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
Refuge (YDNWR) is divided into 4 primary
moose (Alces alces) survey units along the
Yukon and Kuskokwim Rivers. Surveys in
these units are typically conducted using
the GeoSpatial Population Estimator
(GSPE) technique (Ver Hoef 2002, DeLong
2006, Kellie and DeLong 2006, Ver Hoef

2008), which is the preferred method
adopted by the Alaska Department of Fish
and Game (ADFG) and several other federal
agencies including other National Wildlife
Refuges in Alaska. Only one survey unit is
on the lower Kuskokwim River within
YDNWR, and encompasses nearly 2250
km2 of contiguous habitat along the

4Present address: Arctic National Wildlife Refuge, 101 12th Ave, Rm# 236, Fairbanks, Alaska 99701

133



relatively wide riparian corridor. The GSPE
technique overlays a grid of sample blocks
on the study area where each block is strati-
fied into high or low moose density based
on a previous stratification flight. A random
selection of survey blocks in each strata are
surveyed using a fixed-wing aircraft to com-
pletely search each selected block. The ana-
lysis uses the block’s spatial correlation to
increase the estimate’s precision based on
finite population block kriging (Ver Hoef
2002). Complete and adequate depth of
snow cover is essential for this type of survey.
Ideally surveys are conducted approximately
every 3–5 years to monitor trends in moose
abundance. However, the Yukon-Kuskokwim
Delta and other coastal areas of western
Alaska experience moderating climatic effects
from the Bering Sea and have frequent thaw-
refreeze events (1–9 events/winter; Wilson
et al. 2013). As a result, weather and snow
conditions may preclude survey initiation or
completion, extending the typical period
between surveys.

Despite adequate habitat to sustain a
higher moose population, the lower Kuskok-
wim River has historically had a low moose
density (0.03 moose/km2 in 2004; Perry
2010) because of extensive hunting pressure
(Coady 1980). Therefore, a moratorium was
implemented on the lower Kuskokwim
River watershed between 2004 and 2009
when the population increased substantially
(0.23 moose/km2 in 2008; Perry 2010) and
expanded into previously unoccupied, or
occasionally occupied habitat making it
necessary to create an expanded survey
unit. The new survey unit was developed to
include the major tributaries of the lower
Kuskokwim River within the YDNWR,
which are narrow riparian corridors that ori-
ginate from the adjacent mountains (Fig. 1).
These tributaries can support a substantial
population and are important wildlife corri-
dors to other parts of YDNWR and neighbor-
ing conservation units (i.e., Togiak National

Wildlife Refuge; Aderman and Woolington
2006). The Kuskokwim tributary survey unit
was first proposed, designed, and partially
surveyed in the winters of 2009 and 2010
using the GSPE technique; weather and lack
of snow cover prevented completion of both
surveys.

Environmental conditions such as snow
cover are among the most influential vari-
ables that affect survey quality (LeResche
and Rausch 1974, Gasaway et al. 1986,
Quayle et al. 2001, Oehlers et al. 2012).
The GSPE technique recommends that sur-
veys occur after fresh or moderately fresh
snow with complete ground coverage (Gas-
away et al. 1986, Kellie and DeLong 2006),
typically ≥20 cm in this area. Retrospec-
tively, we questioned the suitability of the
GSPE technique for these tributaries because
of the time and cost required to conduct
the survey given the unreliable weather and
snow conditions. In addition, we sought
to evaluate whether this technique is ideal
for use in the narrow linear habitats given
that large portions of many survey blocks
(∼3.7 km � 4.5 km) included non-moose
habitat (i.e., open tundra). The stratified ran-
dom block design of the GSPE is better sui-
ted for larger and more contiguous blocks
of similar habitat (Kellie and DeLong 2006).

A minimum count (termed complete
count, a non-sampling approach) survey is
used in adjacent areas (Aderman 2008) with
a fixed-wing aircraft flown throughout the
entire area, counting all moose observed;
the count is the population estimate (Lancia
et al. 2005). This method requires more fly-
ing time to search all areas completely and
the minimum count has neither an estimate
of precision (i.e., confidence interval) nor
typically a sightability correction factor
(Gasaway and DuBois 1987). Simple aerial
strip-transect surveys require less flying
than minimum counts and incorporate an
estimate of precision (Timmermann 1974,
Timmermann and Buss 2007, Jung et al.

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2009); however, this method assumes equal
detection of animals from the centerline out
to the designated strip width (Burnham and

Anderson 1984). Typically there is no esti-
mate of sightability with strip transect sam-
pling (Evans et al. 1966, Timmermann

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.

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1993), although sightability could be esti-
mated with marked animals (Anderson and
Lindsey 1996), or more intensive flying at
an increased cost (Gasaway et al. 1986, Gas-
away and DuBois 1987).

We determined that a viable survey
method was line-transect distance sampling
(Burnham et al. 1985, Buckland et al.
2001) using a helicopter for several reasons:
1) the area tends to have marginal snow
cover each year making it difficult to com-
plete a GSPE, 2) a helicopter can fly lower
and more slowly with better visibility than
a fixed-wing aircraft, helping to compensate
for minimal snow cover, 3) line-transects
can “fit” in the narrow riparian corridors bet-
ter than GSPE blocks that typically encom-
pass large portions of non-moose habitat, 4)
distance sampling incorporates sightability
corrections (e.g., weather, lighting, snow
conditions, observer experience) provided
that probability of detections at some dis-
tance is known or assumed and, 5) we
expected time, logistics, and costs may be
similar compared to a fixed-wing GSPE sur-
vey in the same region.

Thompson (1979) initially applied a dis-
tance sampling approach to estimate moose
abundance in Ontario, Canada, where it
was later improved upon by Dalton (1990).
Thompson (1979) had problems fitting
detection functions, and both surveys had
difficulties meeting some of the sampling
assumptions (e.g., exact distance measure-
ments, movement of animals before detec-
tion, sightings not always independent) and
were limited to the technological and statisti-
cal challenges of that period (Gasaway and
Dubois 1987, Pollock and Kendall 1987,
Dalton 1990). Significant advances in dis-
tance sampling methodology and statistical
analysis have been recognized over the last
30 years (Buckland et al. 2001, 2004; Tho-
mas et al. 2010), and these improvements
led to the development of distance sampling
protocol for moose in interior Alaska

(Nielson et al. 2006). Although distance
sampling has been used successfully to esti-
mate moose abundance in relatively large
contiguous blocks of boreal forest habitat
with adequate snow conditions, no study has
demonstrated that this technique works in
subarctic tundra along small, narrow riparian
corridors.

Distance sampling analyses typically
involve estimation of semi-parametric detec-
tion functions (Buckland et al. 2001, Thomas
et al. 2010). During early development
and analyses of line-transect distance data,
Burnham et al. (1980) suggested that other
nonparametric methods such as kernel esti-
mators or splines might prove “fruitful” for
estimating probability of detection, and
Mack and Quang (1998) further suggested
that kernel methods could be a viable techni-
que in wildlife distance sampling. The non-
parametric kernel density estimator does not
assume an underlying distribution for the
detection function, and thus has more flex-
ibility by allowing the data to “speak for
themselves” or dictate the shape of the detec-
tion function (Silverman 1986, Wand and
Jones 1995). Kernel estimators are consid-
ered a robust alternative to other density
function estimators (Chen 1996a) and are
computationally more efficient than polyno-
mials (Buckland 1992). Both kernel and
semi-parametric methods are robust against
changing detection functions during a survey
(Gerard and Schucany 2002) and are resili-
ent to changing survey conditions such as
snow depth/coverage, sun angle and overcast
skies, and wind or other environmental con-
ditions that could change during a survey
over time and space (Burnham et al. 1980,
Chen 1996b); it is assumed that no correla-
tion exists between moose density and these
changing conditions. Popular computer pro-
grams such as Distance 6.0 do not include a
kernel-based detection function (Thomas
et al. 2010) for use in analysis of line-
transect data, although the kernel method

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has been used for distance data in other types
of surveys (Buckland 1992, Chen 1996a,
Mack and Quang 1998, Gerard and Schu-
cany 2002, Jang and Loh 2010, Nielson et al.
2013, Nielson et al. 2014), but not for
moose.

The objectives of this study were two-
fold: 1) evaluate helicopter-based aerial
line-transect distance surveys with a double-
observer modification to obtain an estimate
of moose abundance within narrow riparian
corridors during a low snow year, and 2)
compare the nonparametric kernel-based
detection function to the more traditional
semi-parametric models in the program Dis-
tance (Thomas et al. 2010). We investigated
what we presumed was a viable alternative
to traditional moose survey methods for

areas with environmental conditions that pre-
clude traditional surveys.

STUDY AREA
The Yukon Delta NWR is located in

western Alaska and encompasses the delta
formed by the Yukon and Kuskokwim
Rivers which empty into the Bering Sea
(Fig. 1). The Kuskokwim tributary survey
unit includes parts of 4 main lower Kuskok-
wim River tributaries originating from the
mountains to the south and east. These tribu-
taries include the Eek, Kwethluk, Kisaralik,
and Tuluksak Rivers and are characterized
by narrow (0.7–4.3 km wide) riparian corri-
dors (Fig. 2) running through the foothills
and tundra flats that drain the northwest sides
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.

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The Eek and upper Kwethluk Rivers are
represented by open riparian shrubs (Salix
spp. and Alnus spp.) and scattered clumps
of balsam popular (Populus balsamifera),
whereas the lower Kwethluk River transi-
tions to open forests that include sporadic
mixing of spruce (Picea glauca), balsam
popular, and birch (Betula papyrifera) as
the overstory with an understory of open wil-
low and alder. The Tuluksak River riparian
zone is primarily a narrow corridor of spruce
and birch with an understory of willow and
alder. The Kisaralik River riparian zone is
mostly mixed coniferous open woodland
which exhibits a moderate transition between
the Kwethluk and Tuluksak riparian habitats.
All 4 tributary habitats are bounded by
tundra and include variously sized open
meadows, old river channels, and beaver
ponds.

Weather conditions are highly variable
across the survey area. Average temperatures
and snow depth at Bethel, Alaska airport
(2000–2010; NOAA 2011) during the pri-
mary survey months were −21 °C (range
−36 to 4 °C) with 23 cm (0–56 cm) of
snow in January, −10 °C (−37 to 5 °C)
and 23 cm (0–64 cm) of snow in February,
and −9 °C (−27 to 4 °C) with 20 cm
(0–56 cm) of snow in March. In many years
there are freeze-thaw events (Wilson et al.
2013) throughout the winter which ultimately
limit total snow accumulation and duration.
Our study period (2010) was an El Niño year
which affected the winter weather pattern
on the Yukon-Kuskokwim Delta from June
2009 to March 2010 (NOAA 2013).
Repeated high pressure systems over the
Delta kept numerous low pressure systems
south and subsequently pushed easterly,
resulting in unusually clear and dry condi-
tions with periods of colder temperatures
and little snowfall over the study area during
winter 2009–2010. A portion of the survey
unit experiences a “banana belt” effect, espe-
cially along the foothills between the

Kwethluk and Kisaralik Rivers. This area is
usually affected by a warming trend that
typically melts snow more frequently and
rapidly than other parts of the area, perhaps
resulting from an inversion. These condi-
tions can limit GSPE surveys along the
lower Kwethluk and Kisaralik Rivers in
any given year.

Nearly 3 cm of new snow accumulated 4
days prior to the survey. Total snow depth
was 5 cm (Bethel airport) but was 8–10 cm
at 2 snow stakes in the study area (Kwethluk
River) during the survey. Snow coverage
ranged from 85–100% throughout the survey
area with meadow grasses and short vegeta-
tion protruding and snow melted off stumps
and root wads. Weather conditions during
this survey were mostly clear, 9–37 kph
winds, and −12 to 2 °C. Day length was
nearly 12 h with sunrise at 0900 hr and sha-
dows becoming long at about 1500 hr. Sur-
vey times were typically between 0900 and
1700 hr each day and flying conditions
were generally favorable during the entire
survey.

METHODS
Field Survey

Aerial line-transect distance sampling
protocol for moose followed Nielson et al.
(2006). The survey area (i.e., sampling uni-
verse) was limited to the riparian corridor
for the rivers of interest. Polygons were cre-
ated around rivers to encompass riparian
vegetated areas within the floodplain and
between the tundra benches on each side of
the river (ArcMap 9.2, Environmental Sys-
tems Research Institute, Redlands, Califor-
nia, USA; Fig. 1). Satellite imagery was
used to facilitate creation of survey areas
which encompassed nearly 730 km2.

Survey transects were created within
river corridors and varied by length and
number along each river (Fig. 1). Multiple
transects were placed in areas wide enough
to allow equidistance spacing of 700 m,

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providing a maximum 350 m search area on
each side of a transect centerline. Transect
length varied according to stretches of river
that allowed straight transects with sections
changing direction in a saw-toothed manner
as the river corridor meandered (Nielson et al.
2006). Some riparian corridors were suffi-
ciently narrow to allow only a single transect
which had a random start point contingent on
allowing the minimum half transect width
(350 m) to be in moose habitat. The center-
line could not be on the edge of the habitat
(i.e., one side having a hard boundary of no
moose habitat or open tundra and the other
side all moose habitat) to avoid extreme
asymmetry of g(y), although this source of
bias is minimal in most studies (Buckland
et al. 2001). Areas with systematic parallel
transects had a random start point for the first
transect. A total of 46 transects were delin-
eated with a combined length of 698 km
(Fig. 1).

We used a Robinson (R-44) helicopter
with bubble windows to survey moose
during 16–17 March 2010. Helicopters pro-
vide a better platform for observing moose
because of better sightability, smaller var-
iances, and often comparable cost with
fixed-wing surveys (Smits et al. 1994, Gosse
et al. 2002). Protocol recommends a flight
altitude of 122 m above ground level
(AGL) which results in good visibility and
minimal disturbance of moose (Nielson et al.
2006). However, snow conditions were poor,
so flight altitude was adjusted to 100 m AGL
to increase visibility while remaining high
enough to minimally affect moose and pre-
vent ground flash, the visual effect of ground
zooming by too fast when flying at a lower
altitude (Becker and Quang 2009). Our tar-
get ground speed was 64 kph (40 mph)
depending on terrain and wind.

Four people were onboard during this
survey. The pilot was responsible for main-
taining desired altitude, speed, and heading
on transect centerlines using a preprogramed

GPS (Garmin 695). Two observers were
seated in the back (one on each side) and
were the primary observers for the survey.
Their responsibilities were to sight moose
groups, count and classify each group, and
measure the perpendicular distance from the
transect centerline to each group centerpoint.
The data recorder sat in the front-left seat
and was responsible for recording all data
including GPS locations, performing as a
double-observer, frequently measuring heli-
copter AGL, and overall survey coordina-
tion. The front observer recorded survey
data while flying off transect in order to not
interfere with double-observer duties while
flying on transect.

The double-observer method was used
in conjunction with the line-transect survey
to test the assumption that detection was
100% on or near the transect centerline, or
at the minimum available sighting distance
(Buckland et al. 2001, Laake and Borchers
2004, Borchers et al. 2006). This assumption
is sometimes violated (Chen 1999, 2000)
and information regarding heterogeneity in
observer bias should be modeled (Graham
and Bell 1989) because it can produce nega-
tively biased estimates.

The data recorder in the front-left seat
was paired with the rear left observer to con-
duct the double-observer sampling, which is
essentially a mark-recapture method (Borch-
ers et al. 2006). The data recorder focused on
or near the centerline to detect moose, but
recorded all moose observations at any dis-
tance. Double-observer data are used to esti-
mate detection rate on or near the centerline
by the rear seat observers. This requires
that the front and rear seat observers operate
independently of each other (Buckland et al.
2010). Data were recorded on the number of
moose groups detected by both observers,
and groups detected by the front and not
the rear observer. To account for observer
bias, the 2 rear observers rotated sides each
day to be paired with the front-left observer

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to incorporate biases from both observers
into the model (Cook and Jacobson 1979).
Thus, we considered the probability of detec-
tion estimated for the back-left observer
based on the mark-recapture data to be rele-
vant for both backseat observers during ana-
lyses. The recorder also worked with the
pilot to keep flight speed and altitude within
the range of survey protocol. A laser range-
finder (Nikon Forestry 550 Hypsometer)
was frequently used to measure true vertical
distance from the ground to helicopter every
2–3 min to check flight altitude and recom-
mended adjustments as needed.

Moose groups were defined as one or
more moose within a 50 m radius (Molvar
and Bowyer 1994). The distance of groups
perpendicular to the transect centerline was
measured by the rear observer with a laser
rangefinder (Leupold RX-1000 TBR) with
a built-in clinometer that had maximum
range of ∼900 m; clinometers allow for
accurate horizontal measurements regardless
of survey altitude. A group that was hard to
laser-range (e.g., trees, helicopter movement,
animal movement) required flying back over
the group and marking its location with a
GPS (Marques et al. 2006). Distance was
measured to the center of a group using the
laser rangefinder directed at their feet to
avoid over-estimating the distance; this mea-
surement was associated with the location of
the group when first observed. If moose
moved before a distance was acquired, the
observer ranged the location of the initial
observation. Doubling back to mark GPS
locations worked well, but some moose
moved after detection because of the aircraft
hovering directly overhead; tracks in the
snow proved reliable as reference points for
these cases. The distances measured with
the GPS method (∼90% of all groups
observed) were calculated in a GIS. Addi-
tional moose observed “off transect” while
doubling back to obtain GPS locations were
not included in any analysis. Observers

determined group size, composition (i.e.,
adults and calves), and classified percent
habitat cover for ∼50 m radius around each
group.

Data Analysis
Standard distance sampling theory

assumes all individuals (objects) available
to be detected on the centerline, or the mini-
mal available sighting distance, are
observed, and that the probability of detec-
tion is a function of perpendicular distance
from the centerline. There are 3 essential
assumptions for accurately estimating den-
sity using distance sampling. In order of
importance these are: 1) objects at the mini-
mal available sighting distance are detected
with certainty, that is g(W1) = 1.0, or can be
estimated, 2) objects are detected prior to
any movement in response to the survey,
and 3) perpendicular measurements to the
object are accurate (Buckland and Turnock
1992, Buckland et al. 2001). Other design/
analysis assumptions exist but are less strin-
gent, including accurate measurement of
group size and that object density is indepen-
dent of the placement of transects (i.e., uni-
form distance distributions; Fewster
et al. 2008).

Fulfilling these assumptions allow for an
accurate density estimate using:

D̂ ¼ nÊðsÞ
2ðW2 � W1ÞLP̂

ð1Þ

where n is the number of observed groups,
ÊðsÞ is the expected (or average) group
size, W1 and W2 are the minimum and max-
imum search distances from a transect,
respectively, L is the total length of transects
flown, and P̂ is the estimated average prob-
ability of detection within the area searched
(Buckland et al. 2001).

We tested the assumption g(W1) = 1.0,
where g(W1) is the minimum sighting

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distance with the double-observer technique
(Chen 2000, Borchers et al. 2006, Buckland
et al. 2010) using observations from the left
side of the helicopter. Observations collected
independently by individual observers on the
left side were used to estimate the probability
of detecting a moose group at the minimum
available sighting distance. This probability
was used to adjust the estimated detection
curve starting at that distance (Laake and
Borchers 2004).

We used logistic regression (McCullagh
and Nelder 1989) in the mark-recapture ana-
lysis to estimate the probability of detecting
a moose group by the back-left observer
given detection by the front-left observer.
We considered 3 models that 1) treated the
probability that a group was detected by the
back-left observer as constant across all dis-
tances from the transect line (intercept only
model), 2) treated the probability of detec-
tion as a function of distance from the trans-
ect line, and 3) included both linear and
quadratic terms for distance from the transect
line. We used Akaike’s information criterion
for small sample sizes (AICc; Burnham and
Anderson 2002) to identify the best model
for estimating probability of detection by
the backseat observers based on the mark-
recapture data. The AICc was calculated as:

AICc ¼ �2logðLikelihoodÞ þ 2kn/ðn�k�1Þ
ð2Þ

where k was the number of parameters in the
model (including intercept term), n was the
number of observations used to fit the model,
Likelihood was the value of the logistic like-
lihood evaluated at the maximum likelihood
estimates, and ‘log’ was the natural loga-
rithm. The logistic regression model was fit
using the program R (R Development Core
Team 2010).

We designed transect centerlines to be a
minimum of 700 m apart to ensure that

moose groups were not counted more than
once if they moved during the survey. To
meet this assumption, we set the maximum
search width, W2, equal to the maximum dis-
tance a moose group was observed within
300 m of the transect centerline. Since the
backseat observers had a blind spot under-
neath the helicopter, we used a laser range-
finder (hypsometer) to determine the
minimum sighting distance for the backseat
observers. To determine the width of the
blind spot at the survey altitude, the backseat
observer laser-ranged through the bubble
window along their line-of-sight to the
ground, just clear of the helicopter skid.
The minimum available sighting distance
for backseat observers was ∼43 m from the
centerline. Moose were visible to the front-
left observer from 0–43 m through the front
helicopter window, but lumping these data
into a single distance of “zero”, and the fact
that the front-right observer (pilot) was not
focused on observing moose on that side of
the line, precluded using these data in the
analyses; therefore, the front-left observer
observations in the 0–43 m range were not
used. Thus, the minimum available sighting
distance, W1, was set at the minimum dis-
tance at which a moose group was detected
by a backseat observer.

We evaluated whether correlation
existed between expected group size and
detection distance because group size can
influence detectability, especially at longer
distances; larger groups may have a higher
probability of detection than smaller groups
further from the transect line (Drummer and
McDonald 1987, Drummer et al. 1990). We
used a Pearson’s correlation analysis to esti-
mate the correlation (r) between group size
and distance from the transect line, and cal-
culated a 95% confidence interval (CI) for
the statistic (Zar 1999). We determined no
relationship existed between group size and
detection distance if the 95% CI included
0.0. In this situation, we used the average

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of all observed group sizes for ÊðsÞ (equa-
tion 1). If a correlation was detected, we
used the regression method (Buckland et al.
2001) to estimate expected group size. We
examined the habitat covariate, percent
cover as a potential influence on the prob-
ability of detection of groups (i.e., higher
percent cover may reduce probability of
detection; Anderson and Lindzey 1996, Oeh-
lers et al. 2012).

The underpinning of distance sampling
is the detection function g(y) which
expresses the probability of detecting a
group given that the group was observed at
distance (y) from a random transect, and
that the assumption g(W1) = 1.0, or can be
estimated, holds true (Buckland et al.
2001). There are many models that can be
fitted to distance data in order to estimate
the shape of a detection function, and we
used the computer program Distance 6.0
release 2 (Thomas et al. 2010) to model
semi-parametric detection functions for
moose groups. We considered robust key
functions with expansion terms as outlined
in Buckland et al. (2001), including the
half-normal with hermite polynomial and
cosine expansion terms, the hazard-rate
with a cosine expansion, and the uniform
with simple polynomial and cosine expan-
sion terms. Additionally, the half-normal or
hazard-rate key functions allow for predictor
variables to help model the detection func-
tion. We used the half-normal (including her-
mite polynomial and cosine expansion
terms) and hazard-rate (including a cosine
expansion term) key functions for modeling
the detection function while incorporating
the percent cover variable. The number of
expansion terms for each key function was
allowed to vary from 0–5; the AICc was
used to select the number of expansion terms
among the various models. The model with
the lowest AICc value was selected as the
best model to describe the detection function
(Burnham and Anderson 2002).

Use of parametric or semi-parametric
detection functions may not always be the
best approach to fit probability detection
curves (Burnham and Anderson 1976, Buck-
land 1992); instead, a nonparametric kernel
density estimator without an assumed prob-
ability density function may provide a better
fit to the data. We fit a nonparametric kernel
estimator (Silverman 1986, Wand and Jones
1995) to our group observations, and used
the general univariate kernel density estima-
tor described in Wand and Jones (1995):

f̂ xð Þ ¼ nhð Þ�1
Xn
i¼1

K
x � xi

h

� �
ð3Þ

where x is a perpendicular distance within
the range of observed distances, xi is one
of the n observed distances, h is a smooth-
ing parameter, or ‘bandwidth’, and K is a
kernel function satisfying the conditionÐ
K xð Þdx ¼ 1.
Since the bandwidth (h) governs the

function smoothness (Chen 1996a, Gerard
and Schucany 1999), the choice of band-
width is more crucial than the choice of ker-
nel (Mack and Quang 1998, Jang and Loh
2010). We used a Gaussian kernel function
(Silverman 1986, Chen 1996a) and the direct
plug-in bandwidth selection method
(Sheather and Jones 1991, Wand and Jones
1995, Sheather 2004) to develop the detec-
tion function for groups. The direct plug-in
method objectively fits the bandwidth and
is considered to be the best compromise
between bias and variance among the avail-
able methods (Sheather and Jones 1991,
Wand and Jones 1995, Venables and Ripley
2002, Sheather 2004).

Kernel estimators inherently do not per-
form well near sharp boundaries (Jang and
Loh 2010). A boundary bias is created, as
in our case, when distance observations are
not distinguished from the right or left side
of the transect line and where all values are

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non-negative (Buckland 1992, Jang and Loh
2010). In order to model the distances with a
kernel estimator, Chen (1996a, 1996b) and
Silverman (1986) recommended reflecting
the observed distances to both sides of the
transect line in order for the kernel density
estimator to perform properly. After shifting
all observed distances by the left-truncation
distance (W1), we multiplied (reflected) the
observed distances by (−1) and added them
to the dataset (Buckland 1992, Chen 1996a,
1996b). Once the kernel density function
was created from the expanded dataset, the
detection function to the right of the zero
line (positive) was used for the density esti-
mate. The kernel estimator was fit using the
program R (R Development Core Team
2010) and the MASS package in R (Ven-
ables and Ripley 2002).

We used bootstrapping to estimate SEs
and 95% CIs for final estimates of moose
density and abundance within the sampled
region (Efron 1981a, 1981b, Quang 1990,
DiCiccio and Efron 1996). Estimates derived
from the program Distance 6.0 were boot-
strapped within the program, which uses a
default of 999 bootstrap re-samplings with
replacement (Thomas et al. 2009). Standard
errors and confidence intervals for the kernel
estimates were derived from bootstrapping
999 resamples (with replacement) to be con-
sistent with program Distance and because
the bootstrapped estimates (SE, CI) usually
become stable and asymptotic between 500
and 1000 resamples (Efron and Tibshirani
1994). We bootstrapped the 46 line-transects
surveyed in which the bootstrap would rerun
the analysis for all parameter estimates,
including the shape of the detection function
and the average probability of detection dur-
ing each iteration. Additionally, we evalu-
ated bias and precision of the density
estimate using the bootstrap (Efron and Tib-
shirani 1986). We used the percentile method
(Efron 1981b, 1982) for calculating the 95%
confidence intervals using the 2.5th and 97.5th

percentiles of the 1,000 estimates (999 boot-
strap estimates + original estimate). The per-
centile method is the preferred method for
calculation of CIs when bootstrapping,
because using the standard formula (i.e., esti-
mate ± 1.96[SE]) requires the additional
assumption that the bootstrap estimates gen-
erally follow a normal distribution (Buck-
land 1984, Efron and Tibshirani 1994). We
estimated relative percent bias of the density
estimates as:

%Bias ¼ Dboot � Dorig
� �

Dorig

� �
� 100 ð4Þ

where Dboot is the average density esti-
mate from the bootstrap and Dorig was
the original density estimate. We measured
dispersion or the extent of variability in rela-
tion to the final density estimate by calculat-
ing the coefficient of variation (CV) as
CV ¼ ðSE=D̂Þ � 100%. The standard
deviation (SD) of the 1,000 estimates was
used as the estimated SE.

In order to estimate the total length (L)
of transects needed in future surveys to
achieve a certain level of precision (i.e., CV
value), we used the formula from Buckland
et al. (2001):

L ¼ L0 cvðDÞf g2
.

cvtðDÞf g2 ð5Þ

where L0 is the total length of transects sur-
veyed, cv (D) is the coefficient of variation
of the density estimate from this study and
cvt (D) is the desired target coefficient of
variation.

RESULTS
A total of 162 moose (112 adults, 48

calves) in 78 groups were detected on 46
transects along 698 km within a series of
polygons encompassing 730 km2 of riparian
moose habitat. There were 37 cow moose
with calves including 26 singletons and 11

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143



sets of twins (30% twinning rate). Group size
ranged from 1–5 with 73% of groups com-
prised of 1–2 moose and only 6% with 4–5
moose.

Because the mark-recapture portion of
this study was intended to occur only on
the left side of the aircraft, a single group
observation detected by the front-left obser-
ver that was 244 m to the right of the transect
line (and not detected by the back-right
observer) was excluded from the analysis.
Ten of the 78 groups were detected only by
the front-left observer and were recorded as
seen directly on the transect line (i.e., per-
pendicular distance = 0). Since these groups
could not be seen by the back-left observer
and ‘lumping’ of the perpendicular distances
occurred during data recording (i.e., these
moose were likely somewhere ± 43 m from
the transect line and not all directly on the
line), these observations were also excluded
from the analysis. Of the remaining observa-
tions, the minimum observed distance of a
moose group by the backseat observers was
46 m from the transect line, thus W1 was
set to 46 m. We truncated our data to 300
m, which corresponded to a reduction of
approximately 8% of the farthest distance
observations; Buckland et al. (2001) recom-
mend truncating the farthest 5–10% of dis-
tance observations. The maximum observed
distance of a group within 300 m of a
transect line was 299 m, so W2 was set at
299 m.

Analysis of moose observations within
the defined search width (46–299 m from a
transect line) indicated that group size was
not correlated with distance from the transect
line (r = 0.048, 95%, CI = −0.20–0.29). The
average group size by the backseat observers
within the search strip was 2.03 (95% CI
from 1.78–2.32) and was used in the density
estimate.

The mark-recapture trials used 34 obser-
vations to fit logistic regression equations to
estimate the probability of detection by the

back-left observer given detection by the
front-left observer. Only 3 groups were
missed by the back-left observer and these
were deleted for the density estimate. The
logistic equation with linear and quadratic
terms for distance from the transect line had
the lowest AICc value (19.8 versus 22.4
and 24 for the intercept only and linear dis-
tance function models, respectively). The
final estimated logistic regression model
was:

E yi½ � ¼
exp 51:461 � 0:583distancei þ 0:0012distance2i

� 	
1 þ exp 51:461 � 0:583distancei þ 0:0012distance2i

� 	
ð6Þ

where E [yi] was the expected probability
of detection for mark-recapture observa-
tion i.

Based on this final model, the predicted
probability of detection of moose at the mini-
mum sighting distance by the back-left
observer was 1.0. Therefore, the estimated
probability of detection curve was not scaled
by a correction factor prior to integration and
estimation of P̂, and only observations by
the rear seat observers were used to estimate
moose density.

Comparison of models using AICc
values requires that the competing models
are all estimated using the same number of
observations and the same response (Y)
values. Percent cover was not recorded for
one observation so this record was not initi-
ally included during estimation of the prob-
ability of detection curve. In addition, due to
the distribution of percent cover values for
observations (10–70% in 10% increments)
and few observations at the extremes, the ori-
ginal values were collapsed into 3 categories:
1) 10–30, 2) 30–50, and 3) 60–70%.

Comparison of the models with and
without the covariate for percent cover indi-
cated that a hazard-rate key function with
no expansion terms was the best fit to the
data (Table 1). Because the models

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containing the covariate for percent cover
ranked last according to AICc values, we
refit the models without the predictor vari-
able using all the observations from the rear
seat observers within 46–299 m of a transect
line, including the single observation where
percent cover was not recorded. The results
of this analysis were similar to the analysis,
minus the missing observation, in that the
top model was a hazard-rate key function
with no expansion terms (Table 2). We used
the goodness of fit (GOF) test statistic to
determine if the top model fit the data well
(Buckland et al. 2001). There was no evi-
dence of lack of fit for the top model (GOF

test; χ2 = 6.07, df = 4, P = 0.194). Based on
this final model using 59 groups, the esti-
mated average probability of detection was
0.70 (Fig. 3), and the estimated density was
0.48 moose/km2 or a population of 352
moose (95% CI = 237–540); this model
had a CV of 20% and an estimated bias
of ∼1.4%.

The detection function calculated using
the kernel density estimator (without covari-
ates) also had a good fit (GOF test; χ2 = 6.42,
df = 5, P = 0.73) with an estimated average
probability of detection of 0.73 (Fig. 3).
The estimated density was 0.47 moose/km2

or a population of 340 moose (95% CI =

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 (P̂), estimated moose density (D̂), and coefficient of variation (CV) for
each model, Alaska, 2010.

Key Function Expansion
Expansion
Terms k

% Cover
(yes/no) AICc P̂ D̂

%
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 P̂ , estimated moose density D̂, and coefficient of variation (CV) for each
model, Alaska, 2010.

Key Function Expansion Expansion Terms k AICc P̂ D̂ % 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.

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145



238–472); the corresponding CV was 18%
and the estimated bias based on bootstrap-
ping was <0.001%.

Based on an encounter rate of 0.085
moose groups/km (59 groups/698 km) and
the CV from the kernel estimator (18%),
we calculated the total length of transects
needed to achieve a targeted CV of 20, 15,
and 10%. This analysis indicated that trans-
ect lengths of 566, 1006, and 2262 km,
respectively, were required to meet these tar-
geted CVs assuming that the encounter rate
remains constant.

DISCUSSION
Others have utilized distance sampling

with varying degrees of success in model

fitting and achieving adequate levels of esti-
mate precision under adequate snow condi-
tions within boreal transition forest of west-
central Alaska (Nielson et al. 2006) and
central Canadian boreal forest habitats
(Thompson 1979, Dalton 1990, Thiessen
2010, Peters et al. 2014). We evaluated this
method as an alternative technique for sur-
veying moose in a subarctic tundra ecosys-
tem with variable and often minimal snow
conditions, and present an alternative techni-
que for analyzing distance data using a non-
parametric kernel density estimator to fit the
detection function. Overall, distance sam-
pling proved to be a viable technique to
monitor moose along the Kuskokwim

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.

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tributary rivers in the YDNWR in southwes-
tern Alaska.

Assumptions
Distance sampling depends on 3 main

assumptions that need to be met, or nearly
so, in order to produce unbiased and reliable
estimates (Buckland et al. 2001). Although
the assumptions can be relaxed to some
degree in certain circumstances and still pro-
vide dependable estimates (Buckland et al.
2001), we designed our study in an attempt
to meet all assumptions or to estimate our
biases if we failed to adequately meet one.

Assumption (1), that objects at the
minimum available sighting distance were
detected with certainty, is typically
addressed by developing a sightability cor-
rection factor (SCF) through modeling
covariates against mark-recapture data of
collared animals (Gasaway et al. 1986,
Samuel et al. 1987, Anderson and Lindzey
1996). Distance sampling inherently
accounts for, or corrects for, visibility (per-
ception) biases provided that all objects
are detected on the transect centerline or at
the minimum sighting distance (Buckland
et al. 2001, Marques and Buckland 2004).
Although many distance sampling studies
do not address assumption (1) (Bachler
and Liechti 2007), we utilized the double-
observer method (Graham and Bell 1989)
to test the primary assumption that detection
of moose groups on the centerline or at the
minimum sighting distance was certain. The
mark-recapture logistic regression analysis
indicated that we met the assumption with
100% probability of the backseat observer
detecting a moose group that was detected
by the front-left observer at the minimum
sighting distance (g(W1)). Detection cer-
tainty along the transect line in our study
was enhanced by several factors including
that the survey area was within narrow ripar-
ian habitat with a relatively open canopy
(range of percent cover data was 10–70%

with an average of 39%). Additionally,
detection on the centerline was further
increased by the fact that we used a helicop-
ter flying at 100 m AGL at a relatively slow
speed of 48–88 kph; although snow was
shallow, visibility on the centerline was
excellent.

Moose in our study area were assumed
to be available for detection because of the
relatively open habitat (39% canopy clo-
sure). One concern was that root-wads of
wind-fallen trees could hide an adjacent,
bedded moose. However, if we flew directly
over a root-wad we detected the moose on
the transect line (g(W1) = 1.0), and it would
be accounted for in the detection function
at distances off the transect line (Laake et al.
2008). Availability bias could possibly be
removed or reduced if the area was surveyed
at different times (e.g., hours apart) to allow
animals to become available; this is likely
dependent on species (Laake and Borchers
2004) and unlikely of concern with moose
in most conditions.

Assumption (2), that objects are detected
at their initial location, is sometimes difficult
to assess (Fewster et al. 2008), and in our
case, related to disturbed moose “pushed”
by the helicopter some distance before detec-
tion. Thompson (1979) reported that moose
were not disturbed by circling fixed-wing
aircraft and did not move as the airplane
approached; however, Cumberland (2012)
reported that moose usually initiated some
movement from a larger turbine helicopter
(Bell 206) at a lower survey altitude (60 m
AGL). Random movement is acceptable as
long as it is not caused by the observer
(Buckland et al. 2001), but failure to meet
assumption (2) would bias the density esti-
mate low.

We investigated the validity of this
assumption, in part, by reviewing the dis-
tance data histogram and identifying whether
a bump or peak is evident some distance
from the center line. Figure 3 has a slight

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147



bump in frequency at ∼150 m which might
reflect recording bias or movement from
the helicopter prior to detection (Dalton
1990). Our front observer was focused on
the centerline for the double-observer
method, and looking forward of the helicop-
ter to identify any pre-detection movement
(Fewster et al. 2008). Few moose were
observed moving prior to when the backseat
observers detected moose; movement was
mainly in response to the helicopter directly
overhead. Because these few moose did not
move into a zone of detection for the back-
seat observer, movements were considered
moot in our study. Further, observations of
moose within the effective search width
(46–299 m) did not indicate movement prior
to detection by the backseat observer.

A possible explanation for the bump in
our data was that the backseat observers
had a comfortable scanning level or sight
line (i.e., distance) while sitting in the heli-
copter. Observer fatigue increases as a sur-
vey progresses (Briggs et al. 1985,
Schroeder and Murphy 1999), possibly con-
tributing to the desire to scan (subcon-
sciously) at a less strained position. For
example, Jang and Loh (2010) graphed the
classic wooden stake data outline in Burn-
ham et al. (1980) and showed that their histo-
gram had a large bump or spike of detections
that clearly was not associated with move-
ment. We believe that we met assumption
(2) because the front observer scanned for-
ward of the flight path and there was no
change in observation rate moving from the
center line (Fig. 3). Flying at a higher alti-
tude (e.g., 122 m instead of 100 m AGL).
as suggested by Nielson et al. (2006), would
presumably further address assumption (2).

To meet assumption (3), that perpendi-
cular distance measurements are exact, we
utilized both rangefinders with built-in clin-
ometers and GPS units to determine perpen-
dicular distances to moose groups. Although
both methods can be accurate and efficient, it

was difficult to range groups at times, espe-
cially when close to the helicopter which
required a quick response, and when in
cover. Higher quality or industrial-type laser
rangefinders should reduce this problem. We
eventually adopted the technique used by
Marques et al. (2006) and used GPS loca-
tions to measure distances. This required
more flying time and effort to fly off transect
to identify the group location. Because this
process caused some moose to move prior
to marking the location, we followed tracks
in the snow to ascertain the initial location.
Increasing flight altitude while off transect
may alleviate or reduce disturbance while
marking locations. We are confident that
movements were minimal and measured
adequately, and that groups were not double
counted on subsequent transects.

Other assumptions that are not generally
discussed in literature, such as the uniformity
of the distance distribution and indepen-
dence of group observations, are typically
addressed during the survey design process.
The uniformity assumption is addressed by
randomly distributing transect lines across
the study area, or systematically arranging
transects with a random start point, as we
did (Fewster et al. 2008, Jang and Loh
2010). The assumption that observations
are independent is addressed in the same
manner as distance uniformity (Buckland
et al. 2001) provided that moose are not clus-
tered together in one part of the survey area.
Estimates of density are robust to the inde-
pendence assumption especially when boot-
strapping to obtain confidence intervals
(Thomas et al. 2002). Additionally, we did
not incorporate “dependent” moose groups
observed while flying off transect when
obtaining GPS locations for groups that
moved.

Detection Functions
Survey design and protocol are para-

mount for meeting the 3 primary assumptions

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of distance sampling in order to model detec-
tion functions reliably (Thomas et al. 2010).
Our survey transects were systematically dis-
tributed throughout the riparian corridors
with random start points allowing for statisti-
cal inference (Fewster et al. 2009). Although
transects were spaced 700 m apart and a
maximum search width of 350 m could
have been used in the analysis, there were
few observations beyond 300 m. Restricting
the analysis to observations within 300 m
reduced the possibility that moose groups
were counted more than once. We dropped
nearly 8% of the farthest observations which
was within the recommended 5–10% range
suggested because outliers may have undue
influence on the shape and scale of the detec-
tion function (Buckland et al. 2001). Our
effective search width (W1 and W2) was
253 m (46–299 m) which was narrower
than the 700 (Dalton 1990) and 800 m
(Thiessen 2010) widths used in Canada,
and similar to the 250 m search width used
by Thompson (1979). Our search width
was narrow because of the narrow corridor
of habitat, we flew relatively low, and the
relatively poor snow conditions which pre-
sumably reduces visibility. We recommend
using narrow transect search widths during
low or poor snow condition years to increase
effectiveness of the survey.

We measured percent cover because
covariates can improve model precision by
accounting for heterogeneity in the data
(Buckland et al. 2004, Marques and Buck-
land 2004), but at an added cost of sample
size (Giudice et al. 2012). However, it did
not improve the detection function based on
the higher AIC values for the models includ-
ing this covariate. This might reflect the
relatively narrow range of values (range =
10–70%, median = 40%) that were lumped
into 3 categories. Visual obstruction by
vegetation influenced detection of moose in
Minnesota where percent cover was higher
(range = 0–95%, median = 60%) (Giudice

et al. 2012). Buckland et al. (2001) recom-
mend 60–80 observations and at least 10–
20 replicate transects to obtain reliable esti-
mates with relatively good precision; we
had 58 group observations with percent
cover measurements. Seddon et al. (2003)
improved their survey precision (i.e.,
decreased CV values) by increasing
observations.

In an analysis of several surveys, Thies-
sen (2010) found a strong relationship
between the number of observations and
CVs for those surveys; surveys with 60
observations had a CVof ∼20%. Our survey
(59 observations) corroborates this relation-
ship as our model without covariates had a
CV of 20% (using the hazard-rate key func-
tion). Adding covariates or stratifications
would require considerably more observa-
tions to ensure reliable estimates with a CV
of 20%. We examined the possibility of stra-
tifying our study area by each tributary river
but moose density was too low to acquire
sufficient observations for reliable estimates
for all rivers, with the possible exception of
the Kwethluk River (∼60–80 observation in
each strata; Buckland et al. 2001).

Group size influences detection at dis-
tance (Drummer et al. 1990), and can be
included as a covariate in the program Dis-
tance (Laake et al. 2008). We investigated
whether a correlation existed between group
size and detection distance prior to “penaliz-
ing” our analysis with an additional covari-
ate (Giudice et al. 2012). Our analysis
indicated that group size was not correlated
with detection distance in this study which
most likely reflects the group composition
in the study area. Most groups were rela-
tively small (73% had 1–2 moose) and
most observations were cows with calves.
Since there was no correlation between dis-
tance and group size, and the composition
of groups had a narrow range of sizes (no
major outliers), we used the average group
size as equivalent to the expected group

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149



size in the density estimate (Buckland
et al. 2001).

Our model choices were based on
recommendations of Buckland et al. (2001)
and past experience (Nielson et al. 2006) in
order to prevent a “shotgun” approach to
modeling. Models that included the percent
cover covariate were ranked last and did
not contribute to or improve the model
according to AICc; we subsequently
removed the covariate and analyzed the
data without it. Our top model was the
hazard-rate key function with no expansion
terms. As in our study, several other ungulate
studies reported the hazard rate key function
with various expansions to be the top models
(Focardi et al. 2002, Shorrocks et al. 2008,
Young et al. 2010, Schmidt et al. 2011).
Other studies with ungulates found the half
normal key function with various expansions
terms to perform best (Trenkel et al. 1997,
Jathanna et al. 2003, Peters 2010, Thies-
sen 2010).

The kernel estimator used for the prob-
ability of detection curve does not use
maximum likelihood methods, so AICc
values are not available for comparison
with models with semi-parametric detection
functions in the program Distance. However,
the kernel-based estimated probability of
detection, animal density, and CV were simi-
lar to those obtained from the hazard-rate
model in Distance, although the CI was much
narrower for the kernel estimator. Based
on bootstrapping, all the semi-parametric
models estimated that the probability of
detection biased low (i.e., lower than the
kernel’s P̂ ¼ 0:73), thus estimated densities
were biased high. The estimated bias in the
hazard-rate model estimate (1.4%) was
higher than the estimated bias for the kernel-
based estimate (<0.001%). An advantage of
the nonparametric estimator is that it is free
of parametric assumptions on the detection
function. Additionally, using a kernel-based
model does not require that detection is a

monotonically decreasing function of dis-
tance away from the transect centerline,
unlike semi-parametric models (Cassey and
McArdle 1999). One limitation is that it
requires an adequate sample size to produce
a reasonable estimate (Chen 2000), but
sample size was not a problem in our uni-
variate analysis for the level of precision
we achieved. The Hermite polynomial and
kernel estimates are very similar with the
kernel estimate less intensive to compute
(Buckland 1992).

Survey Effectiveness
The study area is characterized by mar-

ginal snow conditions during any given
year with the most reliable conditions in Feb-
ruary (Fig. 4). The daily average snow depth
clearly demonstrates that the area does not
accumulate deep snow and daily variation
is high because of periods of warming and
rain causing snowmelt. We considered ∼20
cm of snow accumulation as moderate to
good conditions, required for the standard
GSPE survey method. Conversely, Dalton
(1990) considered 20 cm “shallow” for a
moose survey in Ontario, Canada.

Comparison of the helicopter line-
transect method with the GSPE method con-
siders time, logistics, cost, and the estimate
of precision. The GSPE method requires a
minimum of 60 units surveyed between 2
moose density strata (30 low and 30 high
strata), with preferably more units in high
density areas assuming greater variation
within that strata (Kellie and DeLong
2006). GSPE survey areas are a minimum
of 777 km2 because smaller areas have insuf-
ficient sample units to generate estimates.
These survey units are approximately 16.6
km2 and require a minimum search intensity
of 40 min/block with cub-like or tandem
style fixed-winged aircraft (Kellie and
DeLong 2006). The time required to fly the
minimum intensity and number of units
would be ∼40 h. Two aircraft for a minimum

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of 5 days would be required to complete the
survey given continuous optimal snow con-
ditions, a situation unlikely in the study area.

The helicopter line-transect survey was
considerably more efficient in terms of area
sampled and flight time than a fixed-wing
GSPE. We flew a total of 16 h in one heli-
copter including about 2.5 h of training prior
to the actual survey (training is highly
recommended to prepare the survey team
for duties and search patterns) and 13.5 h
during the actual survey, including ferry
times from the base of operation. We accom-
plished the survey in 2 days which improves
the chance of continuous, optimal snow con-
ditions. Cost based solely on flight hours
was similar; a fixed-wing survey for the
minimum sampling under the GSPE method
in this area would be approximately 6% less
than the helicopter line-transect technique, a
reasonable compromise given the reduction
in survey days (2 versus 5). Our helicopter
survey had a CV of 18%, a difficult level
of precision to obtain with the minimum

number of GSPE units required to address
potential stratification errors, sample sizes,
and high variability of observations between
units (Kellie and DeLong 2006).

Management Application
The recent expansion and establishment

of moose in the lower Kuskokwim River tri-
butaries prompted our survey efforts. Our
survey indicated that moose density is 0.47
moose/km2 or twice that of the adjacent
lower Kuskokwim River survey unit in
2008 (0.23 moose/km2 without SCF; Perry
2010). The difference can arguably be attrib-
uted to better habitat along the Kuskokwim
tributaries compared to the main channel of
the lower Kuskokwim River, and the 5-year
moose hunting moratorium in the lower Kus-
kokwim drainage that allowed moose to
establish a viable population and disperse
into unoccupied habitat. The exploitation of
underutilized habitat was expressed in popu-
lation production and is emphasized by the
30% rate of twinning during our March sur-
vey, which is high for that time of year.

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).

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151



Comparative twinning rate data are collected
in May during the peak calving period and
can be used in conjunction with other vari-
ables to determine the nutritional status of
moose in an area. Density dependence
occurs at high moose densities in interior
Alaska when May twinning rates are 4–
21% indicating nutritional stress, whereas
in years of low moose densities and recovery
of vegetation, rates are 30–47% (Boertje et al.
2007). The May twinning rate in our study
area has recently been estimated as 47–67%
(concurrent study; unpublished survey data,
YDNWR), corroborating our assumption of
a population at high nutritional status. This
moose population continues to grow and is
an important subsistence resource for local
people and a monitoring program is essential
for sound management regarding appropriate
harvest levels to maintain a healthy, sustain-
able population. We recommend that surveys
occur every 3–5 years to assess population
trends and inform management decisions.

Future surveys along the lower Kuskok-
wim tributaries should follow the same pro-
tocol used here (and potentially the same
transects; Buckland et al. 2001), with the
exception of how moose locations under
the aircraft were recorded. Perpendicular dis-
tances of moose detected by the front-left
observer under the helicopter (i.e., moose
groups approximately ± 43 m of the center
line) should be estimated and recorded in
future surveys. The precision of our density
estimates would have increased if we did
not lump and remove from analyses the 10
observations directly under the helicopter.

The kernel density estimator was fairly
precise (CV = 18%); however, additional
transects are required to increase precision
in future surveys. Attaining a CV closer to
15% would require an additional 307 km of
transects; a precision with CV = 10% would
require an additional 1564 km, given the cur-
rent group encounter rate. Given the narrow
riparian corridors, it would be difficult to

add transects without greatly increasing the
chance of double counting groups. Thus,
improved precision is limited by increasing
the encounter rate; however, if a CV of
20% is acceptable, transect length could be
reduced by ∼133 km.

Another consideration is pooling data
across years to obtain more robust, and
potentially more precise estimates of detec-
tion probability (Burnham et al. 1980, Burn-
ham et al. 2004, Fewster et al. 2005).
Distance sampling is pooling robust and a
common practice in a single study area
because each transect typically has too few
observations to calculate separate detection
functions (Gerard and Schucany 2002).
Pooling by year to increase sample size
(observations) and to account for various
survey conditions (e.g., snow conditions)
could improve the global detection function
for the area if repeated surveys are in the
same area and preferably along the same
transects (Nielson et al. 2014).

If the CV ranges from 13–19%, man-
agers should be able to detect at least a
38% change in abundance using a 90% CI
with 80% statistical power. Given our den-
sity estimate of 0.47 moose/km2 (340
moose), we should detect a change in density
if the population changed by ∼0.18 moose/
km2 (129 moose; 38%). Furthermore, if there
is a 5-year period between surveys, this
would require a finite rate of change (λ =
e{(ln Nt − ln N0) / t}, where N0 is the starting abun-
dance estimate, Nt is the abundance estimate
at time t, and t is the time period between
surveys; Skalski et al. 2005: 295) equal to
λ = 0.909 annually for a decreasing popula-
tion, or λ = 1.066 for an increasing popula-
tion. This is a realistic change for moose in
this area since the lower Kuskokwim survey
unit showed an extreme growth rate of λ =
1.647 over a 4-year period (from 70 to 515
moose; Perry 2010).

Our research provides a viable alterna-
tive method to survey moose in a subarctic

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tundra ecosystem with marginal snow condi-
tions. Presumably this technique could be
applied elsewhere in areas with larger con-
tiguous habitat and variable snow conditions
such as portions of moose range within sub-
arctic Alaska, Canada, Scandinavia, and
Russia. Areas with dense canopy cover may
require accounting for vegetation covariates
affecting sightability which would require a
larger number of group observations. Never-
theless, as climate change increases the dis-
ruption of prevailing weather patterns and
causes more atypical and uncertain scenarios
such as freeze-thaw or rain-on-snow events,
our research and recommendations provide
wildlife managers an accurate, efficient, and
cost-effective option for surveying moose
populations.

ACKNOWLEDGEMENTS
We would like to thank observers M.

Gabrielson and V. Anvil, and pilot S. Her-
mens (Hermen Helicopters) for his expert
flying. We also thank G. Walters for his aer-
ial fixed-wing support and T. Doolittle for
encouraging this effort. We are grateful to
Drs. L. Munn, R. McCormick, J. Beck, M.
Murphy, and S. Miller, as well as the Alces
editors and 2 anonymous reviewers for pro-
viding helpful comments. Funding for this
project was through the US Fish and Wildlife
Service, Yukon Delta National Wildlife
Refuge, Bethel, Alaska, USA. The use of
trade names of commercial products in this
manuscript does not constitute endorsement
or recommendation for use by the federal
government.

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http://www.ruwpa.st-and.ac.uk/distance/

	ESTIMATING MOOSE ABUNDANCE IN LINEAR SUBARCTIC HABITATS IN LOW SNOW CONDITIONS WITH DISTANCE SAMPLING AND A KERNEL ESTIMATOR
	STUDY AREA
	METHODS
	Field Survey
	Data Analysis

	RESULTS
	DISCUSSION
	Assumptions
	Detection Functions
	Survey Effectiveness
	Management Application

	ACKNOWLEDGEMENTS
	REFERENCES