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dissertation entitled

POPULATION ESTMATION AND FIXED KERNEL
ANALYSES OF ELK IN MICHIGAN

presented by

DANIEL PAUL WALSH

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Ph.D. degree in Fisheries and Wildlife

 

 

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POPULATION ESTIMATION AND FIXED KERNEL ANALYSES OF ELK IN
MICHIGAN

By

Daniel Paul Walsh

A DISSERTATION

Submitted to
Michigan State University
in partial ﬁilﬁllment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY
Department of Fisheries and Wildlife

2007

ABSTRACT

POPULATION ESTIMATION AND FIXED-KERNEL ANALYSES OF ELK IN
MICHIGAN

By

Daniel Paul Walsh

Michigan proudly boasts an elk herd heavily utilized by a wide array of
stakeholders from across the Midwest with varying recreational interests. Recently,
signiﬁcant changes have occurred within and surrounding the elk range, which have
created concern among elk managers that historical techniques and management
strategies may no longer be adequate to address the current issues facing Michigan’s elk.
This project was initiated and designed to gain valuable information and develop new
techniques that will provide elk managers with the knowledge and tools for successful
management of one of Michigan’s most unique natural resources. I developed a
population estimation procedure based on a sightability model framework using ﬁxed-
wing aircraft, which allowed for correction for Visibility bias associated with missing elk
groups. Incorporated into this technique was the ability to estimate group sizes, which
reduced bias of population estimates and resulted in near nominal conﬁdence interval
coverage. Using this technique I estimated the Michigan elk herd to be approximately
905 (SE = 125). I collected 13,923 locations using triangulation procedures, and 728
visual observations of 58 radiocollared elk. I estimated individual home ranges for each
animal using ﬁxed-kemel estimation procedures, and determined that mean bull home
range size (9,587 ha) was significantly larger than cow home range size (6,349 ha).

Additionally, kernel surfaces were averaged to allow for population level inference about

range use patterns. Analyses showed an uneven distribution of range use with many
peaks and valleys in the probability density surface. There was considerable joint space
use between elk from different summering areas based on dispersal patterns from capture
sites, movement data and by examining the joint density surfaces calculated from the
independent kernel density functions for each individual elk. Two large ranches in the
center of the elk range, Black River and Canada Creek, received substantial use by elk
throughout the year although use varied seasonally. Elk use within these ranches was
highly localized, and changed in response to habitat manipulations. Also, movement
patterns of bulls inhabiting Canada Creek Ranch indicated that these bulls are likely
breeding bulls from across the range. Using the averaged kernel density surface, I
demonstrated that management efforts focused on maintaining and enhancing wildlife
openings are having the desired effect as elk used managed openings with a signiﬁcantly
higher probability than unmanaged openings. The elk range unfortunately lies within the
endemic region for bovine tuberculosis (TB), which infects free-ranging deer in this area.
Using the averaged kernel density with historical TB prevalence data, I identiﬁed high-
risk areas for elk being exposed to TB. Three high-risk areas were delineated, and these
areas corresponded well with locations of known TB positive elk. Lastly, I examined the
range use patterns of a radiocollared cow that was infected with TB and her joint space
use with other elk in the region. Results showed that this elk had a home range of 8,856
ha, potentially exposing numerous other individuals and species to infection either
through direct or indirect contact. Elk population and management decisions must
account for the dynamic movement patterns that exist in this region of the elk range to

accommodate diverse recreational objectives.

ACKNOWLEDGEMENTS

This project was supported by the Federal Aid in Restoration Act under Pittman-
Robertson project W-147-R, Michigan Agricultural Experiment Station and through
generous contributions from the Rocky Mountain Elk Foundation and Safari Club
International. I sincerely extend my gratitude to all these organizations for their support.

I want to extend special thanks to each of my graduate committee members for
their contributions to this study as well as to my professional development. I especially
want to thank Dr. Connie Page for her assistance when I would hit a “brick wall” while
working out the variance equations for the population estimator. Without her I am not
sure I would have ever ﬁnished this dissertation. I want to thank Dr. Dean Beyer for his
logistical support, for providing an essential agency perspective, and for his amazing
ability to tackle elk. I extend my gratitude to Dr. Scott Winterstein for his ability to put
up with my “toug ” questions, and to ﬁnd the humor in every situation. Also I want to
thank Dr. Graham Hickling for providing insights into TB issues, which stimulated many
of the analyses with regard to elk and TB. Lastly, I want to thank my major professor Dr.
Rique Campa for his friendship, constant support and insights into elk in Michigan which
proved valuable at every step of this project, and for giving me this opportunity.

The success of this project is due in large part to the assistance I received from the
many technicians that worked with me on this study. I learned much from each person
with whom I worked. In particular, Amy Belson, Randy Havens, Greg Hochstetler, Mike
Budd, Katie McIntyre, Tanner Dixson, Leslie Witter, Mark Tessmer and Chris J eszke

were outstanding employees as well as friends. I owe them a deep debt of gratitude.

iv

The support for this project by the MDNR employees working in the elk range
was amazing. I want to recognize, Unit Supervisor, Glen Matthews for his support and
commitment to this project. Also Brian Mastenbrook, Elaine Carlson, Bill Green, Kevin
Jacobs, Keith Fisher, Mark Monroe and Carrie Steen provided critical knowledge and
assistance particularly during the development of the sightability model. I especially
want to thank the Atlanta ﬁeld crew for their help and more importantly their friendship.
I learned more than I can say about elk and wildlife management from Dave Smith, it
was truly a pleasure to have the opportunity to work with him. I will miss the stories and
laughs I shared with Joe Valentine, Bruce Baker and Joe Molnar. They will be some of
my fondest memories of working in the elk range. Lastly, there were numerous
volunteers on this project particular during the ﬂights, thank you all for your help.

I was also privileged to work with and count among my friends the other
members of the Ne Plus Ultra, Ali Felix and Dan Linden. I was truly blessed to have had
the opportunity to cross your paths on the walk of life, and what I have learned from
knowing you and the memories I have shared will not be forgotten.

I must recognize my friends, too numerous to mention, who have always been
there for me; I could never have made it without you all. Also I want to acknowledge my
brothers and sisters, Bill, Rose, Sam, Joe, Rachel, John, Mary and Theresa for always
being there for me, as well as the rest of my family.

Lastly, I am deeply indebted to my parents Bill and Dolores Walsh. Your
sacriﬁces have allowed me to realize my dreams, and all my past, present and future

successes are yours. Words cannot express my gratitude or how much I owe you.

 

 

TABLE OF CONTENTS

LIST OF TABLES ............................................................................................................ IX
LIST OF FIGURES ......................................................................................................... XII
CHAPTER 1: INTRODUCTION ....................................................................................... 1
History ..................................................................................................................... 1
Current Issues .......................................................................................................... 2
Objectives ............................................................................................................... 3
Outline ..................................................................................................................... 5
Study Area .............................................................................................................. 5
Capture Procedures ............................................................................................... 13
Capture Results, Mortalities, Current Status ......................................................... 15
CHAPTER 2: POPULATION ESTIMATION OF MICHIGAN ’S ELK
HERD ................................................................................................................................ 22
Introduction ........................................................................................................... 22
Study Area ............................................. 24
Methods ................................................................................................................. 25
Sightability Model Development—Detection Probability
Estimation ...................................................................................................... 25
Survey—Population Size Estimation .............................................................. 35
Sampling Simulations .................................................................................... 42
Cost ................................................................................................................ 43
Results ................................................................................................................... 43
Sightability Model Development—Estimating Detection
Probability Estimation ................................................................................... 43
Survey—Population Size Estimation .............................................................. 51
Sampling Simulations .................................................................................... 53
Cost ................................................................................................................ 62
Discussion ............................................................................................................. 62
Sightability Model Development—Detection Probability
Estimation ...................................................................................................... 62
Survey—Population Size Estimation .............................................................. 69
Sampling Simulations .................................................................................... 70
Costs .............................................................................................................. 72
Management Implications ..................................................................................... 73
Availability of Estimation Program ...................................................................... 73

CHAPTER 3: DERIVATION OF ELK POPULATION ESTIMATOR
ALLOWING FOR GROUP SIZE ESTIMATION ........................................................... 74

vi

 

Introduction ........................................................................................................... 74
Estimation of Group Sizes Using Multiple Independent Observer

Counts ................................................................................................................... 77
Estimation of the Approximate Variance of T ...................................................... 80
Performance of estimator ...................................................................................... 83
Conclusion ............................................................................................................ 85

CHAPTER 4: EXAMINATION OF ELK HOME RANGES AND

RANGE UTILIZATION .................................................................................................. 88
Introduction ........................................................................................................... 88

Study area .............................................................................................................. 90
Methods ................................................................................................................. 91
Capture ........................................................................................................... 91

Elk Locations ................................................................................................. 91

Analysis ......................................................................................................... 93

Results ................................................................................................................. 1 06
Capture ......................................................................................................... 106

Elk Locations ............................................................................................... 106

Analysis ....................................................................................................... 108

Discussion ........................................................................................................... 173
Management Implications ................................................................................... 183
Conclusion .......................................................................................................... l 85
CHAPTER 5: ELK AND BOVINE TUBERCULOSIS IN MICHIGAN ...................... 186
Introduction ......................................................................................................... 1 86

Study area ............................................................................................................ 190
Methods ............................................................................................................... 191

TB Prevalence in Deer ................................................................................. 191

Elk Range Use ............................................................................................. 192

Identifying High Risk Areas ........................................................................ 194
Examination of Range Use of a TB Positive Elk ........................................ 195

Results ................................................................................................................. 198
Discussion ........................................................................................................... 209
Management Implications ................................................................................... 212
Conclusion .......................................................................................................... 21 3
APPENDIX A ................................................................................................................. 215
APPENDIX B ................................................................................................................. 218
APPENDIX C ................................................................................................................. 224
APPENDIX D ................................................................................................................. 228

vii

LITERATURE CITED ................................................................................................... 231

viii

Table 1.

Table 2.

Table 3.

Table 4.

Table 5.

Table 6.

Table 7.

Table 8.

Table 9.

LIST OF TABLES

Capture record, age, mortalities, and current status (January 2007) of
radiocollared elk in Michigan, 2003—2006. .............................................. 19

Number of elk groups classiﬁed as seen and unseen during aerial ﬂights
for each level of the following class variables: conifer cover“,
behaviorb, light class° and snow conditionsd for elk in Michigan
during the winters of 2004 and 2005. Percentage of groups for a
given response within each level of the class variables is shown in
parentheses. ............................................................................................... 45

Top 10 elk sightability models, AICc values, A AICc values, relative
model likelihoods (RML) and associated Akaike weights (AW) in
Michigan, 2004 and 2005. ........................................................................ 46

Model averaged parameter estimates of group sizea, wind speed,
behaviorb, percent conifer coverc, snow conditionsd and light class'3
for my formulation which estimates group size (GS) and the
Samuel et al. (1987) sightability model (SF) constructed for elk in
Michigan during winters of 2004—2005. Unconditional standard
errors of estimates are presented in parentheses. ...................................... 47

Relative likelihood values for independent variables used in GS and SF
sightability model calculations for elk in Michigan during winters
of 2004—2005. ........................................................................................... 48

Covariance matrix for model averaged beta parameter estimates of
group sizea, wind speed, behaviorb, percent conifer coverc, snow
conditions”1 and light classe calculated using the sightability model,
which allows for estimates of group size (GS). ........................................ 49

Covariance matrix for model averaged beta parameter estimates of
group size“, wind speed, behaviorb, percent conifer coverc, snow
conditionsd and light classe calculated using the sightability model,
which allows for estimates of group size (SF). ......................................... 50

Accuracy assessment of assignment of quadrats to low (0—15 elk),
medium (16—30 elk) and high (31+ elk) density strata in Michigan,
2006 ........................................................................................................... 54

The sample size of quadrats surveyed, the average variance of 1,000 elk
population estimates generated using the optimal number of
samples from each density strata, and the optimal number of
quadrats sampled from each density stratum based on the elk
survey in Michigan, 2006. ........................................................................ 63

ix

Table 10. Costs associated with conducting the elk survey of the entire range in
northern Michigan, 2006 ........................................................................... 65

Table 11. Projected costs for conducting the historical elk survey procedure using
a helicopter in northern Michigan, 2006. .................................................. 66

Table 12. Projected costs for conducting the historical elk survey procedure using
a ﬁxed-wing aircraft in northern Michigan, 2006 ..................................... 67

Table 13. Top 5 values of or that minimized MSE values of method-of-moments
estimates of N across all values of N (1—50) and p (0.50—0.99) ............... 79

Table 14. Average of performance measures for the population estimator that
includes estimates of group size (GS) and for the traditional
sightability model estimator (SF) based on Monte-Carlo
simulations with 20,000 repetitions for each population size from
Michigan elk survey data (2006). ............................................................. 86

Table 15. Estimates of home range size (ha) at the 95% and 50% probability
contour, associated 95% conﬁdence limits (LCL, UCL), number of

locations used in kernel density estimation (n) for radiocollared elk
in Michigan, 2003—2005. ........................................................................ 111

Table 16. Estimates of mean annual home range size (ha) at the 95% probability
contour, associated 95% conﬁdence limits (LCL, UCL), number of
elk (n) for radiocollared elk in Michigan, 2003—2005. ........................... 114

Table 17. Estimates of mean annual home range size (ha) at the 50% probability
contour, associated 95% conﬁdence limits (LCL, UCL), number of
elk (n) for radiocollared elk in Michigan, 2003—2005. ........................... 115

Table 18. Matrix of Mann-Whitney test statistics and associated P—values for sex
and year comparisons of mean annual home range size (ha) at the
95% probability contour, for radiocollared elk in Michigan, 2003—
2005 ......................................................................................................... 116

Table 19. Matrix of Mann-Whitney test statistics and associated P—values for sex
and year comparisons of mean annual home range size (ha) at the
50% probability contour, for radiocollared elk in Michigan, 2003—
2005 ......................................................................................................... l l 7

Table 20. Estimates of bull annual home range size (ha) at the 95% probability
contour, associated conﬁdence limit (LCL, UCL), and number of
locations used to generate kernel density estimates (n), for
radiocollared elk in Michigan, 2003—2005. ............................................ 118

Table 21. Estimates of cow annual home range size (ha) at the 95% probability
contour, associated conﬁdence limit (LCL, UCL), and number of

locations used to generate kernel density estimates (n), for
radiocollared elk in Michigan, 2003—2005. ............................................ 119

Table 22. Estimates of bull annual home range size (ha) at the 50% probability
contour, associated conﬁdence limit (LCL, UCL), and number of
locations used to generate kernel density estimates (n), for
radiocollared elk in Michigan, 2003—2005. ............................................ 120

Table 23. Estimates of cow annual home range size (ha) at the 50% probability
contour, associated conﬁdence limit (LCL, UCL), and number of
locations used to generate kernel density estimates (n), for
radiocollared elk in Michigan, 2003—2005. ............................................ 121

Table 24. Probability of elk use of various cover types and associated standard
errors (SE), coefﬁcients of variation (CV), and standard normal
95% conﬁdence limits (LCL, UCL) in Michigan, 2003—2005 ............... 172

xi

LIST OF FIGURES

Figure 1. The areas of range expansion outside the historical elk range in
Michigan, 2002 (adopted from D.E. Beyer, Michigan Department
of Natural Resources, unpublished report). ................................................ 4

Figure 2. General location of Michigan elk range in Michigan, 2003 ............................... 6

Figure 3. General location of the study area (cross-hatched area) within the elk
range in Michigan, 2006. ............................................................................ 7

Figure 4. Mean monthly temperature (° C) for the study area recorded at the
National Oceanic and Atmospheric Administration weather station
at Alpena Regional Airport, 2006. .............................................................. 9

Figure 5. Differences in mean monthly temperature (° C) from long-term
averages for the study area recorded at the National Oceanic and
Atmospheric Administration weather station at Alpena Regional
Airport, 2006 ............................................................................................. 10

Figure 6. Monthly precipitation totals (cm) for the study area recorded at the
National Oceanic and Atmospheric Administration weather station
at Alpena Regional Airport, 2006. ............................................................ 11

Figure 7. Differences in precipitation totals (cm) from long-term averages for the
study area recorded at the National Oceanic and Atmospheric
Administration weather station at Alpena Regional Airport, 2006. ......... 12

Figure 8. Location of elk captured from the western portion of the study area
(unﬁlled circles represent 2003 capture locations, cross-hatched
circles represent 2004 capture locations, and circles ﬁlled with
lines represent 2005 captures) in Michigan, 2003—2005. ......................... 17

Figure 9. Location of elk captured from the eastern portion of the study area
(unﬁlled circles represent 2003 capture locations and circles ﬁlled
with lines represent 2005 captures) in Michigan, 2003—2005. ................ 18

Figure 10. Region that contains the greatest extent of movement of radiocollared
elk, and the locations of quadrats used in the sightability model
development in Michigan, 2004—2005. .................................................... 28

Figure 11. The location of 0.40 km ﬂight lines in quadrats used to develop an elk
sightability model for Michigan, 2004—2005 ............................................ 29

Figure 12. Location of quadrats of and expected elk densities of quadrats (dark
gray—high elk density, light gray—medium elk density, white—low
elk density) used during the elk survey in Michigan, 2006
(identifying labels are along the margins). ............................................... 36

xii

Figure 13. Location and relative size of elk groups observed during aerial survey
in late winter in Michigan, 2006 (identifying labels are along the
margins). ................................................................................................... 5 2

Figure 14. Location of quadrats correctly (white) and incorrectly (gray) assigned
to expected elk density strata in Michigan, 2006(identifying labels
are along the margins) ............................................................................... 55

Figure 15. Effects on average variance of the population estimate of varying the
sampling rate in the high (31+ elk) elk density and the medium
(16—30 elk) density strata with a low density stratum (1-15 elk)
sampling rate of 50%. ............................................................................... 56

Figure 16. Effects on average variance of the population estimate of varying the
sampling rate in the high (31+ elk) elk density and the medium
(16—30 elk) density strata with a low density stratum (1-15 elk)
sampling rate of 60%. ............................................................................... 57

Figure 17. Effects on average variance of the population estimate of varying the
sampling rate in the high (31+ elk) elk density and the medium
(16—30 elk) density strata with a low density stratum (1-15 elk)
sampling rate of 70%. ............................................................................... 58

Figure 18. Effects on average variance of the population estimate of varying the
sampling rate in the high (31+ elk) elk density and the medium
(16—30 elk) density strata with a low density stratum (1-15 elk)
sampling rate of 80%. ............................................................................... 59

Figure 19. Effects on average variance of the population estimate of varying the
sampling rate in the high (31+ elk) elk density and the medium
(16—30 elk) density strata with a low density stratum (1-15 elk)
sampling rate of 90%. ............................................................................... 60

Figure 20. Effects on average variance of the population estimate of varying the
sampling rate in the high (31+ elk) elk density and the medium
(16—30 elk) density strata with a low density stratum (1-15 elk)
sampling rate of 100%. ............................................................................. 61

Figure 21. The distribution of acquisition times of triangulated locations for
radiocollared elk in Michigan, 2003—2006. ............................................ 107

Figure 22. The distribution of acquisition times of GPS ﬁxes for radiocollared elk
in Michigan, 2003—2006. ........................................................................ 109

Figure 23. Kernel density estimate surface and associated 95% conﬁdence

surfaces (a), and intensity map of kernel density estimates (b) of
elk #12’s home range in Michigan, 2003—2005 ...................................... 113

xiii

Figure 24.

Figure 25.

Figure 26.

Figure 27.

Figure 28.

Figure 29.

Figure 30.

Figure 31.

Figure 32.

Figure 33.

Figure 34.

Figure 35.

Figure 36.

Figure 37.

Averaged kernel density estimates of space use for 58 elk in Michigan,
2003—2005. ............................................................................................. 123

Estimates of standard error associated with averaged kernel density
estimates of space use for 58 elk in Michigan, 2003—2005. ................... 124

Averaged kernel density estimates of annual space use for 36 elk in
Michigan, 2003. ...................................................................................... 125

Estimates of standard error associated with averaged kernel density
estimates of space use for 36 elk in Michigan, 2003. ............................. 126

Averaged kernel density estimates of annual space use for 36 elk in
Michigan, 2004. ...................................................................................... 127

Estimates of standard error associated with averaged kernel density
estimates of space use for 36 elk in Michigan, 2004. ............................. 128

Averaged kernel density estimates of annual space use for 30 elk in
Michigan, 2005. .............. ' ........................................................................ l 29

Estimates of standard error associated with averaged kernel density
estimates of annual space use for 30 elk in Michigan, 2005. ................. 130

Summering areas and general interchange patterns between areas for
radiocollared elk in Michigan, 2003—2005 (arrows represent
movement of at least 1 radiocollared elk). .............................................. 132

Joint density kernel surface depicting areas of joint space use between
7 radiocollared elk from the Black River summering area and 7 elk
from the Camp 30 Hills summering area in Michigan, 2003—2005. ...... 133

Joint density kernel surface depicting areas of joint space use between
7 radiocollared elk from the Black River summering area and 9 elk
from the Canada Creek summering area in Michigan, 2003—2005. ....... 134

Joint density kernel surface depicting areas of joint space use between
7 radiocollared elk from the Black River summering area and 5 elk
from the Osmun summering area in Michigan, 2003—2005. .................. 135

Joint density kernel surface depicting areas of joint space use between
7 radiocollared elk from the Black River summering area and 5 elk
from the Tin Shanty summering area in Michigan, 2003—2005. ............ 137

Joint density kernel surface depicting areas of joint space use between
7 radiocollared elk from the Camp 30 Hills summering area and 9
elk from the Canada Creek summering area in Michigan,
2003—2005. ............................................................................................. 13 8

xiv

Figure 38.

Figure 39.

Figure 40.

Figure 41.

Figure 42.

Figure 43.

Figure 44.

Figure 45.

Figure 46.

Figure 47.

Figure 48.

Joint density kernel surface depicting areas of joint space use between
7 radiocollared elk from the Camp 30 Hills summering area and 5
elk from the Osmun summering area in Michigan, 2003—2005. ......

Joint density kernel surface depicting areas of joint space use between
7 radiocollared elk from the Camp 30 Hills summering area and 5
elk from the Tin Shanty summering area in Michigan, 2003—2005.

Joint density kernel surface depicting areas of joint space use between
9 radiocollared elk from the Canada Creek summering area and 6
elk from the Meaford summering area in Michigan, 2003—2005.

Joint density kernel surface depicting areas of joint space use between
9 radiocollared elk from the Canada Creek summering area and 5
elk from the Osmun summering area in Michigan, 2003—2005. ......

Joint density kernel surface depicting areas of joint space use between
9 radiocollared elk from the Canada Creek summering area and 4

elk from the Voyer Lake summering area in Michigan, 2003—2005.

Joint density kernel surface depicting areas of joint space use between
6 radiocollared elk from the Meaford summering area and 6 elk
from the M-32 South summering area in Michigan, 2003—2005.

Joint density kernel surface depicting areas of j oint space use between
6 radiocollared elk from the Meaford summering area and 4 elk
from the Voyer Lake summering area in Michigan, 2003—2005 ......

Joint density kernel surface depicting areas of joint space use between
6 radiocollared elk from the M-32 South summering area and 4 elk
from the Vienna summering area in Michigan, 2003—2005. ............

Joint density kernel surface depicting areas of joint space use between
4 radiocollared elk from the Voyer Lake summering area and 5 elk
from the Bone Yard summering area in Michigan, 2003—2005. ......

Joint density kernel surface depicting areas of joint space use between
4 radiocollared elk from the Voyer Lake summering area and 6 elk
from the M-32 South summering area in Michigan, 2003—2005.

General movements of at least 1 radiomarked elk away from winter
capture sites (unﬁlled circles represent 2003 capture sites, cross-
hatched circles represent 2004 capture sites, and line-ﬁlled circles
represent 2005 capture sites, and size of circles represent the
relative number of elk captured) in Michigan, 2003—2005. .............

XV

...... 139

...... 140

...... 141

...... 142

..... 143

...... 144

...... 145

...... 146

...... 147

...... 149

...... 150

Figure 49.

Figure 50.

Figure 51.

Figure 52.

Figure 53.

Figure 54.

Figure 55.

Figure 56.

Figure 57.

Figure 5 8.

Figure 59.

Figure 60.

Figure 61.

Figure 62.

Figure 63.

General movements of radiomarked bulls from Canada Creek Ranch
during the rut (August—November) in Michigan, 2003. ......................... 151

General movements of radiomarked bulls from Canada Creek Ranch
during the rut (August-November) in Michigan, 2004. ......................... 152

General movements of radiomarked bulls from Canada Creek Ranch
during the rut (August—November) in Michigan, 2005. ......................... 153

Kernel density map of radiomarked elk use of Black River Ranch
based on 1,443 locations in Michigan, 2003—2005. ............................... 154

Kernel density map of radiomarked elk use of Black River Ranch
based on 503 locations in Michigan, 2003 .............................................. 155

Kernel density map of radiomarked elk use of Black River Ranch
based on 381 locations in Michigan, 2004 .............................................. 156

Kernel density map of radiomarked elk use of Black River Ranch
based on 559 locations in Michigan, 2005 .............................................. 157

Kernel density map of radiomarked elk use of Canada Creek Ranch
based on 1,957 locations in Michigan, 2003—2005. ............................... 159

Kernel density map of radiomarked elk use of Canada Creek Ranch
based on 477 locations in Michigan, 2003 .............................................. 160

Kernel density map of radiomarked elk use of Canada Creek Ranch
based on 805 locations in Michigan, 2004 .............................................. 161

Kernel density map of radiomarked elk use of Canada Creek Ranch
based on 675 locations in Michigan, 2005 .............................................. 162

The number of locations of radiomarked elk (n = 40 in 2003, n = 39 in
2004, and n = 39 in 2005) occurring within the boundaries of
Black River Ranch in Michigan, 2003—2005. ........................................ 163

The number of locations of radiomarked elk (n = 20 bulls and n = 20
cows in 2003) by sex occurring within the boundaries of Black
River Ranch in Michigan, 2003. ............................................................. 164

The number of locations of radiomarked elk (n = 18 bulls and n = 20
cows in 2004) by sex occurring within the boundaries of Black
River Ranch in Michigan, 2004. ............................................................. 165

The number of locations of radiomarked elk (n = 16 bulls and n = 23

cows in 2005) by sex occurring within the boundaries of Black
River Ranch in Michigan, 2005. ............................................................. 166

xvi

Figure 64.

Figure 65.

Figure 66.

Figure 67.

Figure 68.

Figure 69.

Figure 70.

Figure 71.

Figure 72.

Figure 73.

Figure 74.

Figure 75.

The number of locations of radiomarked elk (n = 40 in 2003, n = 39 in
2004, and n = 39 in 2005) occurring within the boundaries of
Canada Creek Ranch in Michigan, 2003—2005. ..................................... 167

The number of locations of radiomarked elk (n = 20 bulls and n = 20
cows in 2003) by sex occurring within the boundaries of Canada
Creek Ranch in Michigan, 2003. ............................................................ 169

The number of locations of radiomarked elk (n = 18 bulls and n = 20
cows in 2004) by sex occurring within the boundaries of Canada
Creek Ranch in Michigan, 2004. ............................................................ 170

The number of locations of radiomarked elk (n = 16 bulls and n = 23
cows in 2005) by sex occurring within the boundaries of Canada
Creek Ranch in Michigan, 2005. ............................................................ 171

Averaged kernel density surface of elk use for 58 radiocollared elk
overlaid with the kriging prediction surface of apparent TB
prevalence of white-tailed deer in Michigan, 1999—2005. ..................... 199

Areas of high-risk of TB transmission based on elk usage and apparent
TB prevalence rates in white-tailed deer in Michigan, 1999—2005,
and locations of harvest/collection of known TB positive elk
(crosses). ................................................................................................. 200

Averaged kernel density surface of elk use for 58 radiocollared elk
overlaid with the kriging prediction surface of apparent TB
prevalence of white-tailed deer in Michigan, 2003—2005. ..................... 201

Areas of high-risk of TB transmission based on elk usage and apparent
TB prevalence rates in white-tailed deer in Michigan, 2003—2005,
and locations of harvest/collection of known TB positive elk
(crosses). ................................................................................................. 202

Locations and movement patterns of a radiocollared TB-positive adult
cow elk in Michigan, 2003 ...................................................................... 203

Kernel density surface estimating the home range of a radiocollared,
TB-positive cow elk (elk #32) based on 121 locations in Michigan,
2003 ......................................................................................................... 205

Average kernel density surface estimating probability of use of 15
radiocollared elk utilizing the eastern portion of the study area in
Michigan, 2003. ...................................................................................... 206

The standard error surface for the average kernel density surface
estimating probability of use of 15 radiocollared elk utilizing the
eastern portion of the study area in Michigan, 2003 ............................... 207

xvii

Figure 76. Joint kernel density surface estimating the joint space use of a
radiocollared, TB-positive cow elk (elk #32), and the 15 other
radiocollared elk utilizing this portion of the elk range in
Michigan, 2003. ...................................................................................... 208

xviii

CHAPTER 1: INTRODUCTION
History

An extinct subspecies of elk (Cervus elaphus‘canadensis) once roamed the Lower
Peninsula of Michigan, however, by the late 1800’s the species was believed to be
extirpated from the state (0’ Gara and Dundas 2002). During the early 20‘h century, the
state of Michigan initiated a series of reintroduction activities aimed at reestablishing the
species in the northeastern region of the Lower Peninsula. It is generally believed among
biologists that the entire Michigan elk herd arose from a 1918 reintroduction of 7 Rocky
Mountain elk (Cervus elaphus nelsom') southeast of Wolverine in Nunda Township of
Cheboygan County (Moran 1973). But, based on historic and genetic evidence presented
by Glenn and Smith (1993), it appears that the herd originated from multiple source
populations with some evidence of founding individuals being Roosevelt elk (Cervus
elaphus roosevelti). Thus, to explain the variability observed in the genetic data, it is
likely that reintroductions other then the 1918 reintroduction were also successful, and/or
private individuals were also releasing elk.

Despite the uncertainty of the origin of Michigan’s elk herd, the population grew
substantially until by 1964 the herd was estimated at over 2,000 elk (Moran 1973). With
a population of this magnitude, tourism based on elk viewing became popular. However,
increasing elk damage to forests, wildlife range and agricultural crops created conﬂicts
that intensiﬁed throughout the 1960’s. To address these conﬂicts, the Michigan
Department of Natural Resources (MDNR) instituted hunts in 1964—1965. During these

years, 477 elk were taken legally (Moran 1973). In the following years the elk herd

decreased substantially. By 1975, when the MDNR conducted a combined aerial-
snowmobile survey, they estimated only 200 animals comprised the entire herd (Beyer
1989). The serious decline was attributed to widespread poaching, lack of habitat
management and human disturbances (Ruhl 1984). To combat these low population
levels the MDNR developed the elk management plan, which focused on increasing the
elk herd to 500—600 individuals through reduction of poaching activities and increased
elk habitat management. By 1984, the population was estimated at 850 individuals, and
conﬂicts similar to those observed in the 1960’s were once again emerging. In response
to these issues, the state began controlled hunting of the elk herd in 1984 (Beyer 1987).
The same year, the MDNR formalized its elk management plan with the following
objectives (Michigan Department of Natural Resources 1984: 24—25):

1. “Maintain a visible herd of 600—800 elk for public viewing.

2. When the elk herd reaches an optimal population level (easily viewable
with minimal damage to agriculture and range), utilize a portion of the
annual production through a controlled annual hunt.

3. Protect elk habitat.

4. Protect elk from illegal kill.”

The elk plan had the desired effects, as the elk population has remained generally above
800 animals. Elk viewing remains a popular tourist attraction, and crop and forest

damage complaints are minimal.

Current Issues
In recent years, there has been a noticeable change in the distribution of elk throughout

their range. The historical elk range encompasses an area of approximately 1550 km2

centered on the Pigeon River State Forest. Recently, there has been a noticeable range
expansion in the southerly and easterly directions (Figure 1), and it has been estimated
the range has expanded by approximately over 5 0% from where it had occurred in 1984
(D. E. Beyer, Michigan Department of Natural Resources, unpublished report). These
range expansions are not entirely understood. However, it is likely that the 1998 ban on
baiting and winter feeding of elk and white-tailed deer (Odocoz'leus virginianus), intended
to minimize the transmission and spread of bovine tuberculosis (TB), is a major causative
factor contributing to this expansion. This expansion created concern among elk
managers and researchers that current management activities are no longer adequate, as
elk are distributing themselves away from areas dominated by public lands to regions
with a greater amount of private lands and agricultural activities. Also the easterly range
expansion shifts elk into regions with higher TB prevalence in the white-tailed deer herd,
creating concerns of increased TB transmission from deer to elk (Hickling 2002). Thus,
understanding how elk in Michigan are currently utilizing the range is crucial from a
management perspective.

' Additionally, elk researchers and managers were concerned the current population
estimation procedure, since it does not account for these changes in elk range utilization

patterns, it is no longer adequate for management purposes.

Objectives
The objectives of this study were focused on addressing the current issues facing elk
managers as described above. The objectives were as follows:
1. Document elk movement patterns and range use throughout both the historical

range as well as areas of range expansion.

 

 

V
1984 Core Elk Range I \\

/ I

,/

 

 

 

 

10 0 10 20 I 30 Kilometers 7 i

55:— - -—"

 

 

Figure 1. The areas of range expansion outside the historical elk range in Michigan, 2002
(adopted from D.E. Beyer, Michigan Department of Natural Resources, unpublished
report).

 

2. Develop a population estimation procedure that will produce accurate and precise
estimates while accounting for shifting elk distributions.
3. Determine areas of the elk range that exhibit a high level of elk usage as well as a

high TB prevalence in the deer herd for targeted management efforts.

Outline
The results of this study are presented in 4 separate chapters. Chapter 2 details the new
population estimation technique. The third chapter provides the derivation of the
estimator used in Chapter 2. The fourth chapter details movement patterns, individual
home range analyses and examines use of managed openings by elk, and the ﬁnal chapter
examines elk range utilization with respect to TB prevalence. A general study area

description and description of capture procedures precede these chapters.

Study Area
The elk range in Michigan encompasses portions of 4 counties, Cheboygan,
Montmorency, Otsego and Presque Isle, in the northeastern comer of the Lower
Peninsula of Michigan (Figure 2). The historic or core elk range occupies approximately
1,550 kmz, and is centered on the Pigeon River State Forest near Vanderbilt, Michigan
(Bender 1992). The entire elk range accounting for areas of recent range expansion
encompasses approximately 3,450 km2 (D.E. Beyer, Michigan Department of Natural
Resources, unpublished report). This study focused mainly on the eastern region of the
elk range near Atlanta in Montrnorency County (Figure 3). Over 33% of the elk range is
publicly owned, with another 3% controlled by 2 large private hunting clubs in the center

of the range (Michigan Department of Natural Resources 2000).

 

 

INDIAN
RIVER

  

VANDERBILT

 
    
 

       

 

 

 

 

Figure 2. General location of Michigan elk range in Michigan, 2003.

 

 

 

 

 

 

 

 

 

 

Topography of the area slopes northerly and consists of ﬂat-topped ridges

interspersed with headwater swamps and outwash plains created through glacial actions
(Moran 1973). Originating in these headwater swamps are the Black, Pigeon and
Sturgeon rivers, which drain the study area (Ruhl 1984). Podzol soils characterize the
region, and range from relatively infertile, dry sandy soils on outwash plains to medium
high fertility soils on till plains and moraines (Moran 1973).

Climatic conditions are less affected by the Great Lakes than other regions in the
state with most noticeable effects being increased cloudiness, moderation of fall and early
winter temperatures and prevalence of westerly winds (Ruhl 1984). Mean annual
temperature is 6.3° C with January having the lowest mean monthly temperature (—7.70
C) and the highest (19.7° C) occurring in July (NCAA 2006). The maximum mean
monthly temperatures during the study (2003—2006) was 20.4° C in July 2005, and the
minimum mean monthly temperature was -10.8° C in January 2004 (Figure 4). With the
exception of 2003, generally mean monthly temperatures were above the long-term
average for the study years (Figure 5). Mean annual rainfall is 67.3 cm, and mean annual
snowfall is 189 cm (NOAA 2006) with precipitation being generally well distributed
throughout the year. The maximum monthly precipitation total, 12.52 cm, occurred in
August 2005, and the minimum monthly precipitation total, 0.48 cm, occurred in January
2003 (Figure 6). Mean monthly precipitation totals throughout the study were generally
below the long-term average (Figure 7).

Due to variations in soil fertility, aspect and moisture levels, vegetation types are
diverse and well interspersed. In addition logging, agriculture, and management

activities further complicate the pattern of vegetation types throughout the area. Moran

 

25.0

 

 

 

 

 

 

 

 

 

6‘
a, 200+ —~
0
g 15.0—
‘3‘. 10.0 J +2003
g ~a~2004
E... 5.0—
% +2005
g 0-0‘ * ” ” +2006
5 -5.0—
E -100 ~1
E
'15.0 V I I F I I I 7 I I I
123456789101112
Month

 

 

 

Figure 4. Mean monthly temperature (° C) for the study area recorded at the National
Oceanic and Atmospheric Administration weather station at Alpena Regional Airport,
2006.

 

 

 

 

 

 

G
8; + 2003
E —-I-— 2004
a
{a + 2005
g ——x—— 2006
H

 

 

 

 

123456789101112
Month

 

 

 

Figure 5. Differences in mean monthly temperature (° C) from long-term averages for the
study area recorded at the National Oceanic and Atmospheric Administration weather
station at Alpena Regional Airport, 2006.

10

 

 

 

 

 

 

 

 

E
3 ——-~-— 2004
i + 2005
33 —x— 2006
9..

 

 

 

 

123456789101112
Month

 

 

 

Figure 6. Monthly precipitation totals (cm) for the study area recorded at the National
Oceanic and Atmospheric Administration weather station at Alpena Regional Airport,
2006.

ll

 

 

 

 

 

 

 

 

 

 

 

6 .n- L L _ v 7 v 7 _ F _ __ _ __

E
.3 +2004
:33 +2005
§ +2006
Du

-6 I" —_ _ _ _ _ _ ~ — #_#_—_ ~e

-8 T I I I I I I f j I I

1 2 3 4 5 6 7 8 9 10 11 12

Month

 

 

 

Figure 7. Differences in precipitation totals (cm) from long-term averages for the study

area recorded at the National Oceanic and Atmospheric Administration weather station at
Alpena Regional Airport, 2006.

12

(1973) gives a detailed description of the vegetation of the region. Typical vegetation
found on moraine uplands consist of sugar maple (Acer saccharum), red pine (Pinus
resinosa), white pine (Pinus strobus), hemlock (T suga canadensis), basswood (Tilia
americana), red maple (Acer rubrum), and northern red oak (Quercus borealis). Aspen
(Populus tremuloides), red oak, red pine and white pine are found on steep morainic
slopes. Red maple, white birch (Betula papyrifera) and aspen characterize the outwash
plain-morainic ecotone. Sandy outwash plains are typiﬁed by jack pine (Pinus
banksiana), cherry (Prunus spp.) and willow (Salix spp.). Riverbanks and bottomlands
support ash (F raxinus spp.), speckled alder (Alnus rugosa), dogwoods (Cornus spp.),
white cedar (Thuja occidentalis) and red elm (Ulmusﬁrlva). Coniferous swamps
typically contain white cedar, balsam ﬁr (Abies balsamea), black spruce (Picea mariana)
and balsam poplar (Populus balsamifera). These typical forest cover types are found

throughout the study area in varying age classes and stocking rates.

Capture Procedures

Capturing and radiocollaring elk was critical to achieving all the objectives for this
project. All capture operations were planned and conducted by MDNR and contractors,
and therefore, this project was exempted by the All University Committee on Animal Use
and Care (D. L. Garling, All University Committee on Animal Use and Care, written
communication, 01 27 2003).

The eastern edge of the traditional elk range and areas of range expansion were
targeted for elk captures, as this region represents areas of elk distribution shifts and
incorporates a portion of the TB endemic area for white-tailed deer in Michigan (Garner

2001, Hickling 2002). Captures were conducted during the winter since elk are more

13

 

readily located from the air against the snow background. Home range sizes tend to be
smaller during this time period (Ruhl 1984) allowing for more consistent relocation of elk
groups by capture crews. Also during winter, group sizes of bull/cow groups and bull
only groups are largest (Beyer 1987, Bender 1992) increasing the probability of large
numbers of individuals being discovered and being captured. Lastly, Moran (1973)
provided some anecdotal evidence of intermingling of elk from various portions of the
elk range during winter, based on dispersal of marked individuals. Thus, winter captures
likely allowed for the marking of a more representative sample of animals from across
the range.

Two different capture techniques were employed to capture animals. Helicopter
net-gunning techniques were used to capture elk in February, 2003 (Carpenter and Innes
1995). Hawkins and Powers Aviation (Greybull, Wyoming, USA) was contracted for
this operation. Once captured, each animal was radiocollared with a 550 g, Telonics
(Mesa, Arizona, USA), MOD-600HC radiocollar transmitting on a unique frequency in
the 150-152 MHz range with brown leather collar bands. Collars have a predicted battery
life of 4 years and are equipped with a MS6A, 6 hr mortality sensor. Upon capture blind
folds and ear plugs were placed on the animal. Personnel recorded the sex of each
animal, ear-tagged, and obtained blood, fecal, and hair samples for analysis if condition
of the animal permitted. Capture personnel monitored the condition of an animal during
handling by observing coloration of mucous membranes, which indicates proper blood
pressure and blood oxygen levels. Also respiration rate, pulse and body temperature
were monitored as indicators of animal condition. Average normal body conditions

include the following: mucous membranes of a pinkish color, respiration rate typically

14

 

between 6—12 breaths/min, pulse of 60—70 beats/min, and temperature of 38.3 °C
(Michigan Department of Natural Resources 2003). If a captured individual’s body
temperature reached a maximum of 40.6 °C, if respiration became shallow and rapid, or
if mucous membranes became gray or blue, the individual was immediately released.
Lastly, personnel gave most animals an intramuscular injection of 5—10 cc of the long-
lasting antibiotic, Flocillian (Bristol Laboratories, Syracuse, New York, USA) to
minimize infection.

Chemical immobilization techniques were used by MDNR personnel in July 2004
to capture elk (Roffe et a1. 2005). Carfentanil was administered by intramuscular
injection using a dart gun (Pneudart, Williamsport, Pennsylvania, USA) in the rear
hindquarter. Once an animal succumbed to the anesthesia, personnel followed the same
procedures as describe for net-gunning. Naltrexone at 125 times the carfentanil dose was
injected into the jugular as a reversal.

In February 2005, MDNR in conjunction with Quiksilver Air (Fairbanks, Alaska,
USA), collared additional elk using net-gunning techniques. Also 4 animals that had
grown signiﬁcantly since 2003 were recollared. Capture techniques and protocol were as
before. However, 5 of these animals were collared with Advanced Telemetry System’s
(Isanti, Minnesota, USA) G2000 GPS collars, rather than the standard VHF radiocollars.

These collars were pro grammed to take ﬁxes every 7 hours.

Capture Results, Mortalities, Current Status
The MDNR personnel captured 58 elk throughout the study (Table 1). Twenty adult
bulls and 20 adult cows were captured in 2003, 2 adult cows were darted in 2004, and 16

adult cows were captured in 2005. No mortalities as a result of capture occurred during

15

this study. Capture locations were distributed throughout the eastern portion of the range
(Figures 8—9). Images in this dissertation are presented in color.

A total of 20 mortalities occurred during the study period (Table 1). Ten of these
elk died as a result of legal or illegal hunting activities. During the mandatory hunter
orientation before the 2003—2006 elk hunts, hunters were asked to avoid shooting
collared animals to allow for collection of long-term datasets, however there were no
legal mandates against shooting a collared animal. Generally, hunters willingly complied
with this request, and many hunters at the check station reported seeing and passing up
shots on collared animals. Of the hunters harvesting collared elk, all but 1 individual
reported that they did not see the collar on the animal prior to harvest.

Other mortalities factors included: 1 cow died of old age (22 yr), 1 cow died of
exhaustion after becoming mired in an old beaver pond, 1 cow broke her neck running
into a fence, 1 cow died of a meningeal worm (Parelaphostroneylus tenuis) infection, and
1 bull died of unknown causes, although age (14 yr) may have been a contributing factor.
Additionally, the 5 GPS collars were removed in October 2005 off of 2 bulls and 3 cows.

As of January 2007, there were currently 33 active collars on 11 bulls and 22 cows.

16

 

Milli

    
  

 

PH 5139113 nu

 

 

 

 

 

 

 

Figure 8. Location of elk captured from the western portion of the study area (unﬁlled
circles represent 2003 capture locations, cross-hatched circles represent 2004 capture
locations, and circles ﬁlled with lines represent 2005 captures) in Michigan, 2003—2005.

 

  
       
 

llllllili

Meaford Rd

  
 

    

 

, «mun. «lIIIIIIIIIi

 

 

 

 

 

 

 

 

1 0 1 2 Kilometers

 

 

 

 

 

Figure 9. Location of elk captured from the eastern portion of the study area (unﬁlled
circles represent 2003 capture locations and circles ﬁlled with lines represent 2005
captures) in Michigan, 2003*2005.

Table 1. Capture record, agea, mortalities, and current status (January 2007) of

radiocollared elk in Michigan, 2003—2006.

 

 

Elk Date Left Ear Right Ear Current Status
Number Capture Tag Tag Sex Age (date recovered)
1 2/12/2003 673 673 F A Active
2 2/9/2003 674 674 F 22.0 Old age (3/30/05)
3 2/12/2003 675 675 M A Active
4 2/9/2003 676 676 F A Active
5 2/9/2003 677 677 F A Active
6 2/12/2003 678 678 M A Active
Broken neck-fence
7 2/9/2003 679 679 F 4.0 (2/16/05)
8 2/9/2003 680 680 F A Shot (1/07)
9 2/12/2003 681 681 F A Illegally shot (9/10/05)
10 2/9/2003 682 682 M A Shot (12/7/04)
1 1 2/1 1/2003 683 683 F A Active
12 2/1 1/2003 684 684 F A Active
13 2/12/2003 685 685 M A Shot (12/7/05)
14 2/12/2003 686 686 M A Active
15 2/9/2003 687 687 M A Active
16 2/9/2003 68 8 688 M Y Active
17 2/12/2003 689 689 F A Active
Unknown cause
18 2/11/2003 690 690 M 14.5 (8/6/2003)
Exhaustion - mired in
19 2/12/2003 691 691 F 11.0 beaver pond ( 6 /9 /0 5)
GPS collar removed
20 2/1 1/2003 692 692 M A (1 0/23/05)
21 2/11/2003 693 693 F A Shot (1/07)
22 2/12/2003 694 694 M 4.5 Shot (12/7/04)
23 2/ 12/2003 695 695 M A Active
24 2/9/2003 696 696 F A Active
GPS collar removed
25 2/11/2003 697 697 M A (10/23/05)
26 2/9/2003 698 698 F A Active
27 2/9/2003 699 699 F A Active

 

a Age estimates are provided for mortalities based on cementum aging (in years), for all other elk age is

classiﬁed as adult = A or yearling = Y.

Table l. (cont’d)

 

 

Elk Date Left Ear Right Current Status
Number Capture Tag Ear Tag Sex Age (date recovered)
28 2/9/2003 602 602 F A Active
29 2/12/2003 618 618 M A Unknown (1/21/07)
30 2/12/2003 621 621 M Y Active
31 2/9/2003 630 630 F A Active
32 2/11/2003 632 632 F A Shot (12/13/03)
33 2/1 1/2003 639 639 M A Active
34 2/1 1/2003 1 10 1 1 1 M A Active
35 2/11/2003 112 1 13 M A Active
36 2/11/2003 1 14 l 15 M Y Active
37 2/12/2003 116 117 M Y Shot (12/10/03)
38 2/12/2003 118 119 M A Shot (12/5/06)
39 2/9/2003 120 121 F A Active
40 2/9/2003 122 123 F 5.5 Brainworm (10/9/03)
Ille all shot
41 7/26/2004 478 477 F 6.5 (1% /1 0y/05)
42 7/28/2004 666 666 F A Active
46 2/12/2005 F A Active
48 2/12/2005 4 4 F A Shot (1/07)
49 2/12/2005 5 5 F A Active
50 2/ 12/2005 6 6 F A Active
51 2/12/2005 7 7 F A Active
52 2/12/2005 P A Shot (8/29/05)
53 2/12/2005 9 9 F A Active
54 2/12/2005 F Y Shot( 1/07)
55 2/12/2005 1 1 1 1 F A Active
56 2/12/2005 12 12 F A Active
57 2/12/2005 F A Active
GPS collar removed
x38 2/12/2005 14 14 F A 00/24/05)

 

20

Table 1. (cont’d)

 

Current Status

 

Elk Date Leﬁ Ear Right Ear
Number Capture Tag Tag Sex Age (date recovered)

GPS collar

59 2/ 12/2005 1 5 l 5 F A removed
(1 0/23/05)
GPS collar

61 2/12/2005 NA NA F A removed
(10/23/05)

64 2/12/2005 NA NA F A Active

66 2/12/2005 21 21 F A Shot (8/ 30/05)

 

21

CHAPTER 2: POPULATION ESTIMATION OF MICHIGAN ’S ELK HERD

Introduction
Estimating the size of free-ranging wildlife populations is one of the most daunting yet
critical tasks faced by wildlife managers (White and Shenk 2001). In Michigan
enumeration of wild elk (Cervus elaphus) populations has been problematic.
Historically, estimation of annual population size was based on pellet group surveys, kill
distributions and ﬁeld observations (Moran 1973). Abundance estimates generated were
both imprecise and likely biased as a result of the subjective nature of the surveys (Moran
1973, Beyer 1987). In 1975, the Michigan Department of Natural Resources (MDNR), in
an effort to improve its elk survey technique, instituted a combined aerial and
snowmobile survey technique to derive population estimates (Otten 1989). This
technique involved gathering a group of 100+ volunteers as well as MDNR personnel,
and assigning them in pairs to survey quadrats using snowmobiles. MDNR personnel
and volunteers would attempt to count all elk within a quadrat. In conjunction with the
snowmobile survey, an aircraft would survey quadrats that could not be accessed by
Snowmobiles such as private lands. Also some quadrats were simultaneously surveyed
by volunteers and the aircraft, which provided an ad hoc check on volunteer counts.
There are several problems with the combined aerial and snowmobile survey
te=Chnique. First, there is no correction for visibility bias (Caughley 1974, Samuel and
1)Ollock 1981) to adjust counts for unseen animals, and therefore projections of
population size are undoubtedly negatively biased (Samuel et a1. 1992). Visibility bias
arises from a multitude of causative factors including group size (i.e., larger groups are

more likely to be observed), vegetation characteristics (i.e., the amount of conifer cover

22

in a region) and animal behavior. Secondly, surveys focus primarily on areas of
historically high elk densities without a standardized procedure for sampling the entire
elk range. This results in areas of lower densities, such as regions of range expansion
being excluded from the survey. Also, this survey provides only an index to the
parameter of interest—population size. Differences in index values across years cannot be
attributed exclusively to changes in elk numbers, but may result from changes in
detection probability (i.e., the parameter of population size is confounded with detection
probability) (Anderson 2001). Confounding of detection probability and population size
prohibits managers from being able to conﬁdently draw conclusions about any observed
changes in counts. Since this technique is an index, and is not made using any sampling
or statistical framework; no associated measure of precision can be developed for
generated population estimates to assess their quality (White et al. 1982). Lastly, in
recent years snow conditions in the elk range have not been adequate to allow the use of
snowmobiles, which effectively crippled this survey technique.

As a result of these problems, Otten et al. (1993) developed an aerial survey
procedure, which utilized sightability correction factors (Samuel et al. 1992) to correct
for visibility bias in aerial counts of Michigan elk. The correction factors allowed for
Statistically defensible estimates of population size and calculation of associated
measures of precision. Otten et al. (1993) also provided a standardized sampling
procedure for conducting counts across the entire elk range to eliminate the problems of
Only sampling areas where elk historically occurred. However, this survey procedure was
never employed. The major drawback was the technique’s reliance on the availability of

the Michigan State Police helicopter to conduct surveys, which is costly and often

23

difﬁcult to obtain during the narrow window of survey conditions allowable under
Otten’s survey protocol . Thus, currently managers still rely on the aerial and
snowmobile survey with associated limitations for their management programs.

In recent years, growing public interest and increasing consumptive and non-
consumptive use of the elk herd has created pressure to have an accurate and defensible
estimation technique for elk managers. To meet these demands, I developed a ﬁxed-wing
survey technique based on sightability models (Samuel et a1. 1987) and the following
objectives:

1) To measure and determine variables which have a signiﬁcant effect on
sightability of elk from ﬁxed-wing aircraft.

2) To use these variables to develop a ﬁxed-wing sightability model for correcting
aerial counts of the Michigan elk herd.

3) To develop a standardized, stratiﬁed sampling procedure to allow for rigorous
survey of elk throughout their range.

4) Develop an economical survey technique that incorporates the sightability model
corrections, allows for estimation of group size, and provides statistically
defensible population estimates with associated measures of precision for the

Michigan elk herd across the entire range.

Study Area
The study site selected for this project is the current elk range located primarily in
Cheboygan, Montmorency, Otsego and Presque Isle counties in the northern portion of
the Lower Peninsula of Michigan (Moran 1973). The historic range was estimated at

approximately 1,5 50 kmz, including the Pigeon River State Forest near Vanderbilt,

24

Michigan (Bender 1992). The current range size is estimated at approximately 3,450 km2
(D. E. Beyer, Michigan Department of Natural Resources, unpublished report). We

focused our study mainly on the eastern region of the elk range near Atlanta in

Montrnorency County.
Topography of the area slopes northerly and consists of ﬂat-topped ridges

interspersed with headwater swamps and outwash plains created through glacial actions

(Moran 1973).

Mean annual temperature is 6.3° C with January having the lowest mean monthly
temperature (81° C) and the highest (19.7° C) occurring in July (NOAA 2006). Mean
annual rainfall is 93 cm, and mean annual snowfall is 378 cm (NOAA 2006) with

precipitation being generally well distributed throughout the year.

Due to wide array of soil fertilities, aspects and moisture levels, vegetation types
are diverse and well interspersed. In addition human activities such as logging,
agriculture and management practices ﬁrrther complicate the pattern of vegetation types

throughout the area. Dominant cover types include deciduous and coniferous forests

i nterspersed with typically human-induced openings. Moran (1973) provides a detailed
description of the vegetation of the region.
Methods

Siglrtability Model Development—Detection Probability Estimation

Capture—To facilitate sightability model development in February 2003, we
captured and radiomarked 20 adult bulls and 20 adult cows using helicopter net- gunning

techniques (Carpenter and Innes 1995). Hawkins and Powers Aviation (Greybull,

25

Wyoming, USA) was contracted for this operation. The capture was exempted by the
Michigan State University Animal Care and Use Committee (D. L. Garling, All
University Cormnittee on Animal Use and Care, written communication, 1 27 2003). In
the summer of 2004, we supplemented our sample of radiomarked animals by capturing
and radiomarking 2 additional adult cows using chemical immobilization techniques
Gtoffe et al. 2005). Thus after mortalities, 36 radiomarked elk were available for
sightability model development during winters of 2004 and 2005.
Data Collection.— Prior to initiation of sightability model development, I met with
MDNR wildlife biologists, MDNR pilots, administrators, and others that would be
involved in the process to discuss protocol and expectations. Once all participants
understood their respective roles, we conducted aerial surveys to develop an elk
sightability model during the winters of 2004 and 2005. I chose winter for model
development, since elk group size tends to be largest during the winter (Moran 1973,
Beyer 1987) increasing the probability of observing elk groups (Samuel et a1. 1987).
Also snow conditions provide a good background against which elk can be observed
from the air. We conducted all ﬂights using Cessna 180 or Cessna 170 between 0900—
1 600 hours to take advantage of good light conditions and minimize shadow effects.
We attempted to make ﬂights under clear skies with calm winds, temperatures at
01‘ above —12° C after a fresh snowfall (Otten 1989). However, due to the time
cOnstraints and the amount of data needed for adequate estimation of the sightability
ﬁ«Inction, we conducted ﬂights when conditions were deemed safe by the pilots. Flights

Consisted of 2 shifts, 2—3 hours in length, with a 1 hour break between shifts to allow for

all‘craft refueling and for recuperation of observers.

26

I divided the region encompassing the greatest extent of movements of
radiocollared elk into 80 quadrats with length (N/ S) 9.66 km and width (E/W) 3.22 km
(Figure 10), and I gave each quadrat a unique identiﬁcation. Parallel, 0.40 km wide,
ﬂight lines were created running north to south within each quadrat, and the starting point
and ending point of each line was recorded (Figure 11). I created ﬂight lines to assure
100% coverage of the quadrat.

We used 2 ﬁxed-wing aircraft equipped with radiotelemetry gear and wheel
covers removed. The ﬁrst plane, the telemetry plane, contained a pilot and a telemetry
operator. The second plane, the observation plane, contained a pilot, 2 experienced
observers and a telemetry operator. Observers were seated at the rear of the plane, and
the telemetry operator next to the pilot. Each plane was equipped with a radio for inter-
plane communications, a book containing all the quadrat and ﬂight line locations,
andGlobal Positioning System (GPS) equipment for locating and ﬂying ﬂight lines and
recording locations of observed elk groups and radiomarked individuals.

In the telemetry plane, the telemetry operator randomly selected a
radiocollared animal for observation. Using the telemetry equipment, the telemetry plane
located the group of animals containing the collared individual. The pilot recorded the
location of the group using a GPS. Based on this GPS location, the operator determined
the quadrat, which contained the marked individual. Lastly, the telemetry operator
scanned all frequencies of marked individuals to determine if any other marked
individuals were in the same quadrat. If additional animals were in the same quadrat,
their location were also determined. Once all animals in the quadrat were located, the

telemetry operator radioed the identification number of both the quadrat and the

27

Atlanta

20 W$B
Ki Iomete rs

S

 

Figure 10. Region that contains the greatest extent of movement of radiocollared elk, and
the locations of quadrats used in the sightability model development in Michigan, 2004—
2005

28

A1 'B1 C1

 

 

A1 B1 Cl D1 E1 F1 G1 H1 I1 J1 K1 L1 iM1NI 01 P1 Q1 R1 81 T1 U1 V1 W1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

o 2 4 8 N
_ _ W®E
Kilometers

 

 

Figure 11. The location of 0.40 km ﬂight lines in quadrats used to develop an elk
Sightability model for Michigan, 2004—2005.

29

radiomarked individual(s), and their GPS location(s) to the second telemetry operator in
the observation plane. The telemetry plane then proceeded to the next closest
radiocollared animal. However, for safety purposes a minimum separation of 1 quadrat
was maintained between the telemetry and observation planes. If an elk group contained
multiple radiomarked animals, this aggregate was treated as a single unit since the
sampling unit is the group not the individual elk (Samuel et a1. 1987).

Once the telemetry plane communicated the quadrat to be surveyed, the
observation plane proceeded to the designated quadrat and ﬂew the designated ﬂight lines
within the quadrat starting in the southwest comer of the quadrat. The observation plane
ﬂew the ﬂight lines at an air speed of approximately 129 km/hr and at a height of 152 m
above the ground. The 2 experienced observers visually scanned out each side of the
plane to a distance of 0.20 km for elk groups. Markers on the wing struts aided searcher
in searching the correct area.

If a group was located, observers communicated to the telemetry operator they
located a group, if the operator determined the group contained the radio-marked
i ndividual(s), the pilot left the designated ﬂight line and reduced altitude while circling
the group, and recording the GPS location. While the pilot circled, 1 observer counted all
elk in the group. A group was deﬁned as all elk visible in an area. However, if distinct
groups were clearly noticeable by the observer over the area (i.e., there is a clear
separation between groups of animals), or if elk were distributed in areas of different
conifer cover classes then these were treated as separate groups. The observer also
1Funded the number of bulls, cows and calves, the percent conifer cover at the group’s

location, behavior of the ﬁrst animal (5) seen, wind speed, snow cover conditions and

30

light conditions. The percent conifer cover was classiﬁed into 3 classes: 1) 0—33%
conifer cover, 2) 34—66% conifer cover and 3) 67-100% conifer cover at a 10 m radius
around the ﬁrst elk initially sighted. Behavior was classiﬁed as bedded (B), standing (S)
or both (B/S). Snow cover conditions were classiﬁed as 1) complete, 2) some low
vegetations showing or some 3) bare ground showing. Lastly, light conditions were
classiﬁed as bright light with high intensity (BH), bright light with medium intensity
(BM), ﬂat light with medium intensity (FM) and ﬂat light with low intensity (FL). A
standardized data sheet was provided to aid in data collection (Appendix A). These
independent variables were selected a priori as likely to inﬂuence sightability of elk.
When the ﬁrst observer completed data collection, the pilot circled the plane in the
opposite direction, and the second observer repeated the process. Observers did not
communicate their ﬁndings until both completed data collection (i.e., observers were
independent). After the group had been counted by both observers, the pilot returned to
the ﬂight line and continued to survey the quadrat if more radiocollared inviduals were in
the quadrat. If the observers located and counted all groups with the radiomarked
individuals then the telemetry operator communicated to the pilot the survey of the
quadrat was complete. The telemetry operator did not communicate with observers until
the group(s) containing the radiomarked individual(s) was located or the surveying of the
quadrat was complete. If observers did not locate the group(s) containing the
radiomarked individual during the survey of the entire quadrat, the telemetry operator
located this animal(s) using the telemetry gear. Observers recorded telemetry equipment

was used to locate the group containing the radiomarked animal (i.e., it will be classiﬁed

31

as unseen) as opposed to the group being located during the normal survey of the quadrat,
and the same procedure for data collection as just described was implemented.

In 2005, we attempted to ensure an even distribution of observations across the
various class levels of the independent variables if possible (e. g., we sampled more
intensively groups located in conifer class level 3 in 2005 as we had fewer observations
of groups in this conifer class level).

To prevent observer expectancy in regards to a cell containing a radiomarked
individual, which could bias results, periodically cells known to not contain any
radiomarked individuals, placebo cells, were surveyed. Due to limited resources we ﬂew

a maximum of 1 placebo cell per week. Only the telemetry operator on the observation

plane knew the cell was devoid of marked animals.

Analysis.— Data collected during the elk sightability surveys resulted in observed
elk groups being classiﬁed as seen or unseen. This dichotomous classiﬁcation was the
dependent variable in a logistic regression analysis with independent variables: group

size, percent canopy cover, animal behavior, wind speed, snow conditions and light

conditions. I followed the Samuel et al. (1987) recommendation of using the natural log

transformation of group size in the analysis since they found it was a better predictor than

the untransformed measure of group size. The logistic regression analysis allowed

estimation of heterogeneous sighting probabilities for each elk group observed. The
10giStic model used in the analysis for estimating sighting probability closely followed
Samue1 et al. (1987):

exp(u) (1)

P0} :1) = 1+ exp(u) ’

32

where P( y =1) = sighting probability, and u = [30 + 01x1 + [32x2 + + 13ij is the usual
linear regression equation of covariates (x1,x2,...,xj) determined to be affecting elk
sightability.

In addition to using the Samuel et al. (1987) formulation (SF) to calculate sighting
probabilities, I modiﬁed their model by replacing group size, one of the covariates, by an
estimate of group size and recalculated probabilities. Group size was estimated using a
method of moments estimator (MME) (DasGupta and Rubin 2005: see Chapter 3):
erillszi'

_ _ , (2)
Xo’Ipr/I’I1

 

”ii-(k) =
where X (W) = maximum of w observer counts of the size of the ith group in the kth

quadrat, X— = mean of the counts, S 2 = sample variance of the counts, and a = 0.10.
This or value was chosen as it was shown to minimize the mean squared error (MSE) for
the range of population size and detection probability typical of elk aerial surveys in
Michigan (see Chapter 3). If all counts of group size were identical then group size was
assumed to be known. This estimator assumes that double counting of individual elk did

not occur, and other species (e. g., white-tailed deer) were not counted as elk (i.e., there

was no misclassiﬁcation).

The approximate estimate of the asymptotic variance for estimate of group size is

as follows:

20‘ 2ﬁi(k)(ﬁ1i(k) - 1) (3)

 

V5r(’;7i(k)) z w

33

For both formulations, I created 63 a priori models based on all linear
combinations of the independent variables. I estimated beta parameters for each model,
and derived model averaged estimates and relative likelihood values based on the entire
suite of models (Burnham and Anderson 2002).

I developed an unconditional covariance matrix for the beta parameters used in
the SF (Burnham and Anderson 2002).

An estimate of the covariance matrix for the beta parameters in my formulation
(GS) was complex and not available in a closed form, as I had to account for
measurement error associated with estimating group size (Carroll et al. 1995). Therefore,
I used a parametric bootstrap procedure to estimate the covariance matrix (Efron and
Tibshirani 1993). I generated 10,000 datasets from the empirical distribution of data
collected during sightability model development. Any observations with missing
independent variable information were excluded from the resampling process. To

incorporate variability associated with estimating group size, group size for each
observation in the bootstrapped datasets, where counts were not identical, were generated

2a2a,(k)(,;.,(k) — 1)
W

 

from a Normal distribution with mean = a“ k) and variance =

distribution where in“ k) = the estimate of group size for the ith group in the kth quadrat,

a = O. 1 0, and w = number of observer counts of group size for the selected observation
(DasGupta and Rubin 2005). The elements of the covariance matrix were then estimated

as follows for i, j = 1 to 7:

 

. 1 10,000 . _ .. __
ij :10,000 El (,Bik ‘ﬂiXﬂjk ‘ﬂji (4)

34

where ﬁik =the ,3 corresponding to the ith predictor variable from the sightability model

at the kth iteration, and E, = the mean of the 0's over the 10,000 iterations.

All analyses were done using SAS Macro Facility and PROC GLIIVIMIX (SAS

Institute 2003).

Survey—Population Size Estimation

Data Collection.— Prior to implementation of the elk survey, 1 met with MDNR
wildlife biologists, MDNR pilots, MDNR technicians, administrators, and others that
would be involved in the process to discuss protocol and expectations. The protocol and
datasheets used are in Appendix B. Once all participants understood their respective
roles, we conducted an elk survey during late January through early February 2006. We
maintained as much similarity as possible in observers, timing of ﬂights and conditions
between the survey and those used during the sightability model development to assure
sightability during the survey mimicked conditions under which the correction factors for
sightability were developed.

We used 2 ﬁxed-wing aircraft to conduct the survey. Multiple aircraft shortened
survey time and minimized potential problems associated with animal movements
between quadrats. Both planes contained a pilot and 2-experienced observers, and were
equipped with a book containing all the quadrat and ﬂight line locations, and Global
Positioning System (GPS) equipment for locating and ﬂying ﬂight lines and recording
location of observed elk groups.

For the elk survey, I divided the entire elk range into 92 (N/S) 9.66 km by (E/W)
3.22 km quadrats (Figure 12), and each quadrat was assigned a unique identiﬁcation.

Parallel, 0.40 km wide, ﬂight lines running north to south within each quadrat were

35

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

. I" .. . ‘ A .
‘ ‘ .r'w-r»; I

AABCDEFGHIJKLMNOPORS]

 

 

 

 

 

 

 

 

 

 

Figure 12. Location of quadrats of and expected elk densities of quadrats (dark gray—
high elk density, light gray—medium elk density, white—low elk density) used during the
elk survey in Michigan, 2006 (identifying labels are along the margins).

36

created, and the starting point and ending point of each line I provided to the pilots
(Figure 11). I created an adequate number of ﬂight lines to assure 100% coverage of the
entire quadrat. Quadrats were classiﬁed into 3 strata of elk density: high (31 or more
elk), medium (16—30 elk) and low (0-15 elk) based on recommendations of Otten (1989).

Radio-telemetry data, local biologists’ knowledge, historic kill data, and
information gained on observations of elk distributions made during past population
surveys and sightability model development ﬂights were the basis of stratiﬁcation.
The entire range was surveyed in 2006. We surveyed high density quadrats ﬁrst, and we
attempted to survey adjacent quadrats on the same day to minimize elk groups moving
between quadrats. Once the high density quadrats were surveyed, we surveyed the
remaining quadrats in a pattern radiating out from the high density quadrats to once again
minimize movement of elk groups between quadrats.

When a quadrat was surveyed, the plane ﬂew to the quadrat’s southwest corner as
a starting point, and then ﬂew all ﬂight lines within the quadrat. Pilots attempted to
maintain the same air speed and altitude as used for development of the sightability
model. The independent variables of group size, behavior, percent conifer cover, wind
speed, snow cover conditions and light conditions for all elk groups observed by the 2
observers were recorded following the same protocol as developed for the sightability
model. In addition to the 2 observers, the pilot also provided an independent count of the
size of observed elk groups.

Analysis.— In conjunction with the sightability models developed, I used data
collected on elk groups during the elk survey to generate population estimates of the

Michigan elk herd using both my formulation correcting for group size (GS) and the

37

Samuel et al. (1987) formulation (SF). The estimate of population size for SF was

calculated as follows (Steinhorst and Samuel 1989):
l 1 nk ..
t = Z—Zmi(k)®i(k): (5)
k pk i
where pk = the probability the kth land unit is selected as part of the sample (known),
m“ k) = size (assumed to be known) of the ith group in the kth land unit, and O“ k) = is the

inverse of the estimated sighting probability (1/ 5700) for the ith group in the k‘h land unit

calculated using the SF sightability model.

Estimating group size resulted in the following estimator:

’ 1 "k ..
= 2—2 mi(k)@ik() (6)
k Pk i

where pk = the probability the kth land unit is selected as part of the sample (known),

17‘2“ k) 2 method of moments estimate (Equation 2) of the size of the ith group in the klh
land unit, and @1110 = is the inverse of the estimated sighting probability (1/ 331(k)) for the
ith group in the kth land unit calculated using GS, which includes n22“ k) as a covariate in
the estimation of 5'“ k) . If there was only 1 count on a group or if all counts for the ith
group in the kth land unit were identical am 2 mi“).

When using the SF, Steinhorst and Samuel (1989) provide the following equation

for estimating the variance of t:

38

II'

1- .
S2 :2 pkM2+Zzpkk —pkpk MkMk'+
k pk k¢k' pkk' kak'

l Ink
2— ' [I-gig](m i(k)®i(k))2+zjzajajs Séjéj"

 

 

(7)

. "k
where M k = 2m“ k) / j)“ k) , PM = probability both the k and k’ land unit are selected in
1'

the sample, aj Z“ k) 1 ,( k) / pk withj indexing all i(k) where the independent variables

_ .+ ..'A_ . ..'A .+ .. /2 '.I‘ .. '
are constant, and sé) é) ,. = e (x! x] )B (x1 ”1 )2“! x] ) [ex] 2x1 —1] wrth
J .1

xj = vector of independent variables, 0 = vector of beta parameters estimated by the SF,

and i = consistent estimator of the covariance matrix . All remaining variables are as in
equation (5).
The approximate variance estimate for t when using GS is as follows (see Chapter

3 for derivation):

39

      

 

 

 

k kstk' Pkk PkPk'
7 . 2
i 1 n2]. -Zli31xz(k)1 . 2
— 1+6 J: (1‘31) A .
k Pi 1' Wk)
r' -2
—j21Bjxi(k)j 2
+2 é— kZ—m mam-(me 63].
J
‘Zﬁjxttkv'
1
+2): Z—Zf. "WW/019
#1 Pk
_ 7. _
1 1 nk e-Zlﬁjmkn
x — x 6- ~
gm 21: mi(k) i(k)j'e 131,014
L _

 

 

 

k+zlzpkk"' PkPk'M Mk +Z— 1an

 

 

I .. ..
+ Z [ mi(k)mi'(k)'SO,-(k),O,"(k)' :|’

i(k)¢i'(k') PkPk'

I

     

9117‘)

1m} 1009100? +

n
where M k = 2,21“ k) / j)“ k) , ,Bj = is the jth beta parameter estimated from the GS

formulation, ,31 = is the estimated beta parameter associated with the independent

variable of estimated group size, xi(k)j

unit from the sightability model, 6'31“)
1

(8)

= is the jth predictor variable ith group in the kth land

= is the estimated variance of the group size

estimate for the 1'“ group in the kth land unit derived 1n equation (3), and 6'2 =

40

ﬁjﬂj’

estimated covariance of ,an and ﬁjv for all j derived in equation (4). If there was only 1

count or if all counts for a group were identical, then a"; '(k) = O.
l

The ﬁrst 2 terms in this equation are the error associated with sampling, the third
term is the error associated with sightability (i.e., the fact that animals are missed during
aerial surveys). The fourth term can generally be thought of as the error associated with
estimating group size with a component accounting for the estimate of sighting
probability being a function of group size. The next 2 terms correspond to the error
associated with estimating the sightability of elk groups with a component accounting for
group size estimation. The last term is accounting for the covariance between each
group’s sighting probabilities, since they were derived from using the same sightability

model. This last term is a point estimate approximation for the following expectation:

A A

Pan’ﬁixk') COV(®i(k)a®i'(k') )i’ With the covléukrémk'1)

Z

i(k)¢i'(k') J J Pkpk'

estimated by

S. . = e""i<k)+xi'<k')""“"i(k>+xi'1k'))'Z/‘3("i(k)”1116)”2 einc) 2P "i'1k'1 _1
@i<k)®i'(k')

, where xm = the vector of predictor variables used in the sightability model for the z'(k)th

group, B = vector of beta parameters estimated using GS, and :ﬁ = estimated

covariance matrix for the beta parameters estimated using GS. This approximation
results in only a slight positive bias in variance estimates (see Chapter 3). Thus, Equation

(8) can be rewritten more succinctly in matrix notation. Let m = vector of estimated or

known group sizes for all groups observed in the survey, [3 = vector of beta parameters

41

. . Iii . . . .
estimated us1ng GS, I] = (fl), 6 = vector of partial der1vat1ves oft Wlth respect to

11‘2“) and ,31- evaluated at n , thus for the ith group in the kth land unit

65,“) = —l—[1 + e—in‘ )B(1 — ’61)) and for the jth beta estimate

Pk
7 . x
1 1 nk ‘ Zﬂjxi(k)j A 20?: 0
6f?- = Z_Z“Mi(k)xi(k)j'e F1 ,and lastly Z = milk)
J k Pk i O i ‘
15
where :02 = a diagonal matrix of (is: '(k) values and :3 = estimated covariance
. l
’"i(k)

matrix for the beta parameters estimated using my formulation. Then equation (8) is

rewritten as follows:

 

1 1 1'
1— I
3:2 =Z— p—z—k-Mz +22% MkMkMk'+Z—‘1-Zkl[1-—](mi(k)@t(k))z

k pk k¢k' Pkk PkPk' k Pk , @( k) (9)
1
+8' 6+ —-—n”1. ' * ‘ -
2 i(k)¢i'(k')[PkPk' ’(k)m'(k)S®’(k)’®“k')]

Sampling Simulations

To investigate the effects of surveying only a portion of the range on precision of the
estimate, I examined if our stratiﬁcation of quadrats into expected elk densities for the
2006 survey was accurate based on the sum of the maximum counts of elk groups in each
quadrat. I also simulated all combinations of sampling rates between 50—100% at 10%
intervals for the different density strata. For each sampling rate and each stratum, I
generated 1,000 datasets from the survey data collected in 2006, and examined the

average variance of population estimates calculated using GS. Lastly, I examined the

42

optimal sampling rates based on the criteria of minimizing cost and maximizing precision
for sample sizes ranging from 45—91 quadrats. Lohr (1999) provided the following
equation for determining the optimal number of samples in each stratum to minimize the
variance of the population estimate:

K NhSh \

1;
ﬁEIAQSb
\1=1 CI )

 

 

"h:

, (10)

 

 

 

where nh = the number quadrats to sample from stratum h, N}, = the total number of
quadrats in stratum h, S}, = the within stratum standard deviation of number of elk in each
quadrat, and c;, = the cost of sampling a quadrat in stratum h. I used the within stratum
standard deviation of the sum of the maximum counts for each quadrat to estimate Sh.
For a given sample size, I calculated average variance of population estimates based on
the optimal sample allocation as determined above using the GS estimation procedure,

and a Monte-Carlo resampling procedure of the 2006 survey data with 1,000 repetitions.

Cost
To evaluate the cost effectiveness of the sightability model estimation procedure, I
compared the costs associated with this technique with the costs associated with the

current estimation procedure.

Results

Sightability Model Development—Estimating Detection Probability Estimation
During the winters of 2004 and 2005, we collected information on 105 elk groups in 2004

and 125 elk groups in 2005 for sightability model development. Fourteen observations

43

were censored due to lack of information about independent variables. We counted a
total of 1,435 elk in 216 groups based on the maximum of observer counts. The mean
group size was 6.6 elk, and the median group size was 4 elk. Group sizes ranged from 1
to 53 elk. Of the 216 groups, observers saw 1028 elk in 110 groups (9.3 elk/group)
without the aid of telemetry equipment (i.e., groups were classiﬁed as seen). Observers
used telemetry equipment (i.e., groups were classiﬁed as unseen) to locate 407 elk in 106
groups (3.8 elk/group). Wind speed during the survey had an average value of 11.9
km/hr with speeds ranging from 0 to 32.2 km/hr. The mean wind speed for groups that
were seen was 12.1 km/hr, and the mean wind speed for elk groups classiﬁed as unseen
was 11.7 mm. Table 2 displays the number of elk groups both seen and unseen for
each level of the various class variables. When calculating the sightability models, class
3 of the variable, snow conditions, was eliminated since no elk groups occurred in this
class. Also to facilitate calculation of sighting probabilities, class 2 and class 3 of the
variable, percent conifer, were combined because no elk groups containing radiomarked
individuals were observed without the aid of telemetry equipment in class 3. The top 10
models selected using infonnation-theoretic approaches are shown in Table 3. Model
averaged beta parameter estimates and associated unconditional standard errors for GS
and the SF sightability models generated during the logistic regression analyses are
shown in Table 4. Relative likelihood values for each of the parameters for both the GS
and SF are presented in Table 5. Covariance matrices for the model averaged beta
parameters for the GS and SF sightability models are presented in Tables 6 and 7

respectively. The 2 most important variables using SP or GS in determining elk

44

Table 2. Number of elk groups classiﬁed as seen and unseen during aerial ﬂights for each
level of the following class variables: conifer cover“, behaviorb, light classc and snow
conditionsd for elk in Michigan during the winters of 2004 and 2005. Percentage of
groups for a given response within each level of the class variables is shown in
parentheses.

 

Class Variable
Conifer Behavior Light Class Snow Ag

 

 

 

Response 1 2 3 B B/S S BH BM FL FM 1 2 3

94 16 55 21 34 23 19 15 53 53 57
Seen (85) (15) 0 (50) (19) (31) (23) (19) (15) (53) (48) (52) 0

53 29 24 7O 8 28 28 15 8 55 47 59

Unseen (50) (27) (23) (66) (8) (25) (24) (13) (7) (47) (44) (56) 0

a Conifer cover has 3 classes: 1 (0—33%), 2 (34—66%) and 3 (67—100%).

b Behavior has 3 classes: B (bedded), B/S (bedded/standing) and S (standing)

c Light class has 4 classes: BH (bright light with high intensity), BM (bright light with medium intensity,
FL (ﬂat light with low intensity) and FM (ﬂat light with medium intensity).

Snow conditions has 3 classes: 1 (complete snow cover), 2 (some low vegetations showing) or 3 (bare

ground showing).

 

 

45

Table 3. Top 10 elk sightability models, AICc values, A AICC values, relative model
likelihoods (RML) and associated Akaike weights (AW) in Michigan, 2004 and 2005.

 

 

Model AICc Value A AICc RML AW
conifer, lngsize, snow 254.12 0.00 1.00 0.36
conifer, lngsize 255.76 1.64 0.44 0.16
conifer, lngsize, snow, windcont 255.97 1.84 0.40 0.14
behave, conifer, lngsize, snow 257.31 3.19 0.20 0.07
conifer, lngsize, windcont 257.44 3.31 0.19 0.07
conifer, lightclass, lngsize, snow 258.12 3.99 0.14 0.05
behave, conifer, lngsize 258.96 4.84 0.09 0.03
behave, conifer, lngsize, snow, windcont 259.19 5.07 0.08 0.03
conifer, lightclass, lngsize 259.20 5.07 0.08 0.03

conifer, lightclass, lngsize, snow, windcont 260.27 6.14 0.05 0.02

 

46

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47

Table 5. Relative likelihood values for independent variables used in GS and SF
sightability model calculations for elk in Michigan during winters of 2004-2005.

 

Group Light
Model Size Wind Behavior Conifer Snow Class

GS 0.99945 0.28578 0.17534 0.99997 0.66933 0.13381
SF 0.99978 0.28741 0.17548 0.99989 0.72540 0.15202

48

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49

 

 

 

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50

sightability were conifer cover and group size based on the RI values. Snow conditions

were of lesser importance, and the remaining predictor variables were of little inﬂuence.

Survey—Population Size Estimation
In the winter of 2006, we completed the ﬁrst elk survey. The entire range was surveyed
with the exception of quadrat C 1 , which was not surveyed as it fell in air space restricted
by the United States Air Force. The survey was completed in 9 days and required 85 hrs
of total ﬂight time. We ﬂew 4,368 mile of transects. During the ﬂights, observers saw
72 unique groups of elk containing 559 individuals based on maximum of observer
counts. Of the 559 individuals observed, 190 were identiﬁed as bulls, 176 as cows, 64 as
calves, and 129 were unable to be classiﬁed. The locations of groups observed during the
survey are shown in Figure 13. Average group size was 7.8 elk/group (SD = 10.4), and
ranged in size from 1—50 elk. The mean difference between observer counts of elk in
groups was 0.32 elk (SE = 0.071), and ranged from 0—5 elk with difference increasing
with group size.

Using the GS sightability model, I estimated the size of the late winter Michigan
elk herd in 2006 at 905 elk (SE = 125) with a CV = 13.8% and standard normal 95%
conﬁdence interval of 660—1 150 elk. The total variance was 15617.2. The largest
component of the total variance was variability due to estimating group size and sighting
probability (10083.8). The remaining error was a result of sightability error (5533.4).
Since we surveyed the entire range there was no variability due to sampling portions of
the range.

I estimated the size of the late winter Michigan elk herd in 2006, using the SF

sightability model, as 872 elk (SE = 107) with a CV of 12.3% and standard normal 95%

51

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52

conﬁdence interval of 65 8-1086 elk. The total variance was 11495, with the smallest
component due to sightability error (4919.1). The remaining error was due to estimating

the sighting probability (6575.9).

Sampling Simulations

The results of the accuracy assessment of stratiﬁcation of quadrats into expected elk
densities are shown in Table 8 by stratum. Fiﬁy—one quadrats were classiﬁed correctly,
and 40 were misclassiﬁed. Of those correctly classiﬁed, the majority (46) were in the
low density strata. Figure 14 displays the location of correctly and incorrectly classiﬁed
quadrats. The medium density stratum had the greatest error in classiﬁcation with only 1
quadrat correctly classiﬁed. The low density stratum was the least variable with regards
to the number of elk in each quadrat, 48.17. The medium density was more variable,
114.14, and the high density stratum had the largest within stratum variability, 1505.99.

The effects of varying sampling rates on the average variance of population
estimates based on the GS procedure are displayed in Figures 15—20. These analyses
demonstrate a continuously decreasing average variance as sampling rate increases in all
3 density strata. However, it appears sampling rate has the most effect on the average
variance in the high density stratum.

The results of the Monte-Carlo simulations based on the optimal sampling rates
for each density stratum demonstrated the high density stratum should be sampled in its
entirety for all sample sizes of quadrats. The medium density stratum should be sampled
at a lesser sampling rate, and the low density stratum should be sampled at the lowest
sampling rate when all quadrats are not surveyed. The optimal number of quadrats from

each density strata for a given sample size and the average variance of the estimated

53

Table 8. Accuracy assessment of assignment of quadrats to low (0—1 5 elk), medium
(16—30 elk) and high (31+ elk) density strata in Michigan, 2006.

 

Correct stratum

 

Assiged Stratum High Medium Low

 

High 4 1 1 1
Medium 2 1 25
Low 1 0 46

 

54

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 14. Location of quadrats correctly (white) and incorrectly (gray) assigned to
expected elk density strata in Michigan, 2006(identifying labels are along the margins).

55

Average variance

72722 W
66802
60882
54962 i
49042
43122

37202 ‘

 

31282

 

 

(%)

 

Figure 15. Effects on average variance of the population estimate of varying the
sampling rate in the high (31+ elk) elk density and the medium (16—30 elk) density strata
with a low density stratum (1-15 elk) sampling rate of 50%.

56

Average variance

69714
63994
58275
52556‘
46836
41117

35397

 

29678

 

23959

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100 xxx}! , ,— ’2‘; . . —->\
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\_

 

 

. . \_ ”if 2.1-» if- 90
Medium density sampling rate 70 \(f \>/"'/ 80
'\ - . 70
o 60 \f 60 High density sampling rate (%)
5O 50

Figure 16. Effects on average variance of the population estimate of varying the
sampling rate in the high (31+ elk) elk density and the medium (16—30 elk) density strata
with a low density stratum (1-15 elk) sampling rate of 60%.

57

Average variance {,2— \..

71 178
65196 '
59215 .,
53234
47253
41272

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Medium density sampling rate 70 \\_ If: _ v/‘V' 80 9°
(%) V”

Figure 17. Effects on average variance of the population estimate of varying the
sampling rate in the high (31+ elk) elk density and the medium (16—30 elk) density strata
with a low density stratum (1-15 elk) sampling rate of 70%.

58

Average variance If f \\

67858 —
62168
56478 "F'—
50787
45097
39406

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%)

Figure 18. Effects on average variance of the population estimate of varying the
sampling rate in the high (31+ elk) elk density and the medium (16—30 elk) density strata
with a low density stratum (1-15 elk) sampling rate of 80%.

59

Average variance ,~—- \\

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(%) - ‘34—" . . .
50 \\\F_,r""' \ 70 ngh dens1ty sarnphng rate (%)
50 50

Figure 19. Effects on average variance of the population estimate of varying the
sampling rate in the high (31+ elk) elk density and the medium (16—30 elk) density strata
with a low density stratum (1-15 elk) sampling rate of 90%.

60

Average variance

 

67791 -

62000

56210

38838

33047

27257

21466 i

 

15676 " _

 

 

Figure 20. Effects on average variance of the population estimate of varying the
sampling rate in the high (31+ elk) elk density and the medium (16—30 elk) density strata
with a low density stratum (1-15 elk) sampling rate of 100%.

61

population is shown in Table 9.

Cost
The total cost estimate and individual expenditures for the 2006 elk survey (Table 10) are
based on 85 hours of total ﬂight time, and it assumed each plane and pilot ﬂew 42.5
hours. I also assumed each plane had a wildlife technician and biologist as observers.
Costs associated with the historical population estimation procedure using a
helicopter with current prices were much higher than those with the sightability technique
(Table 11). Total estimates of individual expenditures are based on values provided by
Otten (1989). Costs of the same procedure using a MDNR ﬁxed-wing aircraﬁ are more

reasonable (Table 12).

Discussion

Sightability Model Development-Detection Probability Estimation

We observed lower mean elk group sizes for elk groups seen by observers and elk groups
missed by observers as well as across all elk groups compared to the values reported by
Otten (1989) for elk in Michigan. He found across all elk groups, a mean elk group size
of 9.8 elk/group. For elk groups seen by observers, he estimated a mean elk group size of
12.3 elk/group, and for elk groups missed 5.1 elk/group. These smaller group sizes are
not surprising given the ban on winter feeding and baiting in this area, which during
Otten’s study created artiﬁcially large groups concentrated at winter feeding sites (Otten
et al. 1993). Also some discrepancy is due to my attempts to ensure an even distribution

of observations throughout the various levels of the class variables when possible. Thus

62

Table 9. The sample size of quadrats surveyed, the average variance of 1,000 elk
population estimates generated using the optimal number of samples from each density
strata, and the optimal number of quadrats sampled from each density stratum based on
the elk survey in Michigan, 2006.

 

Density Stratum

 

Sample Average
Size Variance High Medium Low

45 36,146.65 16 14 15
46 36,312.62 16 14 16
47 34,216.96 16 15 16
48 33,804.08 16 15 17
49 31,700.95 16 16 17
50 31,476.74 16 16 18
51 29,696.22 16 l7 18
52 29,919.18 16 17 19
53 28,539.81 16 18 19
54 28,023.74 16 18 20
55 27,004.65 16 19 20
56 26,650.14 16 19 21
57 25,358.54 16 20 21
58 25,152.73 16 20 22
59 24,364.09 16 21 22
6O 23,822.63 16 21 23
61 23,016.19 16 22 23
62 22,818.90 16 22 24
63 22,870.17 16 22 25
64 21,772.38 16 23 25
65 21,543.66 16 23 26
66 20,774.76 16 24 26
67 20,542.25 16 24 27
68 19,981.18 16 25 27
69 19,833.83 16 25 28
70 19,276.88 16 26 28
71 19,112.97 16 26 29
72 18,533.04 16 27 29
73 18,284.24 16 27 3O

 

63

Table 9. (cont’d)

 

 

 

Density Stratum
Sample Average
Size Variance High Medium Low
74 17,877.18 16 28 30
75 17,702.27 16 28 31
76 17,480.44 16 28 32
77 17,301.66 16 28 33
78 17,129.11 16 28 34
79 16,886.33 16 28 35
80 16,872.79 16 28 36
81 16,689.94 16 28 37
82 16,532.07 16 28 38
83 16,414.07 16 28 39
84 16,312.12 16 28 40
85 16,227.14 16 28 41
86 16,153.53 16 28 42
87 16,000.35 16 28 43
88 15,871.65 16 28 44
89 15,797.02 16 28 45
90 15,706.70 16 28 46
91 15,617.15 16 28 47

64

Table 10. Costs associated with conducting the elk survey of the entire range in northern
Michigan, 2006.

 

Cost component Per unit costj§) Total component cost ($)

 

 

Plane IOO/hr 8,500
Pilot 28/hr - lead pilot 1,190
26/hr - pilot 1,105

Personnel 23/hr - technician 978
29/hr - biologist 1,233
Total cost (S) 13,005

 

65

Table 11. Projected costs for conducting the historical elk survey procedure using a

helicopter in northern Michigan, 2006.

 

 

 

 

Length of Survey

Cost component Per unit cost ($) 2 days 3 days 4 days
Helicopter rental 1275/day 2,550 3,600 4,650
Helicopter fuel 4.00/gal 1,200 1,800 2,400
Pilot lodging 65.00/night 65 130 195
Personnel 23/hr - technician 5,888 8,832 11,776

29/hr - biologist 1,856 2,784 3,712
Snowmobile rental 125.00/day 1,750 2,625 3,500
Total Cost (S) 13,309 19,771 26,233

 

66

Table 12. Projected costs for conducting the historical elk survey procedure using a ﬁxed-
wing aircraﬁ in northern Michigan, 2006.

 

 

 

 

Length of Survey

Cost component Per unit cost (3) 2 days 3 days 4 days
DNR ﬁxed-wing 700/day 1,400 2,100 2,800
Airplane fuel 4.00/gal 1,200 1,800 2,400
Pilot lodging 65.00/night 65 130 195
Personnel 23/hr - technician 5,888 8,832 11,776

29/hr - biologist 1,856 2,784 3,712
Snowmobile rental 125.00/day 1,750 2,625 3,500
Total Cost ($) 12,159 18,271 24,383

 

67

in 2005, we surveyed more groups in the heavier conifer classes where elk groups tended
to be smaller, and thereby reduced my mean group size.

We collected a large number of observations for development of the sightability
models (216) compared to other studies calculating elk sightability. For example, Samuel
et al. (1987) used observations of 111 elk groups for their model development, Otten
(1989) used observations of 79 elk groups and Anderson et al. (1998) used observations
of 55 elk groups.

The sightability model parameter estimates indicate the following about elk
sightability: larger elk groups have a higher sightability than smaller groups; increasing
wind speed increases sightability of elk groups; elk groups which were standing have an
increased probability of being observed over groups which were classiﬁed as bedded or
bedded and standing; groups which were located in conifercover class 1 were more
likely to be observed as opposed to groups in the heavier conifer cover class; elk groups
in areas of complete snow cover had a higher probability of being observed than elk
groups where some vegetation was showing; and elk groups located in ﬂat light with low
intensity, bright light with medium intensity, ﬂat light with medium intensity and bright
light with high intensity had a decreasing probability of being observed, respectively.
However, conifer cover class and group size are the most important variables inﬂuencing
elk sightability based on RI values and standard errors of parameter estimates. Snow
conditions are of lesser inﬂuence, and the remaining variables have insigniﬁcant impact
on elk sightability.

My sightability model results are comparable with those of other studies. Samuel

6t al. (1987) made similar ﬁndings in Idaho. They found that group size and percent

68

vegetation cover were the 2 most inﬂuential variables affecting elk sightability, while
behavior and snow conditions were of lesser importance. Otten et al. (1993) determined
conifer cover inﬂuenced elk sightability in Michigan from a helicopter; however, group
size was not determined to be inﬂuential. McCorquodale (2001) also determined canopy
cover and group size were inﬂuential variables in the elk sightability models developed

for Washington.

Survey—Population Size Estimation

The comparison between the SF and GS estimators demonstrated, as expected, the GS
increased both point estimates of population size as well as variance estimates relative to
the SF. However, we believe that higher estimates produced by the GS estimator are less
biased. Cogan and Diefenbach (1998) demonstrated the SF estimator, in the presence of
undercounting, produced negatively biased population estimates and underestimated the
variance of those point estimates. Given the differences in counts of the same elk group
by multiple observers shown in this study, we believe there is little doubt undercounting
of elk groups is occurring. The GS procedure relaxes the assumption that the size of elk
groups be known constants, and allows for estimation of group size. This estimation
reduces the bias resulting from the violation of the above assumption, and increases the
variance estimates accordingly which produces conﬁdence intervals with closer to
nominal coverage (see Chapter 3). Interestingly, when group size is estimated the largest
component of the variance in the GS model is due to estimating group size and sighting
probability, whereas in the SF the largest component of variability is due to sightability

error. Thus, the ﬁndings of Cogan and Diefenbach (1998) of below nominal conﬁdence

69

interval coverage for the SF are not surprising as the SF formulation does not include a

critical component of variability—the variability associated with estimating group size.

Sampling Simulations

The resulting increases in average variance of population estimates, as a result of
reducing the number of quadrats surveyed, were clearly demonstrated in the analyses
examining the effects of varying sampling rates in each stratum (Figures 15—20).
Reduction in sampling effort, particularly in the high density stratum, resulted in marked
increases in the average variance of population estimates. The surfaces showed that the
average variance continued to decrease as sampling effort increased with no obvious
asymptote for this stratum. In the medium and low density strata there was a continued
reduction in average variance with increasing sampling effort, however, the effects
lessened as sampling rates approach 100%. Thus, effects 0f sampling on average
variance were less dramatic in these 2 strata. This was not surprising given that the high
density stratum was considerably more variable with regards to total number of elk
within quadrats than the low or medium density strata.

The effect of increasing variance was also demonstrated in the analysis examining
optimal sample sizes per stratum given a ﬁxed sample size. The number of samples,
determined to be optimal in each stratum for a given sample size, were a reﬂection of the
variability associated within each stratum. Thus the high, medium and. low density strata
showed decreasing variability in the number of elk groups within quadrats and
consequently decreasing recommended sampling rates, respectively. From these
simulations it was clear that for the most precise population estimates, the high density

stratum should always be completely surveyed, the medium density stratum should be

70

surveyed at the next highest rate, and the low density stratum should be the focus of the
reduction in sampling effort if the range cannot be completely surveyed. Also even
minor reductions in sampling effort can have signiﬁcant impacts on the length of 95%
conﬁdence intervals. For example, if only 41 of the 47 low density quadrats and all of
the quadrats in the other 2 strata were sampled, the length of the conﬁdence interval
increased by 10 elk. If 35 of the 47 low density quadrats and all of the quadrats in the
other 2 strata were sampled, the length of the conﬁdence interval increased by 20 elk.
Given these results and the inability to correctly classify quadrats into density
strata (Table 8), we strongly recommend surveying the entire range if precise population
estimates are desired. At a minimum the range should be surveyed in its entirety for
several years (i.e., 3—5) to examine the temporal variability of the number of elk groups
in each quadrat during the survey and contributing factors (e. g., snow depths, mast
production, recreational pressure, etc.). Such an analysis will likely produce more
accurate assignment of quadrats to density strata. If the range cannot be surveyed
completely, sample sizes for each stratum should be based on Table 9 and drawn using a
probabilistic sampling scheme (e. g., simple random sample from each stratum); however,
precision of population estimates will suffer accordingly. It is also important to note the
sample sizes recommended in Table 9 are based on the 2006 elk survey data and,
therefore, the within stratum variability may change in subsequent surveys. These
changes will alter the optimal sample sizes, and therefore, the within stratum variability
should be assessed over multiple years and the average should be used to calculate

optimal sample sizes.

71

Thus, when determining whether to survey the entire range or sample a portion of
it, the question to ask is: what is an acceptable level of precision associated with the elk
population estimate relative to cost? Given the relatively low cost of the 2006 survey, the
consideration ultimately is only of the desired level of precision of the population
estimate. When the entire range was sampled the SE = 125 elk, which resulted in a CV =
13.8%. The precision of the 2006 elk population estimate is comparable to other elk
surveys across the country (Otten 1989, Steinhorst and Samuel 1989, Anderson et al.
1998, Noyes et al. 2000). However, decreasing the level of precision through sampling
dictates that changes in population size will need to be larger before differences in
population size are designated as statistically different. Thus, as the variance increases

the useﬁrlness of the estimate for management purposes decreases.

Costs

One of my objectives was to create an economical elk population estimation technique
for the MDNR biologists. The technique described above achieved this objective. The
cost of the 2006 elk survey was inexpensive relative to the historical technique with the
exception of 2 days of surveying using MDNR ﬁxed-wing aircraft. However, 2 days of
surveying using the historical technique would only allow for a small portion of the range
to be surveyed and given the range expansion in the last 10 yrs (Figure 1: Chapter 1) the
use of this technique becomes impractical. Also this technique only generated an index
to population size, whereas the 2006 elk survey, which was conducted over the entire

range, allowed for estimation of population size and an associated measure of precision.

72

Management Implications
The population estimation technique developed met all the project objectives: it
incorporated sightability model correction factors, allowed for estimation of group sizes,
utilized a probabilistic sampling scheme for surveying the range, provided statistically
defensible population estimates, and was economically feasible to conduct. It represents
a considerable improvement over the historical aerial/snowmobile technique as it
addresses the shortcomings of this procedure and allows for rigorous population
estimation. Thus, this estimation procedure is a useful tool that MDNR elk biologists can
employ to monitor population size, set harvest objectives, and meet the various demands

of a diverse array of stakeholders utilizing Michigan’s elk herd.

Availability of Estimation Program
The program that I used to estimate population size and associated variances is available
as SAS code. The code has been archived in several locations, and is available upon
request. I have used the code extensively, and I am not aware of any “bugs”, however, I
make no guarantees about the accuracy of the program or the resulting output. Dr. Henry
Campa III and Dr. Scott Winterstein in the Department of Fisheries and Wildlife at
Michigan State University have several archived copies of the program. Also Dr. Dean
Beyer, Michigan Department of Natural Resources, and I, Colorado Division of Wildlife,

have copies available for distribution.

73

CHAPTER 3: DERIVATION OF ELK POPULATION ESTIMATOR ALLOWING
FOR GROUP SIZE ESTIMATION

Introduction
Sightability models have been widely used to estimate population size for a wide array of
wildlife species, particularly large cervids (Samuel et al. 1987, Bodie et al. 1995,
Anderson and Lindzey 1996, Ayers and Anderson 1999). Sightability models are used to
estimate the detection probability of groups of the species of interest, thereby correcting
for groups that are missed by observers. Generally, sightability models are logistic
regression models with various group—speciﬁc as well as environmental covariates used
as predictor variables (Samuel et al. 1987). Estimates of population size are calculated by
summing the quotients of complete counts of groups counted during a survey divided by
their detection probability as determined from the sightability model. The technique was
ﬁrst put forth by Samuel et a1. (1987), and Steinhorst and Samuel (1989) provided the
statistical theory behind the estimation procedure. Unsworth et a1. (1990) validated the
Samuel et a1. (1987) model for elk in Idaho showing the merit of the technique.

Although this estimation procedure has proven useful, a limitation is the
assumption that group sizes of the species of interest are known. Typically, the
maximum of observer counts is used as the estimate of group size, although the
maximum as an estimator of true group size is known to be negatively biased (Olkin et al.
1981, DasGupta and Rubin 2005). Cogan and Diefenbach (1998) conﬁrmed this bias and
the violation of the above assumption using counts of elk groups of known size by
observers from helicopters in Pennsylvania. Findings in Chapter 2 also demonstrated this
assumption was violated when counting elk groups from ﬁxed-wing aircraft in Michigan

by examining multiple counts of groups by independent observers (see Chapter 2).

74

Through simulation, Cogan and Diefenbach (1998) showed when group sizes were
undercounted population estimates based on these estimates of group size showed severe,
negative bias and conﬁdence interval coverage was below nominal.

I developed a bias correction procedure based on estimating group sizes, and
incorporated the variability resulting from this estimation into the approximate variance
estimates. This correction reduces bias and increases variance estimates since group size
is treated as a random variable rather than a known value. The modiﬁed Horvitz-
Thompson estimator (Steinhorst and Samuel 1989) for estimating population size is

shown below:
L Dk Nk
T =Z—2Ri(k)mi(k)®i(k) (1)
k pk i

where 0].: 1 if the kth land unit is sampled and D1,: 0 otherwise, pk = the known

probability that the kth land unit is selected as part of the sample, Rm.) = 1 if the ith group

in the kth land unit is observed and R,- k = 0 otherwise, m- = size of the ith grou in the
( ) ((16) p

kth land unit, 9i( k) = is the inverse of the sighting probability or detection probability for

the 1'"1 group in the km land unit obtained from a sightability model, L = total number of
land units, and M. = the total number of elk groups in the study area. The realization of

this estimator correction for unknown group sizes is:

I
1 A A
t = 2—2 "1101940, (2)
k pk i

where Iii“ k) = estimated group size of the ith group in the kth land unit, 6)“ k) = is the
inverse of the estimated sighting probability or detection probability for the im group in

the kth land unit obtained from a sightability model I = the number of quadrats in the

75

sample and m, = the number of groups observed during the survey. This chapter is about
estimation of T and its approximate variance, and the examination of the performance of
this estimator.

It is assumed throughout that a logistic regression model for estimating detection
probability of groups has been previously developed, and in this logistic regression
model, the natural log transformation of group size is used as a predictor variable
(Samuel et al. 1987) as in Chapter 2. Group size is a common and often signiﬁcant
predictor variable in sightability models (Samuel et al. 1987, Otten et a1. 1993, Anderson
et al. 1998, Walsh 2007). Elk surveys conducted in 2006 in Michigan will serve as an
example for this estimator, and all analysis and discussion will be based on data collected

during these surveys.

In Section 2, I describe an example of how estimates of ﬁrm can be calculated

using multiple, independent observer counts of group size, and I compare a method-of-
moments estimator (DasGupta and Rubin 2005) to a joint-binomial-maximum-likelihood

estimator. However, ﬁrm can be estimated using any statistically valid means beyond

those explored here, and estimation of T is still possible. In Section 3, I derive the
approximate variance for the estimate of T using the conditional variance formula,
assumptions of log normality and the delta method. In Section 4, I examine the
performance of the estimator including bias, coefﬁcient of variation (CV), mean-squared
error (MSE), and asymptotic conﬁdence interval coverage through Monte-Carlo
simulations based on 2006 Michigan elk survey data, and Section 5 is a discussion of the

results.

76

Estimation of Group Sizes Using Multiple Independent Observer Counts
Multiple independent counts of groups of the species of interest can often be obtained
quickly and economically during wildlife surveys when multiple observers are used. For
example, when conducting aerial elk surveys in Michigan, 3 independent counts of
groups can be obtained by using counts from the pilot and the 2 observers attempting to
locate elk groups out each side of the plane. These counts can then be used to estimate
the true group size.

One means of estimating group size, based on the Binomial distribution
assumptions, and assuming a constant probability of detecting individuals within a group
across observers, is the joint binomial likelihood that generates maximum likelihood
estimates (MLE) of true group size. The likelihood is as follows:

3 N ,
L(N1X,, X2, X3)= H[ V‘ (1 — p)N‘Xi . (3)
i=1 Xi
with N = true group size, X,- = count of group size by the ith observer and p = the
probability of observers detecting an individual within a group from the air. However, no
closed form estimator for N exists and numerical techniques must be employed. Olkin et
al. (1981) and Carroll and Lombard (1985) provide 2 estimators of N based on the
likelihood which improve stability through use of a jack-knife procedure and integrating
the likelihood over a beta density for p.
A second estimator is the method-of-moments estimator (MME) proposed by

DasGupta and Rubin (2005):

 

mlUf) : _ _ a (4)

77

where X (w) = maximum of w observer counts of group size, X = mean these counts,

S 2 = sample variance of these counts, and a = constant. The approximate estimate of the

asymptotic variance is as follows:

 

zaz’hi(k)(’;’i(k) - 1)

vér('?1i(k)) '8 w

(5)

This MME requires a ﬁxed a value. DasGupta and Rubin (2005) recommended
a = 1; however, they only examined scenarios of large N values and small p values
where N = group size and p = probability of detecting an individual within the group.
Generally, once a group is detected during a wildlife surveys p is large, and depending on
the species, N may be small. Thus, to determine the optimal value of or, I simulated 3
random counts from a binomial distribution based on values of N ranging from 1—50 and
values of p ranging from (0.70—0.99). These values were chosen as they were the range
of elk group sizes reported during elk surveys in Michigan and probability of success
values reported by Cogan and Diefenbach (1998) for elk in Pennsylvania. For each
combination of N and p values, I varied or from 0.00—1.00, and generated estimates of N
using the MME, associated variance estimates calculated using equation (5), and
calculated MSE values over 10,000 repetitions. I summed the MSE values across all N
and p values for each a, and determined that a = 0.10 minimized this sum (Table 13).
This value of or was used in all subsequent calculations since it minimized MSE across
the expected range of N and p values for elk surveys in Michigan.

Since estimators of N in the binomial often exhibit erratic behavior including the
MLE and other MMEs (Olkin et al. 1981, Hall 1994), I evaluated the stability of this

MME. 1 generated 3 random counts from a binomial distribution with true group sizes

78

Table 13. Top 5 values of a that minimized MSE values of method-of-moments
estimates of N across all values of N (1—50) and p (0.50—0.99)

 

 

or MSE
0.10 15,493
0.09 15,571
0.11 15,621
0.08 15,841
0.12 15,965

 

79

ranging from 1—75 and probability of success (p) ranging from 0.50—0.99, and calculated
the MME of N ata = 0.10. I then added a value of 1 to one of the random counts and
recalculated the MME of N. Stability was evaluated by examining the differences
between the 2 estimates of Nover 1,000 repetitions for all N and p combinations. The
stability of the estimator was good with the mean difference of 2.51 (SD = 1.94) and a
range of 0.50—17.10 between the 2 estimates across all values of true group size and p.
To determine which estimation procedure, MLE or MME, was better for
estimation of true elk group size given 3 independent counts of group size, I once again
generated 3 random counts from a binomial distribution with N ranging from 1—50 (i.e.,
range of elk group sizes seen in Michigan) and values of p ranging from (0.70—0.99). I
then estimated N using the MLE and MME with a = 0.10, calculated associated
variances, and estimated MSE values for 1,000 repetitions of each N and p combination.
I determined the MME yielded the minimum MSE values, summed across all N and p
values over the 1,000 repetitions, with a sum of 3,7933.99 compared to the MLE, which
had a sum of 7,001.69. Thus the MME was used to estimate group sizes for all further

analyses.

Estimation of the Approximate Variance of T

The variance of the estimator of population size T in equation (1) is complicated as the

estimate of group size, ”‘1“, ) occurs both in the numerator as well as in the denominator of
equation (1), since it is a predictor variable in the logistic regression model that produces

O“ 1) . However, an approximate variance estimate can be derived using the following

lemma (Ross 2003) and the delta method. Notation follows that of Steinhorst and

Samuel (1989).

80

Lemma. The variance of the scalar function, T (D, R, B), of 3 random vectors, is
varlT(D,R, B)] = EDlvaIRlD(EB|R,D[TDl + varD(ER,B|D[T]) + EDlERlDlvarB|R,D(T )1].

where D is a random vector with kth element = Dk, which is 1 if the kth land unit is

sampled and 0 otherwise, R' = (R', , - . ., R'L ) withR',‘ being a random vector whose ith

element = Rim, which is 1 if the ith group in the kth land unit is observed and 0 otherwise,
and B; = (B', , . . ., B'L) with B', being a random vector whose ith element =n‘z,~( “(3)“ k ) .
Using this lemma and the E[m mi(k)®,(k)]~ ml-(k)®,-(k) (Appendix C), the ﬁrst 2
variance components are identical to the variance components given in Theorem 1 in
Steinhorst and Samuel (1989) with m“ k) replaced by rig-(k) . They are identical since the
expectation of the ﬁrst 2 terms is taken with respect to rill-(“OK k) ﬁrst. The third

variance component can be approximated using the delta method, the above lemma and

assuming log normality of (9,0,) (Appendix D). The resulting estimate of approximate

variance is as follows:

     

 

 

I 1'
S3221" pkM2+ZZpkk'— pkpk M kMk'+Z— _1_nzlc:[®

k pk k¢k' pkk' kak' k pk 1

1&4} i(k)é)i(k))2

iﬂ‘)

I 1 " A A
+ 5 25 + 2 Em --m [— “remit/o C°V(®i(k)’®i'(k'))]
i(k)¢i"(k) Pkpk

(6)

. ”k . I "k 5,. (3).

where M k = Z’hi(k)®i(k) , 8 =vector of partial derivatives of ZZ—M) 10‘)
i k 1' pk

with

respect to each of mm) and to each of the ,6 ’s from the sightability model (i.e.,

81

Xxx/()5

 

1 —x- 1‘1 . ’"k'iz'ke_ xh‘k .
550(k) :p—k[1+e I“) (FAD and 5’5}: = 21,1212) 1( ) Pk l( ) wlth Xm.) =the
i(

vector of predictor variables used in the sightability model for the z'(k)th group, 61 = the

beta associated with the ln( m“ k) ) as a predictor in the sightability model, and xhak) is the

 

 

62. 0 0 0
m1
hth predictor for the i(k)th observation) 2 = 0 i . O 0 with 6'2
’ 0 0 67: o 41.-(k)
""00
_ 0 0 0 Zbem_

2

411(k) = 01f all counts of group srze are equal,

derived from equation (5), or 6

Ebem = estimated variance-covariance matrix for the ,6 ’s from the sightability model.
The ﬁnal term in equation (6) is a summation of expectations, which can be

approximated using the average value of N simulated values of a“ k) and mac.) , which

are generated from a Normal distribution with mean = 62,. k) and variance =

Zaz’ﬁmcwﬁxk) — 1)

, and the cév(Oi(k)O,-.(k.)) =
w

 

e-(Xr(k)+xi'(k'))'13-(Xi(k)+xi'(k'))'ibeta(xi(k)+xi'(k’))/ {exit/C) ﬁxmk') -1],

This covariance term is identical to the ﬁnal term in the variance equation proposed by
Steinhorst and Samuel (1989), which is valid using an approximation of asymptotic log
normality.

I examined the amount of bias associated with using this approximation of the

ﬁnal term in equation 6, as well as the bias associated with using solely the point

82

estimates as an approximation of the ﬁnal term of equation (6) (i.e.,

l . . . ~ . .
——mi(k)mi'(k') cov(®,-(k),®,«(kr))] ). I generated 1,000 datasets wrth group

i(k)¢i'(k')l:pk Pk'
size being estimated using equation (4) based on 3 random counts generated from a
binomial distribution with N = estimated group size, which was assumed the true group
size, and p = average probability of success from observer counts of group size from the
2006 Michigan elk survey data. I then calculated the ﬁnal covariance term in equation
(6) using the true group sizes and the 2 approximating methods. Bias was then calculated
as the difference between the values of the approximating methods and true group size.
The point estimate approximation yielded the largest bias with an average bias of 47.45
(SD = 39.21), and the averaging approximation had an average bias of -18.04 (SD =
14.55). Both of these approximating methods produced little bias relative to the overall
variance of the population estimate, 0.30% and 0.12%, respectively. The averaging
method appears to produce less biased results, but a considerable amount of computing
time is required for this method. Therefore, if large simulations need to be conducted the
point estimate approximation will yield reasonable results with slightly liberal variance

estimates.

Performance of estimator
To assess the performance of the proposed estimator for estimating elk population size, I
followed the technique used by Cogan and Diefenbach (1998). I ﬁrst created 1,000 elk
sightability models using Monte Carlo simulation techniques based on 2004 and 2005
Michigan elk sightability model datasets (Chapter 2). Each sightability model was

created following the technique outlined in Chapter 2 for generating model-averaged

83

parameter estimates (Bumham and Anderson 2002), and their associated unconditional
variance-covariance matrix, which incorporates the measurement error associated with
estimating group size.

Secondly, I created 20 elk survey datasets by sampling observation of elk groups
with replacement from the 2006 Michigan elk survey until the total number of elk
sampled reached the desired population size. I examined population sizes of 250, 500,
750 and 1,000 elk, which span the range of elk sizes historically seen in Michigan. I
generated 3 random counts from a binomial distribution with N = estimated group size
for each observation, and p = average probability of success across observer counts of
group size from each observation given N. Then group size was estimated using these 3
random counts and equation (4). Each group was classiﬁed as seen by observers if a
Uniform (0, 1) random variable was less than or equal to the “true” detection probability,
otherwise it was considered as missed by observers. Logistic regression was used to
calculate the “true” detection probability using the parameter estimates ﬁom Michigan’s
current sightability model (Chapter 2), and the values of the predictor variables
associated with each observation from the survey datasets. Once all elk groups were
classiﬁed as seen or missed, total population size was estimated for each survey dataset
across all population sizes using equation (2) and each of the 1,000 sightability models.
Thus 20,000 population estimates were generated for each population size. Variances
were calculated using equation (6), where the last term was estimated using the point

estimate approximation to minimize computing time.

84

Performance of the estimator was then assessed by calculating the average bias,
95% conﬁdence interval coverage, average CV, and average MSE for each population
size. Conﬁdence intervals were 95% asymptotic normal conﬁdence intervals.
I also examined the performance of the Steinhorst and Samuel (1989) estimator, using the
same 1,000 sightability models and 20 survey datasets for each population size for
comparison. However, group size was estimated as the maximum of the 3 random counts
generated previously. I examined the same performance measures as described
previously (Table 14). From these results it is apparent that the proposed estimator
outperforms the traditional sightability model estimator, and bias is reduced substantially
when group sizes are estimated. The proposed estimator has increased MSE values due
to increased variances as evidenced by the larger CV values, but conﬁdence interval
coverage is closer to the 95% nominal level compared to the traditional estimator.

These results also demonstrate the approximate variance formula presented in
equation (6) generates acceptable variance estimates based on the conﬁdence interval

coverage reported.

Conclusion
Any statistically valid method (e. g., mark-recapture, distance-sampling, etc.) can
be used to estimate group size for use with this estimator. We chose to use the method-
of-moments estimator based on multiple independent counts to estimate group size, since
it performs reasonably well given the limited number of independent counts used in this
study. Also it provides an effective way for wildlife managers to estimate the size of
each group. It is important to note that the or value used in this study for estimating

Michigan elk group sizes may not be appropriate for other regions or other species, and it

85

Table 14. Average of performance measures for the population estimator that includes
estimates of group size (GS) and for the traditional sightability model estimator (SF)
based on Monte-Carlo simulations with 20,000 repetitions for each population size from
Michigan elk survey data (2006).

 

 

Conﬁdence
Interval
Population Coverage

Estimator Size Bias CV MSE (%)

GS 250 2.90 0.20 7,280.87 90.90
GS 500 -4.04 0.16 16,159.60 92.40
GS 750 3.36 0.15 31,092.33 94.70
GS 1,000 1.93 0.14 50,892.76 93.50
SF 250 -7.40 0.16 3,969.98 86.20
SF 500 -20.19 0.12 8,445.35 87.30
SF 750 —19.92 0.11 14,508.76 88.90
SF 1,000 -30.33 0.10 22,981.58 85.60

 

86

should be independently determined for each study area and species using simulations as
described.

The inclusion of the estimation of the size of individual groups in the traditional
sightability model population estimator allows for less biased population estimates. It
also increases the variance of these point estimates allowing conﬁdence interval coverage
to approach the nominal level, which is desirable given the ﬁndings of Cogan and
Diefenbach (1998) and my ﬁndings of below nominal coverage of the traditional
estimator as a result of undercounting of group sizes.

Thus this new estimator is an important tool for wildlife managers attempting to
derive accurate population estimates for wildlife species using aerial surveys, and can aid

managers in achieving a wide array of management objectives.

87.

CHAPTER 4: EXAMINATION OF ELK HOME RANGES AND RANGE
UTILIZATION

Introduction

Notable changes in the movements and distribution of elk (Cervus elaphus) in Michigan
have occurred in the last 2 decades based on the increase in the number of elk harvested,
observed and reported beyond the boundaries of the historic range as originally deﬁned in
the Elk Management Plan (Michigan Department of Natural Resources 1984). The
causative factors for these changes are not well understood. But undoubtedly, the
discovery of bovine tuberculosis (TB) in free-ranging white-tailed deer (Odocoileus
virginianus) inhabiting areas within and adjacent to the elk range, and the sweeping
management actions aimed at preventing the spread of the disease played a role. In
particular, the ban on winter-feeding of ungulates instituted in 1998, which occurred
historically throughout the elk range, has changed how elk utilize the range (D. Smith,
Michigan Department of Natural Resources, personal communication).

Using historical elk harvest and survey data it was estimated the elk range had
expanded by over 50% since 1984 (D. E. Beyer, Michigan Department of Natural
Resources, unpublished report). This range expansion created concern among biologists
that agricultural depredations will increase, as many areas of expansion have been in
privately owned agricultural lands. Also, this expansion has increased the number of elk
in areas with higher apparent TB prevalence (Hickling 2002, O’Brien et al. 2002),
providing more opportunity for interspecies transmission of the disease. Given these
concerns, developing an understanding of current elk movement patterns and distribution
is critical for determining harvest strategies, habitat management practices, and

minimizing elk-human conﬂicts.

88

Problems with the distribution and browsing pressure exerted by elk on 2 large
private hunt clubs, Black River Ranch and Canada Creek Ranch, in the central portion of
core elk area have also become an increasing concern in recent years (D. Smith,
Michigan Department of Natural Resources, personal communication). These problems,
however, are not new since Moran (1973) described elk issues associated with these
clubs. Perhaps more recently, the lack of elk harvested on the ranches for several years
prior to and during the early portion of this study, combined with deer habitat work,
forest management practices, and several good mast years have exacerbated these issues.

The main goal of this portion of the study was to gain valuable information regarding

current elk movement patterns and distribution particularly on the eastern portion of the
Michigan elk range, which is the region of major range expansion (Figure 1: Chapterl).

The objectives to achieve this goal were as follows:

1. Using elk location data, determine the size of elk home ranges and examine sex-
speciﬁc differences where home range is deﬁned as “the area traversed by the
individual in its normal activities of food gathering, mating and caring for young”
(Burt 1943).

2. Determine areas of high elk usage across years.

3. Determine areas of joint space use of elk from various portions of the range.

4. Examine elk use of large hunting clubs within the core elk range where human-
elk conﬂicts have been increasing.

5. Determine the probability of elk using various cover types, particularly managed

openings.

89

Study area

The study site selected for this project includes the current elk range (Figure 2: Chapter
1) in the northern portion of the Lower Peninsula of Michigan (Moran 1973). The range
occupies approximately 3,450 km2 (D. E. Beyer, Michigan Department of Natural
Resouces, unpublished report), and is centered on the Pigeon River State Forest near
Vanderbilt, Michigan (Bender 1992). We focused our study mainly on the eastern region
of the elk range near Atlanta in Montmorency County (Figure 3: Chapter 1). Based on
examination of landownership pattems over 33% of the elk range is publicly owned, with
another 3% controlled by 2 large private hunting clubs in the center of the elk range
(Michigan Department of Natural Resources 2000).

The region consists of ﬂat-topped ridges interspersed with headwater swamps, the
product of glacial action. Elevation ranges across the area range from 170—460 In above
sea level.

Mean annual temperature is 6.3° C with January having the lowest mean monthly

temperature (-7.7° C) and the highest (19.7° C) occurring in July (NOAA 2006). Mean
annual rainfall is 67.3 cm, and mean annual snowfall is 189 cm (NOAA 2006) with
precipitation being generally well distributed throughout the year.

Vegetation types throughout the region are diverse and intermixed due to
variations in topography, soil types and human activities. Deciduous forests are the
dominant component of the landscape and represent 30.53% of the area. Woody
wetlands represent the second largest land cover type encompassing 28.26% of the area.

Evergreen forests and mixed forests compose the next largest proportion of the land area

90

representing 7.64% and 8.29%, respectively (United States Geological Survey 1999).

Moran (1973) provides a detailed description of vegetation types throughout the region.
Methods

Capture
Michigan Department of Natural Resources (MDNR) personnel captured elk using
helicopter net-gunning techniques (Carpenter and Innes 1995) in early February of 2003
and of 2005. In the summer of 2004, several elk were darted using chemical
immobilization procedures (Roffe et al. 2005). Michigan State University All University
Committee on Animal Use and Care exempted this project (D. L. Garling, AUCAUC,
written communication, 12 27 2003).

Most elk were collared with a 550 g, MOD-600HC radiocollar from Telonics
(Mesa, Arizona, USA). Five individuals captured in 2006 were collared with G2000 GPS
Collars from Advanced Telemtry Systems (Isanti, Minnesota, USA). These collars were

programmed to take ﬁxes every 7 hours.

Elk Locations

Project personnel attempted to locate every surviving animal captured in 2003, a
minimum of 3 times a week, and elk collared in 2005 a minimum of 2 times a week
throughout the study. A less intense sampling regime was used for elk collared in 2005
as a result of limited resources. This amount of effort ensured collection of greater than
50 relocations/animal/year, the minimum sampling intensity suggested to obtain unbiased
annual home range estimates (Otis and White 1999, Seaman et al. 1999 and Garton et al.

2001). Also this level of effort conforms to the recommendations of Borger et al. (2006)

91

Q.

of 10 locations/month, which they found was adequate to generate unbiased home range
estimates using kernel methods based on home ranges of roe deer (Capreolus capreolus)
in Italy. Lastly, this sampling design likely allowed elk the opportunity to move
throughout their annual home range within the sampling period, and allowed for unbiased
temporal coverage with ample time for movement between subsequent locations to
minimize issues of autocorrelation (De Solla et al. 1999, Otis and White 1999).

Radiocollared animals were located using the loudest point method (Springer
1979, White and Garrott 1990) with portable Model R1000 receivers (Communication
Specialists, Orange, California, USA), hand-held, 2 and 3-element yagi antennas
(Telonics, Mesa, Arizona, USA), GPS units (Garmin, Olathe, Kansas, USA) and
compasses to determine receiver location and bearing to each radiocollared animal.
Personnel collected a minimum of 3 bearings to estimate each point location, and
bearings were collected in the shortest amount of time possible to minimize errors
associated with a moving animal (White and Garrott 1990). Every attempt was made to
obtain bearings with a minimum difference of 25° to promote location accuracy and
precision.

Personnel conducted relocations of marked individuals in 2 shifts, a morning shift
(5:30—14:00) and an afternoon shift (15:00—22:00). Order of relocations of individual
animals within each shift followed a cluster sampling technique. Animals were placed
into 3 primary sampling units (psu) based on their geographic distribution to maximize
efﬁciency in relocating animals, and I created a sampling route for each psu based on
locations of marked individuals. Personnel sampled 1 psu each shift with order of

relocations of elk within a psu being selected based on a simple random sample without

92

replacement of marked animals. The selected animal was the individual initially located.
Personnel subsequently located all marked individuals in the vicinity based on scanning
of all radio frequencies. Once animals in the cluster were sampled, personnel proceeded
to follow the sampling route for the psu in the direction that was most temporally
efﬁcient. This procedure was designed to ensure unbiased temporal coverage of
relocations, avoid clumping of observations and alleviate concern over autocorrelation
issues as well as maintain statistical efﬁciency (Otis and White 1999). If marked
individuals were together, these aggregations were treated as a single unit when selecting
an initial animal to relocate until such time as groups dissolved.

Elk have been shown to exhibit differences in habitat selection and space use
between diurnal (800—2000 hours) and nocturnal periods (2000—800 hours) (Beyer and
Hauﬂer 1994). Thus, we attempted to obtain elk locations throughout a portion of both
periods.

We also attempted to obtain a minimum of 2 visual locations on randomly
selected radiocollared elk each week. We used homing techniques to acquire visual
locations (White and Garrott 1990), and locations were determined using a hand-held

GPS unit.

Analysis

Error assessment.—An important component of any radio telemetry study where
animals are not directly located is estimation of both precision and accuracy of the
triangulation system (White and Garrott 1990, Withey et al. 2001). I estimated precision
of bearings for each observer by placing transmitters in various cover types and

topography to incorporate the range of variability within the region of our study (White

93

and Garrott 1990). Every transmitter was attached to a plastic bottle ﬁlled with saline
solution to simulate the absorption of the radio signal by an elk’s body (Hupp and Ratti
1983). Observers then using triangulation techniques (White and Garrott 1990) took
bearings from known locations to the test transmitters. Bias and precision for each
observer were calculated based on differences between estimated bearings and true
bearings using the formula presented by White and Garrott (1990). Bias, averaged across
observers, was tested to determine if it was signiﬁcantly different from zero using a
standard t-test. I lastly calculated average SD of bearings to the test transmitters to test
precision of the loudest point method.

By placing them at a ﬁxed location for approximately 1 week prior to deployment
and examining the variability in estimated locations, I investigated the SD of GPS collar
ﬁxes. It was assumed the ﬁxes were unbiased.

Location estimation. —Prior to location estimation, I visually inspected the point
locations from which bearings were taken in ArcView Version 3.2 (ESRI, Redlands,
California, USA), and corrected data entry errors and removed erroneous data. Next, I
used Lenth’s maximum likelihood estimation (MLE) procedures in Locate III (N ams
2006) to calculate all location estimates based on the bearing data. The standard
deviation of the bearings was ﬁxed as the standard deviation calculated during the error
assessment. I examined the accuracy of all estimated locations using ArcView, and
removed points that were estimated incorrectly based on visual inspection.

Home range estimation. —1 estimated home ranges of individual animals using
multivariate Gaussian ﬁxed kernel estimators (Worton 1987, 1989; Wand and Jones

1995) in R Version 2.4.1 (2006). I placed a grid over the entire study area with 160.9344

94

m spacing, and estimated the probability density at each grid point using the ﬁxed kernel
estimators. Fixed kernel estimators provide several advantages over other types of
estimators. For example, they do not make any assumptions about the underlying
distribution and handle complex multi-modal distributions with multiple centers of
activity well (Kemhonan et al. 2001). These estimators also create a utilization
distribution (UD), which can be a useful metric for analyzing animal space use (Marzluff
et a1. 2001 , 2004; Millspaugh et al. 2006). They also tend to perform better, have less
bias especially in the outer contours of the UD, are robust to outliers, and require a
smaller sample size (i.e., number of locations) compared to other estimators including the
adaptive kernel estimators (Seaman and Powell 1996, Seamann et al. 1999, Borger et al.
2006). The smoothing parameter or bandwidth was determined for each elk using a 2-
stage, direct plug-in (DPI) bandwidth selector (Wand and Jones 1995, Kemohan et al.
2001). The smoothing parameter represents the standard deviation for each of the
individual kernels in the kernel function, and therefore determines the distance from a
particular elk location for which that elk location will have inﬂuence on the density
estimate of surrounding grid points. I chose the DPI method over the more commonly
used least squares cross-validation (LSCV) bandwidth selector, as research based on
simulations suggests that the DPI selector is a better bandwidth selector in the sense it
provides less variable, unbiased estimates of the bandwidth compared to LSCV (Wand
and Jones 1995). Also the rate of convergence to theoretical optimal bandwidth is greater
for the DPI selector compared to LSCV.

Wand and Jones (1995) provide a detailed description of each of these techniques,

which I summarize below for the univariate case. Extensions to the 2-dimensional case

95

are straightforward as h is replaced with H a 2 X 2 bandwidth matrix, and replacing x by

a matrix of (x, y) locations.
LSCV is a bandwidth selector which attempts to choose a bandwidth size that

minimizes mean integrated squared error (MISE). MISE can be calculated as follows:
" . __ " . 2 " . 2
MISE{f(., 12)} — E 1m, h) dx — 2E j/(x. h)f(x)dx + fro) dx.

where f (x, h) is the kernel estimate of the density at point x given bandwidth h, and
f (x) is the true density estimate at point x. However, this expression can be formulated

in the following manner since the ﬁnal term is not dependent on h:

MISE{f‘(.;h)} — jf(x)2dx = E1 thx;h)2dx — 2 Jf(x;h)f(x)dx1.
LSCV(h) is an unbiased estimator of the right hand side of this formulation and is
calculated as follows:

LSCV(h) = If"(x;h)zdx — 2n'12njf”.r(X.-;h)

i=1
n
where f_,-(x;h) = (n — 1)“1 2K h (x — X j) is the leave-one-out kernel density estimator.
j¢i
Thus the Optimal bandwidth under the LSCV technique is the bandwidth that minimizes
LSCV (h).

The DPI selector is based on the notion of using estimates for unknown quantities

5
R(K) ] ,whereK

#2(K)2¢4"

 

in the formula for the AMISE-optimal bandwidth: h A MISE = [

represents the chosen kernel, R(K) = I K (x)2dx , [22(K) = Ix2K(x)dx ,

96

(04 = I f ""(x) f (x)dx , and n = the number of observations. The only unknown quantity

in the AMISE—optimal bandwidth is go4 as it is dependent on f (x). The DPI selector

replaces this quantity in the following estimator:

 

llDPI =[ R(K) ]5 , where
#200 (04(8))!

71 I! n
(254 (g) = n-IZf(4)(X,-;g) =n—ZZ ZLEWX, — Xj) , and L may be a different kernel
i=1 i=1 j=1

2K(4)(O)
- #200606"

 

3
than K with bandwidth g = [ ] , and the sample of locations, X, is given.

However, in this formula g must also be estimated since (06 is a function of f(x)—this
problem does not go away. At each stage this same problem arises since the (a needs to
be estimated (e. g., at the next stage (06 is estimated as a function of gas ). DPI selectors

address this problem by using a normal scale rule as a plug-in at some stage, I, to estimate
(pr. Such a band-width selector is called an l-stage DPI bandwidth selector. The normal

scale rule is used since it is easy to calculate and is available in following form:

r
—l —r! ,. . . . . . .
(p, = ( )2 1 , where a is est1mated from X and rth derivative rs even. For thrs

(2&)’+1[—;—)m3

 

analyses 1 = 2, and we used the same normal kernel for L and K.
Using the ﬁxed kernel estimates, I calculated annual home range sizes at the 95%
and 50% probability contours for individuals in the study for at least 2 years, and overall

home range areas averaged across all study years at the 95% and 50% probability

97

contours for each individual. These probability contours have been commonly used in
wildlife studies (Seaman and Powell 1996, Hooge and Eichenlaub 1997, Anderson et al.
2005). I calculated the variance of these home range areas empirically using
bootstrapping procedures (Efron and Tibshirani 1993) outlined by Kemhonan et al.
(2001) with 1,000 repetitions. In addition, I incorporated radiotelemetry sampling error
into the bootstrapping procedures to account for the uncertainty associated with the
location estimates based on the assumption of asymptotic normality of MLE estimates.
This error was incorporated during each iteration of the bootstrap procedure by taking
each estimated location selected in the bootstrap dataset, and replacing it with a location
generated from a multivariate normal distribution with a mean = the estimated location
and variance-covariance matrix generated from the estimated standard errors for X and Y,
and their correlation, which was produced for each estimated point location in Locate III.
Elk locations selected in the bootstrap datasets, which were conﬁrmed visually on the
ground or from the air, and locations from GPS collars were assumed to have no location
error, as error in these cases is trivial compared to the error associated with triangulation.
Given the 1,000 bootstrap estimates of the probability density function and their
associated area at each probability contour, the quantile method was used to generate
95% conﬁdence intervals for each home range area (Efron and Tibshirani 1993).

Two bulls collared in 2003 with VHF collars were recollared in 2005 with GPS
collars. However, due to design problems these collars malfunctioned within 3 months
post-deployment. Locations were then acquired using triangulation techniques for the
remainder of the season until collar removal. This created a large amount of data while

the GPS receivers were functioning, relative to the amount of data collected during the

98

rest of the year. To avoid biasing kernel estimates as a result of this wealth of data, I
weighted the locations obtained from the GPS collars using a normal density kernel,
based on the following equation suggested by Katajisto and Moilanen (2006):

i=1 2h,
where t represents time a location was taken, and h = bandwidth. For this analysis, t
represented the time since the initial location in decimal days, and h = 1.12 which is
approximately half of the mean time between subsequent locations for the 2 elk of
interest. This bandwidth size was subjectively selected as it represents the standard
deviation of the kernel function, and thus creates a weighting of approximately 1 for GPS
ﬁxes that are the average time apart based on the sampling regime for the VHF collars.
Weights for the ith GPS ﬁx were the inverse of D(t,-). All locations collected using
triangulation techniques were given a weight of 1, assuming temporal independence.
These weights were then used to weight locations in the kernel and variance estimation
procedures described above. However, the kernel had to be modiﬁed to ensure
normalization to unity. This was achieved by dividing by the effective population size
rather than the total number of locations used in the kernel estimator. I calculated the
effective population size by summing the weights of all locations. The following

equation was the result of this procedure:

 

where x is the location at which density is to be estimated, w,- is the weights for the ith

observed location, h is the bandwidth matrix, and X, is the ith observed location. Using

99

this procedure, allows for better estimation of the kernel density function as all
information is being used. Using simulations and a similar technique, Katajisto and
Moilanen (2006) demonstrated that estimates of the kernel density function were
considerably better using this type of approach compared to resampling the data with an
appropriate time interval, which results in the loss of information.

I compared sex-speciﬁc differences between mean home range areas for both
overall, and annual home range areas using two-tailed Mann-Whitney tests, as well as
comparison of standard normal conﬁdence intervals between means of interest.
Variances of means were calculated by summing the individual variances for each home
range area and dividing by the square of the total number of individual home range areas
used to calculate the mean (i.e., I assumed each individual was independent). Using the
same procedures I examined year-speciﬁc differences within and between each sex class.

Overall range use. -To allow for population level inference concerning the
probability of use of the study area, I combined individual kernel estimates to generate an
overall kernel density for the sample of radiocollared individuals. As individuals vary in
the number of years collared and, therefore, the number of locations acquired, combining
all the locations for all elk would bias the population density function, as those with more
locations would be weighted heavier than those with fewer. This data manipulation
would effectively create spikes in the density surface where home ranges of elk collared
and alive all 3 years of the study were located. To address this problem, I created kernel
density estimates for each individual using the techniques described above with
probability density estimated at points on a corrrrnon grid with spacing of 160.9344 m.

The grid was created in Arcview to ensure coverage of the estimated home ranges of all

100

radiocollared elk. I created the population level density function by averaging across all
individual density estimates at each point on the grid in SAS Version 9.1 (2003) (Wand

and Jones 1995). The following equation summarizes the above procedure:
_ 1 ’1 .
fp0p(x) = ZZfzi-x),
i=1

where fp0p(x) is the averaged kernel density estimate for the sample of radiocollared

elk at location x, and fi(x) is kernel density estimate at location x for the ith individual

elk. Variances for each point of the averaged surface were calculated by summing the
individual variances, generated using the bootstrap procedure previously described, and
dividing this summation by the square of the total number of individuals used to calculate
the mean (i.e., 58). This surface and the variance surface were graphically displayed in
ARCGIS 9.0 (ESRI, Redlands, California, USA) using interpolated distance weighting
(IDW) with parameters of K = 2 and 12 nearest neighbors. Areas of high elk use were
noted, and the amount of area used was calculated for the 95% probability contour using
Hawth’s Analysis Tools (Beyer 2006). This process was repeated for each year of the
study to look at annual range use based on average kernel density estimates. However,
for the annual, averaged kernel densities, only animals that had at least 2 years of data
were used, to allow for qualitative comparison of range use across years. These kernel
averaging analyses require the following assumptions to allow population level inference:
1) Individuals collared represent a random sample of the population, and therefore their
range use reﬂects that of the population. 2) Collared elk are independent. 3) Individual

kernel density estimates adequately describe range use.

101

Joint space use between elk groups. —To examine joint space use between groups
of elk from various portions of the range, the study area was subjectively broken into
distinct summering areas based on summer distribution of radiocollared elk. Summer
locations were used to segregate elk into groups, since radiocollared individuals tended to
be in discrete groups and widely distributed during this time of year before rut and
wintering activities. Movements of radiocollared elk among areas were then qualitatively
characterized. To quantitatively assess and delineate areas of joint space use I created
population level kernels for each summering area, using the same kernel averaging
procedure described above, (i.e., l averaged the kernel density estimates for all
radiocollared elk assigned to a speciﬁc summering area). I then multiplied the density
estimates from each summering area’s population level kernel for each point on the
common grid, with the density estimates for the same grid points from the population
level kernels for all other summering areas between which interchange occurred. This
analysis created joint density functions, and delineated areas of interchange and intensity
of joint space use within these areas (Wand and Jones 1995). Variance estimates for the
density function were approximated using the delta method and the bootstrap estimated

variances for each grid point. The following is the approximate variance equation:

.. " " “ 2 42 “ 2 42
vartntx) * fj(x)) 9 fix) a.- + fJ-(x) 0,,
where 1;,(x) is the density estimate of the ith kernel at a common grid point, x, and 6",? is

the estimated bootstrap variance of the density estimate at the common grid point from
the ith kernel. This process assumes that individuals or groups for which joint space use

was examined were independent.

102

However, these joint space use analyses only examine space sharing, and do not
examine temporal aspects of that sharing (i.e., animals may intersect in space, but not in
time). For evidence of intermingling of elk groups from across the range, I examined the
movement patterns and distribution of radiocollared elk from the few isolated locations
where they were initially collared (i.e., they were in the same space at the same time
when they were collared) to summering areas. I assessed the number of summering areas
elk captured in the same location used, as a simple metric of the amount of interchange
between elk from different summering areas.

Elk use of club lands in the core elk range-Immigration and emigration of elk
associated with Black River and Canada Creek Ranches was addressed through the
evaluation of the joint space use of elk groups previously described. Additionally, I
examined the movements of collared bulls from Canada Creek during the rutting season
(i.e., August through November). No radiocollared bulls were on Black River Ranch
prior to the rut. I determined the number of locations of radiocollared elk, radiocollared
bulls and radiocollared cows on each of the ranches annually and for the entire study
period for each month. This allowed for a rough examination of elk use of these 2
ranches, and the distribution of use within a year. Fixed kernel density estimates were
generated for each club using only elk locations that fell within their boundaries. Four
surfaces were developed, 3 annual surfaces and 1 surface using all the locations on the
clubs during the entire study.

Probability of use of various cover types. —Cover types of interest were
determined from IF MAP land classiﬁcation system (Michigan Department of Natural

Resources 2001). I examined 11 different cover types: agricultural (IFMAP code = 5, 6,

103

7 and 9), aspen association (IFMAP code = 16), upland conifers (IFMAP code = 19—21),
lowland forest (IFMAP code = 24—26), mixed conifer/deciduous (IFMAP code = 22),
mixed upland deciduous (IFMAP code = 18), northern hardwood association (IFMAP
code = 14), oak association (IFMAP code = 15), openings (IFMAP code = 10—13), water
(IFMAP code = 23) and other (IFMAP code = 1—4 and 27—35). I also examined the
probability of use of openings managed by the MDNR based on ARCVIEW shapeﬁles of
managed openings provided by local MDNR biologists (B. Mastenbrook and D. Smith,
Michigan Department of Natural Resources, personal communication).

Probability of use for a particular cover type was determined using Spatial
Analyst and 3D Analyst extensions in ARCGIS. I reclassiﬁed all grid cells of that cover
type with a 1 value, and all other cover types were reclassiﬁed with a 0 value. Then
using Raster Calculator this reclassiﬁed raster was multiplied against the IDW raster for
the averaged kernel density estimates for all elk and for all years. This produced a raster
containing only pixels, from the averaged kernel density surface, that were associated
with the cover type of interest. I then calculated the probability of use by
integrating/calculating the volume under this surface. This was repeated for each cover
type previously described.

I estimated variances of these probability estimates by intersecting the point
locations at which averaged kernel density estimates were generated with the reclassiﬁed
raster for each cover type using Hawth’s Analysis Tools. This created a ﬁeld for each
cover type in the shapeﬁle attribute table containing an indicator of whether a point was
contained in the cover type of interest. If the point was contained within the cover type, I

calculated the sum of the variances by summing the bootstrap variance estimates

104

associated with each point multiplied by the square of the grid cell area using R. To
account for spatial autocorrelation of density estimates created by the kernel function, I
generated a correlation structure for the estimates based on distance using a Matem
covariance ﬁrnction (Handcock and Stein 1993, Marzluff et al. 2004). The smoothing
parameter (9) was set at 0.5, which equates to an exponential function. The range or
scale parameter (p) was determined by the averaging the bandwidth matrices, determined
as described previously, across all radiocollared individuals. I calculated covariances
between 2 points by multiplying their correlation by the bootstrapped standard errors for
each point. Total covariance, for the probability of use of the cover type of interest, I
estimated by multiplying each individual covariance estimate for each pair of grid points
by 2 times the square of grid cell area (i.e., 25,900 m2), and summing across all point
combinations. Finally, the total variance for each probability of use estimate was
calculated by adding the sum of variances and sum of the covariance.

I tested if the probability of using managed openings was greater than expected,
by determining if the expected probability of using managed openings was within the
normal conﬁdence intervals for the estimated probability for managed openings. The
expected probability was calculated by taking the percentage of the total area of all
openings (i.e., managed and unmanaged) contained in the study region, occupied by
managed openings, and multiplying this percentage by the probability of use calculated
for all openings. This analysis is based on the assumption that if there is no effect of
management activities on elk use of openings, elk will use all openings with an equal

probability.

105

Results

Capture

Helicopter net gunning in 2003 resulted in 20 adult bulls and 20 adult cows being
captured. The same technique in 2005 yielded an additional 16 adult cows. Darting
activities in the summer of 2004 resulted in 2 adult cows being radiocollared. Only adult
elk were collared, and most bulls were subdominant. No capture related mortalities
occurred ﬁom any of these collating activities.

Of the 5 GPS collars placed on elk, only 3 remained functional throughout the
deployment period. These 3 collars collected data until all collars were retrieved from
the animals in late October 2005.

No mechanical failure of the VHF collars occurred during the duration of the

study. All collars functioned the beyond the length of the study.

Elk Locations
Over the 3 years of the study, personnel collected a total of 13,923 triangulated locations
on radiocollared elk and an additional 728 visual observations by homing in on collars or
incidental sightings. After removal of poorly estimated locations and data entry errors, I
used a total of 16,767 locations across all animals and all location techniques (i.e.,
triangulation, GPS collars, visual sightings and aerial visual sightings) in all subsequent
analyses.

The distribution of the times of acquisition of triangulated locations is bimodal
with peaks at 1000 and 1600 hours (Figure 21). Approximately 95% of the locations
were taken between 0600 and 2100 hours, with 22% of the locations being acquired

during the nocturnal time period. All aerial visual sightings were during the diurnal

106

 

 

 

 

 

 

1200
E: 1000 ~~ -1 e * ~ * ——~~———~ﬂ ~ I -—4 +4;—
8 800 ~ +++++++ - ~ —— ‘- - ~
.2
“5 600 -~-——+-—~-~-* - ~ —4
3'5 400
.o LUL LL ,. - Mr
E I
z 200 +~-—--~*-—-_—-- * k * w » , I I

0 _
1 3 5 7 9 11 13 15 17 19 21 23
Hour

 

 

 

Figure 21. The distribution of acquisition times of triangulated locations for
radiocollared elk in Michigan, 2003—2006.

107

period. GPS ﬁxes from all 5 collared elk were uniformly distributed throughout the day

(Figure 22).

Analysis

Error assessment. —Personnel collected 522 useable bearings to collars placed in
various locations throughout the study area. The average bias across all observers and
collar locations was -l°, however, it was not signiﬁcantly different from zero (1521 = -
1.53, P = 0.126) at a = 0.05. The standard deviation of these bearings was 9.998°, and
this value was used in Locate III for all location estimation. Standard deviation of GPS
ﬁxes over 148 ﬁxes was 14.23 m with an average difference ﬁ'om the mean location of
10.02 m.

Home range areas. —Mean bull home range size averaged across all study years at
the 95% probability contour was 9,587 ha (SE = 143) With a maximum of 17,784 ha and
a minimum of 378 ha. Mean cow home range was 6,349 ha (SE = 96) with a maximum
of 14,004 ha and a minimum of 2,813 ha. Based on examination of 95% standard normal
conﬁdence intervals, the mean bull home range size calculated at the 95% probability
contour was signiﬁcantly larger than the corresponding mean cow home range size. This
was conﬁrmed by a Mann—Whitney test (W20,38 = 599, P $0.001). Mean bull home
range size averaged across all study years for the 50% probability contour was 1,764 ha
(SE = 39) with a maximum of 3,492 ha and a minimum of 72 ha . Mean cow home range
was 1,272 ha (SE = 27) with a maximum of 3,168 ha and a minimum of 368 ha. Based
on examination of 95% standard normal conﬁdence intervals, the mean bull home range
size calculated at the 50% probability contour was signiﬁcantly larger than the

corresponding mean cow home range size. This was conﬁrmed by a Mann—Whitney test

108

 

120

Number of locations

 

 

 

 

 

 

 

Tr'Tr

 

I l

l

 

100‘ * *

80*

60* *

40*

20 *

0 r 1 u'r «r .
3 5 7 9

ll

13 15 17

Hour

19 21 23

 

Figure 22. The distribution of acquisition times of GPS ﬁxes for radiocollared elk in

Michigan, 2003—2006.

109

 

(W20,33 = 555, P = 0.002). Estimates of the size of home range areas at the 95% and 50%
probability contour, number of locations used in the kernel density ﬁrnctions and
associated 95% conﬁdence limits are displayed in Table 15 for each radiomarked elk.
Figure 23 depicts a graphical example of kernel density estimates of an elk home range
and associated 95% conﬁdence limits. Images in this dissertation are presented in color.
I calculated 95% and 50% contour annual home range size for 18 bulls and 18 cows in
2003 and 2004 and for 16 bulls and 14 cows in 2005. Based on standard normal 95%
conﬁdence intervals mean bull home range size was signiﬁcantly larger in 2003
compared to 2004 and 2005 home range size, but there was no statistical difference
between 2004 and 2005 (Table 16). Mean cow home range sizes were different across all
years with decreasing size from 2003 (Table 16). Within all years, mean bull home range
sizes were consistently larger than cow home ranges, and across years they were also
larger with the exception of the mean cow home range size in 2003, which was not
statistically different from mean bull home range size in 2004 and 2005 (Table 16). The
same patterns were generally true for the 50% contour annual home range size. However
at this contour, mean annual cow home range size in 2004 was not different from 2003 or
from 2005 home range sizes (Table 17). Also mean bull home range size in 2004 is not
different from mean cow home ranges in 2003 and 2004 (Table 17). Using the Mann-
Whitney test conﬁrmed these relationships (Table 18 and 19). Individual annual home
range estimates and upper and lower conﬁdence limits for the 95% and 50% probability
contour intervals are shown in Table 20 —23.

Overall range use. —Radiocollared elk used a total area of 58,973 ha over the

study period based on the 95% contour of the kernel density surface created by averaging

110

Table 15. Estimates of home range size (ha) at the 95% and 50% probability contour,

associated 95% conﬁdence limits (LCL, UCL), number of locations used in kernel
density estimation (n) for radiocollared elk in Michigan, 2003—2005.

 

 

ID Sex n LCL 95% Contour UCL LCL 50% Contour UCL
3 Bull 352 7,587 8,685 9,288 1,584 1,836 2,061
10 Bull 229 4,860 6,048 6,552 684 837 999
13 Bull 334 13,896 16,020 16,848 2,952 3,492 3,825
14 Bull 352 6,885 8,622 8,757 1,080 1,278 1,449
15 Bull 355 5,220 6,300 6,768 1,071 1,242 1,368
16 Bull 348 12,852 15,732 16,605 1,728 2,070 2,376
17 Bull 361 8,793 10,287 10,665 1,512 1,818 2,052
18 Bull 56 342 378 900 54 72 108
20 Bull 425 4,535 5,307 5,405 1,145 1,31 1 1,368
22 Bull 232 8,451 10,098 10,548 1,548 1,917 2,187
23 Bull 358 10,953 13,365 13,914 1,359 1,638 1,944
25 Bull 464 6,439 7,659 7,736 1,259 1,489 1,621
29 Bull 345 8,091 9,414 9,837 1,440 1,719 1,935
30 Bull 354 9,675 11,124 11,664 1,800 2,097 2,358
33 Bull 336 9,423 11,421 11,880 1,413 1,773 2,070
34 Bull 363 6,975 7,983 8,460 1,512 1,737 1,881
35 Bull 361 10,989 12,150 12,654 2,772 3,249 3,492
36 Bull 347 5,688 6,948 7,209 981 1,134 1,287
37 Bull 107 5,058 6,408 6,858 882 1,341 1,620
38 Bull 349 15,399 17,784 18,639 2,628 3,231 3,717
l Cow 365 5,022 5,697 6,201 1,251 1,386 1,539
2 Cow 284 5,148 6,435 6,606 801 945 1,089
4 Cow 368 5,778 6,750 7,164 1,188 1,350 1,503
5 Cow 375 4,833 5,499 5,859 765 900 1,044
6 Cow 356 8,091 9,504 9,972 1,422 1,710 1,926
7 Cow 275 8,271 9,846 10,260 1,431 1,746 1,980
8 Cow 378 4,320 4,959 5,346 648 729 882
9 Cow 310 12,267 14,004 14,598 2,691 3,168 3,465
11 Cow 396 4,707 5,310 5,625 1,098 1,251 1,377
12 Cow 394 4,815 5,364 5,742 1,044 1,170 1,305
19 Cow 282 10,557 12,060 12,681 2,223 2,655 2,970

 

111

Table 15. (cont’d).

 

 

ID Sex n LCL 95% Contour UCL LCL 50% Contour UCL
21 Cow 382 7,650 9,045 9,387 1,278 1,530 1,755
24 Cow 372 4,833 5,589 5,886 1,035 1,179 1,323
26 Cow 375 5,319 6,201 6,606 747 882 1,044
27 Cow 364 7,965 8,541 9,036 1,917 2,205 2,385
28 Cow 365 5,058 5,985 6,300 891 1,071 1,206
31 Cow 378 4,311 5,130 5,481 864 981 1,098
32 Cow 121 6,975 8,856 9,630 1,791 2,340 2,565
39 Cow 376 4,923 5,787 6,156 981 1,107 1,224
40 Cow 96 4,338 5,733 6,489 774 1,107 1,386
41 Cow 171 2,853 3,654 3,834 540 711 819

42 Cow 179 3,816 4,644 4,878 801 1,017 1,152
46 Cow 100 3,096 3,789 4,212 684 909 1,035
48 Cow 76 3,429 4,491 4,806 747 1,116 1,332
49 Cow 97 5,526 6,921 7,497 1,188 1,665 1,953
50 Cow 1 14 4,446 5,418 5,931 774 1,089 1,368
51 Cow 81 3,393 4,356 4,752 765 1,071 1,251
52 Cow 49 6,948 10,773 12,564 1,053 1,989 2,691
53 Cow 97 4,806 6,012 6,642 1,044 1,395 1,638
54 Cow 1 12 5,976 7,902 8,424 1,080 1,449 1,737
55 Cow 79 2,529 3,564 4,104 315 477 747

56 Cow 108 7,965 9,927 10,683 1,746 2,277 2,601
57 Cow 93 3,519 4,887 5,940 729 1,053 1,278
58 Cow 681 2,435 2,813 2,797 298 368 414

59 Cow 809 2,989 3,209 3,297 663 746 798

61 Cow 733 4,649 5,654 5,879 427 484 554

64 Cow 97 2,781 3,735 4,059 459 621 792

66 Cow 51 1,755 3,222 3,906 315 495 71 1

 

112

a)
Upper 95%

 

conﬁdence w_m Legend

surface -— 14;, ,._.._.,,,, __

[’1 High :8.59 e-08
U Low : 0
'1 High :7.05 e-08

ﬂLowzo

N High 5.55 e-08

    
 

Lower 95% . :
conﬁdence .1 LOW . 0

surface

It

 

 

 

 

13)

Manila

 

M 31 Legend

I High: 1.33e-09
o 0.5 1 2 3 4
Kilometers ’—‘U_|'J L0" 5 0
Figure 23. Kernel density estimate surface and associated 95% conﬁdence sru'faoes (a),

and intensity map ofkemel density estimates (b) ofelk #12’s home range in Michigan,
2003—2005.

 

 

 

 

 

 

113

Table 16. Estimates of mean annual home range size (ha) at the 95% probability contour,
associated 95% conﬁdence limits (LCL, UCL), number of elk (n) for radiocollared elk in

Michigan, 2003—2005.

 

 

 

Bull Cow
2003 2004 2005 2003 2004 2005
Mean 12,780 7,722 7,401 7,342 6,323 5,459
SE 378 163 179 178 133 134
n 18 18 16 18 18 14

UCL 13,520 8,041 7,751
LCL 12,040 7,404 7,050

7,691 6,583 5,722
6,993 6,063 5,196

114

Table 17. Estimates of mean annual home range size (ha) at the 50% probability contour,

associated 95% conﬁdence limits (LCL, UCL), number of elk (n) for radiocollared elk in
Michigan, 2003—2005.

 

Bull Cow
2003 2004 2005 2003 2004 2005
Mean 2,578 1,557 1,544 1,436 1,365 1,218
SE 200 53 57 48 45 40
n 18 18 16 18 18 14
UCL 2,971 1,661 1,655 1,531 1,454 1,296
LCL 2,185 1,454 1,432 1,341 1,277 1,140

 

115

Table 18. Matrix of Mann-Whitney test statistics and associated P—values for sex and
year comparisons of mean annual home range size (ha) at the 95% probability contour,
for radiocollared elk in Michigan, 2003—2005.

 

 

 

 

 

Bull COW
2003 2004 2005 2003 2004 2005
2003 261 228 273 284 240
($1.001) ($0.001) (0.002) (50.001) (it-001)
161 178 225 190
Bull 2004 (0,287) (0.314) (0.024) (0.007)
144 204 163
2005 (0.5068) (0.019) (0.017)
248 197
2003 (0.003) (0.003)
Cow 133
2004 (0.404)

2005

 

116

Table 19. Matrix of Mann-Whitney test statistics and associated P—values for sex and
year comparisons of mean annual home range size (ha) at the 50% probability contour,
for radiocollared elk in Michigan, 2003—2005.

 

 

 

 

 

Bull Cow

2003 2004 2005 2003 2004 2005

2003 253 212 266 278 221
(0.002) (0.009) (50.001) ($1.001) ($1.001)

139 177.5 221 169.5

Bu“ 2004 (0.5743) (0.318) (0.063) (0.051)
172 204.5 153

2005 (0.1737) (0.019) (0.046)

201 156
2003 (0.1131) (0.1312)
Cow 125
2004 (0.5152)

2005

 

117

 

 

 

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118

 

 

 

 

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119

 

 

 

 

 

 

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120

 

 

 

 

 

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121

across all radiocollared elk. Areas of high use included the following regions in no
particular order: Osmun/Clark Bridge region, Camp 30 Hills, Blue Lakes region, Tin
Shanty Road region, Black River and Canada Creek Ranches, Buttles Road region,
Meaford Hills, Bone Yard/Hubert Road region, and the Chipper Pile Road region (i.e,
region north of Voyer Lake Road between M-33 and Steven Springs Road). These areas
of high probability density are depicted in the kernel density surface and associated
standard error surface displayed in Figures 24 and 25.

The amount of area used in 2003 by 36 radiocollared elk was 58,864 ha based on
the 95% contour of the averaged kernel density surface. In 2004 the area of range used
was 54,112 ha for the same elk, and 30 elk used 48,335 ha in 2005. It also should be
noted that care must be taken in comparing surfaces from 2005 with other years, as 6 elk
(i.e., 1 from Black River Ranch, 2 from Bone Yard, 1 from Elk Hill Trail Camp, 1 from
Camp 30 Hills, and 1 from Canada Creek) were removed due to mortalities. Annual,
averaged kernel density surfaces and associated standard error surfaces are displayed in
Figures 26—3 1. The areas previously described with high elk use for the kernel density
surface averaged across all years and radiomarked elk, are also the regions that were used
heavily by elk for each year of the study. Differences across years in these surfaces
include the following: in 2003 and 2004, the Brush Creek Truck Trail/Grass Lake region
was used; however, this did not occur in 2005 with the marked elk remaining in the Bone
Yard area. In 2004, elk used the region north and northeast of the Morrow/Hubert Road
intersection, an area with elk crop damage complaints. This area was not used during
other years of the study. The Elk Hill Trail Camp region was used in 2003 and 2004, but

not during 2005. However, this was likely due to loss of radiocollared elk in this region.

122

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1 l l, P
W% _
_4
'3.
'6
>
Bum M32
It I I
l
MMWA
‘5}
$4.
0 I ”i
l E
1.53 6 9 12
-:-:—:—Kilomcters

 

 

 

 

 

 

 

 

63¢
L_.C
WW5”
\
Road
i \ﬂ
Legend A
High 22.14 e-08
Low : 0

 

 

 

 

Figure 24. Averaged kernel (husky 086m of space Inc for 58 elk in Michigan,

2003—2005.

123

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

“ Jxl I I Fl 1 2
E M r r
W ' ~- ,
—l l
Webb
V’1 0011me
$-
‘5
Wwas
P
A .-
W 33
t‘ ill \
j M32
rl . '
Legend
High:4.48e-09
2 4 a 12 16161 a Lowzo
c-Z_:— om ers

 

 

 

 

 

 

Figme25. Esﬁmatwofstandardenoramciatedwiﬂlavemgedkemeldensitycsﬁnmus
of space use for 58 elk in Michigan, 2003—2005.

124

 

 

 

IFT

 

 

 

 

 

 

 

 

 

 

 

 

 

 

hi)

6“

conﬁrms” J

Beckett 33 ' Ll:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

It I I _:r L
d _
M33
3' A k

—F- Legend

P :4 High: 1.03e-08
2 4 8 12 16_ Low:0

-:-:—:_Kilometers

 

 

 

 

 

 

Figure 26. Averaged kernel density wtimatw of annual space use for 36 elk in Michigan,
2003.

125

Legend
High : 9.23e-10

Low20

 

Figure 27. Estimates of standard error associated with averaged kernel density estimates
of space use for 36 elk in Michigan, 2003.

126

Legend
High: 9.44e-09

LOW:0

 

Figure 28. Averaged kernel density estimatw of annual space use for 36 elk in Michigan,
2004.

127

Legend
High : 9.83e-10

Lowzo

 

Figure 29. Estimates of standard error associated with averaged kernel density estimates
of space use for 36 elk in Michigan, 2004.

128

Legend
High : 1.40e-08

LOW:0

 

Figure 30. Averaged kernel density estimates of annual space use for 30 elk in Michigan,
2005.

129

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

‘ l I l:Li
01V ' T
l
w . ~ J
l
Webb ‘-
1 comm“
i
‘8-
mmhﬂm "
\2
mm 3
I l
l _
M32 , I r
2 Legend A
F High. 1.33e-09
1.53 6 9' 1'2 Low:0
mﬂlometcrs
L . \ _L_L

 

 

Figure 31 . Estimates of standard error associated with averaged kernel density estimates
of annual space use for 30 elk in Michigan, 2005.

130

Other noticeable differences are associated with varying intensities of use of regions used
across years, which can be assessed by visual inspection of the surfaces in Figures 26-31.

Joint space use between elk groups. —Based on summer locations of radiomarked
elk, 10 summering areas were deﬁned. These are displayed in Figure 32, and are named
as follows: Black River, Bone Yard, Camp 30 Hills, Canada Creek, M-32 South,
Meaford, Osmun, Tin Shanty, Vienna and Voyer Lake. Interchange of elk from various
summering areas occurred across the range (Figure 32), with all summering areas having
an inﬂux of elk from different summering areas. The only summering area to have no elk
depart from the summering area for other regions was the Vienna area. However,
animals utilizing this area were only collared for 1 season, which may have not allowed
adequate time for them to exhibit movement into other summering areas.

Examination of the joint density surface, for 7 radiocollared elk from the Black
River summering area and 7 elk from the Camp 30 Hills area, shows the areas of joint
space use occurs on the southern and eastern portions of Black River Ranch, along Blue
Lakes and Black River roads and in the Tin Shanty Road area (Figure 33). Joint space
use, for elk from the Black River summering area and 9 elk from the Canada Creek,
occurs mainly on the western portion of Canada Creek Ranch, the eastern portion of
Black River Ranch, and the southwest reaches of Black River Ranch (Figure 34). For elk
from the Black River Ranch area and the 5 elk from Osmun Road area, joint space use
occurs throughout Black River Ranch and the region north of Clark Bridge Road to just
west of its intersection with Osmun Road (Figure 35). The western portion of Black
River Ranch and the region between Tin Shanty and Saw Dust Pile Roads are the areas of

joint space use for elk from Black River area and the 5 elk from Tin Shanty summering

131

 

 

 

 

 

 

 

 

 

 

 

 

w 5
3 0 3 6 Kilometers S
E

.4 I I 1 r7); A? 1‘ ' 1 ‘ Lug—A

 

 

Figure 32. Summering areas and general interchange patterns between areas for
radiocollared elk in Michigan, 2003—2005 (arrows represent movement of at least 1

radiocollared elk).

132

 

 

v; j , \
it “i

1 51¢

'. 4...;

ISparr Rd <‘\

 

 

 

 
  
   

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1
Legend ‘
_m High : 5.1464e-Ol7
L051 2 3 i -u LOW : 0
.II_—_—_4Ki.lunem
’ l! l \x \

 

Figure 33. Joint density kernel surface depicting areas of joint space use between 7
radiocollared elk from the Black River summering area and 7 elk from the Camp 30 Hills
summering area in Michigan, 2003-2005.

133

 

 

 

 

 

 

 

 

 

 

 

Legend

.1“ .
n" Hi : 1.4803e-016
l'lf’: 3‘ 8h

 

 

 

 

 

 

 

i l a
1 “W
” lﬂ \\ \

Figure 34. Joint density kernel surface depicting areas of joint space use between 7
radiocollared elk ﬁom the Black River summering area and 9 elk from the Canada Creek

summering area in Michigan, 2003—2005.

 

 

134

 

 

 

 

 

 

 

 

 

 

 

L end
__/ cg

M High : l.0580¢-01

5
C I A
Ian 2 3 4mm“01m l 1 BLOWNO j
}’ lﬂ \\ \

Figure 35 . Joint density kernel surface depicting areas of joint space use between 7
radiocollared elk from the Black River summering area and 5 elk from the Osmun
summering area in Michigan, 2003-2005.

 

 

 

 

 

 

 

 

area (Figure 36). Joint space use mainly occurred on the southwest comer of Canada
Creek Ranch and the southern portion of Black River Ranch between the radiomarked elk
from the Camp 30 Hills summering area and the Canada Creek area (Figure 37). The
majority of the joint space use between the Camp 30 Hills elk and the Osmun Road elk
occurred in the Blue Lakes region and southern portion of Black River Ranch (Figure
38). For theCamp 30 Hills elk and the Tin Shanty Road elk joint space use was primarily
between Tin Shanty and Saw Dust Pile roads and south of Blue Lakes (Figure 39). Joint
space was limited and occurred only at 2 areas along Rouse road, and in the region
between Decheau Lake road and M-33 for elk from the Canada Creek summering area
and the 6 elk from the Meaford area (Figure 40). The western portion of Black River
Ranch and the western portion of Canada Creek Ranch were the sites of j oint space use
for elk from the Canada Creek area and elk from the Osmun summering area (Figure 41).
For Canada Creek elk and the 4 elk from the Voyer Lake area, joint space use was
isolated to the region near the intersection of M-33 and Voyer Lake road (Figure 42).
Meaford road elk and the 6 elk from the M-32 South summering area, jointly used space
throughout the Meaford hills area and the Elk Ridge Golf course region (Figure 43). Elk
from the Meaford area and elk from the Voyer Lake area, had joint space use mainly in
the region between Decheau Lake road and M-33, and in southern portion of the Elk
Ridge Golf Course (Figure 44). M-32 South elk and the 4 elk from Vienna jointly used
space north of M-32 in the Camp 8 road region (Figure 45). Elk from Voyer Lake
summering area jointly used space in the Hubert road and Brush Creek Truck Trail
regions with 5 elk from the Bone Yard area (Figure 46). Lastly, Voyer Lake elk and M-

32 South elk had joint space use in the region between Decheau Lake and M-33, Elk

136

 

 

 

 

 

 

 

 

E Sturgeon Valley Rd 5
County Ron
Span Rd
, Legend
E I"! .. High: 1.5175e-016
L n‘ . -1

 

 

 

 

 

 

 

 

 

 

l{l\\\

Figure 36. Joint density kernel surface depicting areas of joint space use between 7
radiocollared elk from the Black River summering area and 5 elk from the Tin Shanty

summering area in Michigan, 2003—2005.

 

137

 

 

 

 

 

 

t

 

 

”$E ‘ )x' \ l
. 1

e, ‘u

“ _

VF —

7‘)

    
 

 

 

 

 

 

 

 

Legend
n High : 8. 9549e-018
E I I- ‘1:
0.51 2 3 41(an i “Latino
lﬂ \\ \

 

 

Figure 37. Joint density kernel surface depicting areas of joint space use between 7
radiocollared elk from the Camp 30 Hills summering area and 9 elk ﬁ‘om the Canada

Creek summering area in Michigan, 2003—2005.

138

 

 

 

 

 

    

 

 

 

 

 

’1
.l'

  

 

Legend
n High : 4.0751e-017

BLOWZO
TEA k L

Figure 38. Joint density kernel surface depicting areas of joint space use between 7
radiocollared elk from the Camp 30 Hills summering area and 5 elk from the Osmun

summering area in Michigan, 2003—2005.

 

 

 

 

 

 

 

139

 

 

 

 

 

 

 

 

 

 

   

F
I..__._.

ISM ‘

V

H

 

 

 

 

 

 

 

 

 

Legend
HHighzs.76764e-016 r
E I I-
no.512 3 4. i “Latvio —
7;) Kslclnetu _‘~—
VI l\ \ ,1

 

Figure 39. Joint density kernel surface depicting areas of joint space use between 7
radiocollared elk from the Camp 30 Hills summering area and 5 elk from the Tin Shanty
summering area in Michigan, 2003—2005.

140

 

 

 

 

 

1\

County Roao 6

 

 

 

”iv Legend

’ ‘ mI-Iighzl.0000e-018 ,7:

3

 
   

  

mLowzo
. “K m

Figure 40. Joint density kernel surface depicting areas of joint space use between 9
radiocollared elk ﬁ'om the Canada Creek summering area and 6 elk from the Meaford
summering area in Michigan, 2003—2005.

 

 

 

 

 

 

141

 

 

 

 

 

 

 

Legend
m High. 1. 3920e-Ol7

.-
. 4 . . i f H LOW: 0 \\j
2’ m

Figure 41. Joint density kernel surface depicting areas of joint space use between 9
radiocollared elk from the Canada Creek summering area and 5 elk from the Osmun
summering area in Michigan, 2003—2005.

 

 

 

 

 

 

 

 

142

 

 

 

 

 

 

I0.4].8 1.6 2.4 3.2
cut—Kiln

l

 

 

 

 

 

Legend
N High : 2. 0000e-018

 

 

 

Figure 42. Joint density kernel surface depicting areas of joint space use between 9
radiocollared elk from the Canada Creek summering area and 4 elk from the Voyer Lake

summering area in Michigan, 2003—2005.

143

 

 

 

 

 

K
we
I

 

 

 

5\

 

 

 

051 2

 

Co ty Road 622

“I Legend L—
[‘1 High : 3.2041e-016
. 3 4 m Low : 0 L
II-Z—Kilomtm

n

ComtyRoad 628

   

 

 

 

 

 

 

 

 

 

 

I N [LR

 

Figure 43. Joint density kernel surface depicting areas of joint space use between 6
radiocollared elk from the Meaford summering area and 6 elk from the M—32 South
summering area in Michigan, 2003—2005.

144

 

 

 

 

 

Comfy Road 628

 

 

I

3"
\

0.41.8 1.6 2.4 3.2.

ﬂ High : 6.1470e-016
‘ E1 Low : 0
III—z-Ktluneter

   
  

h

 

 

 

 

 

 

 

’[

 

 

 

 

\

C. in 1
Figure 44. Joint density kernel surface depicting areas of joint space use between 6
radiocollared elk from the Meaford summering area and 4 elk from the Voyer Lake
summering area in Michigan, 2003—2005.

145

 

 

A

 

 

 

%\4.'
K

Old State

 

 

. ﬂ 5

 

 

a:

 

Legend
h F ' . _0
n .. .1!“ High .l.9507e 16
[f ..
.3n.7 1.4 2.1 2.8. r u Low : 0
III—:-

 

 

 

 

 

1......— “L. P' I I

Figure 45. Joint density kernel surface depicting areas of joint space use between 6
radiocollared elk from the M-32 South summering area and 4 elk from the Vienna
summering area in Michigan, 2003—2005.

 

 

 

146

 

 

 

 

 

CountyRoad 628

 

 

 

 

 

 

 

Pt V3119?

99W

 

Legend
B"! High : 2.1774e-017

11,222 .

0.51 2 3 4 WLGW:0

a—Z—Kﬂmm 32 / ‘J

 

 

 

 

 

 

Figure 46. Joint density kernel surface depicting areas of joint space use between 4
radiocollared elk from the Voyer Lake summering area and 5 elk from the Bone Yard
summering area in Michigan, 2003—2005.

147

Ridge Golf Course and the region northwest of the intersection of M-32 and Thornton
road (Figure 47).

Elk captured during the winter months dispersed from the few capture sites across
the range. Elk from several different summering areas were oﬁen captured at the same
locations during the major capture operations in 2003 and 2005 (Figure 48). The 2003
capture sites in the Blue Lakes region and the ridges east of M-33 and north of Voyer
Lake Road had the greatest intermingling of elk from various summering areas. The
capture site on Canada Creek Ranch where a large number of individuals were
radiocollared showed limited dispersal to other regions. Dispersal of elk from 2005
capture sites was limited with most animals utilizing summer range near capture sites. A
notable exception was 1 cow from the Bone Yard that moved to the Canada Creek
summering area.

Elk use of club lands in the core elk range-Radiocollared elk used both Black
River Ranch and Canada Creek Ranch throughout the study. In addition, animals
summering on these ranches jointly used space with elk from 7 of the 10 summering
areas (Figure 32). Locations of joint space were previously described. Radiomarked
bulls, which used Canada Creek Ranch (i.e., no radiomarked bulls used Black River
Ranch) during the summer, distributed themselves throughout the elk range during the rut
for all years of the study (Figure 49—51).

Elk use of Black River Ranch averaged across years was typically heaviest on the
eastern portion of the ranch and the region just east of the Vanderbilt gate (Figure 52).
Changes in intensity of use of various regions within the range are evident, and can be

qualitatively assessed by examining Figures 53-55. Most noticeably is a shift of space

148

 

 

E

 

 

 

   
   

 

  

d! ,_

1...... °
-I_=—Kilnmem
M41 [+4.

Figure 47. Joint density kernel surface depicting areas of joint space use between 4
radiocollared elk from the Voyer Lake summering area and 6 elk from the M-32 South
summering area in Michigan, 2003—2005.

 

 

 

 

n High :l.5965e-016

 

 

 

LAP/Mr

 

 

 

149

 

 

 

 

 

 

 

 

 

 

 

 

 

L

 

Figure 48. General movements of at least 1 radiomarked elk away from winter capture
sites (unﬁlled circles represent 2003 capture sites, cross-hatched circles represent 2004
capture sites, and line-ﬁlled circles represent 2005 capture sites, and size of circles
represent the relative number of elk captured) in Michigan, 2003—2005.

150

 

F

p 19AM 9|

 

 

 

 

.(
—T1—‘ :2 IT‘

 

A

 

SE

 

 

_J
4.1

 

 

10123Ki|omdnrs
E

 

 

f

 

Figure 49. General movements of radiomarked bulls ﬁ'om Canada Creek Ranch during

the rut (August—November) in Michigan, 2003.

151

 

 

 

 

 

 

 

. Li:
«kn L
8 N
\
0'
t
5-
i g
a 8
Rd 1
~1 < T ~
_ — 10123Kim
ﬁ— :2 In‘ : E .—

 

 

 

 

 

Figure 50. General movements of radiomarked bulls ﬁ'om Canada Creek Ranch during
the rut (August—November) in Michigan, 2004.

152

 

 

etth

 

«1,

 

 

:g

 

PM?!

 

SSW

 

 

.4

 

45‘
_. 10123Ki|omdnrs
1 5'55

 

 

 

 

(—

Figure 51. General movements of radiomarked bulls from Canada Creek Ranch during

the rut (August—November) in Michigan, 2005.

153

 

Clark Bridge

 

 

 

O
. I! ,.
Legend "
— High : 1.29 e-07 "' E
I 003507 14 21 (2:, \
I Low : 0.000000 - - - - -Kﬂmet\ers\
l

 

.47.?)

 

 

 

Figure 52. Kernel density map of radiomarked elk use of Black River Ranch based on
1,443 locations in Michigan, 2003—2005.

154

 

 

Clark Bridge

 

 

 

0
Legend
_ H E
ngh : 1.08 e-07
I m 5 \
0 0350.7 1 4 21 2.8
Low : 0.000000 -:-:—:_Kilometers\
,J/gtl ﬂ \

 

 

Figure 53. Kernel density map of radiomarked elk use of Black River Ranch based on
503 locations in Michigan, 2003.

155

 

\.

r _ .1 er

,, ‘,
ClarkB-ridge / t

/

     

l

 

 

 

 

 

Legend :7
E
High: 1.10 e-07
I 6‘
0 0350.7 1.4 2.1 2.8
Low 2 0.000000 Kilometers
)1. S ‘2- \

 

Figure 54. Kernel density map of radiomarked elk use of Black River Ranch based on
381 locations in Michigan, 2004.

156

 

 
  
  

Clark Bridge
I

 

I!

 
   

 

 

 

 

-7 ‘ . N
Legend
_ w E
ngh : 1.50 e-07 /
I x 3 \
00370.75 1.5 2.25 3 x,
Low : 0.000000 III—:_Kilometers
Qh‘ri w ‘5—Fr’

 

Figure 55. Kernel density map of radiomarked elk use of Black River Ranch based on
559 locations in Michigan, 2005.

157

use towards the eastern portion of the range during 2004, with the use more widely
distributed in 2003 and 2005. Also in 2005, the area near the Vanderbilt gate received
more intense use than in other years. Lastly, in 2003 the south central portion of the
ranch (i.e., The Burn and Bucket Hill regions) was used more than in other years.
Elk use of Canada Creek Ranch averaged across years was focused primarily in the west
central portion, as well as the northwest and southeast comers of the ranch (Figure 56).
Examination of elk use across years shows shiﬁing distribution of use patterns (Figures
57—59). In 2003, elk activity was focused in the region along the West Fence road near
food plot 5, and in the southwest corner near the Homestead Gate. In 2004, elk use was
more widely distributed throughout the central portion of the ranch, and in the southeast
comer near the South Gate. In 2005, elk use was similar to the previous year, although. it
was concentrated in a narrower band running southeast to northwest through the ranch.
Elk use of Black River Ranch within a year was greatest during the spring months of
March and April, and again in the fall during September—November for all years of the
study (Figure 60) based on the number of locations of radiomarked elk occurring within
the boundaries of the ranch. Elk use by sex followed the same trends across years with
radiomarked bulls using Black River Ranch for the most part only during these peak
times. Radiomarked cows used the ranch more heavily during these peak times, but used
the ranch throughout the year (Figures 61—63).

Canada Creek was used by radiomarked elk throughout the year with peaks in
March, the summer months of J une—August, and in the winter months of November and
December (Figure 64). Bulls used the ranch throughout the year, but showed decrease

use during September—November for all years of the study. They also displayed some

158

 

 

 

 

 

 

 

 

 

 

 

   
  

‘ Legend
High: 7.14 e-08

Low : 0.000000

 

 

 

 

0 0.45 0.9— 1.8 2.7 .
> (It—Kilometﬁ'l
,1 r” K |

Figure 56. Kernel density map of radiomarked elk use of Canada Creek Ranch based on
1,957 locations in Michigan, 2003—2005.

 

159

 

‘V

 

 

 

 

 

 

\ ‘J ..

 

 

 

 

k

 

      

\ Legend .-
High : 6.19 e-08 '
0 0.45 0.9 1.8 2.7
Low: 0.000000 / ,1 Kafmaeé

 

 

Figure 57. Kernel density map of radiomarked elk use of Canada Creek Ranch based on

477 locations in Michigan, 2003.

160

 

 

 

 

 

  

 

 
    

\ V

“W
\ Legend

- High:6.l9 e-08

I 0 0.45 0.9 1.8 2.7 3.6
Low : 0.000000 (IE—Kilometeé
/ ,f l i

 

 

 

 

 

 

Figure 58. Kernel density map of radiomarked elk use of Canada Creek Ranch based on
805 locations in Michigan, 2004.

161

 

 

 

 

 

 

 

 

 

 

 

 

 

' High: 7.51 e-08
o 0.45 0.9 1.8 2.7 3.6 /
Low : 0.000000 -I_:-Kilmd:ts

/ _L 1

Figure 59. Kernel density map of radiomarked elk use of Canada Creek Ranch based on
675 locations in Michigan, 2005.

 

162

 

 

120

 

 

-mow» ~ ~w

 

 

80w~~~ h~—*w-

123456789101112

Month j

 

 

 

60

 

 

Locations

 

 

40

20—

 

 

 

 

0..

 

 

l
J
l
1

Figure 60. The number of locations of radiomarked elk (n = 40 in 2003, n = 39 in 2004,
and n = 39 in 2005) occurring within the boundaries of Black River Ranch in Michigan,

2003—2005.

163

 

 

2003

 

60

 

 

 

 

 

,— I bulls
D cows

 

 

 

 

 

 

Locations

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

123456789101112

 

 

 

Figure 61. The number of locations of radiomarked elk (n = 20 bulls and n = 20 cows in
2003) by sex occurring within the boundaries of Black River Ranch in Michigan, 2003.

164

 

 

40

 

 

 

30 A»---- — —--—+—w
l

25 «——m —- ..
20 I _ I bulls

Clcows
15

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Locations

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 62. The number of locations of radiomarked elk (n = 18 bulls and n = 20 cows in
2004) by sex occurring within the boundaries of Black River Ranch in Michigan, 2004.

165

 

 

 

90

 

 

70
60 ~——
50 Ibulls .
40

 

 

 

 

 

 

 

D cows

 

—ﬁ

 

 

Locations

 

 

20
10 H II

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

l:
°°L::
:3

9101112

 

l
I. _, , .__|

Figure 63. The number of locations of radiomarked elk (n = 16 bulls and n = 23 cows in
2005) by sex occurring within the boundaries of Black River Ranch in Michigan, 2005.

166

 

 

 

 

 

 

 

 

140*
g .2003
"g? .2004
.3 .2005
J
l

123456789101112

, Month
l
l_.___w

Figure 64. The number of locations of radiomarked elk (n = 40 in 2003, n = 39 in 2004,
and n = 39 in 2005) occurring within the boundaries of Canada Creek Ranch in Michigan,

2003—2005.

167

reduction in use during the April and May, but the amount of reduction was variable
across years. Cows showed limited use of the ranch across all years, although use
increased during the study with highest use during the summer and winter months
(Figures 65—67).

Probability of use of various cover types—Based on the averaged kernel density
estimates radiocollared elk used the following cover types with decreasing probability:
openings, aspen, oaks, northern hardwoods, conifers, lowland forest, mixed
conifer/deciduous, other, mixed upland deciduous, agriculture, managed openings and
water (Table 24). The average CV across all probabilities was 13%. Comparison of the
amount of overlap in conﬁdence intervals shows that many of the probabilities are not
statistically different from each other.

Managed openings were used at higher probability than expected. The expected
probability of use was 0.811%, and estimated probability of use was 1.26% (SE =

0.0014).

168

 

 

 

 

I bulls
Cl cows

 

 

 

Locations

 

 

123456789101112

 

l Month
1 J

Figure 65. The number of locations of radiomarked elk (n = 20 bulls and n = 20 cows in
2003) by sex occurring within the boundaries of CanadaCreek Ranch in Michigan, 2003.

169

 

 

 

Locations

 

 

 

 

 

 

Figure 66. The number of locations of radiomarked elk (n = 18 bulls and n = 20 cows in
2004) by sex occurring within the boundaries of Canada Creek Ranch in Michigan, 2004.

170

2005

 

 

l
100 ‘
+ I

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

90 +~~++ ~ -%———
80 -—~
g 70 -
£33 I ”M
W4, III ,wm
:* :3 3o _ - i 2. = I-
a 20 ~ - F
.Ml!ng=u. ..
; 0.2I.I|II.II.!I=I!III_
% 1 2 3 4 5 6 7 8 9 10 11 12
I
Month
l_

 

Figure 0'/. ‘lhe number ot locations or radiomarked elk (n = 16 bulls and n = 23 cows in
2005) by sex occurring within the boundaries of CanadaCreek Ranch in Michigan, 2005.

171

Table 24. Probability of elk use of various cover types and associated standard errors
(SE), coefﬁcients of variation (CV), and standard normal 95% conﬁdence limits (LCL,

UCL) in Michigan, 2003—2005.

 

 

Cover gpe Probability SE CV LCL UCL

Agriculture 0.0152 0.0023 0.1526 0.0107 0.0198
Aspen 0.1558 0.0168 0.1075 0.1230 0.1887
Conifers 0.1178 0.0143 0.1213 0.0898 0.1459
Lowland forest 0.0977 0.0126 0.1288 0.0731 0.1224
Managed openings 0.0126 0.0014 0.1102 0.0099 0.0153
Mixed conifer/deciduous 0.0859 0.0100 0.1164 0.0663 0.1055
Mixed upland deciduous 0.0224 0.0034 0.1519 0.0157 0.0291
Northern hardwood 0.1154 0.0139 0.1201 0.0882 0.1425
Oaks 0.1348 0.0155 0.1151 0.1044 0.1651
Openings 0.1870 0.0205 0.1099 0.1467 0.2272
Other 0.0583 0.0077 0.1321 0.0432 0.0735
Water 0.0094 0.0014 0.1444 0.0068 0.0121

 

172

Discussion
The sampling regime employed during this study allowed for the acquisition of a large
amount of location data from the sample of radiocollared elk. The bimodal distribution
of collection times of triangulated locations is a reﬂection of the 2-shiﬁs used during the
study. Although this distribution is far from uniform, it does demonstrate that there was a
large amount of locations collected in both diurnal and nocturnal periods, and as a result
there is likely negligible bias in our home range or probability estimates as a result
oﬁime-speciﬁc movements or selection of resources (Beyer and Hauﬂer 1994).
Triangulated locations were relatively imprecise compared to GPS ﬁxes, and standard
deviation of bearings was larger than the 6° reported and used for other studies in this
region (Ruhl 1984, Beyer 1987). This discrepancy could be due to differences in types of
cover and topography at which transmitters were placed, distance from transmitters, or
ability of observers.

The GPS collars provided highly precise location information and ﬁxes times
were nearly uniformly distributed throughout the day. Thus they may be more
appropriate for habitat selection studies, or for studies where detailed use information is
required. The major drawback with these collars is reliability and design ﬂaws. Collars
on 2 bulls stopped functioning in March 2005, less than 2 months after deployment. The
malfunction in both cases was due to an exposed antenna wire, which was severed by the
elk during normal activities. The antenna wire was exposed during deployment, as the
collars were being adjusted to ﬁt the bulls’ necks, and sit with both the antenna and
receiver vertically oriented on the animal. This design ﬂaw limited the usefulness of

these collars, and the manufacturers are currently looking for solutions to this problem.

173

 

Thus all these factors should be weighted into the decision of whether to use GPS or
traditional VHF collars.

Estimates of mean home range sizes reported here agree closely with Beyer
(1987), who estimated a mean non-rut, home range size for bulls of 9,363 ha and mean
non-rut, home range size of 6,444 ha for cows. However, Bender (1992) reported home
range sizes of 2,600 ha for bulls and 2,970 ha for cows. The difference may be attributed
to the smaller sample size of elk (i.e., 28), number of locations used, the high quality
habitat in the core of the elk range from which he sampled elk, and the fact that he only
monitored calves and yearlings. Ruhl (1984) reported only seasonal home ranges,
however, if his estimates of fall and spring home range sizes, the times of greatest
movement in Michigan, are summed then his estimates are similar to those reported
herein. All 3 of these studies, however, employ the useof 100% minimum convex
polygon (MCP) home range estimation techniques (Mohr 1947), which for a given
sample size will tend to yield larger home range estimates than those produced by ﬁxed
kernel methods, as used in this study. This is due to the fact that MCP methods assume a
uniform density function, and it includes all boundary points in the delineation of home
ranges. Thus, it is likely elk home range sizes noted in this study are larger than those
reported previously.

Researchers in other eastern states have reported a variety of home range sizes for
elk, all of which are less than those reported herein. Peterson et al. (2006) reported a
mean home range size of 4,156 ha for 54 radiocollared bulls in Arkansas using kernel
methods. In Pennsylvania, bull home range sizes were reported as 5,309 ha and cow

home ranges as 1,748 ha (Pennsylvania Game Commission 2007). In Wisconsin, mean

174

 

home range of 22 cows was estimates as 2,134 ha for summer and 2,841 ha for winter
based on kernel methods (Anderson et al. 2005). Although no annual home range size
was provided for direct comparison, given the non-migratory nature of the Wisconsin elk
herd it is likely the annual home range size would not exceed the sum of summer and
winter home range sizes. Estimates of annual home range sizes of elk in western states
tend to be much larger than in eastern states. These estimates do not provide a good
comparison of this study’s estimates as elk in western states are often at higher
population densities, migratory, and inhabit vastly different topographic terrains and
cover types relative to eastern states. For example, Van Dyke et al. (1998) reported a
range of mean annual home range sizes for different elk herds in south-central Montana
and northwestern Wyoming. These sizes ranged from 8,360 ha to 37,660 ha based on
95% MCP methods. Thus, compared to other elk herds in eastern states, where home
range sizes were available, Michigan elk have the largest estimated mean annual home
range. These large home ranges may be an artifact of over 20 years of hunting pressure,
since it has been shown that ﬂight distances and daily movements have increased in
Michigan since the hunting was resumed in 1984 (Beyer 1987, Bender 1992). Also
differences may be attributed to differences in elk range conditions between the various
states, or overall differences in elk densities between states (Anderson et a1. 2005).
Mean bull annual home range sizes were larger than associated mean cow home
range size across all years of this study at the both the 95% and 50% contours. Beyer
(1987) and Ruhl (1984) made similar ﬁndings during their investigations of the Michigan
elk herd. These ﬁndings are not surprising as bull home ranges are expected to be larger

given the differences in foraging strategies and anti-predator defenses between the sexes,

175

 

as well as rutting behavior (Geist 2002). However, Bender (1992) examining calves and
yearlings in Michigan found no difference in home range size between the sexes. This
ﬁnding is likely due to the fact that both male and female calves and yearlings remain
with their maternal group through much of the year in Michigan (Moran 1973, Bender
1992), and thus would be expected to have similar home range sizes as a result.

Home range sizes decreased throughout the study period for the 95% and 50%
contours. Both bull and cow home range sizes were considerably larger during 2003
than in other years of the study. This difference may be attributed to the below average
temperatures experienced during this year, or differences in mast production, forest
management practices and snow depths. Also age of collared animals may have been a
factor, particularly for the bulls, since we collared primarily subdominant animals, which
tend to move greater distances then older bulls (Bender 1992).

Elk use of the range was highly variable with many peaks and valleys in the
kernel surfaces. Although many high and low use areas remained such throughout the
study, examination of annual averaged kernel density surfaces across times shows
variability in intensity of use of these areas. Some of these changes are undoubtedly due
to habitat and forest management practices as well as natural food production throughout
the range. For example, in 2003 several managed openings northeast of the Osmun/Clark
Bridge road intersection were replanted with clover and buckwheat, and that area
received intense use by radiocollared elk that year. The amount of use lessened in
subsequent years presumably as forage quality lessened, and as forest cutting activities
occurred in adjacent areas distributing the intensity of use more widely throughout the

region.

176

 

Interchange between groups of elk from various portions of the range is likely
common in Michigan based on the joint space use analyses and dispersal from capture
sites. Regions in the central or core elk range as expected had the most joint space use
with other regions. Not surprisingly, the periphery areas such as the Bone Yard and
Vienna summering areas seemed to be characterized by considerably fewer movements
of elk into and out of these areas. Also this interchange between groups appears to be
highest during winter based on a qualitative assessment of location data, and examination
of the dispersal patterns of radiocollared elk from their capture sites. This is supported by
ﬁndings of Moran (1973) and Bender (1992) who noted intermingling of elk from
various portions of the range particularly during the winter when elk groups are the
largest. Intermingling of elk groups is variable from year to year as the different
dispersal patterns from capture sites across years demonstrate (i.e., large amount of
dispersal in 2003 and limited in 2005). In 2003, the sites with the largest concentrations
of elk from across the range were in fresh timber cuts or along oak ridges (i.e., there was
an exceptional acorn crop in fall 2002). During capture operations in February 2005, the
winter was mild with warm temperatures and little snow accumulation relative to the
weather conditions during the 2003 capture. Therefore, it is likely that local
concentrations of elk from across the region are undoubtedly largely affected by weather
conditions and forage availability.

In addition to understanding interchange between elk groups, the delineation of
joint space use areas provides elk managers with knowledge of areas that are used in
common by elk from across the range, which can be targeted for habitat or population

management practices. Also knowledge of the regions that concentrate elk can be useful

177

 

for focused disease surveillance or control efforts. Thus understanding, interchange, joint
space use and knowledge of where and how they occur are important considerations in
elk management in Michigan with implications for population, habitat and disease
management issues.

Private club lands in the central portion of the elk range provide a vital role for elk
in Michigan both currently as well as historically. Black River and Canada Creek
ranches were used by a large number of radiocollared elk throughout the study. This use
does vary by season and sex. Interestingly, most radiocollared elk use of Black River
Ranch, outside the early spring and fall periods, was by cows, whereas the opposite was
true for Canada Creek Ranch with mainly only radiocollared bulls using it during those
time periods. Sexual segregation in elk for a majority of the year is well documented
(Moran 1973, Bender 1992, Geist 2002). The cause of this sexual segregation is oﬁen
habitat related. It is postulated that cows tend to select areas of better security cover for
calf rearing purposes compared to bulls, which select areas with more nutritious forage to
recover from the previous and prepare for forthcoming winter and rutting activities (Geist
2002). Thus, the segregation of sexes in the case of these clubs may be related to the
various habitat conditions and management practices each club employs, or a function of
differences in the amount of disturbance due to human use.

In the early spring during green-up many of the radiocollared elk normally
associated with Canada Creek moved to Black River Ranch. However, by late spring and
early summer the elk returned to Canada Creek. This short-term movement was
presumably due to food availability, which would indicate an earlier green-up or more

nutritious food source in early spring on Black River Ranch.

178

 

The decrease in elk use of Canada Creek during the fall is due to bulls, which
spend most of the year on the ranch, distributing themselves across the range for the
rutting purposes. This suggests that Canada Creek likely supports a large number of bulls
that are important for breeding purposes for a wide area of the range, and it is critical to
consider this fact when determining harvest objectives for this region. Elk on Black
River Ranch demonstrate the opposite trend in the fall as bull use increases, which is
undoubtedly due to the larger number of cows inhabiting this ranch.

Intensity of elk use on both clubs was uneven with a few areas of high
concentration. Interestingly, changes in intensity of use as measured by the kernel
surfaces, particularly, on Canada Creek can be attributed to forest management activities.
Canada Creek has conducted a number of timber harvest operations in various portions of
the club over the duration of this study. These newly cut and regenerating areas attracted
elk to these regions, and these distribution shifts are evident in the kernel surfaces. An
example of this phenomenon is the region south of the Bald Mountain Ravine, east of the
Homestead road. In 2003 and 2004, this area received only minor elk use, but in the
winter of 2004—2005 the timber in this area was harvested. The subsequent year this area
reached a much greater intensity of use, as the elk responded to the additional forage .
available resulting from the harvest. This increased use of recently timbered areas, and
associated regeneration problems has been a source of controversy in recent years.

These issues are not new as historically, the region where Black River and Canada
Creek ranches occur, has had large concentrations of both deer and elk, and similar issues
have constantly arose over the years (Moran 1973). Currently, to address these issues the

MDNR has worked to reduce the population of elk on the club and adjacent areas,

179

 

restructured harvest unit boundaries to facilitate this reduction, and improved habitat in
the region outside the club in an effort to attract and hold elk that inhabited the club (D.
Smith, Michigan Department of Natural Resources, personal communication). However,
these actions alone will likely be insufﬁcient to reduce regeneration problems if forestry
practices and management polices within the boundaries of the club are not altered.
Thus, the weight of responsibility for reducing browse problems ultimately lies with
forest managers of the club. Managers need to set forth realistic objectives at both the
stand and club levels that account for the natural potential of the site (e. g., a hardwood
stand should not be managed for oak regeneration) as well as the other biological
inﬂuences acting on the club such as the high elk and deer densities. Also forest
managers need to accept the fact that by conducting habitat work (i.e., planting food
plots, etc.) to provide habitat for deer, the club is attracting larger number of deer and elk
than would naturally occur in the region. This can lead to browsing problems from both
species when these concentrations of animals browse for food during the winter months.
Therefore, forest management objectives need to incorporate the club’s other objectives
such as maintaining large deer and elk herds for viewing and hunting purposes if they are
to set achievable timber management objectives. Secondly, a continual evaluation of the
success or failure of these objectives should be conducted to determine the most effective
timber management strategies for the range of conditions present on the club lands.
Evaluations should include but not be limited to the following: the effects of the size and
distribution of timber cuts on regeneration success, effects of the removal of security
cover in and around fresh cuts (i.e., removal of conifers and other hiding cover in and

adjacent to cuts), the long-term production and recovery of stands that receive browsing

180

 

pressure (e. g., is the production of heavily browsed stand in 10 years comparable to those

 

without major browsing pressure), and the effects of various harvest strategies for both
deer and elk. These actions and continued cooperation between public and private
stakeholders, I believe, will ultimately lead to a reduction or resolution of these
elk/human conﬂicts.

The ﬁndings, regarding the probability of use of the various cover types of
interest, are similar to the patterns of use reported by other Michigan researchers (Moran
1973, Ruhl 1984, Beyer 1987). Most importantly, these ﬁndings reinforce the
importance of openings for elk, and validate the management efforts of both public and
private entities working to improve opening conditions, as elk are using managed
openings throughout the range at a higher probability than unmanaged openings.

The use of the averaging of kernels of individual animals is a new concept to the
analysis of animal home range and space use. It provides a powerful tool to make
population level inference based on a sample of radiocollared animals, provided its
assumptions are met. Failure to meet these assumptions would result in bias in the
averaged kernel density surface and in associated variance estimates. For this study, I
believe the assumptions were reasonably met. Given the dispersal of collared elk from
capture sites to regions across the range and qualitative examination of the averaged and
individual kernel density surfaces, it appears that most areas with elk use in my study
area are represented in the movements of the collared elk, and thus in the averaged kernel
surface. The assumption of independence of collared elk was likely met based on the fact
that only adult elk were collared, and the lack of any long-term or lasting associations

between collared animals. Lastly, the assumption of the individual kernel density

181

estimates adequately describing each elk’s home range I do not believe was extensively
violated given the large number of locations used to estimate the individual kernel
densities for most animals. However, for animals with fewer locations due to mortalities
or being collared late in the study, kernel density estimates may not have ﬁrlly described
their home range, which would have introduced bias into the averaged kernel surface.
But, the minimum number of locations used in estimating the individual kernel density
across all collared elk was 51, which is above the minimum number recommended for
home range estimation (Otis and White 1999, Seaman et a1. 1999 and Garton et al. 2001).
This averaging technique provides a means of overcoming differences in the
number of locations associated with individuals, which can often be substantial. Also, no
information is lost with this technique; unlike other analysis procedures such as
resampling that discards data to generate equal sample sizes of locations. One of the
utilities of this technique demonstrated here is the ability to calculate the probability that
a population of interest is using a particular region or cover type, utilizing the information
contained in the probability density function. These probabilities can be used by elk
managers to quantify elk range use patterns, measure the effects of habitat and forest
management practices, or even determine the effects of recreational activities in various
regions. Additionally, the estimation of variances associated with the averaged kernel
density estimates is critical for determining the precision associated with probability
estimates generated using the average kernel density estimates, and the variance surfaces
can be examined to determine the precision of kernel density estimates throughout the
averaged kernel surface. However, more study is needed to determine the performance

of this estimator in the context of ecological studies, and examine means of estimating

182

 

parameters of covariance functions associated with calculated probabilities as opposed to
assigning them ad hoc values. But, this technique holds promise for providing a means
to answer a wide array of management and research questions.

I provided a simple means of incorporating the error associated with estimating
animals’ locations into the estimated variances for the kernel density estimates.
Incorporation of this error is important to avoid negatively biased variance estimates,
resulting from the false assumption that locations input into the kernel functions have no
associated measurement error. Also the use of the DPI bandwidth selector provides
another option to the commonly used LSCV selector, and given its asymptotic properties
and simulation results it appears to be the superior of the 2 selectors (Wand and Jones
1995)

Lastly, the use of a joint density function to examine joint space use, as described,
provides several beneﬁts over other metrics of joint space use such as the volume of
intersection index (Seidel 1992). Joint density functions provide measures of the
intensity of use between 2 individuals or groups of interest, and this intensity can be
easily represented graphically. Most importantly, integration of the joint density function
allows for estimation of probabilities of interest, and facilitates examination of joint space
use on a probabilistic basis. Once again more research is needed to determine the
properties and performance of these estimators, but they are appealing and may be an

important component of the study of animal interactions.

Management Implications
The information provided on the movements, range use, and interchange on public and

private lands is important for wildlife and forest managers. This knowledge is critical for

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determining the most effective locations for habitat improvement projects, and the
delineation of areas where habitat manipulations are having or not resulting in the desired
effects with regards to elk use. These data also can help in conservation planning for elk
by identifying areas with high probability of elk use that can be the focus of protection
efforts, or if these areas are in the hands of private land owners they can be targeted for
easements or acquisition. From a forest management perspective, my ﬁndings can be
useful for setting realistic timber production objectives by isolating regions with high elk
use. These areas likely will not be as productive as areas where elk do not occur or
densities are lower, and this needs to be factored into timber planning if achievable
objectives are desired. From a public relations perspective, information regarding elk use
of agricultural areas and surrounding lands is useful for dealing with agricultural
complaints. Also the general range use information can be an asset when attempting to
provide private citizens with elk viewing or hunting opportunities. Lastly, elk population
management strategies can be derived in part based on the results of this study.
Knowledge of how elk from various locations throughout the range interact, how they
distribute themselves, and the variability of this distribution is useful for establishing elk
hunt units and setting harvest objectives that recognize the spatial structure of Michigan’s
elk herd and allow for a more focused targeting of problem animals.

The increase in the understanding and knowledge of Michigan’s elk herd
generated by this study provides a critical element to the management of elk, and will aid
managers as they strive to make sound management decisions that beneﬁt Michigan’s elk

resource.

184

 

Conclusion
The goal of this project was to gain valuable information regarding current elk movement
patterns and distribution particularly on the eastern portion of the Michigan elk range.
This goal was realized by achieving the objectives set forth. The wealth of information
gained, the new ideas and analysis techniques set forth, and the overall increase in
understanding of elk in Michigan, I believe are all valuable constructs resulting from this
research effort. I hope these products will enhance elk management in Michigan for the

enjoyment of current and future generations.

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CHAPTER 5: ELK AND BOVINE TUBERCULOSIS IN MICHIGAN

Introduction
Michigan has the dubious distinction of being home to the ﬁrst documented epidemic
occurrence of bovine tuberculosis (TB; Mycobaterz'um bovis) in free-ranging cervids in
North America (Schmitt et al. 1997). Discovery of TB, in free-ranging white-tailed deer
(Odocoileus virginanus) in the northeastern comer of the lower peninsula of Michigan,
was precipitated by the submission to the Michigan Department of Natural Resources
[MDNR] of a hunter-killed 4.5-yr-old male deer in 1994 that had suspicious thoracic
lesions, which were tentatively diagnosed as TB. Laboratory analysis later conﬁrmed
this diagnosis with the isolation of M. bovis from the lung tissue of this animal (Schmitt
et al. 1997). In 1995, a survey of hunter-harvested deer from the region was initiated to
determine if TB existed in free-ranging white-tailed deer. The survey resulted in the
estimation of an apparent TB prevalence of 4.8% in the study area (O’Brien et al. 2002).
In subsequent years, local and statewide surveys for the disease, documented the highest
prevalence in the area known as DMU 452 (~1561 kmz) with decreasing prevalence
moving away from this core area (Hickling 2002, O’Brien et al. 2002). It was believed
that the biological and social characteristics particular to this region of Michigan allowed
for the perpetuation of the disease in the deer herd. These factors included large-scale
supplemental feeding programs, high deer densities, land ownership patterns (i.e., a large
proportion of the area is owned by private hunt clubs), extensive deer baiting for hunting
purposes, and a local economy based largely on recreational activities with hunting being
foremost (Hickling 2002, O’Brien et al. 2002, Miller et al. 2003, Rudolph et al. 2006).

The MDNR instituted several management polices aimed at controlling the spread and

186

 

[IT

ultimately eradicating the disease from the state based largely on addressing these factors.
In 1998 they instituted a ban on baiting and supplemental feeding of ungulates in the 5-
counties containing and surrounding the core area. They also instituted liberal antlerless
deer harvests throughout the region in an attempt to lower deer densities, continued
extensive disease surveillance of hunter—harvested deer to estimate apparent prevalence
and track any potential spread of the disease, and lastly they instituted an educational
campaign to inform the general public about the health and biological issues associated
with this epidemic (Hickling 2002, Rudolph 2006). The results of these efforts appear to
be positive as deer densities have decreased signiﬁcantly (Rudolph et al. 2006), the
disease does not appear to be spreading (Hickling 2002), and apparent prevalence has
decreased signiﬁcantly (O’Brien et al. 2002).

Although, white-tailed deer are the primary reservoir host for M. bovis, other
spill-over hosts have been documented in Michigan including: black bear (Ursus
americanus), bobcat (F elis ruﬁts) coyote (Cam's latrans), red fox (Vulpes vulpes), and
raccoons (Procyon lotor) (Bruning—Fann et a1. 2001). Additionally, 4 elk (Cervus
elaphus), 2 bulls and 2 cows, have tested TB positive in Michigan the last case being in
2003.

Elk are known to be susceptible to M. bovis, and in the Riding Mountain National
Park region of Manitoba, Canada the species functions as the primary reservoir host with
an apparent prevalence of 1% in the population (Lees 2004). Both deer and elk in
Michigan have been shown to utilize openings in the spring, summer and fall (Ruhl 1984,
Beyer 1987, Sitar 1996, Garner 2001), and demonstrate similar afﬁnities for wooded

vegetation types especially upland deciduous stands and regenerating stands throughout

187

the year (Moran 1973, Ruhl 1984, Beyer 1987, Sitar 1996). Other studies across the
United States have shown potential overlap in habitat use between elk and various
species of deer. Collins and Urness (1983) noted similar use of vegetation types in Utah,
USA between tame mule deer (Odocoz'leus hemionus) and elk especially in late summer,
although intensity of use of the various habitat types varied between species. Hanley
(1984) studying black-tailed deer (Odocoileus hemionus columbianus) and elk in
Washington, USA noted different dietary habits and habitat preference between the
species along a moisture gradient. However, as grarninoids senesced and became less
nutritionally valuable, a greater overlap in habitat preference was documented. Johnson
et al. (2000) noted that mule deer and elk in Oregon selected resources similarly,
however, mule deer exhibited an avoidance of elk.

Thus previous research demonstrates the potential for transmission to occur
between white-tailed deer and elk in Michigan resulting from home range overlap and
concurrent habitat utilization, but elk-deer interactions are generally believed to be
limited (Miller 2002). However, historical human activities in Michigan that mutually
concentrated deer and elk, such as baiting and particularly supplemental feeding,
provided an ample avenue for inter-species transmission either through aerosol
transmission during direct contact, or from ingestion of feed material contaminated by
feces, saliva or nasal secretions of infected animals (Miller et al. 2003, Lees 2004). M.
bovis can also persist in cool, moist and dark environments for months, and infected
animals can potentially shed a substantial amount of infectious material throughout their
home range (Francis 1971, Lees 2004). Thus, elk in Michigan are at risk of contracting

and possibly becoming a second reservoir host for TB either by direct or indirect contact

188

 

with infected deer and their infected environments. In addition, elk social structure and
breeding activities (i.e., harem holding behaviors) puts the species at a high risk of
intraspecies transmission should the disease become established in the elk herd at any
signiﬁcant prevalence.

In December 2003, an elk hunter legally harvested a 2.5-yr-old cow radiocollared
in February 2003 (elk #32). This cow was conﬁrmed to be TB positive. This provided a
rare opportunity to examine the movement patterns of a TB positive elk for a 10-month
period. Also the amount and location of joint space use of this elk with other
radiocollared elk could provide important information regarding the risk to other elk that
may have come contact with this individual post-infection.

Thus, to gain an understanding of the potential risks associated with TB to the elk
herd in Michigan, the following objectives were addressed:

1. Identify areas of the elk range where elk are at high risk for being exposed to M.
bovis based on apparent prevalence of TB in deer and elk use of the region.

2. Calculate the probability of elk using these high-risk areas, and compare these
areas to the location of known TB positive elk. High-risk areas are deﬁned as
areas in which there is a greater risk of elk being exposed to M. bovis as a result
of relatively higher prevalence levels in deer and correspondingly higher
probability of elk use.

3. Determine the range use of elk #32, a radiocollared cow that was TB positive, and
estimate location and amount of the joint space use of this cow with other

radiocollared elk in the region.

189

 

4. Introduce new analytical techniques using ﬁxed kernel analyses to address
previous objectives, and thereby demonstrated their usefulness in epidemiological

investigations.

Study area

The study site selected for this project is the current elk range located primarily in
Cheboygan, Montmorency, Otsego and Presque Isle counties in the northern portion of
the Lower Peninsula of Michigan (Figure 3: Chapter 1). The historic range (i.e., prior to
1990’s) was estimated at approximately 1550 kmz, including the Pigeon River State
Forest near Vanderbilt, Michigan (Bender 1992). The current elk range is estimated at
approximately 3,450 km2 (D. E. Beyer, Michigan Department of Natural Resources,
unpublished report). We focused our study on the eastern region of the elk range near
Atlanta in Montmorency County.

Topography of the area slopes northerly and consists of ﬂat-topped ridges
interspersed with headwater swamps and outwash plains created through glacial actions
(Moran 1973).

Mean annual temperature is 6.3 °C with January having the lowest mean monthly
temperature (-7.7 °C) and the highest (19.7 °C) occurring in July (NOAA 2006). Mean
annual rainfall is 67.3 cm, and mean annual snowfall is 189 cm (NOAA 2006) with
precipitation being generally well distributed throughout the year.

Due to wide array of soil fertilities, aspects and moisture levels, vegetation types
are diverse and well interspersed. In addition, human activities such as logging,
agriculture and forest management practices further complicate the pattern of vegetation

types throughout the area. Dominant cover types include upland and lowland deciduous

190

 

and coniferous forests interspersed with typically human-induced openings. Moran

(1973) provides a detailed description of the vegetation of the region.
Methods

TB Prevalence in Deer

Data acquisition. —O’Brien et al. (2002) documented the procedures used to
determine TB infection in free-ranging deer in detail. Since 1995, the number of TB
positive, free-ranging deer has been determined by personnel at the MDNR Wildlife
Disease Laboratory, East Lansing, Michigan, mainly through surveillance of hunter-
harvested deer heads and carcasses voluntarily submitted to the MDNR. Other deer
collected by various means (e. g., vehicle collisions, crop damage permits) were also
included in the survey, although these animals represent only a limited percentage of the
total deer surveyed. Information generally collected for each submitted specimen
included: date of harvest/collection, sex, age (via tooth eruption/wear patterns) and
harvest location by township, range and section.

Examination of specimens for M. bovis began with gross examination of the
submandibular, parotid and retropharyngeal cranial lymph nodes. If nodes exhibited
gross enlargement with abscessation or granuloma formation, the specimen was
designated as TB suspect, and specimens were then sent for histopathology, acid-fast
staining, and mycobacterial culture for ﬁnal determination of M. bovis infection. The
sensitivity and speciﬁcity of these examination procedures were estimated as 75% and
100%, and apparent prevalence was linearly related to true prevalence (Fitzgerald et al.

2000, O’Brien et al.2004)

191

 

Analysis. —All information was entered into the Bovine Tuberculosis Surveillance
Database (Michigan Department of Natural Resources 2006). From this database, I
extracted TB prevalence data from 1999-2005 for Cheboygan, Montmorency, Otsego
and Presque Isle counties (i.e., the counties containing the elk range). These years
represented the time since the MDNR ban on supplemental baiting and feeding of
ungulates, and also a period of relatively stable deer harvest and management strategies
for this region (Rudolph et al. 2006). The resolution of the data was at the section level
(2.59 kmz) based on the General Land Ofﬁce Survey. I calculated apparent prevalence
by dividing the sum of the number of TB positive deer by the total number sampled for
each section. Apparent prevalence was calculated for 2 time periods, 1999—2005, and for
2003—2005 (i.e., the time period from which elk data was collected). For each time
period, using the Spatial Analyst extension in ARCGIS version 9.0 (ESRI, Redlands,
California, USA), I used ordinary kriging to develop a prediction surface of apparent TB
prevalence. Parameters for the spherical variogram model were calculated automatically
using weighted-least squares to ﬁt the model (Cressie 1985). I chose to use ordinary
kriging since it requires fewer assumptions, as the mean is not assumed to be known.
Also, since the mean surface is estimated this technique does not drift to the global mean

away from sample points as in simple kriging, but only moves to the local mean.

Elk Range Use

Location estimation. —Elk range use was estimated based on the location data
collected from 2003—2005 on 58 radiocollared adult elk (20 bulls, 38 cows). Forty of
these elk were collared in 2003, 2 were collared in 2004 and the remainder were collared

in 2005. Location data were collected primarily using triangulation techniques via the

192

 

loudest point method (Springer 1979, White and Garrott 1990) with locations being
estimated using Lenth’s estimator in Locate III (Nams 2006). I also obtained location
information from visually sighting collared animals either by homing in on collared
animals or incidental sightings. Locations in these instances were determined by using a
hand-held GPS unit (Garmin, Olathe, Kansas, USA). Lastly, 5 animals in 2005 were
collared with radiocollars equipped with GPS units (Advanced Telemetry Systems, Isanti,
Minnesota, USA) which automatically recorded the GPS location of these animals every
7hrs.

Range use estimation. —Based on this location data and using Gaussian ﬁxed
kernel methods (Wand and Jones 1995), for each individual elk I developed probability
density estimates for each point on a common grid that described the probability of each
elk’s use of the elk range at that point. Grid points were spaced at 160.9344 m intervals,
and the grid encompassed all elk locations with an additional 1,609.344 m border. The
bandwidth for each kernel was determined using a direct plug-in automatic bandwidth
selector (Wand and Jones 1995). I used a bootstrap procedure to develop variance
estimates for each grid point at which the kernel density function was evaluated (Efron
and Tibshirani 1993). To allow for population level inference, I averaged the individual
kernel density functions across all radiocollared animals. Variance estimates for this
averaged kernel density function were determined for each grid point by summing the
individual variances for each elk under the assumption that each individual was
independent. These kernel averaging analyses require the following assumptions to allow
population level inference: 1) Individuals collared represent a random sample of the

population and, therefore, their range use reﬂects that of the population. 2) Collared elk

193

 

are independent. 3) Individual kernel density estimates provide unbiased density
estimates and adequately describe range use. A detailed description of the methodologies

used in the above analyses is presented in Chapter 4.

Identifying High Risk Areas

Locations where elk have a high risk of being exposed to M. bovis were determined by
multiplying the averaged kernel density surface for the radiocollared elk with the kriged
surfaces of apparent TB prevalence for the 2 time periods of interest using Spatial
Analyst in ARCGIS. Then I determined the regions with peaks in the joint use surface,
and delineated these locations with high elk use and relatively high TB prevalence as
high-risk areas. The locations of harvest/collection of elk known to be TB positive were
plotted against the high-risk areas in ARCGIS as a qualitative assessment of the
delineation of high-risk areas.

As the prevalence data were problematic since sample size varies markedly from
section to section ranging from 1 to 66 animals sampled, I did not calculate joint
probability estimates between elk use and apparent TB prevalence. However, I did
examine the probability elk used the high-risk areas. These probabilities were calculated
by intersecting the grid of points at which the averaged kernel density was calculated
with the grid of cells associated with the high risk areas using Hawth’s Analysis Tools
(Beyer 2006) in ARCGIS. This provided in indicator variable of the grid points
associated with the high-risk areas. These grid points were taken into R Version 2.4.1
(2006), and the probability of using the high-risk areas was calculated by summing the

density estimates at each of the grid points that were contained within the high-risk areas

194

 

multiplied by the grid cell area (i.e., 25,900 m2). Variance estimates for these
probabilities were estimated as follows:
2 n A n n A A
vEMU?) = (25,900) X Zvar(f(xia)’i)) + Z 200VU(xi,yt),f(xJ-,yj)) ,
i=1 2' tab j
where n = the number of grid points contained in the high risk areas, the

var(f”(x,-, yi)) =bootstrap variance estimate for the averaged kernel density estimate at
the ith grid point, and c6v( f" (xi, y,), f (x j, y j )) is estimated by multiplying the bootstrap

standard errors for the ith and jth grid point by their correlation as determined by a Matem
correlation function. A Matem correlation ﬁrnction, with a smoothing parameter of 0.5
and a range parameter equal to the average bandwidth matrix of all radiocollared elk, was
used in variance calculations to account for the spatial autocorrelation between grid

points associated with the probabilities of interest.

Examination of Range Use of a TB Positive Elk
Location data collection and home range estimation followed the same techniques
previously described. Movement patterns of the TB positive cow were plotted in
ArcView 3.2 (ESRI, Redlands, California, USA) using Animal Movements Extension
(Hooge and Eichenlaub 1997). The 95% and 50% probability contour home range areas
were calculated for this animal using R. The 95% percent upper and lower conﬁdence
limits for home range area were calculated using bootstrapping and the quantile method
(Efron and Tibshirani 1993).

Averaged kernel density estimates for 15 elk (#9, #11, #12, #13, #17, #19, #20,

#21, #23, #25, #33, #34, #35, #36 and #37) from the region for 2003 were multiplied by

195

the kernel density estimates for elk #32 at the common grid points previously described.

 

This created a joint density estimate at each grid point from which the probability of elk
#32 jointly using the elk range with another elk in the area was calculated. It is important
to note that the density estimates at each grid point estimate the probability density of an
“average” elk from the eastern region using exactly same location (i.e., grid cell) as elk
#32. I graphically displayed this joint density surface using ARCGIS. Variance

estimates at the grid points were approximated using the delta method:
.. " ‘ " 2 .2 " 2 .2
var(f,-(x) *fj(x)) z fi(x) O'i +fj(x) O'j ,

where A- x is the densit estimate of the ith kernel at acommon 'd oint, x, and égis
t y grr p r

the estimated bootstrap variance of the density estimate at the common grid point from
the ith kernel. This process assumes that individuals or groups for which joint space use
was examined were independent.

One of the areas that held a large number of elk from across the eastern portion of
the study area, including elk #32, during the winter of 2003 was the Elk Ridge Golf
Course. I determined the probability, of elk #32 and another elk from the region, using
the golf course jointly conditioned on the probability that joint space use occurred, based
on the above joint density surface. I conditioned on the occurrence of joint space use, to
effectively reweight the joint density surface, so probabilities are readily interpretable
(i.e., the unconditional joint density surface yields extremely low probabilities). This
conditioning results in the following biological interpretation: for a particular location of
interest, the estimated conditional probability was the probability there was joint space
use at this location given there was a simultaneous use of some location. Thus the

conditional probability was calculated as follows:

196

Pr(use)

Pr(use l X =1) = -————,
Pr(X =1)

where Pr(use | X = l) is the conditional probability of jointly using the golf course,
Pr(use) is the unconditional probability, and Pr(X = 1) is the probability of joint space use
(i.e., the overall probability of jointly using the elk range, calculated by ﬁnding the
volume under the joint density surface). The variance of the unconditional probability
was approximated using the delta method as follows:

véir(Pr(use I X = 1) z 6'[ var(Pr(use)) c6v(Pr(use), Pr(X = 1))]6

c6v(Pr(use),Pr(X = 1)) var(Pr(X =1))
— Pr(use) l I
(Pr(X =1))2 Pr(X =1)

 

where 6 =[ ] , var(Pr(use)) is estimated as follows:

var(Pr<use>) = (25.900)4 x [Z variety.» + Z Zc6v(i(xi,yi),f(xj,yj>)].

1' =1 i i¢ j
with n = the number of grid points contained in the golf course, the

véir(f, (xi, y,)) = approximate variance estimate for the joint density estimate at the ith grid
point, and the c6v(f”l (xi, y,), f j (x -, y j )) estimated by multiplying the approximate

standard errors for the ith and jth grid points by their correlation as determined by a
Matem correlation function with the same smoothing and range parameters described
previously, the viir(Pr( X = 1)) is estimated in the same manner, however, n = all grid
n m
points, and lastly cov(Pr(use),Pr(X = 1)) = Z Zéid'jco‘rn-j , where 6',- = is the bootstrap
i=li¢ j

estimate of the standard error at the ith grid point, corn-j : is the correlation coefﬁcient

between the ith and jth grid points as determined by the Matem correlation function

197

parameterized as before, and n = the number of grid points contained in the golf course

and m = the total number of grid points.

Results
TB prevalence in the 4 counties averaged across the years of 1999—2005 ranged from
0-0.3333 with a mean of 0.0018 (SD = 0.0169) with 2,360 deer surveyed. For the
interval of 2003—2005, TB prevalence ranged from 0—1 with a mean of 0.0019 (SD =
0.0299) for 1,735 animals examined.

Elk range use was described previously (Chapter 4). Areas with a high
probability of elk use and corresponding relatively high TB prevalence for 1999—2005
were the regions around the Hardwood Lake/Osmun Road intersection, Canada Creek
Ranch, the region along County Road 622 east of Camp 30 Hills, the region around
Steven Springs Road, the Hubert Road region, and the area around Tomahawk Lake
(Figures 68 and 69). Examining just the years of 2003—2005, identiﬁed 3 main locales of
high-risk: the region around Steven Springs Road, the Hubert Road region, and the area
around Tomahawk Lake (Figures 70 and 71).

Locations of known positive cases of TB elk are plotted along with hi gh-risk
areas (Figures 69 and 71). All positive cases were east of M-33, and visual examination
reveals that these 4 cases are all located in or adjacent to identiﬁed high-risk areas.

The probability of using the high-risk areas based on the 1999—2005 TB
prevalence data was 22.27% (SE = 2.04%). The probability of using the high-risk areas
based on the 2003—2005 data was estimated as 8.96% (SE = 0.899%).

The movements of elk #32 were concentrated between Voyer Lake Road and

County Road 634 with forays east to south of Grass Lake (Figure 72). Early locations

198

 

 

 

 

 

 

 

Legend

 

 

TB prevalence

 

 

 

 

High 0.0653

Low : 0
Elk use
i ' High: 1.024 e-016

 

 

 

 

 

 

 

 

1.53 6 9 12 .
I—Kilometers LOW'O

 

 

 

Figure 68. Averaged kernel density surface of elk use for 58 radiocollared elk overlaid
with the kriging prediction surface of apparent TB prevalence of white-tailed deer in

Michigan, 1999—2005.

199

Legend
High 9.745 e-010

 

1.53 6 9 12 Lowzo
tit—Kilometers

 

Figure 69. Areas of high-risk of TB transmission based on elk usage and apparent TB
prevalence rates in white-tailed deer in Michigan, 1999-2005, and locations of
harvest/collection of known TB positive elk (crosses).

200

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

‘3
0‘ Q)”
“2%“an
Q
Beckett
t‘ 1 I
1 Legend
w: 1 TB prevalence
"“ _ High: 0.2067
- K
$1. Low : 0
. ,1 ‘ Elk use
- LEE: High: 1.024 e-016
1.5 3 6 9 12 LOW I 0
mKilometer-s

 

 

 

Figure 70. Averaged kernel density surface of elk use for 58 radiocollared elk overlaid
with the kriging prediction surface of apparent TB prevalence of white-tailed deer in
Michigan, 2003—2005.

201

 

 

 

 

 

 

 

 

 

 

 

- Legend

 

  

 

 

 

 

 

 

High 9.745 e-OlO

 

 
  

 

 

 

_ p— r _
l 2 4 6 8 . LOW20
cut—Kilomet
Wt. l t

 

Figure 71. Areas of high-risk of TB transmission based on elk usage and apparent TB
prevalence rates in white-tailed deer in Michigan, 2003-2005, and locations of

harvest/collection of known TB positive elk (crosses).

A

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203

were centered on the Elk Ridge Golf Course before she moved east across M-33 for the
remainder of the study. Based on 121 locations, the home range of elk #32 at the 95%
contour encompassed 8,856 ha with 95% lower and upper conﬁdence limits of 6,975 ha
and 9,630 ha, respectively. Elk #32 had a larger home range than the mean cow home
range of 7,342 ha (SE = 178) for all radiocollared cows for 2003, although the difference
was not statistically signiﬁcant based on overlap of 95% conﬁdence intervals. Her home
range size at the 50% contour encompassed 2,340 ha with 95% lower and upper
conﬁdence limits of 1,791 ha and 2,565 ha, respectively. This size was signiﬁcantly
different from the mean cow 50% contour home range area of 1,436 ha (SE = 48) based
on overlap of 95% conﬁdence intervals. This elk had 3 main locations with high
probability of use: the Elk Ridge Golf Course, the area near the Brush Creek Truck
Trail/County Road 624 intersection and the area north of Sportsmans Darn (Figure 73).

The average kernel density surface for elk from the eastern portion of the study
area portrays 3 main high use areas: Elk Ridge Golf Course, the region west of the
Decheau Lake/Meaford Road intersection, and the Hubert Road region in Presque Isle
County (Figure 74). The standard error surface demonstrates the precision of the average
kernel density surface with precision changing considerably across the surface (Figure
75).

The joint density surface between elk #32 and the other elk utilizing the eastern
portion of the study area isolates the Elk Ridge Golf Course, as the site with the highest
probability of joint space use (Figure 76). A secondary site is located southeast of the

Brush Creek Truck Trail/County Road 624 intersection.

204

 

Legend
I_l High: 3.146e-08

 

Figure 73. Kernel density surface estimating the home range of a radiocollared, TB-
positive cow elk (elk #32) based on 121 locations in Michigan, 2003.

205

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

15:.
QWROW
\
"-ilﬂ
r- 7b
1—

_ Legend
' - High 1.59 e-08

“r—‘Z—l 1

1.22.5 5 7.5 10 Low 1 0
Kilometers
.. ‘\ s l xC. LL1_—1—.—

 

 

Figure 74. Average kernel density surface estimating probability of use of 15
radiocollared elk utilizing the eastern portion of the study area in Michigan, 2003.

206

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

‘3.
Quyko
J
P1 IV
.4”
‘7 1
Legend
High 2.01 e-09
«Ll
1.22.5 5 7.5 10 -
Kilomet LOW'O

 

 

 

 

 

 

 

Figure 75. The standard error surface for the average kernel density surface estimating
probability of use of 15 radiocollared elk utilizing the eastern portion of the study area in
Michigan, 2003.

207

 

95‘”

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

r
Co. Rd. 622 -
Pl Paint alby
_._‘L._.__/
_11—4 32 T j 1 i
i V
\ Legend _

 

11

I; j I High 1.024e -16
g “mi Low: 0
2

Figure 76. Joint kernel density surface estimating the joint space use of a radiocollared,
TB-positive cow elk (elk #32), and the 15 other radiocollared elk utilizing this portion of
the elk range in Michigan, 2003.

 

 

 

 

 

  
         

l

.51 2 3 4 '
n-z-Krlometers

_

 

 

 

    

 

 

 

H

 

208

The overall probability of joint space use was estimated as 3.01 e-07% (SE = 2.62
e-12%). The conditional probability of jointly using the Elk Ridge Golf Course, the site

of highest probability of joint space use, was 44.59% (SE = 5.17%).

Discussion
All the analyses, based on characterizing TB prevalence, assume that the sample of
heads/carcasses submitted by hunters, upon which prevalence estimates are based
represent, a random sample with regards to infected and non-infected deer ﬁ'om the
region. If diseased deer are harvested at a higher probability, and/or submitted at a higher
probability then resulting prevalence estimates will be biased high. Conversely, if there
is a conscious effort to avoid submitting deer for testing, for example, to avoid regulative
changes (e. g., ban on baiting) then prevalence estimates may be biased low. However,
bias should only arise in the latter case if hunters were able to only avoid submitting
infected deer. Given the fact that many of the TB positive deer do not exhibit readily
distinguishable, clinical signs of infection, particularly to the untrained eye, this is highly
unlikely. These potential sources of bias to my knowledge have not been investigated,
and I assumed for this study they were negligible.

Apparent TB prevalence in deer throughout the elk range is generally low
compared to prevalence further to the east in the core TB area (O’Brien et al. 2002).
However, there exist pockets of higher prevalence where elk are at risk of being exposed
and contracting the disease. My analyses were useful at identifying the locations where
estimated TB prevalence was relatively high, and the probability of elk use was

correspondingly high. The high-risk areas identiﬁed in 2003—2005 were also identiﬁed

as high-risk for the entire time period of 1999—2005, indicating that these areas have been

209

historically and continue to be hi gh-risk locations. Interestingly, a comparison of the
known harvest/collection locations of TB positive elk with the high-risk areas
demonstrates that all 4 positive elk are located in or adjacent to the high-risk areas for
2003—2005. Although, this was only a small sample size, this close correspondence
suggests that this analytical technique is useful for delineating high-risk areas for elk
exposure to M. bovis. Also notable ﬁom these analyses is the reduction in the number of
hi gh-risk areas and corresponding reduction in probability of elk using high-risk areas
when examining only the latter years. This would seem to indicate the management and
disease control efforts are having the desired effects. Future research efforts should
concentrate on targeting the 2003—2005 high-risk areas to determine the causative factors
contributing to their high elk use, as well as, their consistently higher TB prevalence
relative to other locations in the region.

The radiocollared, TB-positive cow had a slightly larger than average home range
size at the 95% contour; however, at the 50% contour it was signiﬁcantly greater than
other cows in the study. This larger core home range area (i.e., the region containing
50% of her locations) could be attributed to her age, more human disturbance in the
region (i.e., this area is open to and receives extensive off-road vehicle trafﬁc), or other
habitat conditions within her core area. Also I noted that she did not bear a calf in 2003,
which may have allowed her to roam more widely than other calf-rearing cows during the
spring and summer.

The standard error surface for the average kernel density surface for the eastern

elk demonstrates the precision of the density surface and how it changes with location. It

210

 

is also a critical component for estimating the variability of any probabilities generated
with the density surface.

Joint space use analyses of elk from the eastern portion of the study area
demonstrated that the overall probability of joint space use of elk #32 and an elk from the
eastern portion of the study area was low. However, it should be noted that this
probability is the probability of elk #32 jointly using space with an “average” elk. Thus,
the probability of joint space use of elk #32 with all elk from the eastern portion of the
study would be calculated as this estimated probability of j oint space use for an average
elk multiplied by the size of the elk population that use the same region as elk #32.
Although population size at this scale is unknown, the estimated probability of joint space
use is still a useful tool for estimating the location of and the probability of joint space
use with all elk from the area, since it only differs by a constant. Thus, the probability of
joint space use with an average elk is a useful metric for assessing the amount and
location of possible elk interactions that could facilitate disease transmission between elk
#32 and another elk.

If I assumed that joint space use did occur, it was evident that Elk Ridge Golf
Course was the most likely site where the interaction occurred. This assumption seems
reasonable given the social structure of elk, particularly, the maternal grouping of cows
and harem gathering behaviors of the bulls. Also it is not surprising that the golf course
has such a high probability of joint space use for 2003. In 2003 there was a large acorn
crop, which concentrated elk during much of the winter in the areas dominated by oak
ridges. Elk Ridge is one of those regions. Also from personal observation deer were also

heavily concentrated throughout the oak ridges providing more opportunity for

211

interspecies transmission of TB. Future work on disease risk should examine the effects
of large mast crops on subsequent prevalence rates, as these range-wide events
concentrate both elk and deer in space and time.

One of the limitations of these joint space use analyses is that time, is not
incorporated into the kernel estimates. Thus, the probability of joint space use should
ultimately be the probability of using the same location at the same time. Examination of

joint space using 3-dimensions is an area of ﬁrture research opportunity.

Management Implications
These ﬁndings are useful for both disease and wildlife managers attempting to control
and eradicate TB from Michigan’s deer herd, as well as, minimize the potential for
interspecies transmission from deer to elk. The high-risk areas identiﬁed, particularly, in
2003—2005 were mostly on public land. This provides an opportunity to effectively
manage these areas through habitat or population management of both deer and elk. Also
the examination of the home range and joint space use of a TB positive elk relative to
other elk in the region demonstrates the large area potentially exposed to input of
infectious material by this elk, and the potential risk of infection to other elk through
direct or indirect contact with this infected elk. Thus, these ﬁndings clearly portray the
potential threat of TB becoming established in the elk herd.

Lastly, the analytical techniques described provide a template for identifying
high-risk areas for other species and infectious diseases, and demonstrate a metric for
examining potential transmission risk by analyzing joint space use. The power of these
techniques is their ability to combine disease or prevalence information with knowledge

of the biology of wildlife species. These tools can also be used to target areas for

212

sampling to determine spread or emergence of infectious diseases or for control efforts,
as well as assessing the risk to various geographic segments of a population based on

how they utilize common resources/space.

Conclusion
Wildlife disease issues are becoming increasingly more prevalent in recent years with
often substantial biological and economical costs. The threat of zoonotics and other
human health issues in conjunction with decreasing habitat resulting in increased
human/wildlife interactions assures that these issues will remain in the forefront both
locally as well as nationally. I hope that the techniques and ﬁndings described herein will
provide useful information and ideas that will help combat the spread and control of

current and emerging wildlife diseases.

213

 

 

APPENDICES

214

APPENDIX A

SIGHTABILITY MODEL DATA SHEETS

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216

Comments:

 

 

 

 

 

Snow Age:

1. Fresh — Generally less than or equal to 1 week since snowfall or greater than 3
inches. Old tracks are covered.

2. Moderate — Generally greater than 1 and less than or equal to 2 weeks since fresh
snow conditions. Newly fallen snow of less than 3 inches often is inadequate to renew
the snow surface so that it appears smooth and disturbance-free; therefore, shallow new
snow may be classed as moderate-aged based on appearance.

3. Old — Generally greater than 2 weeks since fresh snow conditions. However,
newly fallen snow subjected to melting conditions can rapidly appear like old snow, i.e.,
depressions around trees and shrubs, irregular surface, and enlarge animal tracks.
Therefore, new snow may be classed as old after only 2 or 3 days.

Snow Cover:

1. Complete — Low vegetation covered. Generally 6 to 12 inches of snow are
required.

2. Some low vegetation showing — Tops of some grasses, forbs, or very low shrubs
protruding through snow. Snow cover has brownish cast.

3. Distracting amounts of bare ground or herbaceous vegetation showing — Distinct
brown patches exist that reduce observer efﬁciency.

Crown Density Scale

 

 

 

 

APPENDIX B

 

SURVEY DATA SHEETS AND PROTOCOL

218

PROTOCOL FOR ELK SURVEY
Daniel Walsh, Henry Campa 111, Scott Winterstein
January 2005

Flight time and weather conditions. Surveys for sightability model development
will be conducted in late January through early February, since elk group size tends to be
largest during this time of year (Moran 1973, Beyer 1987) increasing the probability of
observing elk groups (Samuel et al. 1987). Also snow conditions generally provide a
good background against which elk can be easily observed from the air. All ﬂights will
be conducted between 0900-1600 hrs to take advantage of good light conditions and
minimize the effects of shadows.

Flights will ideally be made under clear skies with calm winds, temperatures at or
above —12 C° after a fresh snowfall (Otten 1989). However, due to the time constraints
and the amount of data needed for adequate estimation of the sightability function, ﬂights
will be conducted whenever conditions have been deemed safe by the pilots. For safety
reasons, the pilots will make the ﬁnal determination of whether a ﬂight will occur. Thus,
it is possible ﬂights will be conducted under less than ideal conditions.

Surveys will be conducted in two 3 hr shifts with a 1hr break between shifts to
allow for aircraft refueling and for recuperation of observers.

Personnel and equipment. The survey procedure will require 1-2 ﬁxed-wing
aircraft with wheel covers removed. The planes will contain a pilot and 2 experienced
observers. Observers will be seated at the rear of the plane. Each plane will be equipped

with a radio for inter-plane communications, a book containing all the quadrat and ﬂight

219

line locations, and Global Positioning System (GPS) equipment for locating ﬂight lines
and recording location of observed elk groups and radio-marked individuals.

Quadrat design. The study area is divided into quadrats/cells with length (N/S)
9.66 km (6 mi) and width (E/W) 3.22 km (2 mi). The study area will be deﬁned by MSU
and DNR personnel. Each quadrat was given a unique identiﬁcation. Parallel, 0.40 km
(0.25 mi) wide, ﬂight lines running north to south were created within each quadrat, and
the starting point and ending point of each line was recorded. Enough ﬂight lines have
been delineated to assure 100% coverage of the quadrat.

Survey plane procedures. The survey plane(s) will ﬂy to the designated cell and
begin to ﬂy the designated ﬂight lines within the cell starting in the southwest corner of
the quadrat. I will provide location of the starting points and ending points of these ﬂight
lines for each quadrat in the sampling area to the observation plane pilot. Pilots will ﬂy
at an air speed of approximately 129 km/hr at a height of 152 m above the ground. The 2
experienced observers will visually scan out each side of the plane to a distance of 0.20
km for elk groups, which will be delineated by markers on the wing struts. Once a group
is located, observers will communicate to the pilot they located a group. The pilot will
leave the designated ﬂight line and reduce altitude while circling the group, and record
the GPS location. One observer will count all elk in the group. A group will be deﬁned
as all elk visible in an area. However, if distinct groups are clearly noticeable by the
observer over the area (i.e. there is a clear separation between groups of animals), or if
elk are distributed in areas of different conifer cover classes then these will be treated as
separate groups. He/she will also record the number of bulls, the number of cows and the

number of calves, as well as the percent conifer cover and behavior of the animals. The

220

 

percent conifer cover will be classiﬁed into 3 classes: 1) O—33% conifer cover, 2)

34—66% conifer cover and 3) 67—100% conifer cover at a 10 m radius around the ﬁrst elk
initially sighted. Behavior will be classiﬁed as bedded, standing or moving. A
standardized data sheet will be provided to aid in data collection. Once the ﬁrst observer
has completed his/her data collection, the pilot will circle the plane in the opposite
direction, and the second observer will repeat the process. Observers will not
communicate their ﬁndings until both have completed their data collection (i.e., observers
will remain independent). The pilot will also count the number of the elk in the group
and provide his independent estimate of group size to the observers whom will record the
pilot’s count on the datasheet (The pilot will only be involved in counting elk group size
not in detecting elk groups while ﬂying ﬂight lines! I). Once the group has been counted
the pilot will return to the ﬂight line and continue to survey the quadrat. Once the survey
of the quadrat is complete, the pilot will ﬂy to nearest quadrat and begin the process
again. Observers will record any problems or unusual circumstances they encounter
during the ﬂight on the provided data sheet.

Literature cited

Beyer, D. E. 1987. Population and habitat management of elk in Michigan.
Dissertation, Michigan State University, East Lansing, Michigan, USA.

Moran, R. J. 1973. The rocky mountain elk in Michigan. Michigan Department of
Natural Resources, Wildlife Division Report 267.

Otten, M.R. M. 1989. An aerial censusing procedure for elk in Michigan. Thesis,
Michigan State University, East Lansing, Michigan, USA.

Samuel, M. D., E. O. Garton, M. W. Schlegel, and R. G. Carson. 1987. Visibility bias in
aerial surveys of elk in Northcentral Idaho. Journal of Wildlife Management 55:
622—60.

221

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Comments:

Snow Age:

1. Fresh - Generally less than or equal to 1 week since snowfall or greater than 3 inches. Old tracks are
covered.

2. Moderate — Generally greater than 1 and less than or equal to 2 weeks since fresh snow conditions.
Newly fallen snow of less than 3 inches often is inadequate to renew the snow surface so that it
appears smooth and disturbance-free; therefore, shallow new snow may be classed as moderate-aged
based on appearance.

3. Old — Generally greater than 2 weeks since fresh snow conditions. However, newly fallen snow

subjected to melting conditions can rapidly appear like old snow, i.e., depressions around trees and
shrubs, irregular surface, and enlarge animal tracks. Therefore, new snow may be classed as old after
only 2 or 3 days.

Snow Cover:

4.
5.

6.

Complete — Low vegetation covered. Generally 6 to 12 inches of snow are required.

Some low vegetation showing — Tops of some grasses, forbs, or very low shrubs protruding through
snow. Snow cover has brownish cast.

Distracting amounts of bare ground or herbaceous vegetation showing — Distinct
brown patches exist that reduce observer efﬁciency.

CROWN DENSITY SCALE

 

 

 

 

 

.r-l-

 

APPENDIX C

EXPECTATION ANALYSIS

224

Let a“ k) = the estimate of group size for the i1h group in the km land unit, and let

(3)“ k) =the probability of detecting that group which is estimated from some sightability
model whose parameters were derived independently of the estimation of a“ k) and
includes a“ k) as a predictor variable. Then by the conditional expectation formula
(Ross 2003) the following is true:

E[rh,-(k)é),-(k)] = E[Eltﬁr(k)®i(k) I ”Won
= Elﬁn-(nEléxk) l ”hr/c)“

Since the parameters for the sightability model used to estimate (3)“ k) are derived

independently from the estimation of ﬁzz-(k) thus

E[691(k) Vim/()1: ('9,
and therefore,
EWi(k)é)i(k)] = E[Eliﬁi(k)®i(k) Wi(k)]] = ®i(k)E[’;7i(k)]-
Although the estimator of a“ k) in equation (4) is asymptotically unbiased (DasGupta and

Rubin 2005), with only 3 independent counts on group size the estimator shows some
bias. The amount of bias was assessed by generating 3 random counts from a binomial
distribution with N ranging from 1—50 and p ranging from 0.70—0.99. These values were
chosen based on ﬁeld observations of elk group size and values of p from the literature
(Cogan and Diefenbach 1998). N was then estimated using equation (4). For each
combination of N and p, 1,000 estimates were generated and the average bias was
calculated. Figure 1 shows the simulation results. Based on these results the bias of the

estimator of "a“ k) even with only 3 counts is relatively small with the mean percent bias

225

Avmge Bias

 
 
 

0.61

 

-7.52 ‘77: ﬂ»

Figure C. 1. The average bias of the method-of-moments estimator of group size
(DasGupta and Rubin 2005) given 3 independent counts with 1,000 repetitions at each
combination of N and p.

226

of -0.047 (SD = 0.049). The largest bias occurs at the lowest p and highest N values and
reaches a maximum of -7.52 atp = 0.70 and N: 50.

Based on these simulation results, it is reasonable to approximate the following:
E[ﬁhrkﬂ e mat),
and therefore the following statement can be inferred:

®i(k)E[’hi(k)] z @i(k)mi(k)-

227

APPENDIX D

COVARIANCE ANALYSIS

228

The last term in the lemma can be estimated as follows:

9
varBlR D(T)_ _ Var[zzk mi(k) pki___(__k)]_

(3) m- (3) ‘- (39.
Zivar[’i’_____ mo :00] + zcov[ .(k) z(k),’"z(k) :00}

pk i(k)¢i'(k') pk pk

 

The variance can be approximated using the delta method as previously described. The
COV(7;li(k )éi(k)’ IﬁiI(kv)é)l-r(ko) ) = E[COV(ﬁli(k)©i(k) , Ihiv(kt)c:)iv(kv) l 511(k), ﬁzi'(k'))]
+ cov(E[m,-(k)®,-(k) l ﬁi(k)].E['ﬁi'(k')®i'(k') I’hi'(k')])

However, based on the independence of mm and ﬁll-'(kv) , and the independence of the

parameters of the sightability model used to estimate 6?)“ k) and ﬁzz-(k) the following is

true:

cov(E[riti(k)(:9,-(k) I lili(k)]aE[’hi'(k')é)i'(k') I ’hi'(k')])
= cov(m,-(k)E[O,-(k) I lili(k)]a’hi'(k')E[éi'(k') ”hit/(9])
= COV(’hi(k)®i(k)i’hi'(k')®i'(k')1)

= ®i(k)®i'(k') °°V(’ﬁi(k)”;’i'(k‘)

= 0.

Thus,

COV(’;1i(k)é)i(k)a ﬁli'(k')(:)i'(k'))
= E[COV(I;li(/()(:)i(k),ﬁli'(k')®i'(k') I mi(k)’mi'(k'))]
= Eltiti(k)'i’i'(k')°°"(®i(k)’éilk') I’hiﬁwﬁilklh’

and EDlER|DlvaTB|R,D(T)]] is estimated as follows:

1
626+ Z Emi(k)mi"(k)p mi(k)m m1”(k)cov(®i(k)’ 69100)]
i(k)¢i"(k)

229

LITERATURE CITED

230

LITERATURE CITED

Anderson, C. R. and Lindzey, F. G.. 1996. Moose sightability model developed from
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