U.S. Department of the Interior

U.S. Geological Survey

Open-File Report 2018–1085

Prepared in cooperation with Colorado State University and the National Park Service

Development of an Aerial Population Survey Method for Elk 

(Cervus elaphus) in Rocky Mountain National Park, Colorado
Cover. Left: Elk group observed from helicopter. Photograph by K.A. Schoenecker, USGS. Right: Observers and pilot. 

Photograph by K.A. Schoenecker, USGS.
Development of an Aerial Population 

Survey Method for Elk (Cervus elaphus) 

in Rocky Mountain National Park, Colorado

By Kathryn A. Schoenecker, Bruce C. Lubow, and Therese L. Johnson

Prepared in cooperation with Colorado State University and the 

National Park Service

Open-File Report 2018–1085

U.S. Department of the Interior

U.S. Geological Survey
U.S. Department of the Interior

RYAN K. ZINKE, Secretary

U.S. Geological Survey

James F. Reilly II, Director

U.S. Geological Survey, Reston, Virginia: 2018

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Suggested citation:

Schoenecker, K.A., Lubow, B.C., and Johnson, T.L., 2018, Development of an aerial population survey method for elk 

(Cervus elaphus) in Rocky Mountain National Park, Colorado: U.S. Geological Survey Open–File Report 2018–1085, 

45 p., https://doi.org/10.3133/ofr20181085. 

ISSN 2331-1258 (online)
iii

Acknowledgments

We thank volunteer aerial observers Sheri Huwer (Colorado Parks and Wildlife), Jason Ransom 

(National Park Service [NPS]), and Zac Wiebe (Larimer County Parks and Recreation). Thanks to 

NPS helicopter managers Craig Brower, Mark DeGregorio, and Patti Shafer; and our pilots Jim 

Hennessey (TransAero), Dave Stinson (Sky Aviation), and Lanny Coulter (Coulter Aviation). We 

thank the NPS elk ground darting and capture crew, who made the radio-collar work possible: 

Dan Baker, Scott Esser, Ryan Monello, Jenny Powers, Scott Ratchford, Lindsay Reynolds, Mary 

Kay Watry, Margaret Wild, and NPS volunteer Fred Renner. We are grateful for logistical and 

overall project support from John Mack and Judy Visty, NPS, and Colorado State University. 

This project was funded by the U.S. Geological Survey Natural Resources Preservation 

Program, Washington, D.C., with additional funding from the Rocky Mountain National Park 

Resources Management program.

Contents

Acknowledgments........................................................................................................................................iii

Executive Summary.......................................................................................................................................1

Introduction.....................................................................................................................................................1

Study Area.......................................................................................................................................................3

Background.....................................................................................................................................................4

Objectives...............................................................................................................................................4

Part 1. Developing the Survey Design ....................................................................................................5

Selection of the Survey Method.........................................................................................................6

Sightability Correction Model....................................................................................................6

Radio Mark-Recapture Method ................................................................................................6

Simultaneous Double-Observer Method .................................................................................6

Line-Transect or Distance Sampling ........................................................................................6

Hybrid Methodology....................................................................................................................6

Methods..................................................................................................................................................6

Radio-Collar Location Data ........................................................................................................6

Very High Frequency Telemetry .......................................................................................8

Global Positioning System Telemetry ..............................................................................8

Geographic Information System Analysis ......................................................................8

Defining the Survey Area ...........................................................................................................8

Transect Layout............................................................................................................................8

Results ..................................................................................................................................................10

Survey Area Boundary Results ...............................................................................................10

Transect Layout Results............................................................................................................10

Spatial and Temporal Variation of Elk Use of the Park ........................................................12

Altitude.........................................................................................................................................15

Tree Cover...................................................................................................................................15

Bull Elk Locations on Aerial Survey Days..............................................................................19

Elk Park Boundary Crossings...................................................................................................19
iv

Part 2. Implementing and Testing the Survey Design.........................................................................21

Using a Hybrid Double-Observer Model with Sighting Covariates to Estimate the Elk

Population in Rocky Mountain National Park, 2008–2011 ..............................................22

Methods.......................................................................................................................................22

Population Estimation Analysis ...............................................................................................22

Data.....................................................................................................................................22

Model Structure................................................................................................................22

Model Fitting and Selection ............................................................................................25

Point Estimate Method.....................................................................................................26

Estimating Variance in Abundance Estimates with Bootstrapping..........................26

Results ..................................................................................................................................................28

Model Fitting and Support........................................................................................................28

Population Estimates and Precision.......................................................................................29

Discussion............................................................................................................................................29

References Cited..........................................................................................................................................33

Appendix 1. Description of Aerial Survey Methods Considered for Elk Surveys in Rocky 

Mountain National Park, Colorado..............................................................................................36

Radio (Known-Fates) Mark-Recapture Method ............................................................................36

Simultaneous Double-Observer Method ........................................................................................36

Distance Sampling Method...............................................................................................................36

Sightability Bias Correction Method ...............................................................................................37

Hybrid Methods...................................................................................................................................37

Appendix 2. Discussion of Considerations for Aerial Work in Rocky Mountain National 

Park, Colorado.................................................................................................................................39

Appendix 3. Instructional Protocols and Datasheets for Simultaneous Double-Observer 

Aerial Surveys in Rocky Mountain National Park, Colorado ..................................................41

Field Protocols for Simultaneous Double-Observer Aerial Elk Surveys....................................41
v

Figures

1. Elk population estimates for Rocky Mountain National Park, Colorado, 2000–2005 .........2

2. The general elk winter range in Rocky Mountain National Park and the Estes Valley,

Colorado .........................................................................................................................................3

3. Modified bull elk radio collars showing expandable section developed by

T. Johnson for elk population study in Rocky Mountain National Park, Colorado,

2008–2011 .......................................................................................................................................9

4. Final survey area boundary, showing key elk habitat elevation contours of

2,800 meters and 3,300 meters in Rocky Mountain National Park, Colorado ...................10

5. Final north and south aerial survey routes for Rocky Mountain National Park elk

surveys .........................................................................................................................................11

6. Percent of winter very high frequency collar locations east of the Continental

Divide that were inside Rocky Mountain National Park, Colorado, by month

and year........................................................................................................................................12

7. Percent of winter global positioning system bull collar locations inside Rocky

Mountain National Park (RMNP), Colorado, by month of the study, 2008–2011...............13

8. Winter elk telemetry locations from multiple sources in Rocky Mountain National

Park, Colorado.............................................................................................................................14

9. Winter altitude distribution of elk locations in elk population study in Rocky

Mountain National Park, Colorado, 2008–2011 ......................................................................16

10. Use of dense cover by bull elk wearing global positioning system collars within

Rocky Mountain National Park, Colorado, by month of the study, 2008–2011..................18

11. Use of dense tree cover by global positioning system-collared bull elk during the

winter period by hour of the day in Rocky Mountain National Park, Colorado,

2008–2011 .....................................................................................................................................18

12. Locations of radio-collared bull elk during aerial helicopter surveys in Rocky

Mountain National Park, Colorado, 2008-2011.......................................................................20

13. Distribution of elk groups by group size in Rocky Mountain National Park, Colorado,

elk population estimation study, 2008–2011, demonstrating the tendency toward

larger groups in winter ..............................................................................................................23

14. Distribution of elk groups by major sighting characteristics, percent vegetation

cover and percent snow cover, in elk population study in Rocky Mountain

National Park, Colorado, 2008–2011 ........................................................................................24

15. Distribution of sighting probabilities for combined front and rear observers for all

elk groups marked with radio collars, illustrating how groups varied widely in

visibility.........................................................................................................................................29

16. Sighting probability for combined front and rear observers, using rear observer with

highest sighting probability, for elk population estimation study in Rocky Mountain

National Park, 2008–2011...........................................................................................................30

17. Sighting probability for combined front and rear observers, using rear observer with

lowest sighting probability, for elk population estimation study in Rocky Mountain

National Park, 2008–2011...........................................................................................................31
vi

Tables

1. Dataset description, source, and how the information was used in our analysis to

develop an improved aerial survey method for estimating the elk population in

Rocky Mountain National Park, Colorado, 2008–2011 ............................................................7

2. Summary of global positioning system telemetry data collection showing

deployment and collection date of each bull collar in study of elk population in

Rocky Mountain National Park, Colorado, 2008–2011 ..........................................................12

3. Altitude distribution of winter elk locations reported in different datasets and

studies ..........................................................................................................................................15

4. Distribution of winter bull elk global positioning system locations by cover class

and vegetation type in study of elk population in Rocky Mountain National Park,

Colorado, 2008–2011...................................................................................................................17

5. Covariates and corresponding model coefficients for each unique elk group used

in the population estimation model for elk in Rocky Mountain National Park,

Colorado, 2008–2011...................................................................................................................25

6. Sightability model alternatives with fit and selection statistics for elk population

estimation study in Rocky Mountain National Park, Colorado, 2008–2011 .......................27

7. Sightability model parameters and model weighted average estimates for elk

population estimation study in Rocky Mountain National Park, Colorado, 2008–2011 ...28

8. Elk population estimates and precision, comparing analyses with and without

radio-collar data, for elk population estimation study in Rocky Mountain National

Park, 2008–2011...........................................................................................................................32
vii

Conversion Factors

U.S. customary units to International System of Units

Multiply By To obtain

Length

foot (ft) 0.3048 meter (m)

Flow rate

mile per hour (mi/h) 1.609 kilometer per hour (km/h)

International System of Units to U.S. customary units

Multiply By To obtain

Length

centimeter (cm) 0.3937 inch (in.)

meter (m) 3.281 foot (ft) 

Area

hectare (ha) 2.471 acre

Flow rate

kilometer per hour (km/h) 0.6214 mile per hour (mi/h)

Datum

Altitude, as used in this report, refers to distance above the vertical datum.

Abbreviations

> greater than

< less than

≤ less than or equal to 

AIC Akaike information criterion

CV coefficient of variation

GPS global positioning system

NPS National Park Service

RMNP Rocky Mountain National Park

USGS U.S. Geological Survey

VHF very high frequency

Development of an Aerial Population Survey Method for 

Elk (Cervus elaphus) in Rocky Mountain National Park, 

Colorado

By Kathryn A. Schoenecker,1 Bruce C. Lubow,2 and Therese L. Johnson3

1

U.S. Geological Survey

2

Colorado State University

3

National Park Service

Executive Summary

Since the early 1990s, substantial effort and funding have 

been expended to conduct research to guide development of 

a 20-year Elk and Vegetation Management Plan for Rocky 

Mountain National Park (RMNP) in Colorado. One goal of the 

plan is to maintain the elk (Cervus elaphus) population size at 

the lower end of the natural range of variation. To implement 

management actions called for in the plan, accurate and reliable 

population estimates are needed, as well as a better understanding of the spatial and temporal distribution of elk. The previous 

aerial survey protocol and population estimation model used by 

the park had not been updated since the model’s initial calibration more than 15 years ago and the model was developed with 

an insufficient number (n=44) of observations. Thus we initiated research to reevaluate, update, and improve elk population 

estimation protocols for RMNP. 

We considered several alternative survey and analysis 

methods, and concluded that a hybrid population-estimation 

model using a simultaneous double-observer technique with 

sighting covariates was the most appropriate and effective 

aerial survey methodology for this population and the environmental conditions in RMNP. Instructional protocols for 

conducting these surveys in the future, along with datasheets, 

are provided in this report’s appendixes.

To develop an improved method for aerial elk surveys, 

we used elk radio-collar location data from our study and other 

studies, and applied geographic information system analyses to 

define the survey area and develop effective, repeatable survey 

transect lines. We used telemetry data from radio-collared elk 

to inform our understanding of the temporal and spatial scale of 

elk movements across the park boundary, elk use of tree cover 

during potential survey hours, and elk use of different elevations 

within their range. Determining where elk were during surveys 

helped to fine-tune a survey design that improved spatial coverage and decreased costs where possible, while standardizing the 

method to make it repeatable from year to year. We conducted 

aerial helicopter surveys to test our methodology in an adaptive, 

iterative process during three winters: 2007–2008, 2008–2009, 

and 2009–2010. We gained new information on each survey and 

used results to refine subsequent surveys. 

Our results confirm that elk movements were highly 

dynamic with respect to park boundary crossings; an average 

of six round trips from the park to Estes Park, Colorado, and 

back per month were taken by global positioning systemcollared bull elk. We observed a strong diurnal temporal pattern of bull elk use of trees; elk were found in dense tree cover 

from 15:00−22:00 but not as often during morning and early 

afternoon hours when surveys were conducted. We used information on elk use of different altitudes to refine and establish a 

more efficient survey area. 

During the time of our study, a concurrent study in the park 

deployed 120 very high frequency radio collars on elk cows. 

We used those collar locations during our flights to increase 

sample size and to evaluate the level of precision we would 

gain by using “known fates analysis” (in which elk were known 

to be in the survey area, out of the survey area, or deceased 

based on radio-collar locations collected simultaneously during 

aerial surveys). Using radio-collar locations reduced bias by 

1.1–8.8 percent and increased precision (that is, reduced the 

width of confidence intervals). This report provides final population estimates analyzed with and without radio-collar data to 

demonstrate what is gained by using marked individuals.

Introduction

Public surveys have shown that wildlife viewing is 

extremely important to Rocky Mountain National Park 

(RMNP) visitors. Many visitors visit the park in autumn 

specifically to view elk (Cervus elaphus), as well as the fall 

colors provided by willow (Salix spp.) and aspen (Populus 

tremuloides). An important part of this experience is the 

opportunity to observe natural elk behavior and healthy 
2 Development of an Aerial Population Survey Method for Elk in Rocky Mountain National Park, Colorado

vegetation conditions. Visitors also visit the park to observe 

beaver and a large variety of bird and butterfly species that 

depend on aspen and willow. Management of elk and vegetation is a high priority in the park due to habitat damage from 

previous elk herbivory (Singer and Zeigenfuss, 2002) and 

potential other causes (Kacynski, 2013). 

Beginning in the 1990s, substantial effort and funding 

were expended to conduct research and develop a 20-year Elk 

and Vegetation Management Plan for the park (National Park 

Service, 2008). The goals of the plan are to maintain the elk 

population size near the lower end of the natural range of variation, and to restore vegetation, particularly in aspen and willow 

communities. A number of activities have been, and continue to 

be, implemented to address different aspects of the plan. The elk 

population size was reduced by culling, and temporary fences 

were built to begin restoration of vegetation by protecting aspen 

and willow from elk herbivory. The elk winter range extends 

over multiple jurisdictions, so park staff work in cooperation 

with personnel from Colorado Parks and Wildlife (formerly 

Colorado Division of Wildlife), which has management authority for elk beyond the park boundary.

In order to take the management actions called for in the 

plan, accurate and reliable population estimates are needed 

to guide elk population reductions. Inaccurate estimates of 

population size or an incomplete understanding of the spatialtemporal distribution patterns could result in unknowingly 

missing the target population levels, with potentially long-term 

0

500

1,000

1,500

2,000

2,500

2000 2001 2002 2003 2004 2005 Mean

Survey year

Elk population (number)

Figure 1. Elk population estimates for Rocky Mountain National Park (RMNP), Colorado, 2000–2005 (National 

Park Service, 2007), illustrating large annual differences. Error bars show 95 percent confidence intervals. 

herd or ecosystem impacts. Estimates of the number of elk 

wintering inside the park can shift by several hundred animals overnight; recent population estimates from sequential 

years have differed by as much as 100 percent and have been 

characterized by nonoverlapping confidence intervals despite 

no evidence of significant change in elk mortality or productivity (fig. 1). These differences are thought to be attributed 

to differences in elk distribution in winter in response to 

different foraging conditions and snow cover. Changes in elk 

distribution between the park and Estes Valley outside the 

park are a plausible explanation for the marked variation in 

estimates of population size, supported by both earlier movement (Bear, 1989; Larkins, 1997) and modeling (Lubow and 

others, 2002) studies. Thus, an improved understanding of the 

fluctuating elk distribution and updated elk population survey 

method were vital to guiding management under the new plan 

(National Park Service, 2008).

All wildlife survey techniques are based on a set of 

assumptions about how the data are collected. If the biology or 

behavior of the animals, the conditions in the field, the skills of 

the observers, or the technology of field methods lead to violations of assumptions, required accuracy will not be achieved, 

and results may appear to be precise when they are actually 

substantially biased, and management will have no indication that the survey is misleading. In conducting our study, we 

considered that survey methods must be implemented so that 

fundamental assumptions can be met in practice.
Study Area 3

Study Area

Our study area was the low-elevation elk winter range of 

RMNP encompassing approximately 15,000 hectares (ha) in 

the upper montane zone on the eastern slope of the Continental 

Divide (fig. 2). This winter range spans both sides of the 

eastern boundary of the park. Elk are free to move between 

the national park and a mix of public and private lands in the 

Estes Valley and areas further east. Glacial moraines running 

Figure 2. The general elk winter range (black dashed line) in Rocky Mountain National Park and the Estes Valley, 

Colorado. The cities of Estes Park and Loveland, Storm Mountain, and the Continental Divide are indicated for reference. 

Inset shows location of Rocky Mountain National Park within Colorado.

0 50 100 KILOMETERS

Colorado Shaded Relief derived from U.S. Geological 0 50 100 MILES

Survey digital elevation model data.

105°50'

40°30'

40°20'

40°10'

105°40' 105°30' 105°20' 105°10'

EXPLANATION

Primary elk winter range

Rocky Mountain National

 Park boundary

Primary elk winter range

COLORADO

Map

area

east-west divide the park area into four major valleys, and 

the town of Estes Park lies in the middle of a broad, park-like 

valley (Gysel, 1960; Stevens, 1980; Hobbs and others, 1982; 

Zeigenfuss and others, 1999). Elevations in the study area 

range from 2,300 meters (m) at the lower end of the Estes 

Valley to 2,800 m on moraine ridge tops. Elk habitat on the 

alpine tundra ranges from approximately 3,300 m to 3,800 m. 

Mean annual precipitation is 41 centimeters, mostly occurring 

as wet spring snow.
4 Development of an Aerial Population Survey Method for Elk in Rocky Mountain National Park, Colorado

Background

Prior to our study, a single aerial survey to count elk was 

conducted annually, usually between January and March when 

snow and flying conditions permitted, with a single observer 

in the helicopter. The aerial observer counted the number of 

animals in each elk group that was found and recorded several 

covariates describing the sighting conditions for each group. 

These counts were conducted within predefined count units 

bounded by easily recognizable landmarks. However, the 

helicopter flight path (coverage of the survey area) was left 

to the discretion of the aerial observer and pilot, sometimes 

resulting in areas being missed or surveyed inadequately, and 

inconsistencies from year to year. Surveys were limited to 

within park boundaries at elevations where elk were believed 

to overwinter. A minimum count of elk in the adjacent Estes 

Valley was made by volunteer ground observers from the 

existing road network on the same day as the aerial survey in 

the park. 

These previous aerial surveys were analyzed with a 

sightability bias correction model (Samuel and Pollock, 1981; 

Samuel and others, 1987; Steinhorst and Samuel, 1989) developed under an earlier project conducted by the National Park 

Service (NPS) and U.S. Geological Survey (USGS) (Lubow 

and others, 2002). The model used the number of elk within 

each elk group, their activity, and snow cover to estimate the 

probability that each group would be sighted. Using these 

estimates, adjustments were made for the proportion of similar 

groups that would be expected, by chance, to be missed during 

a typical survey. The adjusted estimate was then used for management purposes. The calibration of this sightability model 

was completed greater than (>) 15 years ago and utilized only 

44 elk groups for model development, which is far fewer than 

the minimum of 100 observations recommended to develop 

such a model based on statistical simulation studies (Wong, 

1996). Due to these limitations, we initiated research to update 

and improve elk population estimation protocols. We determined that a complete winter survey of this entire population 

over its full spatial range in the park, Estes Valley, and further 

east was logistically almost impossible, far too costly, and 

probably unnecessary. What was needed by park management 

was the ability to quantify elk use of park resources during 

the critical winter months (November, December, January, 

February, and March). To do this, we also needed to understand the temporal variation in elk numbers on the eastern 

slope within the park.

Original drawings by Dale Crawford, U.S. Geological Survey

Objectives

Our objectives were to:

1. Determine temporal variation in the number of elk present in the park over winter and elk movement patterns 

that could affect detection probability and population 

estimates. 

2. Update the design of, and revise field protocols for conducting, aerial surveys. 

3. Develop statistical models for estimating elk detection 

probabilities fitted to the most current and complete data 

available and provide procedures for continuously updating this model with data from ongoing annual surveys.

4. Develop population estimates for elk within RMNP with 

statistical confidence intervals from multiple aerial surveys conducted under differing environmental and aerial 

sighting conditions. 

We present the results of this study in two parts: 1. Developing the Survey Design, and 2. Implementing and Testing the 

Survey Design. Part 1 presents a discussion of aerial survey 

methods we considered and how we selected the survey 

method to apply in RMNP. We present analyses of radio-collar 

telemetry data from this and other studies that provided information about spatial and temporal patterns of elk use in the 

park, which we used to determine the survey area boundaries 

and survey design. Part 2 describes how we tested the aerial 

survey method, statistical methods used to analyze aerial survey data, and the resulting population estimates with measures 

of precision. The alpine tundra could not be surveyed annually 

due to high wind, thus results are presented independently for 

this area of the park.
Part 1. Developing the Survey Design 5

Part 1. Developing the Survey Design
6 Development of an Aerial Population Survey Method for Elk in Rocky Mountain National Park, Colorado

Selection of the Survey Method

We evaluated the potential utility of the following survey 

methodologies to estimate elk abundance in RMNP: (1) sightability correction model, (2) radio mark-recapture method, 

(3) simultaneous double-observer method, (4) line-transect or 

distance sampling, and (5) a hybrid methodology that applies 

a combination of several techniques. Each technique offers 

advantages and disadvantages, as well as tradeoffs between 

cost and precision, and each requires different assumptions to 

be met during application. A brief description of these survey 

methods is presented in appendix 1. We reviewed all potential aerial survey methods and their limitations in light of the 

environmental conditions in RMNP. 

Sightability Correction Model

Lubow and others (2002) demonstrated that obtaining 

an adequate sample size of detected elk groups to properly 

calibrate a sightability model was very difficult—their study 

recorded data on only 44 groups over 5 years. This obstacle 

is primarily caused by elk behavior; most of the elk on winter 

range are clustered into a small number of very large groups. 

Also, this method does not account for differences in the sighting abilities of individual observers or changes in sighting rates 

due to other factors or over time, which we suspected were 

likely and would not even be known if this method were chosen. 

Radio Mark-Recapture Method

The mark-resight (also known as mark-recapture) 

method using radio-marked animals is often considered the 

“gold standard” for population surveys (Seber, 1982; Bowden 

and Kufeld, 1995; White, 1996). The major advantage of 

this approach is that sighting probabilities do not need to be 

homogeneous, because the marked groups have 100 percent 

sighting probability due to the radios. The greatest obstacle 

to applying this method is the high cost and intrusiveness of 

placing and maintaining radio collars on a large number of 

elk, especially given the requirement that they be randomly 

distributed across all elk in the study area. 

Simultaneous Double-Observer Method

The simultaneous double-observer method is another form 

of the broader methodology of mark-resight survey (Seber, 

1982; Bowden and Kufeld, 1995; White 1996). The double 

sample is obtained by having two observers record sightings in 

such a way that sightings of the same individual elk or groups 

can be determined concurrently or post hoc. Advantages of 

this method are that animals do not need to be marked and 

that variation in sighting probability that occur with different 

survey conditions can be accounted for. However, this method 

does not account for variation in sighting probability among elk 

groups, which we believed to be prevalent in this population.

Line-Transect or Distance Sampling

Distance sampling would not be effective because the 

number of independent elk groups would be far too small 

for an adequate sample size. Most elk surveys in the park 

record 10–12 groups per survey. To compensate, it would be 

necessary to fly multiple passes over the park during each 

survey—both a costly and impractical option due to challenging flying conditions in the park. Also, accurate measurement 

of distances from an aerial platform in the rugged topography 

of the park would be very difficult to implement with available 

technology. 

Hybrid Methodology

We concluded that combining simultaneous doubleobserver methodology with a sightability correction model 

would be most effective and appropriate for this population. 

Given variable availability of specific personnel to conduct 

surveys in the park and the likelihood of personnel changes 

over time, a method such as simultaneous double-observer 

that accounts for differences in observers is important. At the 

same time, variability in sighting conditions related to factors 

such as snow cover, tree cover, and elk group size make a 

sightability correction model to address heterogeneity in elk 

detection important. This method allows for pooling observations across surveys to cumulatively increase the sample size 

and potentially detect changes in detection effects over time. 

Finally, collecting data on animal sighting covariates during 

a simultaneous double-observer survey would not increase 

survey costs. 

Methods

Radio-Collar Location Data

We used elk radio-collar location data collected during our study and other studies (table 1) to define the spatial 

survey area. Radio-collar locations came from both very high 

frequency (VHF) and global positioning system (GPS) collars 

deployed at different times during different captures, sometimes within and outside of the park and other times solely 

within the park boundaries, depending on the study (table 1). 

For this reason, the locations are not a representative sample 

of overall elk movements but helped us understand and answer 

questions about how often and for what duration elk moved 

in and out of the park, and the spatial extent of their movements. We used radio-collar data to evaluate elk use of tree 

cover during potential survey hours, and elk use of different 

elevations within their range to inform our selection of the 

survey area boundary and survey timing. The radio-collar data 

we utilized for analysis varied by capture technique between 

studies (table 1). Because of this variability in radio-collar 

deployments, we caution that these results should not be used 

to extrapolate in other ways. 
Part 1. Developing the Survey Design 7

Table 1. Dataset description, source, and how the information was used in our analysis to develop an improved aerial survey method 

for estimating the elk population in Rocky Mountain National Park (RMNP), Colorado, 2008–2011.

[GPS, global positioning system; VHF, very high frequency]

Dataset Description Source How used in our analysis

Larkins, 1997 Data from locations of 62 cow elk and 

11 bulls radio collared via helicopter 

netgun in RMNP and dart gun in town. 

Elk were located several times per 

month from the ground and fixed-wing 

aircraft between February 1995 and 

November 1996.

Larkins, K. F., 1997, Patterns of elk 

movement and distribution in and 

adjacent to the eastern boundary 

of Rocky Mountain National Park: 

Greeley, Colo., University of Northern 

Colorado, Master’s Thesis, 89 p.

Data were plotted to 

determine survey area 

boundary and elevation 

boundary.

Lubow and others, 

2001

Ground and fixed wing locations of 

elk from 1994 to 2001, using collars 

deployed on 62 cow elk and 11 bulls 

radio collared via helicopter netgun in 

RMNP and dart gun in town. 

Lubow, B. C., Singer, F.J., Johnson, T.L., 

and Bowden, D.C, 2002, Dynamics of 

interacting elk populations within and 

adjacent to Rocky Mountain National 

Park: Journal of Wildlife Management, 

v. 66, p. 757–775.

Data used for mark-resight 

population estimation. 

Also plotted to determine 

survey area boundary and 

elevation boundary. 

Baker and others, 

2007

VHF radio collars were deployed on 

120 cow elk within RMNP boundaries 

in winters 2006–2007, 2007–2008, and 

2008–2009. Cows were captured using 

ground darting along park roads.

Baker, D.L.., Wild, M.A., and Powers, 

J.G., 2007, Evaluation of methods 

for managing elk population health 

and abundance in Rocky Mountain 

National Park, Colorado: Estes Park, 

Colo., National Park Service Research 

Study Plan, 16 p.

Collars were located during 

helicopter aerial surveys 

for “known fates” analysis 

to know whether elk were 

within park, and sighting 

conditions.

GPS bulls; this study We deployed 12 GPS radio collars 

on bull elk in winters 2008–2009, 

2009–2010, or 2010–2011. Fixes were 

taken every 1/2 hour. All bulls were 

collared within RMNP boundaries 

using ground darting from park roads. 

Schoenecker, K.A., Lubow, B.C., and 

Johnson, T.L., 2018, Development of 

an aerial population survey method 

for elk (Cervus elaphus) in Rocky 

Mountain National Park, Colorado: 

U.S. Geological Survey Open-File 

Report 2018–1085, 44 p., https://doi.

org/10.3133/ofr20181085.

Locations during surveys, 

movements in and out of 

the park, distribution of 

locations by vegetation 

cover type and elevation. 

Fixed-wing locations; 

this study

We located the 120 Baker and others 

(2007) cow collars and our GPS bull 

collars with a fixed-wing (Cessna 182 

or Supercub) aircraft 1–2 times/month 

from November through March in 

winters 2007–2008, 2008–2009, and 

2009–2010.

Schoenecker, K.A., Lubow, B.C., and 

Johnson, T.L., 2018, Development of 

an aerial population survey method 

for elk (Cervus elaphus) in Rocky 

Mountain National Park, Colorado: 

U.S. Geological Survey Open-File 

Report 2018–1085, 44 p., https://doi.

org/10.3133/ofr20181085.

Movements in and out of the 

park, distribution of locations by vegetation cover 

type and elevation; used 

to refine survey area.

Helicopter surveys; 

this study

Helicopter survey data are from our 

five aerial surveys conducted within 

the park, and include locations of 

uncollared and collared bull and cow 

elk locations.

Schoenecker, K.A., Lubow, B.C., and 

Johnson, T.L., 2018, Development of 

an aerial population survey method 

for elk (Cervus elaphus) in Rocky 

Mountain National Park, Colorado: 

U.S. Geological Survey Open-File 

Report 2018–1085, 44 p., https://doi.

org/10.3133/ofr20181085.

Data used for mark-resight 

population estimation. 

Also plotted to determine 

survey area boundary and 

elevation boundary.
8 Development of an Aerial Population Survey Method for Elk in Rocky Mountain National Park, Colorado

Very High Frequency Telemetry

As shown in table 1, we used VHF telemetry data from 

Larkins (1997) and Lubow and others (2002) to evaluate 

spatial and temporal patterns of elk use within the park and to 

determine our survey area. We collected data from 120 VHF 

radio collars deployed on cow elk in a previous study (Baker 

and others, 2007). We located the Baker and others (2007) cow 

collars and our GPS bull collars (see the “Global Positioning 

System Telemetry” section of this report) with a fixed-wing 

(Cessna 182 or Supercub) aircraft 1–2 times per month from 

November through March in winters 2007–2008, 2008–2009, 

and 2009–2010 (table 1). 

Global Positioning System Telemetry

To better understand spatial movements of elk at small 

temporal scales, we placed 12 store-on-board GPS radio collars (Sirtrack Limited, New Zealand) on bull elk in winters 

2007–2008, 2008–2009, and 2009–2010. Bull elk are often 

missed in aerial surveys (McCorquodale, 2001) and were not 

represented among the 120 Baker and others (2007) collars, 

which were all placed on cows. We fitted GPS collars on bull 

elk captured inside the park boundaries, and redeployed collars 

if recovered before the end of the study. Working with the capture team of the NPS Wildlife Health Branch, we captured bull 

elk by dart gun at locations along park roadsides where they 

were accessible and approachable. We worked with Sirtrack 

to develop an expandable collar that bulls could break out of 

if needed, but the elastic on the expandable section disintegrated within 6 weeks after deployment. T. Johnson (USGS) 

developed a canvas cover modification to protect the Sirtrack 

expansion pieces (fig. 3), which was successful. Collars were 

programmed to release after 1 year, and the final drop-off date 

was March 2011. These GPS collars were also equipped with a 

VHF signal, so they were located during all helicopter surveys 

as well as independent fixed-wing flights. Collar fix intervals 

were every 1/2 hour during winter. One collar did not record 

any data, one collar released while the bull was in the alpine 

tundra when road access was closed and we could not recover 

the collar, and one collar did not release as programmed and 

the collar was not recovered.

The GPS data provided accurate locations at frequent 

time intervals during winter, making it the most useful for 

identifying frequency and duration of bull movements in and 

out of the park. Conclusions are limited, however, by the 

small number of individual bulls monitored, and by the bias in 

capture distribution (all bulls were ground darted near roads 

within park boundaries).

Geographic Information System Analysis

The Geospatial Centroid at Colorado State University conducted analyses of GPS and VHF radio-collar locations, which 

were downloaded and plotted in a geographic information 

system using ArcMap Version 10. Time and date stamps from 

GPS data were used to filter for winter locations (November 

16–March 15). We analyzed locations using the geographic 

information system to determine the percent of elk that were in 

or outside of the park and east or west of the Continental Divide 

during winter. We used the park’s vegetation raster-based coverage and reclassified it into “cover types” to estimate when elk 

were in the open versus under tree cover where they could be 

missed by aerial observers in winter. Attributes generated by the 

geographic information system were IN_OUT (inside or outside 

of the park boundary), elevation (derived from a digital elevation model), West_East (east or west of the Continental Divide), 

and cover type (reclassified from the RMNP vegetation raster 

into five categories: dense tree, mixed–low shrub, mixed–open 

tree, open, or no data).

Defining the Survey Area

To define the aerial survey area, we started by including 

all the area inside the park boundary below 3,000 m and east 

of the Continental Divide. Although it is known that some 

elk overwinter in the tundra above 3,000 m, they were not the 

focus of this study. We used evidence of past elk locations 

from multiple datasets (table 1), slope, and vegetation to determine which portions of the park within the 2,750- to 3,000-m 

altitude range to include in the survey area.

At the beginning of the study, we surveyed areas that 

were not within these criteria to confirm we were not missing 

elk groups (by searching for tracks in snow) or important 

areas of habitat. In these initial two surveys, we included 

nearly the entire region defined by the park boundary and the 

3,000 m contour east of the Continental Divide. As we continued with annual surveys, we used additional data gained 

from helicopter surveys to refine or confirm criteria for slope 

and vegetation. 

Transect Layout

We developed the survey flight path in an adaptive process. After each survey, we modified transect lines and survey 

routes to obtain the best coverage for the terrain, taking into 

consideration sighting conditions based on vegetation cover 

and a reasonable and safe flight path for the helicopter. Our 

goal was to define a repeatable flight path that pilots could 

program into their GPS, placing full navigation responsibilities 

on the pilot and leaving observers free to look for elk. We consulted with a pilot from TransAero Helicopters (Fort Collins, 

Colo.) to develop final transect lines. We arranged transects 

so distinct areas of the park would be surveyed within a short 

time, and to cover one area before moving to another so 

observers would not double count elk that moved during the 

survey. We drew transect lines in Google Earth so they could 

be viewed against 3-dimensional satellite photographs of the 

terrain and vegetation cover of the survey area. 

We conducted aerial helicopter surveys to test our 

methodology in an adaptive, iterative process in winters 

2007–2008, 2008–2009, and 2009–2010. We gained new 

information on each survey and used results to inform subsequent surveys.
Part 1. Developing the Survey Design 9

Figure 3. Modified bull elk radio collars showing expandable section developed by T. Johnson for elk population 

study in Rocky Mountain National Park, Colorado, 2008–2011. Photograph by K.A. Schoenecker, USGS.
10 Development of an Aerial Population Survey Method for Elk in Rocky Mountain National Park, Colorado

Results

Survey Area Boundary Results

We found several areas of the park had little evidence of 

winter elk use based on radio-collar location data from multiple 

sources and lack of tracks in snow. The largest of these was 

the southern portion, south of Bierstadt Moraine and Emerald Mountain. There were also several areas of steep terrain 

(> 45° slope) that were not habitat for elk according to Skovlin 

and others (2002), and confirmed by an absence of recorded 

locations in these areas. Steep terrain included portions of 

Lumpy Ridge, Castle Mountain, the ridge north of Horseshoe 

Park (stretching between Bighorn and McGregor Mountains), 

the walls of Spruce Canyon (Cub Lake area), and some smaller 

sections of the study area (fig. 4). These were removed from 

the flight survey route. We found little or no evidence from 

radio-collar locations of elk use in elevations between 2,750 m 

and 3,000 m; most telemetry locations in this altitude were 

from Hidden Valley where former ski runs provided unforested 

Figure 4. Final survey area boundary, showing key elk habitat elevation contours of 2,800 meters 

and 3,300 meters in Rocky Mountain National Park, Colorado.

Colorado Shaded Relief derived from U.S. Geological Survey

Digital elevation model data. 

0 5 10 KILOMETERS

0 5 10 MILES

40°10'

40°20'

40°30'

105°50' 105°40' 105°30'

EXPLANATION 

Final survey area boundary

Helicopter survey routes

slopes, or from Deer Mountain where forest cover is sparse on 

the relatively flat, wind-blown top of the mountain. The remainder of this altitude range is heavily forested and moderately 

steep. Except for Hidden Valley and Deer Mountain, we found 

little support for including altitudes >2,800 m. We excluded the 

elevation range between 2,750 and 2,800 m south of Hollowell 

Park, as well as a few other small portions of this range. Otherwise, all areas less than (<) 2,800 m inside the park and east of 

the Continental Divide were included in the final survey area 

(fig. 4), except for south of Bierstadt Moraine where absence of 

elk and elk tracks in snow helped confirm previous anecdotal 

and telemetry data indicating lack of elk in this area.

Transect Layout Results

We found that evenly spaced transect lines were too wide 

for dense tree cover, and too narrow for open meadow valleys. 

Our final aerial survey transect lines were drawn narrower 

over heavy cover and wider over open meadow valleys with 

high visibility (fig. 5). 
Figure 5. Final north and south aerial survey routes for Rocky Mountain National Park elk surveys. Dashed white line is the park boundary, and the 2,800-meter elevation contour. (ft, foot) den18-0018_fig 05 0 

EXPLANATION 0 

Aerial survey routes North route South route

105°39'

40°24'40°21'

105°39' 105°39' 10
12 Development of an Aerial Population Survey Method for Elk in Rocky Mountain National Park, Colorado

Figure 6. Percent of winter very high frequency collar locations east of the Continental Divide that were inside 

Rocky Mountain National Park (RMNP), Colorado, by month and year. White bars are based on less than 30 elk 

locations for that month. Data are from very high frequency locations of cow elk from Larkins (1997), Lubow and 

others (2002), and this study (2008–2011).

0

50

100

11 12 1 2 3 11 12 1 2 3 2 3 11 12 1 2 3 12 1 2 11 12 2 11 1 2 3 2

1992 1993 1994 1995 1996 1997 2008 2009 2010

Percent of locations inside RMNP

Observation time (year and month)

Table 2. Summary of global positioning system telemetry data collection showing deployment and collection 

date of each bull collar in study of elk population in Rocky Mountain National Park, Colorado, 2008–2011.

Bull elk

identification

First 

date

Last

date

Number days of

recorded data

Number of locations 

recorded

819 10/3/2009 9/16/2010 115 4,684

819b 11/13/2010 5/15/2011 120 5,521

831 10/9/2009 6/30/2010 117 5,124

831b 11/6/2010 3/31/2011 52 1,887

856 10/9/2009 8/23/2010 120 4,859

881 10/7/2009 4/27/2011 223 6,192

894 11/8/2008 4/29/2009 120 5,063

894b 11/5/2010 4/23/2011 120 4,677

906 11/8/2008 2/15/2009 92 3,867

906x 12/19/2009 9/29/2010 87 3,599

918 1/6/2010 4/22/2011 189 6,952

Total 1,355 52,425

Spatial and Temporal Variation of Elk Use of the 

Park

We obtained 52,425 winter elk locations from GPS 

collars over a total of 1,355 elk-days (table 2). We discarded 

eight GPS locations we classified as anomalies where a single 

location was far from the previous and subsequent location. 

All elk that were radio collared for the different studies were 

captured and collared either on the low elevation winter range 

in the park or just outside the park boundary in the town of 

Estes Park. Constraints on capture methods prevented us from 

obtaining a true random sample of collared individuals, so we 

cannot draw conclusions about the percent of time either bulls 

or cows spent inside the park, but it is clear that both bulls and 

cows spend time both inside and outside the park. 

Although all bulls were captured and radio collared inside 

the park, only 59.9 percent of winter bull locations were inside 

the park boundaries (fig. 6). Of the winter GPS bull locations, 
Part 1. Developing the Survey Design 13

Figure 7. Percent of winter global positioning system bull collar locations inside Rocky Mountain National Park (RMNP), 

Colorado, by month of the study, 2008–2011. The three distinct winter periods are distinguished by unique shading. 

0

50

Percent of location inside RMNP

Month and year

100

Nov 08

Dec 08

Jan 09

Feb 09

Mar 09

Nov 09Dec 09

Jan 10

Feb 10

Mar 10

Nov 10

Dec 10

Jan 11

Feb 11

Mar 11

100 percent were east of the Continental Divide. Radio collars 

put on cow elk in both the park and in the town of Estes Park 

as discussed in Larkins (1997) and Lubow and others (2002) 

revealed 61.1 percent of winter cow elk locations were inside 

the park, with 99.7 percent east of the Continental Divide 

(fig. 6). The 120 cows that were radio collared inside the park 

boundary for the Baker and others (2007) study were relocated 

inside the park 74.2 percent of the time during winter. Our 

sample size of GPS bull collars was small and collars were 

deployed for different time periods on each elk, so quantitative conclusions are limited. Similar to the 120 VHF-collared 

cows, bull elk were radio collared only within park boundaries, so these results cannot be used to quantify the percent 

of time bulls spend in the park. However, some qualitative 

patterns were observed and can be informative. Winter use 

of the park by GPS-collared bull elk was highly variable 

among years and months, ranging from a low of 0.4 percent of 

locations during February 2009 to as high as 70.1 percent in 

January 2010 (fig. 7). 

The majority of bull elk winter use occurred in the lower 

altitude, open park areas, including Horseshoe Park, Beaver 

Meadows, Moraine Park, and Hollowell Park (fig. 8). GPS 

telemetry locations revealed more limited bull elk use of the 

Cow Creek, Hidden Valley, and Deer Mountain areas. Based 

on both VHF and GPS location data, we found almost no cow 

or bull elk use of the Glacier Basin drainage in the southern 

portion of the park (fig. 8). 
Figure 8. Winter elk telemetry locations from multiple sources in Rocky Mountain National Park, Colorado. For data description and source see tabl

0 10 

EXPLANATION 0 

GPS bulls (12 individuals) Helicopter surveys within Park Fixed wing 120 VHF collars Ground VHF (Larkins 1997) Colorado Shaded Relief derived from U.S. Geological Survey N digital elevation model data.
Part 1. Developing the Survey Design 15

Table 3. Altitude distribution of winter elk locations reported in different datasets and studies. For detailed description of 

each dataset see table 1.

[GPS, global positioning system; VHF, very high frequency; ≤, less than or equal to; %, percent; >, greater than]

Elevation range

(meters)

Data source

11 GPS radio-collared

elk bulls

(this study)

12 fixed-wing surveys 

of the Baker and others 

(2007) elk cows

(this study)

Larkins (1997; ground 

data of 73 VHF-collared 

cows and bulls)

Helicopter locations 

from five elk surveys

(this study)

≤2,800 76.8% 94.0% 95.8% 91.2%

2,801–3,000 5.1% 1.6% 3.7% 0%

3,001–3,299 0.1% 0.8% 0.3% 0%

>3,300 (alpine) 17.2% 3.7% 0.2% 8.8%

Tree Cover 

Of winter bull elk GPS locations inside the park 

(≤3,000 m altitude), 21.7 percent were in dense tree cover 

with montane Douglas-fir composing the largest portion 

of the vegetation (table 4). Another 25.9 percent were in 

mixed low shrubs, mostly riparian shrubs. An additional 

18.4 percent were in mixed open trees. The remaining 

34 percent of GPS locations were in open habitats composed 

of herbaceous cover types (table 4). Daily GPS elk locations 

in dense tree cover varied widely among winter days from 

a low of 0 percent to a high of 100 percent (mean=24.2 percent, standard deviation=22.6 percent). Monthly averages for 

GPS elk locations in dense trees ranged from 12.4 percent to 

27.6 percent (fig. 10). There appeared to be more GPS locations in dense tree cover during February and March than 

earlier months of 2010 and 2011 (fig. 10).

Winter bull elk GPS locations combined over months 

and years showed a strong diurnal temporal pattern of 

increased use of dense trees during the evening hours, 

rising above 20 percent between 15:00 and 22:00, but 

remaining relatively consistent across the morning and 

early afternoon daylight hours when surveys are typically 

conducted (fig. 11).

Altitude

Of the GPS bull locations, 76.8 percent were at altitudes 

less than or equal to (≤) 2,800 m and 17.2 percent were at 

altitudes >3,300 m, which is alpine tundra habitat (table 3). In 

the altitude band between these extremes, only 5.1 percent of 

locations were between 2,801 and 3,000 m, and 0.1 percent 

were between 3,000 and 3,300 m (table 3). Bull elk locations 

between 2,800 and 3,000 m were almost exclusively in 

Hidden Valley or on top of Deer Mountain. In the helicopter, fixed-wing, and Larkins (1997) telemetry datasets we 

evaluated, the altitude pattern was very similar to the GPScollared elk in this study (fig. 9). Locations between 2,800 

and 3,300 m constituted only 2.4 percent of our fixed-wing 

data, 0 percent of helicopter sightings in our test flights, and 

4.0 percent from Larkins (1997).
Figure 9. Winter altitude distribution of elk locations in elk population study in Rocky Mountain National Park, Colorado, 2008–2011, from fixobservations of 120 very high frequency-collared cows (Baker and others, 2007), helicopter observations of both bull and cow groups (this shigh frequency-collared elk from Larkins (1997). (Helo, helicopter) 0102030 2,300 2,400 2,500 2,600 2,700 2,800 2,900 3,000 3,100 3,200 3,300 3,400 3,500 3,600 3

Percent of elk locations

Altitude, in meters

Fixed

EXPLANATION

HeloLarkins
Part 1. Developing the Survey Design 17

Table 4. Distribution of winter bull elk global positioning system locations by cover 

class and vegetation type in study of elk population in Rocky Mountain National Park, 

Colorado, 2008–2011. (Totals may not equal due to rounding.)

[No., number; >, greater than; m, meter; %, percent; <, less than]

Vegetation type No. of elk

locations

Percent of elk

locations

Dense tree

Lodgepole pine—High elevation (>2,900 m) 104 0.4%

Lodgepole pine—Low elevation (<2,900 m) 962 3.7%

Mixed conifer with aspen (Douglas-fir) 69 0.3%

Mixed conifer with aspen (lodgepole pine) 170 0.7%

Mixed conifer with aspen (ponderosa pine) 200 0.8%

Montane Douglas-fir 2,457 9.5%

Riparian aspen 919 3.5%

Riparian lower montane mixed conifer (<2,590 m) 101 0.4%

Riparian upper montane mixed conifer (>2,590 m) 374 1.4%

Subalpine limber pine 2 0.0%

Subalpine mixed conifer 272 1.0%

Subtotal 5,630 21.7%

Mixed low shrub

Juniper 5 0.0%

Shrub riparian cross zone (<2,925 m) 5,644 21.7%

Shrub upland lower montane—Big sagebrush 5 0.0%

Shrub upland lower montane—Bitterbrush 157 0.6%

Shrub upland lower montane—Undifferentiated 903 3.5%

Subtotal 6,714 25.9%

Mixed open tree

Cottonwood 26 0.1%

Disturbance—Dead and down 1 0.0%

Ponderosa pine, graminoid 2,453 9.4%

Ponderosa pine, rockland 702 2.7%

Ponderosa pine, shrubland 1,384 5.3%

Upper montane aspen 220 0.8%

Subtotal 4,786 18.4%

Open

Herbaceous upland montane (<2,925 m) 5,206 20.0%

Herbaceous wetland cross zone—Marsh 5 0.0%

Herbaceous wetland cross zone—Wetland 2,578 9.9%

Herbaceous wetland subalpine/alpine meadow 24 0.1%

Natural lakes—Ponds 13 0.1%

Outwash 427 1.6%

Reservoirs—Stock tanks 32 0.1%

Rock (alpine–upper subalpine) 3 0.0%

Rock (foothill–lower subalpine) 74 0.3%

Streams—Rivers 1 0.0%

Unvegetated surface 479 1.8%

Subtotal 8,842 34.0%

Total 25,972 100.0%
18 Development of an Aerial Population Survey Method for Elk in Rocky Mountain National Park, Colorado

Figure 10. Use of dense cover by bull elk wearing global positioning system collars within Rocky 

Mountain National Park, Colorado, by month of the study, 2008–2011. White bars indicate months 

when fewer than 4 of the 11 GPS-collared bulls spent time inside the park.

0

10

20

30

40

50

60

70

Nov 08

Dec 08

Jan 09

Feb 09

Mar 09

Nov 09

Dec 09

Jan 10

Feb 10

Mar 10

Nov 10

Dec 10

Jan 11

Feb 11

Mar 11

Perecnt of elk locations in dense tree cover

Month and year

Figure 11. Use of dense tree cover by global positioning system-collared bull elk during the winter 

period by hour of the day in Rocky Mountain National Park, Colorado, 2008–2011.

0

10

20

30

40

0 6 12 18

Percent of elk locations in dense tree cover

Hour of day
Part 1. Developing the Survey Design 19

Bull Elk Locations on Aerial Survey Days

We plotted the location of radio-collared bull elk on 

helicopter survey days to see where they were located during our surveys (fig. 12). Of the observed radio-collared bull 

elk, 47 percent (n=7) were outside of the survey area during 

aerial helicopter surveys and 53 percent (n=8) were inside the 

survey area boundary (fig. 12). Four radio-collared bulls were 

not located on survey days. Pilots invested ample flight effort 

to find missing radio-collared individuals during surveys, but 

if the collared individual was too far outside the survey area 

boundary, it may have been recorded as “not found.” All collars were functioning with audible signals at the time of our 

surveys. If the four bulls that were searched for but not found 

during aerial helicopter surveys are assumed to be outside of 

the survey area boundary (see fig. 4), then 58 percent (n=11) 

of radio-collared bulls were outside the survey area boundary 

during helicopter surveys and 42 percent (n=8) were within. 

During our study years, the majority of bull elk winter use 

occurred in Horseshoe Park, Beaver Meadows, Moraine Park, 

and Hollowell Park, with more limited bull elk use of the Cow 

Creek, Hidden Valley, and Deer Mountain areas. Based on both 

VHF and GPS location data, we found almost no cow or bull 

elk use of the Glacier Basin drainage in the southern portion of 

the park. 

Elk Park Boundary Crossings

We recorded GPS-collared bull elk crossing the park 

boundary 801 times during winter. The GPS bulls were 

captured only within park boundaries and the information 

on boundary crossings provides a relative indication of the 

amount of movement by bulls, but should not be interpreted 

or used as a firm number of crossings because of the nonrandomized capture method we used. Our data indicated there 

were 711 crossings lasting 1 hour or more, of which 581 

were ≤1 day, 124 were between 1 and 30 days, and 6 were 

>30 days. We recorded GPS-collared bull elk locations over 

1,838 winter elk-days with an average of 0.387 crossings per 

elk-day of 1 hour or longer duration, or 11.8 crossings per 

elk-month. That is approximately six round trips from park 

to Estes Park and back per month per bull during the winter 

period. In addition to these crossings, there were 90 crossings 

of <1 hour duration. Some of these may have resulted from 

bulls wandering near the boundary, but others may have been 

due to error in GPS location estimates.
20 Development of an Aerial Population Survey Method for Elk in Rocky Mountain National Park, Colorado

Figure 12. Locations of radio-collared bull elk during aerial helicopter surveys in Rocky Mountain National Park, 

Colorado, 2008-2011 (n=11 radio-collared bull elk located on five aerial surveys during three winters). Dates when individual 

frequencies were not found during the survey are shown. (Freq., frequency)

EXPLANATION 

Aerial Surveys 

2-29-2008

Map 

Area 11-10-2009 

1-11-2010

2-23-2010 

Survey area boundary 

Rocky Mountain National Park

1/16/2009 162.904

1/16/2009

11/10/2009

2/23/2009

Date Freq Status

162.894

162.831

162.831

Not Found

Not Found

Not Found

Not Found

40°16'

40°20'

40°24'

40°28'

40°32'

105°40' 105°36' 105°32' 105°28' 105°24' 105°20' 105°16'
Part 2. Implementing and Testing the Survey Design 21

Part 2. Implementing and Testing the Survey Design

Photograph by K.A. Schoenecker, USGS.
22 Development of an Aerial Population Survey Method for Elk in Rocky Mountain National Park, Colorado

Using a Hybrid Double-Observer Model 

with Sighting Covariates to Estimate the Elk 

Population in Rocky Mountain National Park, 

2008–2011

In order to achieve a more precise and accurate estimate 

for the elk population within RMNP, we used information 

obtained as discussed in part 1, and incorporated it into a 

methodology using a hybrid population-estimation model; 

we used simultaneous double-observer protocols and collected sighting covariates for all surveys. Instructions for this 

method and the flight forms for data collection are provided in 

appendix 3.

Methods

We flew five combined helicopter–fixed-wing surveys 

over three winters: 2007−2008, 2008−2009, and 2009−2010 

using a Lama helicopter (pilot J. Hennessey of TransAero) 

and Supercub or Cessna 182 fixed-wing aircraft (pilots 

Dave Stinson of Sky Aviation and Lanny Coulter of Coulter 

Aviation, respectively). We flew predefined transects (fig. 5) 

using an onboard GPS (Garmin GPSmap, Garmin International, Olathe, Kansas). 

USGS ecologist K. Schoenecker was located in the frontleft seat of the helicopter for all surveys. A second observer, 

NPS biologist T. Johnson, and a third observer (NPS, USGS, 

Colorado Parks and Wildlife, or volunteer) switched positions between the left and right rear seats at each refueling to 

be able to calculate individual sighting probabilities against 

the front-left seat observer. The pilot was not asked to search 

for elk, although any elk detected by the pilot contributed to 

the recorded detections for the primary front observer. The 

pilot would discretely notify the front seat observer of any elk 

groups spotted without notifying the rear seat observers.

During helicopter surveys, a fixed-wing aircraft, occupied 

only by the pilot, flew near but above the helicopter to locate 

elk with radio collars. Using the 120 VHF radio collars from 

the Baker and others (2007) study enabled us to use a knownfates, mark-resight population estimation for our trials; that is, 

during our aerial surveys, elk not seen by the helicopter crew 

were known to be available or unavailable (outside of the survey area or dead) because of simultaneous collar location data 

collected by the fixed-wing pilot. 

Initially, we had the fixed-wing pilot record covariates for 

all radio-collared elk, and at the end of the survey we compared the group size, time of observation, presence of radio 

collars in a group, and Universal Transverse Mercator locations to determine which groups with radio collars were seen 

or not seen by the observers in the helicopter. But because 

fixed-wing pilots were not always able to get a group size 

or record covariates, it became difficult to match up groups 

to determine if they were seen or not seen by the helicopter. Thus, we modified communication so the pilots would 

remain in continuous radio contact with the helicopter pilot; 

the fixed-wing pilot flew ahead of the helicopter’s path to 

locate radio-collared elk and then climbed to a higher altitude 

while the helicopter pilot and observers surveyed an area. 

The fixed-wing pilot watched the helicopter and informed the 

helicopter pilot and crew about any radio-marked elk that had 

been passed and appeared to have been missed (because the 

helicopter did not circle or slow down to count). The helicopter crew then flew to the missed elk and recorded sighting 

conditions for these groups. To maintain safe separation, we 

restricted the helicopter to fly <300 ft above ground level and 

the airplane to fly >500 ft above ground level.

Population Estimation Analysis

Data

Our final dataset included five helicopter surveys and 

data from three fixed-wing surveys conducted at the same 

time as the helicopter surveys. Two additional fixed-wing 

flights had missing values and were dropped. We had a total 

of 27 groups with radio collars located by the fixed-wing that 

were available to helicopter observers during surveys. During 

the 5 helicopter surveys, 67 elk groups were located by the 

fixed-wing aircraft that were available to helicopter observers 

(27 elk groups with known locations and covariates due to 

radio collars and 40 groups without). Lubow and others (2002) 

provided data on an additional 44 groups with radio collars. 

The combined dataset includes 111 observations. 

Observations were well distributed among the major 

covariates: 59.1 percent of groups were moving when sighted, 

group sizes ranged from 1 to 491 (fig. 13), and cover of vegetation that could obscure elk observations, such as trees and 

(or) tall shrubs, was fairly uniformly distributed across the full 

range from 0 percent to 100 percent (fig. 14). Snow cover was 

most commonly either 0 percent or 100 percent, but partial 

snow cover occurred for 44.5 percent of groups (fig. 14). The 

wide distribution of covariates across all possible conditions 

means that we were able to obtain information about this full 

range of sighting conditions to build our models.

Model Structure

The observed number of elk in a survey underestimates 

the true number because of detection bias—the failure to 

detect elk groups that were present but not seen. Thus, the 

inverse of each group’s detection probability (1/p̂

i

) is an 

expected correction factor (θ̂

i

) that represents the number of 

elk present in the surveyed area per elk seen in that group. 

Applying the group-specific correction factor to the group 

sizes and composition of observed elk groups leads to point 

estimates of abundance and composition that account for 

detection bias. 

We prepared data from detection of elk groups by 

individual observers as detection events in a mark-releaserecapture analysis framework. We used a closed-capture 

modeling approach that allowed for individual elk group 

covariates to influence detection probability (Huggins, 1991). 
Part 2. Implementing and Testing the Survey Design 23

In all of the candidate models that we tested, we set the recapture probability, c, equal to the initial detection probability, p. 

This reflects the explicit assumption of double-observer 

analyses (Barker, 2008) that each observer’s detection records 

are independent. 

The sightability calibration surveys (Lubow and others, 2002) were two-occasion mark-resight trials, where the 

presence of a radio collar was the first marking occasion and 

the observation (or failure to observe) by the aerial helicopter 

crew was the second resighting occasion. In our study, there 

could be three sighting occasions: (1) by the fixed-wing pilot 

if a radio-collared elk was in the group, (2) by the helicopter 

front observer, and (3) by the helicopter rear observers. There 

were only two possible sighting occasions for each elk that 

was not marked with a radio collar. 

To model these differing structures, we defined four 

potential sighting-resighting occasions: one for each radiocollared group, one for the single aerial observer in Lubow 

and others (2002), and one each for the front and rear 

observers in the helicopter in the current study. No single 

survey actually had all four of these sighting occasions. For 

example, the study by Lubow and others (2002) did not have 

sightings by front and rear observers, and only the pilot in 

the fixed-wing aircraft could locate elk groups with radio 

collars. Consequently, probabilities were fixed at 0 for occasions that did not apply to a particular group and this model 

structure was reduced mathematically to a two-occasion 

survey for the Lubow and others (2002) data (radio and 

aerial) and to three occasions (radio, front, and back) for 

the current dataset. Structuring the model this way enabled 

us to estimate common parameters for the effects of covariates, such as group size and vegetation, across the different 

studies while maintaining separate intercept parameters for 

the different sighting occasions. We fixed the probability of 

detection of a radio-collared group by the fixed-wing pilot at 

pradio=1. 

Figure 13. Distribution of elk groups by group size in Rocky Mountain National Park, Colorado, elk 

population estimation study, 2008–2011, demonstrating the tendency toward larger groups in winter.

0

50

100

0

50

100

0 100 200 300 400 500

Cumulative nu

mber of groups of smaller size

Cumulative percent of groups of smaller size

Group size (number of elk)
24 Development of an Aerial Population Survey Method for Elk in Rocky Mountain National Park, Colorado

Figure 14. Distribution of elk groups by major sighting characteristics, A. percent vegetation cover, and 

B. percent snow cover, in elk population study in Rocky Mountain National Park, Colorado, 2008–2011.

0

5

10

15

20

25

0 10 20 30 40 50 60 70 80 90 100

Number of elk groups

Vegetation cover, in percent

0

5

10

15

20

25

30

35

40

0 10 20 30 40 50 60 70 80 90 100

Number of elk groups

Snow cover, in percent

A

B
Part 2. Implementing and Testing the Survey Design 25

In all candidate models, the sighting probability for an 

elk group was defined by the logistic function, which specifies that detection probabilities are a logit function of the 

summed products of covariates multiplied by beta (β) coefficient parameters. Sighting probability for each elk group i on 

occasion j can be thought of as having a unique intercept beta 

parameter, and potentially including a number of other additive effects represented by the product of other covariates and 

beta parameters (eq. 1). 

Pi,j = e

e

x

x

i j

i j

β

β

,

'

,

'

( )

( ) 1+

(1)

where 

β is a vector of fitted coefficients for the logistic 

model (beta parameters); and 

x′

i,j is a transpose of the vector of observed 

covariates for an elk group i on occasion j.

The β and x′

i,j vectors for a given elk group consist of the 

intercept for one of the observers, plus additional covariates 

that might affect the sighting probability of elk groups with 

those characteristics. 

We considered structuring a general model with parameters for each observer and each survey. However, the number 

of groups sighted during many of the surveys is too small to 

effectively estimate unique effects for each. Consequently, we 

dropped consideration of parameters to describe effects due to 

individual surveys. 

In a fully parameterized model, the probability of detecting elk could differ for the left and right sides of the aircraft. 

In the rear, this is due to different observers on each side; in 

the front, it is due to different angles and obstructions affecting visibility for the front observer and the extent to which the 

pilot assists in observing. We included two intercepts for the 

front observer: for elk on the left, βL, and right, βR, sides of the 

aircraft. We considered four intercepts for the four different 

individuals who observed from the rear on various surveys; 

however, we determined that it was necessary to pool data for 

two observers (Jason Ransom [JR] and Sheri Huwer [SH]) 

due to insufficient data for SH. Thus, the effects of JR and SH 

were assumed to be the same, which we believe is reasonable 

because these are both highly experienced observers. This left 

three intercept parameters for the rear: βJR=βSH, βTJ , βZW (where 

TJ stands for Therese Johnson and ZW stands for Zac Wiebe).

In the Lubow and others (2002) study, the observer and 

pilot worked as a team to record elk groups; therefore, we 

considered a single parameter, βAll, for the sighting probability 

of the aerial observer during that study. 

A difficulty arises in incorporating the radio-collar data 

into this model structure. When a radio-collared group is missed 

by all helicopter observers, there is no way to know which side 

of the aircraft it was on when the helicopter flew by it. Consequently, we structured the model to use the mean of the estimated left and right sighting probabilities for these groups. 

In addition to the six intercept parameters described 

above, we considered the following five covariates unique to 

each elk group: (1) number of elk in group, (2) percent vegetation cover, (3) activity of elk group (moving or not moving), 

(4) percent snow cover, and (5) squared value of percent snow 

cover (table 5). We included only additive effects for these 

five covariates, rather than considering unique effects for each 

observer, because of the insufficient data for each observer. 

We also did not consider interactions among the covariates 

because of the small sample size. We included snow cover 

squared, xS

2

, because of the likelihood that snow cover affects 

sightability in a nonlinear manner. In total, there were up to 

6 intercepts and four linear covariates, as well as a quadratic 

covariate, for a maximum of 11 parameters to be estimated for 

the most general model. Given the 111 observations, there is a 

ratio of 10 observations for each parameter to be estimated. 

Model Fitting and Selection

The influence of covariates on detection probability 

was unknown, so we used a model-comparison framework 

(Burnham and Anderson, 1998) to assess which covariates 

influenced detection probability. We used optimization software (Frontline Systems Inc., Incline Village, Nevada) in program Excel (Microsoft Corp., Redmond, Washington) to find 

the maximum likelihood, Akaike information criterion (AIC) 

Table 5. Covariates and corresponding model coefficients for each unique elk group used in the population estimation model for elk 

in Rocky Mountain National Park, Colorado, 2008–2011.

Observed

covarariate

Model

coefficient Description

xN βN Group size (number of elk)

xC βC Proportion of ground in vicinity of elk group covered by vegetation tall enough to obscure elk (0.0–1.0)

xA βA Activity: 0 if inactive (bedded or standing), 1 if active (elk moving)

xS βS Proportion of ground in vicinity of elk group covered by snow (0.0–1.0)

xS

2 βS2 Squared value of proportion of ground in vicinity of elk group covered by snow (0.0–1.0)
26 Development of an Aerial Population Survey Method for Elk in Rocky Mountain National Park, Colorado

values, and beta parameter estimates for each of the alternative 

models. Based on the resulting model weights and matrix of 

parameter estimates, we then found the group-specific correction factors using equation 1 for each alternative model. 

We compared the parsimony of the candidate models 

using AIC adjusted for small sample size, AICc (Burnham 

and Anderson, 1998). We examined the evidence supporting 

various effects by evaluating the evidence ratio between the 

alternative models both with and without the effect of interest. 

The evidence ratio is the ratio between the support for the better model and the weaker model; that is, a ratio of 2.0 means 

there is twice as much support for the stronger model. We 

selected models with ΔAICc <4.0 to include in our inference 

set, which we used to estimate population size. We also compared the strength of evidence for the models in this set using 

AICc model weights. 

The most general model (11 parameters) fit the data 

well, with a variance inflation factor of c=1.54 (values <2 

are considered indicative of an adequate model structure). 

Consequently, we did not use a variance inflation adjustment 

to the likelihood estimation. 

In addition to the general model, we fit and evaluated 

alternatives with each slope parameter removed, one at a time, 

and with two different constraints on the observer-specific 

intercepts: (1) βFL=βFR, (FL stands for front-left and FR stands 

for front-right) and (2) βTJ=βJH=βSH=βZW (subscripts are 

initials of observers). After concluding that βN (group size), βA 

(elk activity), and βC (vegetation cover) were strongly supported and that the constraint βTJ=βJH=βSH=βZW was strongly 

disfavored, we considered all combinations of the remaining variables with intermediate support: βS

 (snow cover), βS

2

(snow cover squared), and βFL=βFR. In total, we considered 

12 models. Of these, eight had ΔAICc <4.0, and so were sufficiently supported to include in our final inference set (table 6). 

We used these eight models to estimate population size and 

used the model-weighted average of these to generate the final 

estimate of population size.

Point Estimate Method

The unconditional overall detection probability ( pi) for 

elk group i is one minus the probability that it was missed by 

all observers (eq. 2). 

pi=1-(1-pradio,i)(1-pall)(1-pFL)(1-pFR)(1-pTJ)(1-pJR=SH)(1-pZW) (2)

Note that elk groups with at least one radio-collared 

animal have ρradio =1, so their ρi =1. For elk groups with no 

radio-collared animals, ρradio =0, the ρi for those elk groups is a 

function of ρall, ρFL, ρFR, ρTJ, ρJR=SH and ρZW. Recall that, for any 

given survey and elk group, only some of these observers are 

present, so all inapplicable values are fixed at 0. The groupspecific correction factor (θ̂

i

) is the inverse of the group’s 

unconditional overall detection probability (Steinhorst and 

Samuel, 1989; eq. 3). 

θ̂i = 

1

pi

(3)

Correction factors can be thought of as the per-observedelk contribution to the overall estimate of abundance; it is 

one plus a corresponding number of unseen elk that occur in 

groups with the same covariates as that observed. The contribution to an abundance estimate coming from group i is the 

product of its observed group size (ni) times its group-specific 

correction factor, θ̂

i

. For a given survey, the total estimated 

abundance (N) is the sum of the products of group size 

weighted by group-specific correction factors (eq. 4). 

Ni=Σθj * nj (4)

Estimating Variance in Abundance Estimates with 

Bootstrapping

The variance of abundance estimates was calculated from 

bootstrapped simulations of the observation data (Wong, 1996; 

Lubow and others, 2002). The motivation for this method 

comes from the notion that the observed elk groups were 

drawn from a larger set of elk groups that could have been 

observed. This larger set is considered to be a “super-population” in the statistical sense (Hartley and Sielken, 1975). 

We use the group-specific correction factors estimated 

from the double-observer sightability model to simulate a set of 

potentially observable groups in the super-population, having 

group size and other sighting covariates identical to those in 

the observed dataset. Each simulated elk group retains covariates corresponding to those in the actual dataset and retains its 

membership as belonging to a certain survey. Observed groups 

“represent” themselves as well as additional, undetected groups 

in the super-population. The correction factor is a measure of 

how many groups each observed group represents. So, each 

observed group was replicated θ̂

j

 times, to define the superpopulation. By definition, each elk group with one or more 

radio-collared elk has a θ̂

j

 value of one, because such groups 

are always detected via radio telemetry. However, for each 

iteration of generating a super-population, decimal fractions 

of simulated groups were either included or not included 

depending on a comparison against a random number. As an 

example, an observed group with an estimated sighting probability of 0.4 and θ̂

j

 of 2.5 represents two and one-half comparable elk groups with identical covariates. In this example, 

two elk groups would be included in the super-population in 

every iteration of the bootstrap dataset creation; in addition, to 

account for the additional fraction of a group, another group 

would be added during each iteration only if a randomly generated number (uniform distribution ranging from 0–1) was less 

than the remaining fraction (in this case, 0.5). 

From that putative super-population, we simulated observations that were included in the dataset by testing whether each 

elk group, in turn, was detected by the front or rear observer, 

or if the group had a radio-collared elk, by the radio telemetry 
Table 6. Sightability model alternatives with fit and selection statistics for elk population estimation study in Rocky Mountain National Park, Colorad[obs., observer; Ln(L), natural log; no., number; N, observations; K, parameters; AIC, Akaike information criterion; %, percent]

Model

Rank 1 2 3 4 5 6 7 8 9 10 

Interceptsa

Front 1 1 1 1 2 2 2 2 1 1 Rear 3 3 3 3 3 3 3 3 3 1 combined (single obs.) 1 1 1 1 1 1 1 1 1 1 

Slopesa

Group size 1 1 1 1 1 1 1 1 1 1 Cover 1 1 1 1 1 1 1 1 1 1 Activity 1 1 1 1 1 1 1 1 0 1 Snow 0 0 1 1 0 0 1 1 1 1 Snow squared (Snow2) 1 0 1 0 1 0 0 1 1 1 

Model fit and selection statistics

Ln(L) –78.40 –79.77 –77.61 –78.83 –78.40 –79.77 –78.83 –77.60 –81.04 –82.4Deviance 156.8 159.5 155.21 157.7 156.8 159.5 157.7 155.2 162.1 164.9 no. Observations (N) 111 111 111 111 111 111 111 111 111 111 No. of Parameters (K) 9 8 10 9 10 9 10 11 9 8 Degrees of freedom 102 103 101 102 101 102 101 100 102 103 Variance Inflation Factor (ĉ) 1.54 1.55 1.54 1.55 1.55 1.56 1.56 1.55 1.59 1.6AIC

c

176.6 177.0 177.41 177.5 179.0 179.3 179.9 179.9 181.9 182.3 

Delta AIC

c

0.00 0.37 0.82 0.86 2.42 2.74 3.28 3.28 5.28 5.6

Relative model weight 1.00 0.83 0.66 0.65 0.30 0.25 0.19 0.19 0.07 0.0Model weightb 25.7% 21.4% 17.0% 16.7% 7.7% 6.5% 5.0% 5.0%Evidence ratios 1.0 1.2 1.5 1.5 3.3 3.9 5.1 5.2 14.0 17.2 

aValues indicate number of parameters included in given model.bModel weights computed for inference set only.
28 Development of an Aerial Population Survey Method for Elk in Rocky Mountain National Park, Colorado

Table 7. Sightability model parameters and model weighted 

average estimates for elk population estimation study in Rocky 

Mountain National Park, Colorado, 2008–2011.

[See table 5 for definitions of the variables βN, βA, βC, βS, and βS

2

. βL, left side 

of aircraft; βR, right side of aircraft; βTJ , observer TJ; βJR=SH , observers JR 

and SH; βZW , observer ZW; βAll, all observers]

Parameter Model weighted

average estimates

Intercepts

βL –1.0837

βR –1.0804

βTJ –0.8642

βJR=SH 1.8375

βZW –0.5570

βAll 0.4786

Slopes

βN 0.0156

βA 1.9910

βC –2.1014

βS –0.5846

βS

2 1.1128

observer. Front, rear, combined, and radio telemetry observer 

detections were simulated for each elk group from the simulated 

super-population of elk groups. Each simulated elk group in the 

super-population was recorded as either detected or not detected 

by each observer, based on evaluating a random number against 

the original estimates of detection probabilities for that observer. 

The simulated observation dataset for each iteration only 

included elk groups that were detected by at least one of the 

simulated observers. 

Each dataset of simulated observations was used to solve 

for the parameter estimates and AICc estimates for each of the 

eight contributing models in our inference set. These lead to 

group-specific correction factors (θ̂

j

) for the simulated groups, 

which were multiplied by group sizes to yield the abundance (N̂) estimates for each simulated survey. We generated 

100 such simulated observation datasets, solved for model 

parameters and weights, applied correction factors, and found 

estimated abundances from each. The coefficient of variation 

for the point estimate of abundance, CV^ (N̂), and associated 

confidence limits were calculated based on the range of simulated abundance estimates. 

Results

Model Fitting and Support

The most strongly supported model received 25.7 percent 

of the model weight (table 6). This model included nine 

parameters, which did not include the βS, but did include βS

2

and constrained βFL=βFR. Of the eight models in the inference set, snow effects (linear or quadratic) were supported by 

73.4 percent of the model weight. Differences between front 

left and front right sighting probabilities were supported by 

only 23.9 percent of model weight. Comparison of the best 

model to others revealed overwhelming support (evidence 

ratios given for each effect; table 6) for inclusion of parameters for population size (evidence ratio=6,136), activity (evidence ratio=1,034), cover (evidence ratio=14), and differences 

among rear observers (evidence ratio=17.2). 

Several effects received some support, which justified 

including models with these parameters in the final inference 

set. We included the eight models in this set that had ΔAICc

<4.0. The base model had 33.7 percent of the model weight 

among those in this set. 

Model-weighted averages of the parameters using the 

inference set (see table 5) indicated effects in the expected 

direction: higher sighting probabilities for larger groups, 

active groups, and less cover (table 7). Sighting probability 

for the pooled data on the two most experienced rear observers was highest, followed by the combined observers in the 

Lubow and others (2002) study, then by the front observer, 

and finally by the two less experienced rear observers. Snow 

effects involve both positive linear and negative quadratic 

terms in two of the models, which result in higher estimated 

sighting probabilities for very low and very high snow cover, 

and lower for intermediate snow cover, which corresponds to 

patchy conditions (table 7).

Predicted sighting probabilities varied greatly (fig. 15) 

and were strongly affected by the observer, group size, 

activity, vegetation cover, and snow cover (figs. 16 and 

17). There was no evidence of a difference between sighting probabilities of groups with and without radio collars 

(x2=0.91). Under the worst possible conditions of a single 

inactive elk in 100 percent vegetation cover and 20 percent snow cover, sighting probability for the front and rear 

observers, combined, was only 1.5 percent when using the 

least experienced rear observer. However, this worst case 

improved to 5.5 percent when using the best rear observer. 

Nevertheless, the worst conditions actually encountered 

resulted in a combined sighting probability of 6.7 percent. 

Only 11.3 percent of radio-collared groups and 9.0 percent 

of all groups had ≤30 percent sighting probability because 

worst-case conditions were rarely encountered. For a more 

typical sighting, an inactive group of 10 elk in 50 percent 

vegetation cover and 100 percent snow cover, combined 

sighting probability was 73.2 percent using the best observer 

in the rear, but dropped to 37.0 percent with the less experienced observer in the rear.
Part 2. Implementing and Testing the Survey Design 29

Figure 15. Distribution of sighting probabilities for combined front and rear observers for all elk groups 

marked with radio collars, illustrating how groups varied widely in visibility. Bar heights indicate the number 

of groups observed that had the indicated sighting probability estimate. (%, percent)

0

5

10

15

20

25

30

35

0 10 20 30 40 50 60 70 80 90 100

Nu

mber of elk groups

Sighting probability, in percent

All

With radios

EXPLANATION

Population Estimates and Precision

Population estimates (table 8) had very good estimated 

precision (≤16 percent standard error [SE]). Snow conditions 

were ideal (100 percent cover) for the February 2010 survey, which resulted in the excellent precision of 3.1 percent 

CV. Although snow conditions were not as good in January 

2010, our most experienced observer was in the rear and that 

overcame the reduced sighting probabilities caused by snow 

conditions, resulting in the best precision of the five surveys 

(2.7 percent CV). The earliest two surveys did not have data 

from radio-marked elk, which reduced their precision. 

For comparison, we also estimated the populations during the three surveys where radio-collar data were available 

without including the data from these collared elk (table 8). 

These estimates reflect what would have been obtained had 

the surveys been conducted by only the helicopter crew using 

the double-observer method with the corrections estimated in 

this study. Without the radio-collar data, precision dropped, as 

expected. The worst case was November 2009 when precision without radio-collar data would have been 27.0 percent 

CV. This was due to a combination of patchy snow conditions and the absence of the most experienced rear observers. 

The estimates without radio-collar data also ranged from 

8.8 percent lower to 1.1 percent higher (mean=–4.1 percent, 

SE=2.9 percent). This suggests the possibility of a small residual negative bias due to uncorrected sighting heterogeneity, 

although the confidence intervals overlap 0 percent, so evidence for a residual bias is inconclusive. 

Our estimates indicate that between 84 percent and 97 percent of elk were seen by the combined observers during these 

surveys, with the lowest estimated portion of the population 

seen during the November 2009 survey for the same reasons 

the precision on that survey was lowest, as discussed above. 

Although sighting probability can be very low for some groups, 

larger groups have higher sighting probability. Therefore, the 

number of elk missed by aerial observers is relatively low. 

Discussion

One of the major challenges of estimating the number of 

elk in RMNP is the difficulty of obtaining an adequate sample 

size of observed elk groups to fit sighting probability models. 

This is primarily caused by the clustering of elk into a small 

number of very large groups and a few smaller groups. The 

cost and logistical difficulty of aerial surveys exacerbate this 

problem. One of the benefits of the double-observer method 

used in our study is that each survey cumulatively adds to the 

dataset of observations used to calibrate the sighting probability models. Consequently, results can continue to improve over 

time as regular monitoring adds additional observations. 

Furthermore, if observers and sighting conditions change 

over time, these changes can eventually (with enough data) 

be detected and accounted for using our method, which was 

not possible with just the sightability calibration approach that 

was previously used. For example, our results strongly support 

differences in sighting probability among individual observers, 
30 Development of an Aerial Population Survey Method for Elk in Rocky Mountain National Park, Colorado

Figure 16. Sighting probability for combined front and rear observers, using rear observer with highest sighting 

probability, for elk population estimation study in Rocky Mountain National Park, 2008–2011. 

0

50

100

0 50 100 

0 

50

100 

0 50 100 

1

10

50

100

200

0 

50

100 

0 50 100 

Sighting probability, in percent Sighting probability, in percent

0 

50

100 

0 50 100 

0 

50

100 

0 100

Snow cover, in percent

50

0 

50

100 

0 50 100 

EXPLANATION

Sighting probability, in percent

Snow cover, in percent
Part 2. Implementing and Testing the Survey Design 31

Figure 17. Sighting probability for combined front and rear observers, using rear observer with lowest 

sighting probability, for elk population estimation study in Rocky Mountain National Park, 2008–2011.

0 

50

100 

0 50 100 

0 

50

100 

0 50 100 

1

10

50

100

200

0 

50

100 

0 50 100 

0 

50

100 

0 50 100 

0 

50

100 

0 50 100

0 

50

100 

0 50 100

Sighting probability, in percent Sighting probability, in percent

Snow cover, in percent

Sighting probability, in percent

Snow cover, in percent

EXPLANATION
32 Development of an Aerial Population Survey Method for Elk in Rocky Mountain National Park, Colorado

so the ability to account for these differences in our method 

improves precision of estimates. The result showing differences in sighting probability among observers emphasizes 

the importance of retaining observers for multiple surveys so 

that their individual sighting probabilities can be adequately 

measured and accounted for in statistical corrections. Frequent 

changes in personnel will reduce the precision of the estimates 

and risk uncorrected biases as well. 

A second challenge to reliable elk population estimation 

in RMNP is heterogeneous sighting probabilities. A simple 

double-observer approach would underestimate the population 

because it assumes that all groups have equal probability of 

being sighted. By combining a double-observer method with a 

sighting covariate model, we corrected for the major sighting 

probability differences among elk groups. Nevertheless, comparison of estimates made with and without radio collars suggests a small residual bias remains unexplained by our models. 

A larger sample size with radio-collared elk would enable a 

future analysis to fit models to correct for this additional bias 

following the methods of Griffin and others (2013). 

Our models predicted poor sighting probabilities for 

worst-case conditions. Two of these, snow cover and observer 

ability, can be managed to some extent. It is likely that surveys 

conducted under low and patchy snow conditions using less 

experienced observers will have low precision and may not be 

worth the cost. Nevertheless, it is possible to obtain adequate 

sighting probability, even in dense vegetation, if these other 

factors are optimized. But restricting surveys to ideal snow 

conditions and the availability of the most experienced observers exacerbates the logistical difficulty of scheduling and 

conducting surveys. 

The study was limited by the small number of radio 

collars on bull elk combined with the small sample size of 

elk groups overall, which precluded estimation of different 

sighting probabilities for bull groups. This raises concerns 

about the applicability of our method to estimation of the bull 

population segment. Of particular concern was the possibility 

that bulls were out of the sampling area or in different sighting conditions that could make them more difficult to observe 

during our surveys. 

The park allocated funds to purchase and deploy 12 GPS 

radio collars on bull elk in order to help answer this question. 

We found that bulls were typically in smaller groups than 

females and single bulls wearing radio collars were missed 

more frequently in aerial surveys than radio-collared cows, 

consistent with McCorquodale (2001); however, our corrections for group size allowed us to address this effect for bulls. 

In addition, the GPS collars allowed us to obtain evidence 

suggesting that dense tree cover may not be an important 

contribution to biased bull estimates. Only 22 percent of radiocollared bull locations in winter were in dense tree cover, 

whereas the remaining locations were in open meadow, low 

shrub, or open mixed trees, all vegetation types with higher 

sightability. Also, bulls used dense tree cover more frequently 

Table 8. Elk population estimates and precision, comparing analyses with and without radio-collar data, for elk population estimation 

study in Rocky Mountain National Park, 2008–2011.

[No., number; —, no data; SE, standard error; CV, coefficient of variation; %, percent, Cl, confidence interval]

Survey date Survey date

Feb-10 Jan-10 Nov-09 Jan-09 Feb-08 Feb-10 Jan-10 Nov-09 Jan-09 Feb-08

Using radio-collar data in population estimates Without using radio-collar data in population estimates1

No. elk groups 17 15 11 — — No. elk groups 14 14 7 6 8

No. elk seen 464 523 586 — — No. elk seen 432 508 526 508 381

Estimate (no. elk) 476 532 683 — — Estimate (no. elk) 454 538 623 559 402

SE 14.6 14.3 115.0 — — SE 70.8 36.8 168.2 76.3 56.4

CV 3.1% 2.7% 16.8% — — CV 15.6% 6.8% 27.0% 13.6% 14.0%

% seen 97% 98% 86% — — % seen 95% 94% 84% 91% 95%

Lower 95% CI 458 514 550 — — Lower 95% CI 372 492 442 469 336

Upper 95% CI 495 551 847 — — Upper 95% CI 555 587 877 666 482

Alpine count2 — 71 82 — — — —

Radio versus no radio

%Diff –4.5% 1.1% –8.8%

1

Estimates based on double-observer helicopter survey only; radio collars ignored. 

2

We developed elk survey protocols and transect flight lines for the alpine tundra area of the park, however, tundra surveys are only conducted when wind 

conditions allow for safe flying, which is not an annual occurrence. Therefore, population estimates for the alpine are shown independently, and are not included 

in other population estimates shown.
References Cited 33

between 15:00 and 22:00, as opposed to mornings and early 

afternoons when aerial surveys were conducted. Mean daily 

use of dense trees by bulls was approximately 24 percent and 

monthly average use was approximately 28 percent. This was 

similar to the percentages of cow groups observed during 

surveys that were in dense vegetation cover. Given that there 

is little evidence of differences in cover use between age-sex 

classes, the estimated sightability corrections for vegetation 

cover in our models should be adequate to address the effect 

of dense tree cover.

Of greater concern, however, is our finding that between 

47 percent and 58 percent of radio-collared bulls were out of 

the survey area during aerial surveys, and were more often 

outside the park than simply outside of the survey area. This 

finding is limited by small sample size, but suggests that 

roughly half of the bulls are not within the survey area at the 

time of a survey. Bulls remain challenging to count because 

of their movement rates, particularly in and out of the park. 

Bull elk in our study made approximately 6 round trips from 

the park to Estes Park and back per month per bull during 

1,838 winter elk-days. Despite fine tuning the survey area to 

account for elevation limits and areas that do not appear to 

be used by elk, little can be done to account for bulls that are 

not present during the survey. This emphasizes the importance of interpreting survey results as only an estimate of the 

elk present at the time of the survey, and not as an estimate 

of a fixed population. 

Our study defined a survey area boundary that included 

nearly all winter elk locations within the park and east of the 

Continental Divide (excluding the tundra). These boundaries 

excluded large, mostly densely wooded areas in the southern 

portion of the park, despite meeting our elevation criteria. 

Reconfirming that elk continue to avoid these areas in winter 

may be warranted every 3 to 5 years. 

Obtaining accurate estimates of the elk population that 

use winter range in RMNP is challenging. We considered 

and reconsidered these challenges throughout our study and 

developed an aerial survey methodology that can be applied 

into the future to provide repeatable and reliable estimates 

of the elk population. Consistent, repeatable surveys of the 

defined survey area will provide data needed to support future 

decisions by park managers. However, given the frequent 

movements of elk in and out of the survey area, it is important 

that the results of individual surveys be interpreted correctly 

as estimates of elk use of the park at the time of each survey. Probably the most useful measurement for management 

purposes is an average of estimates from multiple surveys 

conducted on multiple dates (three or more) selected randomly 

from the time window of interest. This approach provides an 

estimate of the average elk use of the park during the time 

window sampled, rather than an estimate of the total population of elk inhabiting the park and Estes Valley.

References Cited

Anderson, D.R., and Southwell, C., 1995, Estimates of 

macropod density from line transect surveys relative to 

analyst experience: Journal of Wildlife Management, v. 59, 

p. 852–857.

Baker, D.L., Wild, M.A., and Powers, J.G., 2007, Evaluation of 

methods for managing elk population health and abundance 

in Rocky Mountain National Park, Colorado: Estes Park, 

Colo., National Park Service Research Study Plan, 16 p.

Barker, R., 2008, Theory and application of mark-recapture 

and related techniques to aerial surveys of wildlife: Wildlife 

Research, v. 35, p. 268–274.

Bayliss, P., and Yeomans, K.M., 1989, Correcting bias in aerial 

survey population estimates of feral livestock in northern 

Australia using the double-count technique: Journal of 

Applied Ecology, v. 26, p. 925–933.

Bear, G.D., 1989, Seasonal distribution and population characteristics of elk in Estes Valley, Colorado: Fort Collins, 

Colo., Colorado Division of Wildlife Special Report No. 65, 

52 p.

Bodie, W.L., Garton, E.O., Taylor, E.R., and McCoy, M., 

1995, A sightability model for bighorn sheep in canyon habitats: Journal of Wildlife Management, v. 59, p. 832–840.

Borchers, D.L., Buckland, S.T., Goedhart, P.W., Clarke, E.D., 

and Hedley, S.L., 1998a, Horvitz-Thompson estimators for 

double-platform line transect surveys: Biometrics, v. 54, 

p. 1221–1237.

Borchers, D.L., Zucchini, W., and Fewster, R.M., 1998b, 

Mark-recapture models for line transect surveys: Biometrics, v. 54, p. 1207–1220.

Bowden, D.C., and Kufeld, R.C., 1995, Generalized marksight population size estimation applied to Colorado moose: 

Journal of Wildlife Management, v. 59, p. 840–851.

Buckland, S.T., Anderson, D.R., Burnham, K.P., and Laake, 

J.L., 1993, Distance sampling—Estimating abundance of 

biological populations: London, Chapman and Hall, 446 p.

Burnham, K.P., and Anderson, D.R., 1976, Mathematical 

models for nonparametric inferences from line transect data: 

Biometrics, v. 32, p. 325–336.

Burnham, K.P., and Anderson, D.R., 1998, Model selection 

and inference—A practical information-theoretic approach: 

New York, Springer-Verlag, 355 p.

Cook, R.D., and Jacobson, J.O., 1979, A design for estimating visibility bias in aerial surveys: Biometrics, v. 35, 

p. 735–742.
34 Development of an Aerial Population Survey Method for Elk in Rocky Mountain National Park, Colorado

Daigle, G., Rivest, L.P., and Crepeau, H., 1995, Statistical 

methods for aerial surveys using the double observer technique to correct visibility bias: Biometrics, v. 51, p. 461–470.

Gogan, P.J.P., Thompson, S.C., Pierce, W., and Barrett, R.H., 

1986, Line transect censuses of fallow and black-tailed deer 

on the Point Reyes Peninsula: California Game and Fish, 

v. 72, p. 47–61.

Graham, G.W., and Bell, R., 1989, Investigating observer bias 

in aerial survey by double observers: Journal of Wildlife 

Management, v. 53, p. 1009–1016.

Griffin, P.C., Lubow, B.C., Jenkins, K.J., Vales, D.J., Moeller, 

B.J., Reid, M., Happe, P.J., McCorquodale, S.M., Tirhi, 

M.J., Schaberl, J.P., and Beirne, K., 2013, A hybrid doubleobserver sightability model for aerial surveys: Journal of 

Wildlife Management, v. 77, p. 1532–1544.

Gysel, L.W., 1960, An ecological study of the winter range of 

elk and mule deer in the Rocky Mountain National Park: 

Journal of Forestry, v. 58, p. 696–703.

Hartley, H.O., and Sielken, R.L., 1975, A “super-population 

viewpoint” for finite population sampling: Biometrics, v. 31, 

p. 411–422.

Hobbs, N.T., Baker, D.L., Ellis, J.E., Swift, D.M., and Green, 

R.A., 1982, Energy- and nitrogen-based estimates of elk 

winter range carrying capacity: Journal of Wildlife Management, v. 46, p. 12–21.

Huggins, R.M., 1991, Some practical aspects of a conditional 

likelihood approach to capture experiments: Biometrics, 

v. 47, p. 725–732. 

Johnson, B.K., Lindzey, F.G., and Guenzel, R.J., 1991, 

Use of aerial line transect surveys to estimate pronghorn 

populations in Wyoming: Wildlife Society Bulletin, v. 19, 

p. 315–321.

Kacynski, K., 2013, Riparian willow decline in Colorado—

Interactions of ungulate browsing, native birds, and fungi: 

Fort Collins, Colo., Colorado State University, Ph.D. dissertation, 94 p.

Larkins, K.F., 1997, Patterns of elk movement and distribution 

in and adjacent to the eastern boundary of Rocky Mountain 

National Park: Greeley, Colo., University of Northern Colorado, Master’s Thesis, 89 p.

Lubow, B. C., Singer, F.J., Johnson, T.L., and Bowden, D.C., 

2002, Dynamics of interacting elk populations within and 

adjacent to Rocky Mountain National Park: Journal of Wildlife Management, v. 66, p. 757–775.

Manly, B.F.J., McDonald, L.L., and Garner, G.W., 1996, 

Maximum likelihood estimation for the double-count 

method with independent observers: Journal of Agricultural, 

Biological, and Environmental Statistics, v. 1, p. 170–189.

McCorquodale, S.M., 2001, Sex-specific bias in helicopter 

surveys of elk—Sightability and dispersion effects: Journal 

of Wildlife Management, v. 65, p. 216–225.

National Park Service, 2007, Final Environmental Impact 

Statement, Elk and Vegetation Management Plan, Rocky 

Mountain National Park, Colorado: Washington, D.C., 

National Park Service, 535 p.

National Park Service, 2008, Record of Decision/Final Environmental Impact Statement—Elk and Vegetation Management Plan, Rocky Mountain National Park, Colorado: 

Washington, D.C., National Park Service, 21 p. 

Pollock, K.H., and Kendall, W.L., 1987, Visibility bias in 

aerial surveys—A review of estimation procedures: Journal 

of Wildlife Management, v. 51, p. 502–510.

Samuel, M. D., Garton, E.O., Schlegel, M.W., and Carson, 

R.G., 1987, Visibility bias during aerial surveys of elk in 

northcentral Idaho: Journal of Wildlife Management, v. 51, 

p. 622–630.

Samuel, M. D., and Pollock, K.H., 1981, Correction of visibility bias in aerial surveys where animals occur in groups: 

Journal of Wildlife Management, v. 45, p. 993–997.

Seber, G. A. F., 1982, The estimation of animal abundance and 

related parameters (2d ed.): New York, MacMillian, 653 p.

Singer, F.J., and Zeigenfuss, L.C., comps., 2002, Ecological 

evaluation of the abundance and effects of elk herbivory in 

Rocky Mountain National Park, Colorado, 1994–1999: U.S. 

Geological Survey Open-File Report 2002–208, 268 p.

Skovlin, J.M., Zager, P., and Johnson, B.K, 2002, Elk habitat 

selection and evaluation, in Toweill, D.E., Thomas, J.W., 

and Metz, D.P., eds., North American elk—Ecology and 

management: Washington, D.C., Smithsonian Institution 

Press, p. 531–555.

Southwell, C., 1994, Evaluation of walked line transect counts 

for estimating macropod density: Journal of Wildlife Management, v. 58, p. 348–356.

Steinhorst, R.K., and Samuel, M.D., 1989, Sightability adjustment methods for aerial surveys of wildlife populations. 

Biometrics, v. 45, p. 415-425.

Stevens, D.R., 1980, The deer and elk of Rocky Mountain 

National Park—A 10-year study: Estes Park, Colo., Rocky 

Mountain National Park, Park Report ROMO-N-13, 67 p. 

Thomas, L., Buckland, S.T., Rexstad, E.A., Laake, J.L., 

Strindberg, S., Hedley, S.L., Bishop, J.R.B., Marques, T.A., 

and Burnham, K.P., 2010, Distance software—Design and 

analysis of distance sampling surveys for estimating population size: Journal of Applied Ecology, v. 47, p. 5–14.
References Cited 35

Trenkel, V.M., Buckland, S.T., McLean, C., and Elston, 

D.A., 1997, Evaluation of aerial line transect methodology for estimating red deer (Cervus elaphus) abundance 

in Scotland: Journal of Environmental Management, v. 50, 

p. 39–50.

Unsworth, J.W., Leban, F.A., Leptich, D.J., Garton, E.O., 

and Zager, P., 1994, Aerial survey–User’s manual (2d ed.): 

Boise, Idaho, Idaho Department of Fish and Game, 84 p.

White, G.C., 1996, NOREMARK—Population estimation 

from mark-resighting surveys: Wildlife Society Bulletin, 

v. 24, p. 50–52. 

White, G.C., Bartmann, R.M., Carpenter, L.H., and Garrott, 

R.A., 1989, Evaluation of aerial line transects for estimating 

mule deer densities: Journal of Wildlife Management, v. 53, 

p. 625–635.

Wong, C., 1996, Population size estimation using the modified Horvitz-Thompson estimator with estimated sighting 

probabilities: Fort Collins, Colo., Colorado State University, 

Ph.D. Dissertation, 131 p. 

Zeigenfuss, L.C., Singer, F.J., D. Bowden, D., 1999, Vegetation responses to natural regulation of elk in Rocky 

Mountain National Park: Denver, Colo., U.S. Government Printing Office, Biological Science Report 

USGS/BRD/BSR–1999-0003, 23 p.

Publishing support provided by the Science Publishing Network, 

Denver Publishing Service Center

For more information concerning the research in this report, contact the

Center Director, USGS Fort Collins Science Center

2150 Centre Ave., Bldg. C

Fort Collins, CO 80526-8118

(970) 226-9398

Or visit the Fort Collins Science Center website at

https://www.fort.usgs.gov/
36 Development of an Aerial Population Survey Method for Elk in Rocky Mountain National Park, Colorado

Appendix 1. Description of Aerial Survey Methods Considered for Elk Surveys 

in Rocky Mountain National Park, Colorado

Radio (Known-Fates) Mark-Recapture Method

The mark-resight method using radio-marked animals is 

often considered the “gold standard” for population surveys 

(Seber, 1982; Bowden and Kufeld, 1995; White, 1996). The 

method is implemented by marking individual elk with radio 

collars. Surveys are then conducted by one group of observers, 

while another group independently locates each of the marked 

elk (or, more precisely, the groups containing these marked 

elk) utilizing radio telemetry, either from the ground or from 

the air. Subsequently, the two sets of locations are compared 

to determine which marked groups were seen and which were 

not seen by the aerial observers. These mark-resight data can 

then be analyzed in Program MARK using the known fates 

model structure. The major advantage of this approach is that 

sighting probabilities do not need to be homogeneous, because 

the marked groups have 100 percent sighting probability due 

to the radios. However, to meet model assumptions, the radios 

must be distributed randomly among all elk groups in the 

study area. In addition, to obtain precise estimates, either a 

large portion of the elk groups must be marked, or the survey 

must be conducted several times over a brief interval (short 

enough so that elk do not leave or enter the population over 

the course of the repeated surveys). This method requires that 

the radios be present and located each time a survey is done. 

The greatest obstacle to applying this method is the high 

cost and intrusiveness of placing radio collars on a sufficient 

sample of elk, especially given the requirement that they be 

randomly distributed across all elk present. 

Simultaneous Double-Observer Method

The simultaneous double-observer method is another form 

of the broader methodology of mark-resight survey (Seber, 

1982; Bowden and Kufeld, 1995; White, 1996). Specifically, 

the population is sampled simultaneously by two independent 

(typically aerial) observers and the numbers of elk seen by each 

observer and by both observers are used to estimate abundance 

(Cook and Jacobson, 1979; Seber, 1982; Pollock and Kendall, 

1987; Bayliss and Yeomans, 1989; Graham and Bell, 1989; 

Daigle and others, 1995; Manly and others, 1996). The sample 

is obtained by having two observers record sightings in such a 

way that sightings of the same individual elk or groups can be 

determined concurrently or post hoc. Group size, location, and 

observation time are typically sufficient to determine whether 

the same group was detected by both observers. This method 

can easily be combined with a sampling of count units within 

the total area to be surveyed. The assumptions underlying this 

method are (1) the two observers are completely independent—

observations by one cannot affect the other, (2) sighting 

probability varies only between the two observers and is not 

different for different animals or groups of animals, and (3) the 

population within a count unit remains relatively immobile during the duration of the survey so that animals neither leave nor 

enter the count unit or move so as to evade observation or be 

observed more than once. Advantages of this method include 

(1) no marked animals are needed and (2) a single survey can 

provide all of the data required for each population estimate. 

Sighting probability corrections are thus based on current 

observers and conditions. 

Distance Sampling Method

Line-transect, or distance sampling, methodology uses 

distances from a transect line to observed animals or groups 

to correct for visibility bias that varies with distance from 

the observer (Burnham and Anderson, 1976; Buckland and 

others, 1993; Anderson and Southwell, 1995). Hundreds of 

applications of this technique have been published that cover 

a wide range of vertebrate and invertebrate animal species, as 

well as plants and other inanimate objects, in both terrestrial 

and marine ecosystems. Sampling can use varied observation 

platforms and vehicles, including manned and unmanned, 

powered and self-propelled, aerial, land surface, water surface, 

and underwater. The largest number of applications pertain to 

marine mammals and small terrestrial vertebrates, especially 

birds and mammals. Examples involving large terrestrial 

mammals include Gogan and others (1986), White and others 

(1989), Johnson and others (1991), Southwell (1994), and 

Trenkel and others (1997).

Line-transect surveys use a random or systematic sample 

of lines located within the study area. These lines do not need 

to be straight and, in fact, are often placed to follow natural 

contours such as elevation or shorelines. Surveys are conducted by following the selected lines and observing animals 

on and near the line. When animals are spotted, distances to 

these animals are measured and recorded, along with group 

size and animal activity. In aerial surveys, this can be done by 

leaving the line and going to the location where the animal 

was first observed and recording the location with a global 

positioning system receiver and data recorder. Distance can 

also be estimated without leaving the transect line by measuring sighting angle, altitude, and location. Three critical 

assumptions underlie this technique: (1) the measured distance 

from the observed animal to the transect line is estimated 

accurately, which implies that the exact location of both the 
Appendix 1 37

observed animals and the transect line can be determined; 

(2) animals on or very near the line are sighted with certainty 

and those further from the line are sighted with smoothly 

decreasing probability; and (3) observed locations of animals 

are not systematically influenced by the approach of the survey team. In other words, detection occurs before any animal 

movement toward or away from the transect line. 

Distance sampling theory is based on sampling with 

replacement, which has several important consequences. A 

positive consequence is that there is no requirement that the 

entire survey area be observed; a random sample of distances 

is all that is required, so groups may be counted multiple 

times but other groups are never approached closely enough to 

have any chance of being seen. However, a downside of this 

method is that large sample sizes are typically required to gain 

the same precision provided by other methods. This method is 

often the most efficient when the population of interest is large 

and dispersed over vast areas. 

Sightability Bias Correction Method

The sightability bias correction method is a two-phase 

approach (Samuel and Pollock, 1981; Samuel and others, 

1987; Steinhorst and Samuel, 1989; Unsworth and others, 

1994; Bodie and others, 1995; Wong, 1996). During the first 

phase, a model of sighting probability as a function of various 

covariates is developed using surveys of known individuals or 

groups of animals. These can be animal groups under constant 

surveillance by ground observers or radio-marked groups. 

The model provides an estimate of the probability that a given 

animal or group is observed, given the covariates associated 

with each group. Typically, these covariates include group 

size, some measure of potentially concealing cover or habitat, 

weather and lighting conditions, and possibly observer location and experience. The model most often used is a logistic 

regression model of these covariates against the dichotomous 

variable, that is, seen versus not seen. Data for this model 

are obtained by observing (or failing to observe) a series of 

animals that are independently under observation by other 

observers. Once the model is developed, it is then applied to 

subsequent surveys to estimate population size by adjusting 

the number of observed animals to account for those that were 

unobserved. Survey areas can be subdivided into count units 

to facilitate counting, and these count units can be sampled to 

reduce survey effort, but at the cost of reduced precision. 

Sightability models have been developed primarily for 

large mammals. The critical assumptions of the method are 

(1) the conditions measured during the model calibration 

remain the same when the model is applied—in other words, 

the sighting probability function does not change over time, 

observers, or locations; (2) animal movement during the 

duration of the survey does not cause animals to systematically leave or enter count units in response to the observer or 

to be counted more than once; (3) an adequate sample size is 

obtained for model calibration; (4) the known groups under 

independent observation during calibration are a random 

sample of all groups in the study area; (5) a logistic model 

fits the data well; (6) sighting probabilities are relatively 

large (greater than 30 percent) under all conditions so that no 

animal groups have very low probability of being sighted; 

and (7) all covariates are measured accurately, especially the 

size of each group.

Hybrid Methods

The above methods can be used in several combinations 

to produce hybrid methods. The distinct advantage of this 

approach is that any limitations of a single method can often 

be largely overcome by combining it with a complementary 

second method. 

The theory to integrate the several techniques described 

above into a single methodology has been under development. 

This work was pioneered by Manly and others (1996) and 

Borchers and others (1998a, b) and is partially supported by 

software (Thomas and others, 2010). This method is a hybrid 

version of distance sampling that incorporates sighting covariates and a double-observer method. Under this approach, line 

transects are surveyed; however, covariates in addition to distance are recorded, and multiple observers are used to obtain 

independent simultaneous counts. Thus, in a single pass, a 

model that factors in sightability covariates and distance can 

be fitted and used to estimate population. In addition, this 

single dataset can be analyzed by several of the other methods 

by disregarding the supplemental data, so the hybrid method 

can be compared to the results of any of the single methods, 

all using the same dataset collected on a single survey.

The strength of this method is that multiple sources of 

data serve to offset the deficiencies inherent in each of the 

individual methods when used alone. For example, sightability 

bias correction models rely on a single calibration period and 

the implausible assumption that a fixed model is applicable 

in the future without further updating or ongoing validation. However, using a double-observer platform enables the 

calibration of the sightability model to be updated with new 

data from each survey. Another example of the complementary 

nature of the hybrid technique is the requirement in a simple 

double-observer survey for all groups to have similar sighting 

probabilities, which is never met in reality; some groups, due 

to their size or location, are inherently much more or less visible than others. However, use of sightability covariates helps 

to overcome these differences by modeling them explicitly; 

adding distance sampling can provide information to ameliorate this difficulty. Finally, the requirement in distance sampling that all groups be sighted on and near the transect line is 

not required when the probability of sighting within this first 

distance category can be estimated through double observer, 

sightability corrections, or both. 

A simpler hybrid technique combines only the simultaneous double-observer method with sighting covariates. This 

approach avoids the need to meet the stringent conditions for 

distance sampling. The heterogeneity problems of a simple 

double-observer method can be addressed with the sighting 
38 Development of an Aerial Population Survey Method for Elk in Rocky Mountain National Park, Colorado

covariates. The static nature of the sightability calibration 

method is overcome by the ongoing enhancement of the dataset with new sightability data from each survey. The theory 

for this approach is largely drawn from Huggins (1991). An 

extension of this approach can also incorporate radio-marked 

animals in addition to the simultaneous double-observer and 

sighting covariates. Incorporating this additional source of 

data helps to evaluate the effectiveness of the heterogeneity 

bias corrections by the sighting covariates and potentially 

provides the information to correct any residual bias. 
Appendix 2 39

Appendix 2. Discussion of Considerations for Aerial Work in 

Rocky Mountain National Park, Colorado

3. Elk behavior and habitat use

a. Few observations obtained per survey. Most elk 

in RMNP during winter cluster into a few very 

large groups. Typically only 10–12 elk groups are 

observed per flight, in which each elk group constitutes one data point. Consequently, it takes many 

surveys to obtain a sample size sufficient for rigorous model development.

b. Undercounting of bull elk. In a study of elk in tree 

cover, cow elk were more than nine times more 

likely than bulls to be seen in helicopter surveys 

(McCorquodale, 2001). Bull elk are more likely to 

be undercounted during aerial surveys because they 

are segregated from cow/calf groups in winter, tend 

to be in higher elevation habitat, stay in the trees 

when aircraft fly over, and are in smaller groups 

or alone. Our models attempt to correct for these 

differences by taking vegetation and group size into 

account in predicting sighting probability, but the 

models may not fully address disparate detection 

between the sexes. 

4. Logistics

a. Finding available vendors was a significant challenge to conducting aerial surveys, second only to 

wind. We had considerable difficulty finding qualified vendors. Personnel from Aviation Management 

Directorate informed us that there were almost no 

Lama helicopter models in the Federal fleet, and 

this specific helicopter is needed for high elevation 

flying in RMNP. Helicopter vendors are phasing out 

the Lama model due to difficulty in maintenance and 

finding parts, and it is being replaced by the A-Star. 

Although appropriate for high elevation rugged 

terrain, the A-Star has substantially decreased visibility with much smaller windows and solid/opaque 

surfaces (as opposed to clear) across the lower part 

of the aircraft. Finding fixed-wing vendors was also 

a challenge. Fixed-wing pilots typically had other, 

larger contracts with State agencies (for example, 

Colorado Parks and Wildlife or Wyoming Game and 

Fish Department) and these contracts were prioritized on good weather days and our project (which 

needed only 3–4 flights/year) received low priority. 

No replacement vendors were available within a reasonable distance. Aviation Management Directorate 

carding delays, as well as aircraft maintenance, also 

postponed flights.

For this study, we initially proposed to conduct surveys 

four times per winter over 2 years to accumulate sufficient 

data for fitting sightability models and to test methods, but 

more importantly, to observe and measure the patterns of 

elk population fluctuation in Rocky Mountain National Park 

(RMNP). It became clear that this would not be possible due 

to constraints on flight time from frequent high winds and 

poor visibility throughout the winter, with occasional 1-day 

windows of suitable flying weather. Suitable flight days were 

mostly timed directly after a large storm system had moved 

through the area the night before, and before winds usually 

picked up the next day (the survey day) by 1300–1400. In 

order to complete our surveys during this short window, there 

was a substantial “on-call” status all winter long required of 

research personnel (National Park Service resource management, National Park Service aviation safety team, observers 

from the U.S. Geological Survey, National Park Service, 

Colorado Parks and Wildlife, and others) and vendors (both 

fixed-wing and helicopter companies), which was not always 

feasible. Some cautions and considerations in conducting 

aerial missions in RMNP include:

1. Environmental factors

a. Wind and high elevation. Surveys were limited by 

high winds and severe winter conditions more than 

any other factor. The alpine tundra was the most difficult to access on most survey days. By early afternoon after we completed the core elk winter range, 

winds had usually picked up enough to preclude 

flying over the alpine tundra. We were able to survey 

the alpine tundra during only two of five surveys. 

b. Stormy conditions. Precipitation, and especially low 

cloud cover or cloud ceiling, prevented aerial activity, especially fixed-wing aircraft activity. On occasion, a storm moved in after the survey had started 

and we were forced to cancel the survey before it 

was completed.

c. High mountainous and rugged terrain. This required 

aircraft to climb and descend often, sometimes 

approaching safety boundaries. 

2. Sighting conditions

a. Difficult sighting conditions in low and patchy 

snow cover. Low heterogeneity in sighting conditions could not be matched to good flying conditions 

because contiguous snow cover and low wind rarely 

occur simultaneously.
40 Development of an Aerial Population Survey Method for Elk in Rocky Mountain National Park, Colorado

b. Helicopter pilots initially had difficulty following 

transect lines and underwent a steep learning curve 

during the study. Fixed-wing pilots could not always 

collect the needed covariates, such as group size, due 

to their flight altitude.

c. Scheduling a fixed-wing aircraft and pilot, an available Lama and pilot, a RMNP helicopter manager, 

and three observers usually from three different 

agencies, and obtaining a good-weather day to fly, 

required immeasurable patience and daunting efforts 

in coordination. To simultaneously select a day with 

good sighting conditions (that is, not patchy snow) 

proved nearly impossible. 
Appendix 3 41

Appendix 3. Instructional Protocols and Datasheets for 

Simultaneous Double-Observer Aerial Surveys in Rocky 

Mountain National Park, Colorado

Field Protocols for Simultaneous DoubleObserver Aerial Elk Surveys

The simultaneous double-observer method is a form of 

mark-resight abundance estimator in which the observations 

by the front seat observer are considered one independent 

survey (the “mark”), and the rear observer acts as a second 

independent survey (the “resight”). Therefore, no communication, visual or verbal, can occur between front and rear observers until after both observers have had adequate opportunity 

to detect independently each elk group. The front observer 

must wait until the elk group is completely aft of the aircraft 

to be sure the rear observer has an adequate chance to see the 

group before calling it out. If the pilot spots an elk group, the 

pilot can nonverbally identify it to the front observer, so that 

the rear observer(s) is not alerted. Usually a group is circled 

to obtain a better count or classification to age and sex. Once 

a group has been identified and the observers who saw it independently have recorded their observations, all crew members 

can participate in the count, record sighting covariates, and 

take digital photographs of the group for more careful recounting after the flight. The helicopter pilot gently pushes elk 

groups away from future transect lines to avoid recounting the 

same group. 

A “group” is considered to be one or more individual 

animals that are close enough together so that spotting any 

part of the group leads to locating the entire group. When a 

group is spotted, observers record (1) the size of the group, 

(2) the vegetation type and percent canopy cover as described 

by Unsworth and others (1994), (3) whether the group was 

moving or not when first spotted, (4) which observers in 

the aircraft saw the group and their positions in the aircraft, 

(5) where the elk group was located relative to the aircraft 

(right, left, or centerline), (6) the percent snow cover in the 

patch where the group was first observed, (7) the time of the 

observation, (8) the presence and number of radio-collared 

elk in the group, and (9) the global positioning system location. A photo is taken of groups of more than 10 individuals 

to confirm or adjust aerial counts. Datasheets for helicopter 

surveys and fixed-wing surveys are provided in this instructional protocol. Several observers can record data to compare, 

or the datasheet can be split among observers so one records 

sighting covariates, another records elk numbers and classifications, and the third observer obtains a waypoint for each elk 

group. The helicopter should fly predetermined transect lines 

developed for Rocky Mountain National Park in this study 

(see figs. 4 and 5) so observers can remain focused on searching for elk groups.

The flight forms used for data collection are presented 

below. The abbreviations used in the forms are: ROMO, 

Rocky Mountain National Park; AGL, above ground level; 

ft, foot; mph, mile per hour; km/hr, kilometer per hour; LF, 

left front; RF, right front; LR, left rear; RR, right rear; grp, 

group; no., number; hh, hour; mm, minute; GPS, global positioning system; wypt, waypoint; A/C, aircraft; obs, observers; veg, vegetation; L, left of transect; R, right of transect; 

C, centerline; B, both; A, active; N, not active; O, open; S, 

shrub; T, tree. 
Sample Datasheets

ROMO Aerial Elk Survey Information

Date of Survey: _____________________

Observer 1

Name________________________________ Agency______________________________

E-mail_________________________________ Telephone (______)_________________

Observer 2

Name________________________________ Agency______________________________

E-mail_________________________________ Telephone (______)_________________

Observer 3

Name________________________________ Agency______________________________

E-mail_________________________________ Telephone (______)_________________

Pilot

Name_____________________________________ Company__________________________

Office Address_________________________________________________________________

E-mail________________________________ Telephone (______)___________________

Aircraft

Type (helicopter/fixed wing)_______________________________________________

Planned altitude AGL____________ ft

Planned air speed ___________ statute mph / nautical mph / km/hr (circle one)

General comments: (conditions that might affect observer’s ability to spot elk or the number counted. 

Examples: general weather, lighting, and sky conditions; description of sun, clouds, shadows, visibility, 

turbulence during flight, gusty conditions, etc. Include lighting condition changes during survey if possible [“started cloudy, became sunny in early afternoon”]). _____________________________________

____________________________________________________________________________________

____________________________________________________________________________________

____________________________________________________________________________________

____________________________________________________________________________________

__________________________________________

42 Development of an Aerial Population Survey Method for Elk in Rocky Mountain National Park, Colorado
ROMO Aerial Elk Survey_HELICOPTER

(Start a new datasheet for each leg of flight; each time you takeoff)

Date: ______________ Page ____ of _____. Observer positions in aircraft (LF, RF, LR, RR; use initials): 

Survey segment start time:___________ Segment End time:____________.

Grp. No. Time hh:mm GPS Wypt Observed by: “X” who saw

Side of A/C 

(where grp first 

obs)

Total

Bulls

Spikes

Cows

Classification

Activity (Active/Not) Veg Class (Open/ Shrub/ Tree)

 percent Veg Cover

Snow percent Comments? Photo?(circle

Calves

No. Collars

L C R B A N O S T 

L C R B A N O S T L C R B A N O S T 

L C R B A N O S T 

L C R B A N O S T L C R B A N O S T L C R B A N O S T L C R B A N O S T L C R B A N O S T L C R B A N O S T 
Instructions for Helicopter Flight Form: 1. Use a new datasheet each time you start a new leg of the survey flight, so observer position is updated in the squares at the top, and it is 

refuel, for example. It’s important that observer position on each segment of the survey is clear. 2. All observers should search for horses or burros with equal effort (not one recording while others search). Ok to divide datasheet betwe

3. Use a reliable GPS unit to record each elk group location separately, and call out the waypoint to the other observers. The waypoint is t

that group. It will also have the timestamp for each group. Codes: Grp No. Sequential list of groups Time (hh:mm) This can be filled in later using GPS timestamp if desired. GPS Waypoint Get a waypoint for each group and call it out to the others to coordinate datasheets. A timestamp from the waypoint in the 

to get this after the flight – a timestamp on each group. Obs by: (Who Saw) X = in each seat position for who saw the elk grp on their own without assistance from other observers. If an observer another observer pointed it out, leave that seat position blank. See example below. Note: all observers should be looking (not one recording while others search). The idea of a mark-resight is that the front- and backseat observers detect each other, and either front or back observers (or both) are expected to miss some groups. If either misses the groubased on that miss. Also, backseat observers and frontseat observers are compared to estimate individual observers’ sighare used in the correction for animals missed. To estimate all observers’ sighting probabilities, back-seat observers must behind the front observer (that’s why you need to rotate seats). The front seat observer can remain the same through the 

Side of A/C Group location when first spotted. L = Left of transect; R = Right of transect; C = Centerline (right under aircraft, never v

B = both (this can be for large groups that span the transect and could be seen from both rear seats (even if they were nothat runs from one side to the other under aircraft and was available to the back-seat observers on both sides of the aircra

Classification Fill in total number of elk in a group, and number of each age class. Note number of radio collars if needed. The Data Rec

sus of total count, based on what observers see together. Guestimates can be made and then amended using photographs>10 individuals. Activity A=active, N=Not active (not moving) when observer first saw the elk group. Veg Class O = Open (grass, bare ground) S = Shrubs (not tall enough to hide an elk); T = Trees (tall enough to hide an elk). percent Veg Estimated percent shrub and/or tree canopy cover (within the patch) of the elk group; based on area including entire animal 

 percent Snow Estimated percent snow cover surrounding (within the patch) around the elk group; based on area including entire animal Comments Photo? Comments can include things such as: geographic area (“Cow creek”, or “just over the park boundary” e.g.), any violation 

“pilot shouted out group b4 we had a chance to see”). Take photos of groups >10 elk. To break up photo sequence and btween groups after the survey, take a photo of floor of aircraft in between groups .

Example: Front of aircraft

X ←Pilot seatX (In this example, the two left side observers both saw the group independently, 

while neither pilot nor back-right observer saw the group)
ROMO Aerial Elk Survey Data Sheet _FIXED WING

Date: ________________ Observer(s) and Position in Aircraft: _____________________________________________________ Pilot: _______________ Aircraft model:_____________________ Conditions (wind, snow, temp):_______________________________

Grp. Number Collar Frequency Time hh:mm

GPS Waypt 

No.

Total Count (small 

Groups only)

Activity 

(active/ 

not active) Veg Class

 percent 

Veg Cover 

 percent 

Snow 

Cover

C

1 : A N O S T2 : A N O S T3 : A N O S T4 : A N O S T5 : A N O S T6 : A N O S T7 : A N O S T8 : A N O S T9 : A N O S T

10 : A N O S T
Schoenecker and others—Development of an Aerial Population Survey Method for Elk in Rocky Mountain National Park, Colorado—OFR 2018–1085

ISSN 2331-1258 (online)

https://doi.org/10.3133/ofr20181085