compensate Burnham et al. (1980) suggested that other for minimal snow cover, 3) line-transects nonparametric methods such as kernel esti- can “fit” in the narrow riparian corridors bet- mators or splines might prove “fruitful” for ter than GSPE blocks that typically encom- estimating probability of detection, and pass large portions of non-moose habitat, 4) Mack and Quang (1998) further suggested distance sampling incorporates sightability that kernel methods could be a viable techni- corrections (e.g., weather, lighting, snow que in wildlife distance sampling. The non- conditions, observer experience) provided parametric kernel density estimator does not that probability of detections at some dis- assume an underlying distribution for the tance is known or assumed and, 5) we detection function, and thus has more flex- expected time, logistics, and costs may be ibility by allowing the data to “speak for similar compared to a fixed-wing GSPE sur- themselves” or dictate the shape of the detec- vey in the same region. tion function (Silverman 1986, Wand and Thompson (1979) initially applied a dis- Jones 1995). Kernel estimators are consid- tance sampling approach to estimate moose ered a robust alternative to other density abundance in Ontario, Canada, where it function estimators (Chen 1996a) and are was later improved upon by Dalton (1990). computationally more efficient than polyno- Thompson (1979) had problems fitting mials (Buckland 1992). Both kernel and detection functions, and both surveys had semi-parametric methods are robust against difficulties meeting some of the sampling changing detection functions during a survey assumptions (e.g., exact distance measure- (Gerard and Schucany 2002) and are resili- ments, movement of animals before detec- ent to changing survey conditions such as tion, sightings not always independent) and snow depth/coverage, sun angle and overcast were limited to the technological and statisti- skies, and wind or other environmental con- cal challenges of that period (Gasaway and ditions that could change during a survey Dubois 1987, Pollock and Kendall 1987, over time and space (Burnham et al. 1980, Dalton 1990). Significant advances in dis- Chen 1996b); it is assumed that no correla- tance sampling methodology and statistical tion exists between moose density and these analysis have been recognized over the last changing conditions. Popular computer pro- 30 years (Buckland et al. 2001, 2004; Tho- grams such as Distance 6.0 do not include a mas et al. 2010), and these improvements kernel-based detection function (Thomas led to the development of distance sampling et al. 2010) for use in analysis of line- protocol for moose in interior Alaska transect data, although the kernel method
136 ALCES VOL. 50, 2014 WALD AND NIELSON – ESTIMATING MOOSE ABUNDANCE has been used for distance data in other types areas with environmental conditions that pre- of surveys (Buckland 1992, Chen 1996a, clude traditional surveys. Mack and Quang 1998, Gerard and Schu- cany 2002, Jang and Loh 2010, Nielson et al. STUDY AREA 2013, Nielson et al. 2014), but not for The Yukon Delta NWR is located in moose. western Alaska and encompasses the delta The objectives of this study were two- formed by the Yukon and Kuskokwim fold: 1) evaluate helicopter-based aerial Rivers which empty into the Bering Sea line-transect distance surveys with a double- (Fig. 1). The Kuskokwim tributary survey observer modification to obtain an estimate unit includes parts of 4 main lower Kuskok- of moose abundance within narrow riparian wim River tributaries originating from the corridors during a low snow year, and 2) mountains to the south and east. These tribu- compare the nonparametric kernel-based taries include the Eek, Kwethluk, Kisaralik, detection function to the more traditional and Tuluksak Rivers and are characterized semi-parametric models in the program Dis- by narrow (0.7–4.3 km wide) riparian corri- tance (Thomas et al. 2010). We investigated dors (Fig. 2) running through the foothills what we presumed was a viable alternative and tundra flats that drain the northwest sides to traditional moose survey methods for of the Eek and Kilbuck Mountains.
Fig. 2. Tributary rivers within the study area are characterized by narrow riparian corridors bounded by open tundra. The relatively open forest and shrub habitat is conducive to sighting moose during a line-transect survey with a helicopter. This corridor is a part of the Kwethluk River and is approximately 800 m wide.
137 ESTIMATING MOOSE ABUNDANCE – WALD AND NIELSON ALCES VOL. 50, 2014
The Eek and upper Kwethluk Rivers are Kwethluk and Kisaralik Rivers. This area is represented by open riparian shrubs (Salix usually affected by a warming trend that spp. and Alnus spp.) and scattered clumps typically melts snow more frequently and of balsam popular (Populus balsamifera), rapidly than other parts of the area, perhaps whereas the lower Kwethluk River transi- resulting from an inversion. These condi- tions to open forests that include sporadic tions can limit GSPE surveys along the mixing of spruce (Picea glauca), balsam lower Kwethluk and Kisaralik Rivers in popular, and birch (Betula papyrifera)as any given year. the overstory with an understory of open wil- Nearly 3 cm of new snow accumulated 4 low and alder. The Tuluksak River riparian days prior to the survey. Total snow depth zone is primarily a narrow corridor of spruce was 5 cm (Bethel airport) but was 8–10 cm and birch with an understory of willow and at 2 snow stakes in the study area (Kwethluk alder. The Kisaralik River riparian zone is River) during the survey. Snow coverage mostly mixed coniferous open woodland ranged from 85–100% throughout the survey which exhibits a moderate transition between area with meadow grasses and short vegeta- the Kwethluk and Tuluksak riparian habitats. tion protruding and snow melted off stumps All 4 tributary habitats are bounded by and root wads. Weather conditions during tundra and include variously sized open this survey were mostly clear, 9–37 kph meadows, old river channels, and beaver winds, and −12 to 2 °C. Day length was ponds. nearly 12 h with sunrise at 0900 hr and sha- Weather conditions are highly variable dows becoming long at about 1500 hr. Sur- across the survey area. Average temperatures vey times were typically between 0900 and and snow depth at Bethel, Alaska airport 1700 hr each day and flying conditions (2000–2010; NOAA 2011) during the pri- were generally favorable during the entire mary survey months were −21 °C (range survey. −36 to 4 °C) with 23 cm (0–56 cm) of snow in January, −10 °C (−37 to 5 °C) METHODS and 23 cm (0–64 cm) of snow in February, Field Survey and −9°C(−27 to 4 °C) with 20 cm Aerial line-transect distance sampling (0–56cm)ofsnowinMarch.Inmanyyears protocol for moose followed Nielson et al. there are freeze-thaw events (Wilson et al. (2006). The survey area (i.e., sampling uni- 2013) throughout the winter which ultimately verse) was limited to the riparian corridor limit total snow accumulation and duration. for the rivers of interest. Polygons were cre- Our study period (2010) was an El Niño year ated around rivers to encompass riparian which affected the winter weather pattern vegetated areas within the floodplain and on the Yukon-Kuskokwim Delta from June between the tundra benches on each side of 2009 to March 2010 (NOAA 2013). the river (ArcMap 9.2, Environmental Sys- Repeated high pressure systems over the tems Research Institute, Redlands, Califor- Delta kept numerous low pressure systems nia, USA; Fig. 1). Satellite imagery was south and subsequently pushed easterly, used to facilitate creation of survey areas resulting in unusually clear and dry condi- which encompassed nearly 730 km2. tions with periods of colder temperatures Survey transects were created within and little snowfall over the study area during river corridors and varied by length and winter 2009–2010. A portion of the survey number along each river (Fig. 1). Multiple unit experiences a “banana belt” effect, espe- transects were placed in areas wide enough cially along the foothills between the to allow equidistance spacing of 700 m,
138 ALCES VOL. 50, 2014 WALD AND NIELSON – ESTIMATING MOOSE ABUNDANCE providing a maximum 350 m search area on GPS (Garmin 695). Two observers were each side of a transect centerline. Transect seated in the back (one on each side) and length varied according to stretches of river were the primary observers for the survey. that allowed straight transects with sections Their responsibilities were to sight moose changing direction in a saw-toothed manner groups, count and classify each group, and as the river corridor meandered (Nielson et al. measure the perpendicular distance from the 2006). Some riparian corridors were suffi- transect centerline to each group centerpoint. ciently narrow to allow only a single transect The data recorder sat in the front-left seat which had a random start point contingent on and was responsible for recording all data allowing the minimum half transect width including GPS locations, performing as a (350 m) to be in moose habitat. The center- double-observer, frequently measuring heli- line could not be on the edge of the habitat copter AGL, and overall survey coordina- (i.e., one side having a hard boundary of no tion. The front observer recorded survey moose habitat or open tundra and the other data while flying off transect in order to not side all moose habitat) to avoid extreme interfere with double-observer duties while asymmetry of g(y), although this source of flying on transect. bias is minimal in most studies (Buckland The double-observer method was used et al. 2001). Areas with systematic parallel in conjunction with the line-transect survey transects had a random start point for the first to test the assumption that detection was transect. A total of 46 transects were delin- 100% on or near the transect centerline, or eated with a combined length of 698 km at the minimum available sighting distance (Fig. 1). (Buckland et al. 2001, Laake and Borchers We used a Robinson (R-44) helicopter 2004, Borchers et al. 2006). This assumption with bubble windows to survey moose is sometimes violated (Chen 1999, 2000) during 16–17 March 2010. Helicopters pro- and information regarding heterogeneity in vide a better platform for observing moose observer bias should be modeled (Graham because of better sightability, smaller var- and Bell 1989) because it can produce nega- iances, and often comparable cost with tively biased estimates. fixed-wing surveys (Smits et al. 1994, Gosse The data recorder in the front-left seat et al. 2002). Protocol recommends a flight was paired with the rear left observer to con- altitude of 122 m above ground level duct the double-observer sampling, which is (AGL) which results in good visibility and essentially a mark-recapture method (Borch- minimal disturbance of moose (Nielson et al. ers et al. 2006). The data recorder focused on 2006). However, snow conditions were poor, or near the centerline to detect moose, but so flight altitude was adjusted to 100 m AGL recorded all moose observations at any dis- to increase visibility while remaining high tance. Double-observer data are used to esti- enough to minimally affect moose and pre- mate detection rate on or near the centerline vent ground flash, the visual effect of ground by the rear seat observers. This requires zooming by too fast when flying at a lower that the front and rear seat observers operate altitude (Becker and Quang 2009). Our tar- independently of each other (Buckland et al. get ground speed was 64 kph (40 mph) 2010). Data were recorded on the number of depending on terrain and wind. moose groups detected by both observers, Four people were onboard during this and groups detected by the front and not survey. The pilot was responsible for main- the rear observer. To account for observer taining desired altitude, speed, and heading bias, the 2 rear observers rotated sides each on transect centerlines using a preprogramed day to be paired with the front-left observer
139 ESTIMATING MOOSE ABUNDANCE – WALD AND NIELSON ALCES VOL. 50, 2014 to incorporate biases from both observers determined group size, composition (i.e., into the model (Cook and Jacobson 1979). adults and calves), and classified percent Thus, we considered the probability of detec- habitat cover for ∼50 m radius around each tion estimated for the back-left observer group. based on the mark-recapture data to be rele- vant for both backseat observers during ana- Data Analysis lyses. The recorder also worked with the Standard distance sampling theory pilot to keep flight speed and altitude within assumes all individuals (objects) available the range of survey protocol. A laser range- to be detected on the centerline, or the mini- finder (Nikon Forestry 550 Hypsometer) mal available sighting distance, are was frequently used to measure true vertical observed, and that the probability of detec- distance from the ground to helicopter every tion is a function of perpendicular distance – 2 3 min to check flight altitude and recom- from the centerline. There are 3 essential mended adjustments as needed. assumptions for accurately estimating den- Moose groups were defined as one or sity using distance sampling. In order of more moose within a 50 m radius (Molvar importance these are: 1) objects at the mini- and Bowyer 1994). The distance of groups mal available sighting distance are detected perpendicular to the transect centerline was with certainty, that is g(W1) = 1.0, or can be measured by the rear observer with a laser estimated, 2) objects are detected prior to rangefinder (Leupold RX-1000 TBR) with any movement in response to the survey, a built-in clinometer that had maximum and 3) perpendicular measurements to the ∼ range of 900 m; clinometers allow for object are accurate (Buckland and Turnock accurate horizontal measurements regardless 1992, Buckland et al. 2001). Other design/ of survey altitude. A group that was hard to analysis assumptions exist but are less strin- laser-range (e.g., trees, helicopter movement, gent, including accurate measurement of animal movement) required flying back over group size and that object density is indepen- the group and marking its location with a dent of the placement of transects (i.e., uni- GPS (Marques et al. 2006). Distance was form distance distributions; Fewster measured to the center of a group using the et al. 2008). laser rangefinder directed at their feet to Fulfilling these assumptions allow for an avoid over-estimating the distance; this mea- accurate density estimate using: surement was associated with the location of the group when first observed. If moose ^ moved before a distance was acquired, the ^ nEðsÞ 1 D ¼ ^ ð Þ observer ranged the location of the initial 2ðW2 W1ÞLP observation. Doubling back to mark GPS locations worked well, but some moose where n is the number of observed groups, ^ moved after detection because of the aircraft EðsÞ is the expected (or average) group hovering directly overhead; tracks in the size, W1 and W2 are the minimum and max- snow proved reliable as reference points for imum search distances from a transect, these cases. The distances measured with respectively, L is the total length of transects the GPS method (∼90% of all groups flown, and P^ is the estimated average prob- observed) were calculated in a GIS. Addi- ability of detection within the area searched tional moose observed “off transect” while (Buckland et al. 2001). doubling back to obtain GPS locations were We tested the assumption g(W1) = 1.0, not included in any analysis. Observers where g(W1) is the minimum sighting
140 ALCES VOL. 50, 2014 WALD AND NIELSON – ESTIMATING MOOSE ABUNDANCE distance with the double-observer technique moose groups were not counted more than (Chen 2000, Borchers et al. 2006, Buckland once if they moved during the survey. To et al. 2010) using observations from the left meet this assumption, we set the maximum side of the helicopter. Observations collected search width, W2, equal to the maximum dis- independently by individual observers on the tance a moose group was observed within left side were used to estimate the probability 300 m of the transect centerline. Since the of detecting a moose group at the minimum backseat observers had a blind spot under- available sighting distance. This probability neath the helicopter, we used a laser range- was used to adjust the estimated detection finder (hypsometer) to determine the curve starting at that distance (Laake and minimum sighting distance for the backseat Borchers 2004). observers. To determine the width of the We used logistic regression (McCullagh blind spot at the survey altitude, the backseat and Nelder 1989) in the mark-recapture ana- observer laser-ranged through the bubble lysis to estimate the probability of detecting window along their line-of-sight to the a moose group by the back-left observer ground, just clear of the helicopter skid. given detection by the front-left observer. The minimum available sighting distance ∼ We considered 3 models that 1) treated the for backseat observers was 43 m from the probability that a group was detected by the centerline. Moose were visible to the front- – back-left observer as constant across all dis- left observer from 0 43 m through the front tances from the transect line (intercept only helicopter window, but lumping these data “ ” model), 2) treated the probability of detec- into a single distance of zero , and the fact tion as a function of distance from the trans- that the front-right observer (pilot) was not ect line, and 3) included both linear and focused on observing moose on that side of quadratic terms for distance from the transect the line, precluded using these data in the analyses; therefore, the front-left observer line. We used Akaike’s information criterion observations in the 0–43 m range were not for small sample sizes (AICc; Burnham and used. Thus, the minimum available sighting Anderson 2002) to identify the best model distance, W , was set at the minimum dis- for estimating probability of detection by 1 tance at which a moose group was detected the backseat observers based on the mark- by a backseat observer. recapture data. The AICc was calculated as: We evaluated whether correlation existed between expected group size and AICc ¼ 2logðLikelihoodÞþ2kn/ðn k 1Þ detection distance because group size can ð2Þ influence detectability, especially at longer distances; larger groups may have a higher where k was the number of parameters in the probability of detection than smaller groups model (including intercept term), n was the further from the transect line (Drummer and number of observations used to fit the model, McDonald 1987, Drummer et al. 1990). We Likelihood was the value of the logistic like- used a Pearson’s correlation analysis to esti- lihood evaluated at the maximum likelihood mate the correlation (r) between group size estimates, and ‘log’ was the natural loga- and distance from the transect line, and cal- rithm. The logistic regression model was fit culated a 95% confidence interval (CI) for using the program R (R Development Core the statistic (Zar 1999). We determined no Team 2010). relationship existed between group size and We designed transect centerlines to be a detection distance if the 95% CI included minimum of 700 m apart to ensure that 0.0. In this situation, we used the average
141 ESTIMATING MOOSE ABUNDANCE – WALD AND NIELSON ALCES VOL. 50, 2014 of all observed group sizes for E^ðsÞ (equa- Use of parametric or semi-parametric tion 1). If a correlation was detected, we detection functions may not always be the used the regression method (Buckland et al. best approach to fit probability detection 2001) to estimate expected group size. We curves (Burnham and Anderson 1976, Buck- examined the habitat covariate, percent land 1992); instead, a nonparametric kernel cover as a potential influence on the prob- density estimator without an assumed prob- ability of detection of groups (i.e., higher ability density function may provide a better percent cover may reduce probability of fit to the data. We fit a nonparametric kernel detection; Anderson and Lindzey 1996, Oeh- estimator (Silverman 1986, Wand and Jones lers et al. 2012). 1995) to our group observations, and used The underpinning of distance sampling the general univariate kernel density estima- is the detection function g(y) which tor described in Wand and Jones (1995): expresses the probability of detecting a group given that the group was observed at Xn ^ 1 x xi fxðÞ¼ ðÞnh K ð3Þ distance (y) from a random transect, and h i¼1 that the assumption g(W1) = 1.0, or can be estimated, holds true (Buckland et al. 2001). There are many models that can be where x is a perpendicular distance within fitted to distance data in order to estimate the range of observed distances, xi is one the shape of a detection function, and we of the n observed distances, h is a smooth- ‘ ’ used the computer program Distance 6.0 ing parameter, or bandwidth , and K is a release 2 (Thomas et al. 2010) to model Ðkernel function satisfying the condition 1 semi-parametric detection functions for KxðÞdx ¼ . moose groups. We considered robust key Since the bandwidth (h) governs the functions with expansion terms as outlined function smoothness (Chen 1996a, Gerard in Buckland et al. (2001), including the and Schucany 1999), the choice of band- half-normal with hermite polynomial and width is more crucial than the choice of ker- cosine expansion terms, the hazard-rate nel (Mack and Quang 1998, Jang and Loh with a cosine expansion, and the uniform 2010). We used a Gaussian kernel function with simple polynomial and cosine expan- (Silverman 1986, Chen 1996a) and the direct sion terms. Additionally, the half-normal or plug-in bandwidth selection method hazard-rate key functions allow for predictor (Sheather and Jones 1991, Wand and Jones variables to help model the detection func- 1995, Sheather 2004) to develop the detec- tion. We used the half-normal (including her- tion function for groups. The direct plug-in mite polynomial and cosine expansion method objectively fits the bandwidth and terms) and hazard-rate (including a cosine is considered to be the best compromise expansion term) key functions for modeling between bias and variance among the avail- the detection function while incorporating able methods (Sheather and Jones 1991, the percent cover variable. The number of Wand and Jones 1995, Venables and Ripley expansion terms for each key function was 2002, Sheather 2004). allowed to vary from 0–5; the AICc was Kernel estimators inherently do not per- used to select the number of expansion terms form well near sharp boundaries (Jang and among the various models. The model with Loh 2010). A boundary bias is created, as the lowest AICc value was selected as the in our case, when distance observations are best model to describe the detection function not distinguished from the right or left side (Burnham and Anderson 2002). of the transect line and where all values are
142 ALCES VOL. 50, 2014 WALD AND NIELSON – ESTIMATING MOOSE ABUNDANCE non-negative (Buckland 1992, Jang and Loh percentiles of the 1,000 estimates (999 boot- 2010). In order to model the distances with a strap estimates + original estimate). The per- kernel estimator, Chen (1996a, 1996b) and centile method is the preferred method for Silverman (1986) recommended reflecting calculation of CIs when bootstrapping, the observed distances to both sides of the because using the standard formula (i.e., esti- transect line in order for the kernel density mate ± 1.96[SE]) requires the additional estimator to perform properly. After shifting assumption that the bootstrap estimates gen- all observed distances by the left-truncation erally follow a normal distribution (Buck- distance (W1), we multiplied (reflected) the land 1984, Efron and Tibshirani 1994). We observed distances by (−1) and added them estimated relative percent bias of the density to the dataset (Buckland 1992, Chen 1996a, estimates as: 1996b). Once the kernel density function was created from the expanded dataset, the Dboot Dorig %Bias ¼ 100 ð4Þ detection function to the right of the zero Dorig line (positive) was used for the density esti- mate. The kernel estimator was fit using the where Dboot is the average density esti- program R (R Development Core Team mate from the bootstrap and Dorig was 2010) and the MASS package in R (Ven- the original density estimate. We measured ables and Ripley 2002). dispersion or the extent of variability in rela- We used bootstrapping to estimate SEs tion to the final density estimate by calculat- and 95% CIs for final estimates of moose ing the coefficient of variation (CV) as density and abundance within the sampled CV ¼ðSE=D^ Þ 100%. The standard region (Efron 1981a, 1981b, Quang 1990, deviation (SD) of the 1,000 estimates was DiCiccio and Efron 1996). Estimates derived used as the estimated SE. from the program Distance 6.0 were boot- In order to estimate the total length (L) strapped within the program, which uses a of transects needed in future surveys to default of 999 bootstrap re-samplings with achieve a certain level of precision (i.e., CV replacement (Thomas et al. 2009). Standard value), we used the formula from Buckland errors and confidence intervals for the kernel et al. (2001): estimates were derived from bootstrapping . 999 resamples (with replacement) to be con- 2 2 L ¼ L0fgcvðDÞ fgcv ðDÞ ð5Þ sistent with program Distance and because t the bootstrapped estimates (SE, CI) usually become stable and asymptotic between 500 where L0 is the total length of transects sur- and 1000 resamples (Efron and Tibshirani veyed, cv (D) is the coefficient of variation 1994). We bootstrapped the 46 line-transects of the density estimate from this study and surveyed in which the bootstrap would rerun cvt (D) is the desired target coefficient of the analysis for all parameter estimates, variation. including the shape of the detection function and the average probability of detection dur- RESULTS ing each iteration. Additionally, we evalu- A total of 162 moose (112 adults, 48 ated bias and precision of the density calves) in 78 groups were detected on 46 estimate using the bootstrap (Efron and Tib- transects along 698 km within a series of shirani 1986). We used the percentile method polygons encompassing 730 km2 of riparian (Efron 1981b, 1982) for calculating the 95% moose habitat. There were 37 cow moose confidence intervals using the 2.5th and 97.5th with calves including 26 singletons and 11
143 ESTIMATING MOOSE ABUNDANCE – WALD AND NIELSON ALCES VOL. 50, 2014 sets of twins (30% twinning rate). Group size back-left observer given detection by the ranged from 1–5 with 73% of groups com- front-left observer. Only 3 groups were prised of 1–2 moose and only 6% with 4–5 missed by the back-left observer and these moose. were deleted for the density estimate. The Because the mark-recapture portion of logistic equation with linear and quadratic this study was intended to occur only on terms for distance from the transect line had the left side of the aircraft, a single group the lowest AICc value (19.8 versus 22.4 observation detected by the front-left obser- and 24 for the intercept only and linear dis- ver that was 244 m to the right of the transect tance function models, respectively). The line (and not detected by the back-right final estimated logistic regression model observer) was excluded from the analysis. was: Ten of the 78 groups were detected only by 2 the front-left observer and were recorded as exp 51:461 0:583distancei þ 0:0012distance Ey i ½ i ¼ 1 51:461 0:583 0:0012 2 seen directly on the transect line (i.e., per- þ exp distancei þ distancei pendicular distance = 0). Since these groups ð6Þ could not be seen by the back-left observer and ‘lumping’ of the perpendicular distances where E [yi] was the expected probability occurred during data recording (i.e., these of detection for mark-recapture observa- moose were likely somewhere ± 43 m from tion i. the transect line and not all directly on the Based on this final model, the predicted line), these observations were also excluded probability of detection of moose at the mini- from the analysis. Of the remaining observa- mum sighting distance by the back-left tions, the minimum observed distance of a observer was 1.0. Therefore, the estimated moose group by the backseat observers was probability of detection curve was not scaled 46 m from the transect line, thus W was by a correction factor prior to integration and 1 ^ set to 46 m. We truncated our data to 300 estimation of P, and only observations by m, which corresponded to a reduction of the rear seat observers were used to estimate approximately 8% of the farthest distance moose density. observations; Buckland et al. (2001) recom- Comparison of models using AICc mend truncating the farthest 5–10% of dis- values requires that the competing models tance observations. The maximum observed are all estimated using the same number of distance of a group within 300 m of a observations and the same response (Y) transect line was 299 m, so W2 was set at values. Percent cover was not recorded for 299 m. one observation so this record was not initi- Analysis of moose observations within ally included during estimation of the prob- the defined search width (46–299 m from a ability of detection curve. In addition, due to transect line) indicated that group size was the distribution of percent cover values for not correlated with distance from the transect observations (10–70% in 10% increments) line (r = 0.048, 95%, CI = −0.20–0.29). The and few observations at the extremes, the ori- average group size by the backseat observers ginal values were collapsed into 3 categories: within the search strip was 2.03 (95% CI 1) 10–30, 2) 30–50, and 3) 60–70%. from 1.78–2.32) and was used in the density Comparison of the models with and estimate. without the covariate for percent cover indi- The mark-recapture trials used 34 obser- cated that a hazard-rate key function with vations to fit logistic regression equations to no expansion terms was the best fit to the estimate the probability of detection by the data (Table 1). Because the models
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Table 1. Estimated semi-parametric detection functions fit to 58 moose group observations using the program Distance (Thomas et al. 2010), including the number of expansion terms, whether the covariate for percent cover was included in the model, the number of parameters (k), AICc value, and estimated average probability of detection (P^), estimated moose density (D^), and coefficient of variation (CV) for each model, Alaska, 2010. Expansion % Cover % Key Function Expansion Terms k (yes/no) AICc P^ D^ CV Hazard-rate Cosine 0 2 N 627.85 0.71 0.480 19.1 Uniform Cosine 2 2 N 629.26 0.67 0.505 25.3 Uniform Simple Polynomial 1 1 N 629.47 0.70 0.485 17.3 Half-normal Cosine/Hermite Polynomial* 0 1 N 629.48 0.62 0.547 21.0 Half-normal Cosine 1 4 Y 631.40 0.85 0.398 18.2 Hazard-rate Cosine 0 4 Y 631.42 0.68 0.498 18.4 Half-normal Hermite Polynomial 1 4 Y 631.68 0.82 0.413 18.4
*No expansion terms were selected using AICc values.
Table 2. Estimated semi-parametric detection functions fit to 59 moose group observations using the program Distance (Thomas et al. 2010), including the number of expansion terms, whether the covariate for percent cover was included in the model, the number of parameters (k), AICc value, and estimated average probability of detection P^, estimated moose density D^, and coefficient of variation (CV) for each model, Alaska, 2010. Key Function Expansion Expansion Terms k AICc P^ D^ %CV Hazard-rate Cosine 0 2 643.25 0.70 0.482 20.0 Uniform Cosine 1 1 643.53 0.60 0.562 19.1 Half-normal Cosine/Hermite Polynomial* 0 1 643.67 0.64 0.533 20.4 Uniform Simple Polynomial 1 1 644.47 0.72 0.472 17.4
*No expansion terms were selected using AICc values. containing the covariate for percent cover test; χ2 = 6.07, df = 4, P = 0.194). Based on ranked last according to AICc values, we this final model using 59 groups, the esti- refit the models without the predictor vari- mated average probability of detection was able using all the observations from the rear 0.70 (Fig. 3), and the estimated density was seat observers within 46–299 m of a transect 0.48 moose/km2 or a population of 352 line, including the single observation where moose (95% CI = 237–540); this model percent cover was not recorded. The results had a CV of 20% and an estimated bias of this analysis were similar to the analysis, of ∼1.4%. minus the missing observation, in that the The detection function calculated using top model was a hazard-rate key function the kernel density estimator (without covari- with no expansion terms (Table 2). We used ates) also had a good fit (GOF test; χ2 = 6.42, the goodness of fit (GOF) test statistic to df = 5, P = 0.73) with an estimated average determine if the top model fit the data well probability of detection of 0.73 (Fig. 3). (Buckland et al. 2001). There was no evi- The estimated density was 0.47 moose/km2 dence of lack of fit for the top model (GOF or a population of 340 moose (95% CI =
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Fig. 3. Histogram of the 59 moose group distance observations with corresponding detection functions superimposed. The final hazard- rate detection function was fit using the program Distance (Thomas et al. 2010). The non-parametric kernel-based detection function was fit using the program R (R Development Core Team 2010). Perpendicular distances were shifted left by 46 m prior to analysis, but shifted back for graphing visual clarity.
238–472); the corresponding CV was 18% fitting and achieving adequate levels of esti- and the estimated bias based on bootstrap- mate precision under adequate snow condi- ping was <0.001%. tions within boreal transition forest of west- Based on an encounter rate of 0.085 central Alaska (Nielson et al. 2006) and moose groups/km (59 groups/698 km) and central Canadian boreal forest habitats the CV from the kernel estimator (18%), (Thompson 1979, Dalton 1990, Thiessen we calculated the total length of transects 2010, Peters et al. 2014). We evaluated this needed to achieve a targeted CV of 20, 15, method as an alternative technique for sur- and 10%. This analysis indicated that trans- veying moose in a subarctic tundra ecosys- ect lengths of 566, 1006, and 2262 km, tem with variable and often minimal snow respectively, were required to meet these tar- conditions, and present an alternative techni- geted CVs assuming that the encounter rate remains constant. que for analyzing distance data using a non- parametric kernel density estimator to fit the DISCUSSION detection function. Overall, distance sam- Others have utilized distance sampling pling proved to be a viable technique to with varying degrees of success in model monitor moose along the Kuskokwim
146 ALCES VOL. 50, 2014 WALD AND NIELSON – ESTIMATING MOOSE ABUNDANCE tributary rivers in the YDNWR in southwes- with an average of 39%). Additionally, tern Alaska. detection on the centerline was further increased by the fact that we used a helicop- Assumptions ter flying at 100 m AGL at a relatively slow Distance sampling depends on 3 main speed of 48–88 kph; although snow was assumptions that need to be met, or nearly shallow, visibility on the centerline was so, in order to produce unbiased and reliable excellent. estimates (Buckland et al. 2001). Although Moose in our study area were assumed the assumptions can be relaxed to some to be available for detection because of the degree in certain circumstances and still pro- relatively open habitat (39% canopy clo- vide dependable estimates (Buckland et al. sure). One concern was that root-wads of 2001), we designed our study in an attempt wind-fallen trees could hide an adjacent, to meet all assumptions or to estimate our bedded moose. However, if we flew directly biases if we failed to adequately meet one. over a root-wad we detected the moose on Assumption (1), that objects at the the transect line (g(W1) = 1.0), and it would minimum available sighting distance were be accounted for in the detection function detected with certainty, is typically at distances off the transect line (Laake et al. addressed by developing a sightability cor- 2008). Availability bias could possibly be rection factor (SCF) through modeling removed or reduced if the area was surveyed covariates against mark-recapture data of at different times (e.g., hours apart) to allow collared animals (Gasaway et al. 1986, animals to become available; this is likely Samuel et al. 1987, Anderson and Lindzey dependent on species (Laake and Borchers 1996). Distance sampling inherently 2004) and unlikely of concern with moose accounts for, or corrects for, visibility (per- in most conditions. ception) biases provided that all objects Assumption (2), that objects are detected are detected on the transect centerline or at at their initial location, is sometimes difficult the minimum sighting distance (Buckland to assess (Fewster et al. 2008), and in our et al. 2001, Marques and Buckland 2004). case, related to disturbed moose “pushed” Although many distance sampling studies by the helicopter some distance before detec- do not address assumption (1) (Bachler tion. Thompson (1979) reported that moose and Liechti 2007), we utilized the double- were not disturbed by circling fixed-wing observer method (Graham and Bell 1989) aircraft and did not move as the airplane to test the primary assumption that detection approached; however, Cumberland (2012) of moose groups on the centerline or at the reported that moose usually initiated some minimum sighting distance was certain. The movement from a larger turbine helicopter mark-recapture logistic regression analysis (Bell 206) at a lower survey altitude (60 m indicated that we met the assumption with AGL). Random movement is acceptable as 100% probability of the backseat observer long as it is not caused by the observer detecting a moose group that was detected (Buckland et al. 2001), but failure to meet by the front-left observer at the minimum assumption (2) would bias the density esti- sighting distance (g(W1)). Detection cer- mate low. tainty along the transect line in our study We investigated the validity of this was enhanced by several factors including assumption, in part, by reviewing the dis- that the survey area was within narrow ripar- tance data histogram and identifying whether ian habitat with a relatively open canopy a bump or peak is evident some distance (range of percent cover data was 10–70% from the center line. Figure 3 has a slight
147 ESTIMATING MOOSE ABUNDANCE – WALD AND NIELSON ALCES VOL. 50, 2014 bump in frequency at ∼150 m which might was difficult to range groups at times, espe- reflect recording bias or movement from cially when close to the helicopter which the helicopter prior to detection (Dalton required a quick response, and when in 1990). Our front observer was focused on cover. Higher quality or industrial-type laser the centerline for the double-observer rangefinders should reduce this problem. We method, and looking forward of the helicop- eventually adopted the technique used by ter to identify any pre-detection movement Marques et al. (2006) and used GPS loca- (Fewster et al. 2008). Few moose were tions to measure distances. This required observed moving prior to when the backseat more flying time and effort to fly off transect observers detected moose; movement was to identify the group location. Because this mainly in response to the helicopter directly process caused some moose to move prior overhead. Because these few moose did not to marking the location, we followed tracks move into a zone of detection for the back- in the snow to ascertain the initial location. seat observer, movements were considered Increasing flight altitude while off transect moot in our study. Further, observations of may alleviate or reduce disturbance while moose within the effective search width marking locations. We are confident that (46–299 m) did not indicate movement prior movements were minimal and measured to detection by the backseat observer. adequately, and that groups were not double A possible explanation for the bump in counted on subsequent transects. our data was that the backseat observers Other assumptions that are not generally had a comfortable scanning level or sight discussed in literature, such as the uniformity line (i.e., distance) while sitting in the heli- of the distance distribution and indepen- copter. Observer fatigue increases as a sur- dence of group observations, are typically vey progresses (Briggs et al. 1985, addressed during the survey design process. Schroeder and Murphy 1999), possibly con- The uniformity assumption is addressed by tributing to the desire to scan (subcon- randomly distributing transect lines across sciously) at a less strained position. For the study area, or systematically arranging example, Jang and Loh (2010) graphed the transects with a random start point, as we classic wooden stake data outline in Burn- did (Fewster et al. 2008, Jang and Loh ham et al. (1980) and showed that their histo- 2010). The assumption that observations gram had a large bump or spike of detections are independent is addressed in the same that clearly was not associated with move- manner as distance uniformity (Buckland ment. We believe that we met assumption et al. 2001) provided that moose are not clus- (2) because the front observer scanned for- tered together in one part of the survey area. ward of the flight path and there was no Estimates of density are robust to the inde- change in observation rate moving from the pendence assumption especially when boot- center line (Fig. 3). Flying at a higher alti- strapping to obtain confidence intervals tude (e.g., 122 m instead of 100 m AGL). (Thomas et al. 2002). Additionally, we did as suggested by Nielson et al. (2006), would not incorporate “dependent” moose groups presumably further address assumption (2). observed while flying off transect when To meet assumption (3), that perpendi- obtaining GPS locations for groups that cular distance measurements are exact, we moved. utilized both rangefinders with built-in clin- ometers and GPS units to determine perpen- Detection Functions dicular distances to moose groups. Although Survey design and protocol are para- both methods can be accurate and efficient, it mount for meeting the 3 primary assumptions
148 ALCES VOL. 50, 2014 WALD AND NIELSON – ESTIMATING MOOSE ABUNDANCE of distance sampling in order to model detec- et al. 2012). Buckland et al. (2001) recom- tion functions reliably (Thomas et al. 2010). mend 60–80 observations and at least 10– Our survey transects were systematically dis- 20 replicate transects to obtain reliable esti- tributed throughout the riparian corridors mates with relatively good precision; we with random start points allowing for statisti- had 58 group observations with percent cal inference (Fewster et al. 2009). Although cover measurements. Seddon et al. (2003) transects were spaced 700 m apart and a improved their survey precision (i.e., maximum search width of 350 m could decreased CV values) by increasing have been used in the analysis, there were observations. few observations beyond 300 m. Restricting In an analysis of several surveys, Thies- the analysis to observations within 300 m sen (2010) found a strong relationship reduced the possibility that moose groups between the number of observations and were counted more than once. We dropped CVs for those surveys; surveys with 60 nearly 8% of the farthest observations which observations had a CV of ∼20%. Our survey was within the recommended 5–10% range (59 observations) corroborates this relation- suggested because outliers may have undue ship as our model without covariates had a influence on the shape and scale of the detec- CV of 20% (using the hazard-rate key func- tion function (Buckland et al. 2001). Our tion). Adding covariates or stratifications effective search width (W1 and W2) was would require considerably more observa- 253 m (46–299 m) which was narrower tions to ensure reliable estimates with a CV than the 700 (Dalton 1990) and 800 m of 20%. We examined the possibility of stra- (Thiessen 2010) widths used in Canada, tifying our study area by each tributary river and similar to the 250 m search width used but moose density was too low to acquire by Thompson (1979). Our search width sufficient observations for reliable estimates was narrow because of the narrow corridor for all rivers, with the possible exception of of habitat, we flew relatively low, and the the Kwethluk River (∼60–80 observation in relatively poor snow conditions which pre- each strata; Buckland et al. 2001). sumably reduces visibility. We recommend Group size influences detection at dis- using narrow transect search widths during tance (Drummer et al. 1990), and can be low or poor snow condition years to increase included as a covariate in the program Dis- effectiveness of the survey. tance (Laake et al. 2008). We investigated We measured percent cover because whether a correlation existed between group covariates can improve model precision by size and detection distance prior to “penaliz- accounting for heterogeneity in the data ing” our analysis with an additional covari- (Buckland et al. 2004, Marques and Buck- ate (Giudice et al. 2012). Our analysis land 2004), but at an added cost of sample indicated that group size was not correlated size (Giudice et al. 2012). However, it did with detection distance in this study which not improve the detection function based on most likely reflects the group composition the higher AIC values for the models includ- in the study area. Most groups were rela- ing this covariate. This might reflect the tively small (73% had 1–2 moose) and relatively narrow range of values (range = most observations were cows with calves. 10–70%, median = 40%) that were lumped Since there was no correlation between dis- into 3 categories. Visual obstruction by tance and group size, and the composition vegetation influenced detection of moose in of groups had a narrow range of sizes (no Minnesota where percent cover was higher major outliers), we used the average group (range = 0–95%, median = 60%) (Giudice size as equivalent to the expected group
149 ESTIMATING MOOSE ABUNDANCE – WALD AND NIELSON ALCES VOL. 50, 2014 size in the density estimate (Buckland monotonically decreasing function of dis- et al. 2001). tance away from the transect centerline, Our model choices were based on unlike semi-parametric models (Cassey and recommendations of Buckland et al. (2001) McArdle 1999). One limitation is that it and past experience (Nielson et al. 2006) in requires an adequate sample size to produce order to prevent a “shotgun” approach to a reasonable estimate (Chen 2000), but modeling. Models that included the percent sample size was not a problem in our uni- cover covariate were ranked last and did variate analysis for the level of precision not contribute to or improve the model we achieved. The Hermite polynomial and according to AICc; we subsequently kernel estimates are very similar with the removed the covariate and analyzed the kernel estimate less intensive to compute data without it. Our top model was the (Buckland 1992). hazard-rate key function with no expansion terms. As in our study, several other ungulate Survey Effectiveness studies reported the hazard rate key function The study area is characterized by mar- with various expansions to be the top models ginal snow conditions during any given (Focardi et al. 2002, Shorrocks et al. 2008, year with the most reliable conditions in Feb- Young et al. 2010, Schmidt et al. 2011). ruary (Fig. 4). The daily average snow depth Other studies with ungulates found the half clearly demonstrates that the area does not normal key function with various expansions accumulate deep snow and daily variation terms to perform best (Trenkel et al. 1997, is high because of periods of warming and Jathanna et al. 2003, Peters 2010, Thies- rain causing snowmelt. We considered ∼20 sen 2010). cm of snow accumulation as moderate to The kernel estimator used for the prob- good conditions, required for the standard ability of detection curve does not use GSPE survey method. Conversely, Dalton maximum likelihood methods, so AICc (1990) considered 20 cm “shallow” for a values are not available for comparison moose survey in Ontario, Canada. with models with semi-parametric detection Comparison of the helicopter line- functions in the program Distance. However, transect method with the GSPE method con- the kernel-based estimated probability of siders time, logistics, cost, and the estimate detection, animal density, and CV were simi- of precision. The GSPE method requires a lar to those obtained from the hazard-rate minimum of 60 units surveyed between 2 model in Distance, although the CI was much moose density strata (30 low and 30 high narrower for the kernel estimator. Based strata), with preferably more units in high on bootstrapping, all the semi-parametric density areas assuming greater variation models estimated that the probability of within that strata (Kellie and DeLong detection biased low (i.e., lower than the 2006). GSPE survey areas are a minimum ^ kernel’s P ¼ 0:73), thus estimated densities of 777 km2 because smaller areas have insuf- were biased high. The estimated bias in the ficient sample units to generate estimates. hazard-rate model estimate (1.4%) was These survey units are approximately 16.6 higher than the estimated bias for the kernel- km2 and require a minimum search intensity based estimate (<0.001%). An advantage of of 40 min/block with cub-like or tandem the nonparametric estimator is that it is free style fixed-winged aircraft (Kellie and of parametric assumptions on the detection DeLong 2006). The time required to fly the function. Additionally, using a kernel-based minimum intensity and number of units model does not require that detection is a would be ∼40 h. Two aircraft for a minimum
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Fig. 4. Average daily snow depth at Bethel, Alaska airport (2000–2010) during typical moose survey months. In this area the minimum snow depth for GSPE type surveys is ∼20 cm (dashed line). The variability in snow depth is due to periodic and rapid warming trends (NOAA 2011). of 5 days would be required to complete the number of GSPE units required to address survey given continuous optimal snow con- potential stratification errors, sample sizes, ditions, a situation unlikely in the study area. and high variability of observations between The helicopter line-transect survey was units (Kellie and DeLong 2006). considerably more efficient in terms of area sampled and flight time than a fixed-wing Management Application GSPE. We flew a total of 16 h in one heli- The recent expansion and establishment copter including about 2.5 h of training prior of moose in the lower Kuskokwim River tri- butaries prompted our survey efforts. Our to the actual survey (training is highly survey indicated that moose density is 0.47 recommended to prepare the survey team moose/km2 or twice that of the adjacent for duties and search patterns) and 13.5 h lower Kuskokwim River survey unit in during the actual survey, including ferry 2008 (0.23 moose/km2 without SCF; Perry times from the base of operation. We accom- 2010). The difference can arguably be attrib- plished the survey in 2 days which improves uted to better habitat along the Kuskokwim the chance of continuous, optimal snow con- tributaries compared to the main channel of ditions. Cost based solely on flight hours the lower Kuskokwim River, and the 5-year was similar; a fixed-wing survey for the moose hunting moratorium in the lower Kus- minimum sampling under the GSPE method kokwim drainage that allowed moose to in this area would be approximately 6% less establish a viable population and disperse than the helicopter line-transect technique, a into unoccupied habitat. The exploitation of reasonable compromise given the reduction underutilized habitat was expressed in popu- in survey days (2 versus 5). Our helicopter lation production and is emphasized by the survey had a CV of 18%, a difficult level 30% rate of twinning during our March sur- of precision to obtain with the minimum vey, which is high for that time of year.
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Comparative twinning rate data are collected add transects without greatly increasing the in May during the peak calving period and chance of double counting groups. Thus, can be used in conjunction with other vari- improved precision is limited by increasing ables to determine the nutritional status of the encounter rate; however, if a CV of moose in an area. Density dependence 20% is acceptable, transect length could be occurs at high moose densities in interior reduced by ∼133 km. Alaska when May twinning rates are 4– Another consideration is pooling data 21% indicating nutritional stress, whereas across years to obtain more robust, and in years of low moose densities and recovery potentially more precise estimates of detec- of vegetation, rates are 30–47% (Boertje et al. tion probability (Burnham et al. 1980, Burn- 2007). The May twinning rate in our study ham et al. 2004, Fewster et al. 2005). area has recently been estimated as 47–67% Distance sampling is pooling robust and a (concurrent study; unpublished survey data, common practice in a single study area YDNWR), corroborating our assumption of because each transect typically has too few a population at high nutritional status. This observations to calculate separate detection moose population continues to grow and is functions (Gerard and Schucany 2002). an important subsistence resource for local Pooling by year to increase sample size people and a monitoring program is essential (observations) and to account for various for sound management regarding appropriate survey conditions (e.g., snow conditions) harvest levels to maintain a healthy, sustain- could improve the global detection function able population. We recommend that surveys for the area if repeated surveys are in the occur every 3–5 years to assess population same area and preferably along the same trends and inform management decisions. transects (Nielson et al. 2014). Future surveys along the lower Kuskok- If the CV ranges from 13–19%, man- wim tributaries should follow the same pro- agers should be able to detect at least a tocol used here (and potentially the same 38% change in abundance using a 90% CI transects; Buckland et al. 2001), with the with 80% statistical power. Given our den- exception of how moose locations under sity estimate of 0.47 moose/km2 (340 the aircraft were recorded. Perpendicular dis- moose), we should detect a change in density tances of moose detected by the front-left if the population changed by ∼0.18 moose/ observer under the helicopter (i.e., moose km2 (129 moose; 38%). Furthermore, if there groups approximately ± 43 m of the center is a 5-year period between surveys, this line) should be estimated and recorded in would require a finite rate of change (λ = {(ln Nt − ln N0) / t} future surveys. The precision of our density e , where N0 is the starting abun- estimates would have increased if we did dance estimate, Nt is the abundance estimate not lump and remove from analyses the 10 at time t, and t is the time period between observations directly under the helicopter. surveys; Skalski et al. 2005: 295) equal to The kernel density estimator was fairly λ = 0.909 annually for a decreasing popula- precise (CV = 18%); however, additional tion, or λ = 1.066 for an increasing popula- transects are required to increase precision tion. This is a realistic change for moose in in future surveys. Attaining a CV closer to this area since the lower Kuskokwim survey 15% would require an additional 307 km of unit showed an extreme growth rate of λ = transects; a precision with CV = 10% would 1.647 over a 4-year period (from 70 to 515 require an additional 1564 km, given the cur- moose; Perry 2010). rent group encounter rate. Given the narrow Our research provides a viable alterna- riparian corridors, it would be difficult to tive method to survey moose in a subarctic
152 ALCES VOL. 50, 2014 WALD AND NIELSON – ESTIMATING MOOSE ABUNDANCE tundra ecosystem with marginal snow condi- ———, and J. WOOLINGTON. 2006. Demo- tions. Presumably this technique could be graphics and home ranges of moose at applied elsewhere in areas with larger con- Togiak National Wildlife Refuge, South- tiguous habitat and variable snow conditions west Alaska: March 1998–March 2005. such as portions of moose range within sub- Progress Report. U.S. Fish and Wildlife arctic Alaska, Canada, Scandinavia, and Service, Togiak National Wildlife Refuge, Dillingham, Alaska, USA. Russia. Areas with dense canopy cover may ANDERSON, C. R., JR., and F. G. LINDZEY. 1996. require accounting for vegetation covariates Moose sightability model developed affecting sightability which would require a from helicopter surveys. Wildlife Society larger number of group observations. Never- Bulletin 24: 47–259. theless, as climate change increases the dis- BACHLER, E., and F. LIECHTI. 2007. On the ruption of prevailing weather patterns and importance of g(0) for estimating bird causes more atypical and uncertain scenarios population densities with standard dis- such as freeze-thaw or rain-on-snow events, tance-sampling: implications from a tele- our research and recommendations provide metry study and a literature review. Ibis wildlife managers an accurate, efficient, and 149: 693–700. cost-effective option for surveying moose BECKER, E. F., and P. X. QUANG. 2009. A populations. gamma-shaped detection function for line-transect surveys with double-count and covariate data. Journal of Agricul- ACKNOWLEDGEMENTS tural, Biological, and Environmental Sta- We would like to thank observers M. tistics 14: 207–223. Gabrielson and V. Anvil, and pilot S. Her- BOERTJE, R. D., K. A. KELLIE,C.T.SEATON,M. mens (Hermen Helicopters) for his expert A. KEECH,D.D.YOUNG,B.W.DALE,L. flying. We also thank G. Walters for his aer- G. ADAMS, and A. R. ADERMAN. 2007. ial fixed-wing support and T. Doolittle for Ranking Alaska moose nutrition: signals encouraging this effort. We are grateful to to begin liberal antlerless harvests. Jour- Drs. L. Munn, R. McCormick, J. Beck, M. nal of Wildlife Management 71: Murphy, and S. Miller, as well as the Alces 1494–1506. editors and 2 anonymous reviewers for pro- BORCHERS, D. L., J. L. LAAKE,C.SOUTHWELL, viding helpful comments. Funding for this and C. G. M. PAXTON. 2006. Accommo- project was through the US Fish and Wildlife dating unmodeled heterogeneity in dou- Service, Yukon Delta National Wildlife ble-observer distance sampling surveys. – Refuge, Bethel, Alaska, USA. The use of Biometrics 62: 372 378. BRIGGS, K. T., W. B. TYLER, and D. B. LEWIS. trade names of commercial products in this 1985. Comparison of ship and aerial sur- manuscript does not constitute endorsement veys of birds at sea. Journal of Wildlife or recommendation for use by the federal Management 49: 405–411. government. BUCKLAND, S. T. 1984. Monte Carlo confi- dence intervals. Biometrics 40: 811–817. REFERENCES ———. 1992. Fitting density functions with ADERMAN, A. R. 2008. Demographics and polynomials. Journal of the Royal Statis- home ranges of moose at Togiak National tical Society, Series C-Applied Statistics Wildlife Refuge, southwest Alaska, 1998 – 41: 63–76. 2007. Progress Report. U.S. Fish and ———,D.R.ANDERSON,K.P.BURNHAM, Wildlife Service, Togiak National Wildlife J. L. LAAKE,D.L.BORCHERS, and L. Refuge, Dillingham, Alaska, USA. THOMAS. 2001. Introduction to Distance
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