Nathaniel Thomas Yost

A THESIS

Submitted to

Michigan State University

in partial fulfillment of the requirements

for the degree of

Fisheries and Wildlife

Master of Science

20
20

ABSTRACT

Nathaniel Thomas Yost

To monitor the status of waterfowl populations, the Michigan Department of Natural Resources
(MDNR) beg
an surveying abundance of breeding ducks and geese in 1991 and developed goals
for waterfowl population and habitat management tied to the spring waterfowl survey. The
spring waterfowl survey
required

flying a series of fixed
-
width transects using fixed
-
wi
ng
aircraft to estimate statewide abundance

of Canada geese (
Branta canadensis
), mallards (
Anas
platyrhynchos
), mute swans (
Cygnus
olor
), and sandhill cranes (
Grus canadensis
)

among others
.

To get consistent results, standard operating procedures (SOP) hav
e been implemented and
maintained across the years.
Since
observers did
not

see
all birds
from
the fixed
-
wing aircraft,
estimation of waterfowl abundance require
d

surveying a portion of transects with helicopters to
establish visibility correction factors (VCF).
MDNR used the VCF
to adjust fixed
-
wing estimate
s

assuming

observers saw

all birds
in
transects flown with helicopters.
To potentially improve
precision and

reduce costs, w
e developed a
lternate VCFs
and aerial survey designs

to understand
how the accuracy
and precision
of the waterfowl population estimate change
d

from the existing
SOP methodology
. To meet MDNR standards,
we considered

alternate population est
imate
s

that
produced a
coefficient of variation (
CV
)

of less than 20%

to be acceptable and worth
consideration
.
We found comparable population estimates and CVs from eleven alternate VCFs
and three alternate aerial survey designs compared to the SOP.

iii

ACKN
OWLEDGMENTS

This research was made possible due to the funding provided by the
U.S. Fish and
Wildlife Service through the Pittman
-
Robertson Wildlife Restoration Act Grant MI W
-
155
-
R,
Michigan Department of Natural Resources (MDNR)
,

and the Department of F
isheries and
Wildlife at Michigan State University (MSU).
This work was also partially supported by salary
support for Scott R. Winterstein from the USDA National Institute of Food and Agriculture
(Project No. M
I
CL02588). I

will forever be indebted to thes
e organizations for their support.
I
would like to thank my graduate committee,
which was

made up of
Dr. David Luukkonen
, Dr.
Scott Winterstein, and Dr. Elise Zipkin. Their guidance, expertise, and support were instrumental
in the completion of this
project, as well as developing the skills to become a wildlife
professional. In particular, I thank Drs. Luukkonen and

Winterstein for being truly supportive
advisors and
mentors
for providing me the opportunity to work on this project. They promoted
me to

grow professionally and personally during my time at MSU.

I thank the MDNR for graciously letting me use their historic aerial survey data. I thank
their observers, Bruce Barlow,
John Darling, Brandy Dybas
-
Berger, Caleb Eckloff, Jeremiah
Heise, Josh Imber, Nik Kalejs, Nate Levitte, Ben Luukkonen, Terry McFadden,
Melissa Nichols,
Mike Richardson, Joe Robinson, and Barry Sova,

who helped with the data collection

for 2018
and 2019
, as well as anyone else who has helped in previous years.

I also thank Trey McClinton
and Ashley Huinker for participating in the helicopt
er surveys. I thank the pilots and support
personnel of the Michigan State Police, Aviation Section for their assistance in completing the
surveys each year.

, Dr. Sarah Mayhew,

for pr
oviding
and managing the database
used in the spring waterfowl survey, as well as her expertise and
guidance throughout the project.

Lastly,

program at MSU was exceptional for the supportive academic community I was

surrounded by.

my fellow graduate students who supported me with friendship and
guidance throughout my masters.

Lastly,
I would like to thank my parents, Debbie and Gary,

who have supported me from the beginning. Thank you for e
ncouraging my love for science and

supported me along the way.

TABLE OF CONTENTS

LIST OF TABLE
S

................................
................................
................................
.......................

v
i

LIST OF FIGURES

................................
................................
................................
...................

viii

INTRODUCTION
................................
................................
................................
..........................
1

Research Objectives

................................
................................
................................
...........
9

METHODS

................................
................................
................................
................................
...
10

Study Area

................................
................................
................................
........................
10

Data Collection

................................
................................
................................
.................
1
1

Data Analysis

................................
................................
................................
....................
1
3

Statistical Analysis

................................
................................
................................
...........
1
8

Alternate Visibility Correction Factors

................................
................................
1
8

Alternate Aerial Survey Designs
................................
................................
...........
21

Helicopter Bootstrap

................................
................................
.............................
2
5

Fixed
-
wing Bootstrap

................................
................................
............................
2
6

RESULTS

................................
................................
................................
................................
.....
2
8

Survey
Timing and Sample Sizes
................................
................................
....................
2
8

Alternate Visibility Correction Factors

................................
................................
.........
29

He
l
icopter Bootstrap

................................
................................
................................
........
5
5

Fixed
-
wing Bootstrap
................................
................................
................................
.......
6
1

Alternate Aerial Survey Design
s
................................
................................
.....................
7
1

DISCUSSION

................................
................................
................................
...............................
9
1

Alternate Visibility Correction Factors

................................
................................
.........
9
1

Survey Timing and Sample Sizes
................................
................................
....................
9
6

Bootstrap Methods

................................
................................
................................
...........
9
7

Alternate Aerial Survey Designs
................................
................................
.....................
98

MANAGEMENT IMPLICATIONS

................................
................................
........................
10
6

APPENDI
X

................................
................................
................................
................................
.
1
09

LITERATURE CITED

................................
................................
................................
.............
1
1
4

LIST OF TABLES

Table 1.
D
escriptions
of methods to estimate Visibility Correction Factors (VCFs) for the
Michigan DNR spring
waterfowl survey, including

seven VCFs to compare against the
Standard
Operating Procedure (
SOP
)

VCF

................................
................................
................................
...
19

Table 2. Annual Visibility Correction Factor (VCF) for a) Canada goose, b) mallard, and c)
sandhill crane
, 1992
-
2019
. A VCF with 1 and SE of 0 is an ass
umed value in table
c

before
sandhill cranes were counted on VCF flights

................................
................................
................
30

Table
3
.
P
opulation estimates,
Coefficient of Variation
s

(
CV
s
)
, and costs to evaluate the
helicopter
-
only design for Canada goose and mallard
, 2003
. Two costs were
calculated based on
the 2018 or 2019 helicopter survey costs to determine helicopter
-
only design costs

....................
8
0

Table
4
.
P
opulation estimates,
Coefficient of Variation
s

(CV
s
)
, and costs to evaluate the
helicopter
-
only design for Canada goose, mallard, and sandhi
ll crane
, 2010
. Two costs were
calculated based on the 2018 or 2019 helicopter survey costs to determine helicopter
-
onl
y design

costs
................................
................................
................................
................................
................
8
1

Table
5
.
P
opulation estimates,
Coefficient of Variation
s

(CV
s
)
, and costs to evaluate the
helicopter
-
only design for Ca
nada goose, mallard, and sandhill crane
, 2014
. Two costs were
calculated based on the 2018 or 2019 helicopter survey costs to determine helicopter
-
only design

costs
................................
................................
................................
................................
................
8
2

Table
6
.
P
opulation estimates,
Coefficient of Variation
s

(CV
s
)
, and costs to
evaluate the
helicopter
-
only design for Canada goose, mallard, sandhill crane, and mute swan
, 2018
. Two
costs were calculated based on the 2018 or 2019 helicopter survey costs to determine helicopter
-
only design
costs

................................
................................
................................
............................
8
3

Table
7
.
P
opulation estimates,
Coe
fficient of Variation
s

(CV
s
)
, and costs to evaluate the
helicopter
-
only design for Canada goose, mallard, sandhill crane, and mute swan
, 2019
. Two
costs were calculated based on the 2018 or 2019 helicopter survey costs to determine helicopter
-
only design c
osts

................................
................................
................................
............................
8
4

Table
8
.
P
opulation estimates,
Coefficient of Variation
s

(CV
s
)
, and costs to evaluate the
modified SOP design for Canada goose, mallard, and mute swan
, 2003
. Two costs were
calculated based on the 2018 or 2019 MDNR spring waterfowl survey costs to
determine
modified SOP
design

costs

................................
................................
................................
............
8
5

Table
9
.
P
opulation estimates,
Coefficient of Variation
s

(CV
s
)
, and costs to evaluate the
modified SOP design for Canada goose, mallard, sandhill crane, and mute swan
, 2010
. Two
costs were calculated based on the
2018 or 2019 MDNR spring waterfowl survey costs to
determine modified SOP design costs

................................
................................
...........................
8
6

vii

Table 1
0
.
P
opulation estimates,
Coefficient of Variation (CV)
, and costs to evaluate the modified
SOP design for Canada goose, mallard, sandhill crane, and mute swan
,

2014
. Two costs were
calculated based on the 2018 or 2019 MDNR spring waterfowl survey costs to determine
modified SOP design costs

................................
................................
................................
............
8
7

Table 1
1
.
P
opulation estimates,
Coefficient of Variation (CV)
, and costs to evaluate the modified
SOP design for Canada
goose, mallard, sandhill crane, and mute swan
, 2018
. Two costs were
calculated based on the 2018 or 2019 MDNR spring waterfowl survey costs to determine
modified SOP design costs

................................
................................
................................
............
8
8

Table 1
2
.
P
opulation estimates,
Coefficient of Variation (CV)
, and costs t
o evaluate the modified
SOP design for Canada goose, mallard, sandhill crane, and mute swan
, 2019
. Two costs were
calculated based on the 2018 or 2019 MDNR spring waterfowl survey costs to determine
modified SOP design costs

................................
................................
................................
............
8
9

Table 1
3
. Waterfowl grouping

types for the M
ichigan DNR

spring waterfowl survey

..............
1
1
3

viii

LIST OF FIGURES

Figure 1.
Map of M
ichigan
DNR

spring waterfowl survey with east
-
west survey transects (4
-
digit numbers) shown as solid lines. Transect numbers 5901
-
5912 (segment numbers 1
-
93)

f
arm
u

-
5811 (segment numbers 1
-
18
and 20
-
49) are in

n
orthern
f

forested stratum was removed
. Farm urban stratum is shown in green, northern forested stratum
is shown in red, and non
-
surveyable areas are shown in light blue

................................
.................
5

Figure 2.
Maps of

a) Standard Operating Procedure (SOP), b) helicopter
-
only, and c) modified SOP. East
-
west
survey transects (4
-
digit numbers) are shown as solid lines, fixed
-
wing surveys are shown
in the
red outlined box, helicopter surveys are shown in the yellow outlined box, and non
-
surveyable
areas are shown in light blue

................................
................................
................................
..........
2
2

Figure 3. Comparison of Canada goose alternate Visibility Correction Factors (VCFs) using
fixed
-
wing and helicopter survey
s over the state of Michigan for a) 2003, b) 2010, c) 2014, d)
2018, and e) 2019. The black bars represent ninety
-
five percent confidence interval
s

.................
3
2

Figure 4. Comparison of mallard alternate Visibility Correction Factors (VCFs) using fixed
-
wing
and helic
opter surveys over the state of Michigan for a) 2003, b) 2010, c) 2014, d) 2018, and e)
2019.
The black bars represent ninety
-
five percent confidence intervals

................................
......
36

Figure 5. Comparison of sandhill crane alternate Visibility Correction Factors (VCFs) using
f
ixed
-
wing and helicopter surveys over the state of Michigan for a) 2010, b) 2014, c) 2018,
d
)
2019.
The black bars represent ninety
-
five percent confidence intervals

................................
......
4
0

Figure 6. Comparison of Canada goose population estimates for alternate Visibility Corr
ection
Factors (VCFs) using fixed
-
wing and helicopter surveys over the state of Michigan for a) 2003,
b) 2010, c) 2014, d) 2018, and e) 2019.
The black bars represent ninety
-
five percent confidence
intervals

and n represents the number of segments to calcu
late the VCF for each VCF estimation
method
................................
................................
................................
................................
............
4
3

Figure 7. Comparison of mallard population estimates for alternate Visibility Correction Factors
(VCFs) using fixed
-
wing and helicopter surveys over the state of Michigan for a) 2003, b) 2010,
c) 2014, d) 2018
, and e) 2019.
The black bars represent ninety
-
five percent confidence intervals

and n represents the number of segments to calculate the VCF for each VCF estimation method
................................
................................
................................
................................
........................
4
7

Figure 8. Comparison of sandhill crane population estimates for alternate Visibility Correction
Factors (VCFs) using fixed
-
wing and helicopter surveys over the state of Michigan for a) 2003,
b) 2010, c) 2014, d) 2018, and e) 2019.
The black bars represent
ninety
-
five percent confidence
intervals

and n represents the number of segments to calculate the VCF for each VCF estimation
method
................................
................................
................................
................................
............
5
2

Figure 9. Comparison of average Coefficient of Variation (CV) on population estimates for
alternate Visibility Correctio
n Factors (VCFs) using fixed
-
wing and helicopter surveys over the
state of Michigan for a) Canada goose (2003, 2010, 2014, 2018, and 2019), b) mallard (2003,
2010, 2014, 2018, and 2019), and c) sandhill crane (2010, 2014, 2018, and 2019).
CV

of 20%

is
sho
wn as the red dashed line.
The black bars represent ninety
-
five percent confidence intervals

....
................................
................................
................................
................................
........................
5
6

Figure 10. The bootstrap method population estimates for the helicopter
-
only aerial survey
design using helicopter surveys over the state of Michigan for the f
ive most recent VCF years for
a) Canada goose, b) mallard, c) sandhill crane, and d) mute swan.
The black bars represent
ninety
-
five percent confidence intervals

................................
................................
........................
5
8

Figure 11. The bootstrap method Coefficient of Variation (CV) on population estimates from
the
helicopter
-
only aerial survey design using helicopter surveys over the state of Michigan for the
five most recent VCF years for a) Canada goose, b) mallard, c) sandhill crane, and d) mute swan.

CV
of 20%
is shown as the red dashed line

................................
................................
...................
6
2

Figure 12. Th
e bootstrap method population estimates for the modified SOP aerial survey design
using fixed
-
wing and helicopter surveys over the state of Michigan for the five most recent VCF
years for a) Canada goose, b) mallard, c) sandhill crane, and d) mute swan.
Th
e black bars
represent ninety
-
five percent confidence intervals

................................
................................
........
6
5

Figure 13. The bootstrap method Coefficient of Variation (CV) on population estimates from the
modified SOP aerial survey design using fixed
-
wing and helicopter surveys over the state of
Mi
chigan

for

the five most recent VCF years for a) Canada goose, b) mallard, c) sandhill crane,
and d) mute swan.
CV
of 20%
is shown as the red dashed line

................................
....................
6
8

Figure 14. Comparison of population estimates among alternate aerial survey designs using
fixed
-
wing and helicopter surveys over the state of Michigan for a) Canada goose, b) mallard, c)
sandhill crane, and d) mute swan. The black bars represent a ninety
-
five percent confidence
interval

................................
................................
................................
................................
...........
7
2

Figure 15. Comparison of average Coefficient of Variati
on (CV) on population estimates among
alternate aerial survey designs using fixed
-
wing and helicopter surveys over the state of
Michigan for a) Canada goose (2003, 2010, 2014, 2018, and 2019), b) mallard (2003, 2010,
2014, 2018, and 2019), and c) sandhill
crane (2010, 2014, 2018, and 2019), and d) mute swan
(2018 and 2019).
CV of 20%

is shown as the red dashed line.
The black bars represent ninety
-
five percent confidence intervals

................................
................................
................................
...
7
6

Figure 16.
Comparison of indicated birds on the fixed
-
wing survey to the C
oefficient of
Variation (CV) on population estimates from the Standard Operating Procedure (SOP) aerial
survey design using fixed
-
wing and helicopter surveys over the state of Michigan for a) Canada
goose (1992
-
2019), b) mallard (1992
-
2019), c) sandhill cr
ane (2005
-
2019), and d) mute swan
(2007
-
2019). CV of 20% is shown as the red dashed line

................................
...........................
10
0

Figure 17. Fixed
-
wing
S
tandard
O
perating
P
rocedure

(SOP)

for conducting the Michigan

DNR

spring waterfowl survey

................................
................................
................................
...............
11
2

INTRODUCTION

Highly mobile species can be difficult to monitor as the
y cover

large areas, including
areas with restricted or limited access due to terrain or private
land
ownership (Caughley et al.
1976, Tracey et al. 2008).
S
ome population surveys may be difficult and expensive to conduct
when surveying over a state or regional l
evel. One solution is to conduct aerial surveys to
estimate population size, particularly for large mammals and birds (Norton
-
Griffiths 1975,
Caughley 1977). Aerial surveys have been extensively conducted to estimate regional and local
abundance
of North A
merican waterfowl using fixed
-
wing aircraft (Martin et al. 1979, Smith
1995).

One of the largest wildlife surveys takes place during the
spring

to estimate population
sizes of waterfowl species in
important breeding areas of
Canada and
the
United States

(
USFWS
2018); t
he Waterfowl Breeding Population and Habitat Survey
provides information on a wide
variety of duck and goose species and
helps to inform annual
waterfowl
hunting regulations. The
MDNR collaborates with the U.S. Fish and Wildlife Service (USFW
S), the Canadian provinces,
and the Canadian Wildlife Service (CWS) to conduct aerial surveys from April to June to
monitor important waterfowl populations across Canada and the northern United States (USFWS
2018).

Beginning in 1991, MDNR began a pilot s
tudy

to survey
distribution and
abundance
of
waterfowl
.
Since 1991
, t
h
e MDNR

has annually conducted the spring waterfowl survey to
monitor

population trends of breeding ducks and geese and develop
ed

goals for waterfowl
population and habitat management (Cleveland 1994, Soulliere and Chadwick 2003). The
MDNR spring waterfowl survey uses fixed
-
wing aircraft and helicopter
s

to estimate statewide
2

abundance of
waterfowl with an emphasis on
Canada geese (
B
ranta canadensis
), mallards (
Anas
platyrhynchos
), mute swans (
Cygnus olor
), and sandhill cranes (
Grus canadensis
). These species
are of management concern because
Canada goose and mallard

are hunted

species
, and in some
cases, high abundance
s

of Canada goo
se, sandhill crane, and mute swan h
as resulted in human
-
wildlife conflicts. In addition, waterfowl provide economic value and are good indicators of
wetland habitat conditions (Grado et al. 2011, Hagy et al. 2016).

Canada goose populations

in Michigan

hav
e increased in the past 50 years

with a
corresponding

increase in management demand to reduce human
-
goose conflicts through harvest
or nest destruction

as populations

increased to over 300,000 birds in 2015
(Ankney 1996, United
States Department of the Int
erior 2005, Luukkonen et al. 2008). More recently, the MDNR
has
tried
to
reduce the population and
achieve a statewide Canada goose
abundance
goal
of
between
175,000
-
225,000

birds

based on the spring waterfowl survey
(MDNR 2019).

A concern for mallard abu
ndance has recently become prominent due to the increase in
droughts which has negatively impacted the number of wetland habitats in the prairie pothole
region (PPR),
one of

the most productive waterfowl habitat
s

in the world (Johnson et al. 2005).
Michigan mallard
abundance is an indicator of breeding habitat conditions and so population
monitoring can help detect

wetland habitat loss.
Ducks, especially mallards,
use wetlands
throughout their life for food, breeding, brood rearing, and cover from pr
edators, so wetlands are
an important habitat for ducks and a good predictor for where duck density may be the greatest
(Krapu and Reinecke 1992, Austin et al. 2001, Anteau 2012
, Bartzen et al. 2017
). With a
potential decrease in wetland abundance, mallard

productivity could decrease and impact mallard
abundance, specifically in southeast Michigan
based on
a
predictive model of mallard
distribution (
Yerkes et al. 2007, Singer et al. 2016).
Although

not been
as
negatively aff
ected as the
PPR
, recent mallard abundance estimates for Michigan
have been below expectations
.
E
stimated
wetland abundance

in 2018 was

slightly above the
long
-
term average, although long
-
term climatic change predicts decreased quantity and quality of
mall
ard habitat (Singer
et al.
2016, USFWS 2018).

Sandhill crane abundance in Michigan has rebounded from declines caused by historic
overharvesting and wetland habitat loss, and now significant human
-
crane conflicts through crop
depredation
are occurring (
Me
ine and Archibald 1996,
Avers et al. 2017). Due to their
aggressive behavior, mute swans have been out
-
competing and displacing native species
including trumpeter swans (
Cygnus buccinator
)

and destroying native wetland habitat (Stone and
Marsters 1970, Cia
ranca 1990, MDNR 2012). In the case of the invasive mute swan, a DNR
policy calls for reducing their abundance with a short
-
term goal of stabilizing numbers and a
long
-
term goal of fewer than 2,000 birds (MDNR 2012).

While these four species are the most
abundant
or

important species counted using the
MDNR spring waterfowl survey, other waterfowl species are recorded as well. Other species of
dabbling ducks like wood duck (
Aix sponsa
), gadwall (
Mareca strepera
), American wigeon
(
Anas americana
), green
-
wing
ed teal (
Anas carolinensis
), northern pintail (
Anas acuta
), and
northern shoveler (
Anas clypeata
) and diving ducks like
ring
-
necked duck (
Aythya collaris
),
canvasback (
Aythya valisineria
), lesser scaup (
Aythya affinis
), and greater scaup (
Aythya
marila
),
bufflehead (
Bucephala albeola
), long
-
tailed duck (
Clangula hyemalis
), hooded merganser
(
Lophodytes cucullatus
), and common merganser (
Mergus merganser
) are detected on the aerial
survey. Although the abundance of these waterfowl species is estimat
ed from the spring
waterfowl survey, they are not
as well
represented due to their
low breeding abundance in
Michigan
. While the wood duck is a common species in Michigan, they are more prone to take
4

cover in forested wetland habitat which makes it difficu
lt for observers to detect

them
, resulting
in
highly variable
underestimates of their population size (Bellrose and Holm 1994).

The MDNR spring waterfowl survey is a statewide survey
with
observers

flying a series
of 21 fixed
-
width transects using fixed
-
w
ing aircraft (Figure 1; CWS and USFWS 1987, Smith
1995).
Each transect is then made up of varying numbers of segments
depending

on the length of
the transect.
To get consistent results, standard operating procedures (SOP)
have been
implemented and maintain
ed across
the
years

(CWS and USFWS 1987; see Appendix for
a
full
description of the
SOP).
Fixed
-
wing observers
can fail to

detect all birds and
may

misidentify
waterfowl species which can result in population estimates with low precision and high bias
(Gre
en et al. 2008).
Since detection is imperfect for observers in fixed
-
wing aircraft,
a sample

of
fixed
-
winged
segments

have historically been resurveyed using helicopters (Caughley 1974).
Helicopters provide
d

more reliable detection for observers
.

Additiona
lly, helicopters are more
maneuverable and efficient compared to fixed
-
wing aircraft (Ross 1985, Cordts et al. 2002).
The
MDNR has used
visibility correction factor
s

(VCF
s
), based on the helicopter flights,

to correct
fixed
-
wing counts, yield
ing

species
-
specific statewide abundance estimates

that are thought to be
less biased than uncorrected estimates
. Helicopter surveys have not been flown every year

due to
expensive costs and labor constraints
, so
mean
statewide species
-
specific VCFs from all
VCF
years
have been used

to correct annual fixed
-
wing survey counts.
A new VCF is calculated for
each VCF year,
with
a VCF year
defined as a year in which
both the fixed
-
wing and helicopter
survey
s

are conducted. The
n, the

MDNR

used c
orrected
mean
fixed
-
wi
ng density estimates from
segment
s

to expand
for the area of Michigan to compute population estimates.

Figure 1.
Map of M
ichigan
DNR

spring waterfowl survey with east
-
west survey transects (4
-
digit numbers) shown as solid lines. Transect numbers 590
1
-
5912 (segment numbers 1
-
93)

-
5811 (segment numbers 1
-
18
and 20
-

forested stratum was removed. Farm urban str
atum is shown in green, northern forested stratum
is shown in red, and non
-
surveyable areas are shown in light blue
.

To provide reliable results, s
urvey methodologies need to periodically be examined and
reevaluated
,

as many factors (e.g., weather, obse
rvers, population demographics, and survey
cost) could change over time (Cowardin and Blohm 1992,
Tracey
et al.
2008,
Mills 2012,

evaluated once. MDNR has

not

formally evaluated their current SOP survey design since 1994
(Cleveland 1994), so another evaluation of the survey is needed to
determine

if abundance
estimates are reliable, cost
-
effective,
and
precise
. A
dditionally,
the
costs of aircraft, observers,
an
d survey stratification have changed.

Since 199
1
,

the MDNR has been using the same aerial
survey field methods

to provide consistent data collection
.

aerial survey
designs can be evaluated to determine utility for Michigan. For example, an
assessment of wintering American black ducks (
Anas rubripes
) in the Atlantic flyway changed
from a

systematic sampling design to a stratified sampling design with multiple strata (
Conroy et
al. 1988). This modification in their survey methodology helped to increase precision and adjust
for underestimation from fixed
-
wing aircraft. Moreover, a recommendation for the Atlantic
Flyway Breeding Waterfowl Survey to use hierarchical models

to estimate waterfowl abundance
instead of stratified random sampling was based on evaluating historical aerial survey data
(Sauer
et al.
2014). Lastly, the CWS and the USFWS jointly monitor American black duck
populations in eastern Canada and the northe
astern United States (Zimmerman

et al.

2012). The
CWS uses a helicopter plot survey while the USFWS uses a fixed
-
wing transect survey. After
considering

alternative models, they used a hierarchical model to aggregate and analyze
data
from both survey metho
ds to obtain one population estimate for this region.

Since many survey
7

might improve survey efficiency.

Recently, helicopter costs for MDNR
were

reduced through a p
artnership with the
Michigan State Police

(MSP)
.
Helicopter surveys are expensive but detect more birds compared
to the fixed
-
wing survey.
The MDNR
was

able to increase the

number of

helicopter

flights
,
which also opened the possibility of
using
alternative aerial survey designs. One
possibility

could
be to conduct the entire spring waterfowl survey only using helicopters.
If the MDNR budget
was not constrained, h
elicopter surveys
c
ould be surveyed ever
y
year
if possible,
as observers in
a
helicopter have higher detection rates than observers in
a
fixed
-
wing

aircraft
.
Currently
,
reduced expenses in helicopter costs may make a helicopter
-
only aerial survey design feasible.
Alternatively,

the MDNR could us
e a modified SOP where some fixed
-
wing transects are
removed to allocate more
effort to

helicopter surveys. An improved aerial survey design might
minimize variance or achieve comparable precision on population estimates to the SOP from
fewer transects, re
ducing time and expenses for the spring waterfowl survey.
To quantify
precision, the MDNR uses the coefficient of variation (CV) which is a standardized measure of
dispersion.
The MDNR attempt
s

to achieve a

CV of 20% or less on annual estimates of
abundanc
e

for

the spring waterfowl survey.

A component that affect
s

the accuracy of the waterfowl population estimate using the
SOP survey methodology
is

the
species
-
specific VCFs used to correct the fixed
-
wing counts.
Currently, the SOP uses
an all
-
year (long
-
te
rm)

average species
-
specific VCFs.

When the
helicopter survey is conducted, each historic VCF is averaged with the current VCF. For
example, eight VCF years exist from 1992
-
1996, 2003, 2010, and 2014. To determine the 1995
all
-
year VCF, the MDNR average
d

t
he 1992, 1993, 1994, and 1995 VCF values. From 1992
-
8

1996
, the number and location of helicopter surveys were determined by cost, aircraft, and
personnel time which might result in bias since the VCF segments were not representative of the
state of Michigan

(Cleveland 1994). The number of years selected to estimate VCFs will impact
population estimates as well as the variance. If the MDNR
uses all

year
s to estimate VCFs
,
population estimates may have increased precision, but th
e

long
-
term average VCF may not
accurately estimate annual detection
if there are changes to the system over time
(i.e., changes in
weather, observers, pilots, etc.; Soulliere and Chadwick 2003).
A rolling average like a three or
five
-
year statewide VCF est
imate may be a viable alternative to accurately
represent

how the
detection may change over time while also maintaining a CV of 20% or less on population
estimates.

Research Objectives

The purpose of this research
wa
s to evaluate the current SOP for the MDNR spring
waterfowl survey by analyzing historical data (1992
-
2017) and by conducting two years of
expanded helicopter
surveys (2018
-
2019). This research also address
ed

if other aerial survey
designs may be more
cost
-
effective.
The specific research objectives were as
follows
:

T
o determine if modifications to existing
MDNR survey
methodologies can improve
the precision of their aerial survey and estimation of waterfowl abundance.

T
o estimate
visibility correction fact
or
s

(VCFs) and determine if the current
aerial survey methodologies are

appropriate for estimating waterfowl
abundance
in Michigan
.

develop alternative aerial survey designs that estimate waterfowl abundance
precisely
and are comparable to the SOP metho
dology (coefficient of variation [CV]
less than 20%).

evaluate
helicopter
-
only and modified SOP aerial survey designs to
estimate precise waterfowl abundance (coefficient of variation [CV] less than
20%).

determine the
most efficient alternative
aerial survey design
s

waterfowl.

conduct a statistical
analysis to

predict

and compare waterfowl population
estimates, coefficient
s

of variation

(CV)
, and cost
s

to determine the best
aerial survey design
s
.

METH
ODS

Study Area

from
the spring waterfowl survey, the
MDNR developed a stratified systematic sampling framework to survey the whole state of
Michigan.
MDNR biologists believed that
the
detection probability of wate
rfowl was not
constant throughout the state of Michigan (Cleveland 1994, Soulliere and Chadwick 2003).
Thus,
the MDNR considered
stratification for the state of Michigan
due
to variations in cover
type and land use.

The MDNR

divided

Michigan

into two strat
a
,

the MDNR surveyed a
sample of segments
within each stratum
(Figure 1). The
farm

urban stratum encompasses approximately the southern 1/3 portion of Michigan. The
northern forested stratum consists of the remaining northern 2/3 portion of the state.

The farm

urban stratum is mostly defined by agricultural and urban land where plant
pr
oductivity and waterfowl densities are high.
Wetlands are abundant in the farm urban stratum
as loam soils dominate this stratum while clay and sandy soils
comprise

the northern forested
stratum which retain
s

fewer

wetlands. Ducks, geese, and swans are fou
nd
in and
near wetlands,
so high waterfowl abundance is associated with a higher number of wetlands in the
farm urban
stratum.
Plant productivity and waterfowl densities are more variable

in the northern forested
stratum

but mostly

lower

than
in
the
farm u
rban

stratum. Although the spring waterfowl survey
is a statewide survey, some areas of both strata were excluded from the survey. Portions of the
hilly west
ern

Upper Peninsula, urban centers, and large airports, especially the Detroit
Metropolitan Wayne C
ounty Airport, were not surveyed due to safety concerns.

Data
C
ollection

While historical data were used to conduct this project,
we

participated as observer
s

for
the helicopter portion of the 2018 and 2019 spring waterfowl survey.
The MDN
R typically
cond
ucted the
spring waterfowl survey during the months of April and May, but the start and end
dates were variable

and

based on many factors.
Survey t
iming was
critical

for the MDNR spring
waterfowl surveys to get the most accurate local breeding pair estimates (Dzubin 1969, CWS and
USFWS 1987). The MDNR aimed to complete aerial surveys before nests from Canada geese
hatched, when about half of the mallard females starte
d nests,
after migrant waterfowl have
moved through an area, and
when there was still good visibility by having less than 20% leaf
-
out
on trees and shrubs (Soulliere and Chadwick 2003).

W
eather
in Michigan can rapidly change
within a season and

vary among
year
s
, resulting in earlier or later springs

that
can
impact when
the survey would begin
.
Surveys were not conducted on days with rain, fog, high winds, or other
conditions that reduce
d

waterfowl detection and safety. Thus, long delays for the aerial surve
y
could occur if

harsh weather persist
ed

for days.

To get consistent results, the MDNR
maintain
ed

standard operating procedures (SOP) for
the spring waterfowl survey (see Appendix for
a
full description of the
SOP
).

Since there is a
higher concentration o
f breeding ducks and geese in the farm urban stratum,

more transects were
surveyed in th
is

stratum compared to the northern forested stratum.

Hence, transects in the
northern forested stratum are spaced 45.1 km (28 mi) apart while transects in the farm urb
an
stratum are spaced 22.5 km (14 mi) apart (Cleveland 1994).

Once
the MDNR collected the
data,
they grouped
waterfowl observations

into six categories: singles, flocked drakes, pairs, nesting
pairs, nesting singles, and groups.
The MDNR entered the data into a relational database used to
estimate abundance by species. The relational database was a quick and efficient way to organize
12

large amounts of related data. The MDNR created quality control checks to eliminate most data
entr
y errors. They then entered each waterfowl observation into the database with the transect
number, segment number, date, species
,

grouping type, and wetland type.
Waterfowl

the
total n
umber of

estimated for each segment.

The number of singles, flocked drakes, pairs,
nesting pairs,

and

nesting singles seen in a segment were

each

multiplied by two while the
number of birds in a group were not adjusted to get the tota
l number of indicated birds.

Thus,
indicated birds may include birds that were not seen but were

assumed

associated with a pair, for
example.

Since helicopter flights are expensive, the MDNR
only
conducted

helicopter
surveys in
eight years
prior to 2018
:
1992
-
1996, 2003, 2010, and 2014
.
The MDNR began and has
maintained
an all
-
year averaged VCF

for each species
.

The MDNR has surveyed from 139 to
152 segments for the fixed
-
wing flights. The number of segments surveyed with helicopters
within a year ranged f
rom six to 29

prior to 2018
. Some years had fewer segments surveyed
because no flights were flown in the northern forested stratum in that year.

In 2018 and 2019, we maintained
the
current survey methodology for

transect numbers,

transect configuration,
t
iming, and
da
ta

collection

for the spring waterfowl survey
. However, we
changed some survey methodology

to
evaluate changes in costs and
precision
. We aimed to
conduct 40 helicopter segments for
2018 and 2019

VCF years
,
which was
an increase
from
previous

VCF years
. We
also
changed to a new randomization for selecting helicopter segments
to increase spatial representation for the state of Michigan
(see below for a discussion of the new
randomization).

Data Analysis

The SOP
aerial survey
design

use
d

fixed
-
wing density estimates and a statewide species
-
specific VCF to compute population estimates

(Smith 1995)
.
The MDNR calculated d
ensity
estimates from the fixed
-
wing survey through
the

relational database and extrapolated for the
whole stat
e of Michigan
, including areas of the state that are not surveyed
. The
y have

used
statewide species
-
specific
VC
F,
based on the helicopter flights, to correct fixed
-
wing counts

to
add the number of indicated birds that were missed on the fixed
-
wing survey
.

h
elicopter surveys
were

not flown every year

due to budget
and labor
constraints
, so
average

statewide species
-
specific VCFs from all VCF years
were

used to correct annual fixed
-
wing
survey counts.
Then, the MDNR used c
orrected mean fixed
-
wing d
ensity estimates from
segments

expand for the area of Michigan to compute population estimates.

We assumed that
observers in
helicopter surveys had a 100% detection
, detections were statistically independent
events
,

the
number of birds in surveyed areas
did not change in a segment between the

fixed
-
wing and helicopter survey, and

all birds were not double
-
counted

and
did not move before
detection.

While these are estimates, we do not fully know the true population
size

95%
confidence intervals are used to deal with uncertainty in our estimates.

We
generated

p
opulation estimates using the SOP methodology

as:

where

is
the
total abundance by species,

is the total number of strata, j is th
e stratum type,

A
j

is the total area in stratum j
,

is the observed density per stratum, and

is the average
statewide species
-
specific VCF that is applied to each stratum j.

(1)

We estimated

as:

(
2
)

where y
f

is the
total
number of indicated birds on the helicopter in
year
f

that is summed
statewide
, x
f

is the number of indicated birds on the fixed
-
wing aircraft in
year f

that is summed
statewide
, and
F

is the
total
number of
years

surveyed
(Cochran 1977
). For mallards, indicated
birds can be expanded as:

Indicated birds = (2*singles) + (2*flocked drakes
) + (2*pairs) + (2*nesting pairs) + (2*nesting
singles) +
number of birds in a
group

(Cowardin et al. 1995). The formula for Canada geese
, sandhill crane, and mute swan

is the
same, except there are no flocked drakes to consider
:

Indicated birds =
(2*singles) + (2*pairs) + (2*nesting pairs) + (2*nesting singles) + number of
birds in a group

is the observed density per stratum and calculated as

(
3
)

where

is the mean indicated birds
from

the transects in stratum j from a fixed
-
wing, and

is
the

mean

area of the transects in stratum j (Martin et al
.

1979).

The variance on the population estimate is:

(
4
)

where
T is the total number of transects in stratum j,
A is the area
for
transect t

stratum j,
R
is
the average statewide VCF
applied to

transect t
,

B is
the observed density per segment

(Martin et
al. 1979). T
he variance components are:

(
5
)

where

is the fixed
-
wing indicated birds per transect in stratum j, and B is defined in equation
3
.

The associated variance on R is:

(
6
)

where
k

is the number of
VCF
segments in the
stratum
,

is the helicopter indicated birds in
stratum j,

are
defined in equation
4,
and R is defined in equation
2
.

Ninety
-
five percent confidence intervals on population
estimates for the SOP can be
calculated as:

(
7
)

where

is defined in equation
1
,

is defined in equation
4
, and 1.96 is the critical z value
when estimating a 95% confidence inter
val

using the normal distribution
.

To determine if the estimate from the survey method was precise, the coefficient of
variation (CV) was computed. The MDNR uses a CV of 20% or less on annual estimates of
abundance as a guideline for reasonable precision
for the spring waterfowl survey. The CV was
calculated as:

(
8
)

pilot s
tudy

(which will not be included in our analyses). Additionally,
high
helicopter costs have

limite
d the

number of years
in which
to conduct the helicopter survey,
and

the
number of
helicopter

segments sampled.
Past VCF years (1992
-
1996)
lacked randomness in th
e
selection

of
the s
urveyed s
egments and
targeted
areas with
high waterfowl abundance.
In 2003,
the MDNR
switched to a systematic random sampling approach. Beginning in the southernmost transect,
the
MDNR
randomly selected
a segment
in every other transect
, as well as the closest segment
immediately north of the random segment.
The MDNR a
ttempted

target of 30 randomly
selected segments across the state to achieve spatial coverage

and assure representation in low
and high waterfowl segments
,

but
it
was nev
er fully achieved
.
The MDNR surveyed 27, 29, and
28 segments in 2003, 2010, and 2014, respectively.
W
e
decided

to achieve a target of 40
segments for

each of
the
2018 and 2019

survey years to determine if adding more than 10
helicopter segments was feasible

under reduced helicopter expenses
.

To evaluate the SOP survey
17

methodology,
we compared
VCF years using surveys with more than 25 segments which include
2003, 2010, 2014, 201
8, and 2019
.
F
ewer than 25
segments
resulted in

higher variance on VCF
estimates
.

In addition,
the
n
orthern
f
orested stratum was not surveyed
with a helicopter
in
1992
and 1996.

Starting in 2018,
we used
a generalized random tessellation stratified desig
n (GRTS) to
randomly select segments
for VCF flights
while maintaining a representative

spatial coverage
.
GRTS sampling uses an algorithm that creates specific polygons called Dirichlet tessellation that
is overlaid on a specified area (Gitzen et al. 2012)
. Then, a randomly selected point will be
surveyed within each polygon. GRTS sampling is more spatially balanced than a simple random
sample. Furthermore, the least spatially balanced GRTS sample is comparable to the most
spatially balanced

simple random
s
ample (Gitzen et al. 2012). To compute a GRTS sample, we
used R
programming software (Version 3.6.1;
https://www.R
-
project.org/
)
with package grts.

Mute swans and sandhill cranes have limited data compared to mal
lards and Canada
geese.
We did not analyze m
ute swans for alternate VCF comparisons since
we assumed that
mute swans

had

a VCF value of 1 and
a
standard error of 0.
Mute swans are large birds that are
easily detected in a fixed
-
wing

aircraft
, so both surveys should have a 100% detection of seeing a
mute swan on a segment.
Additionally, helicopter surveys
only
began to count mute swans
starting in 2018, so there were
only
two years of mute swan data
with which
to compare
population estimate
s

t
o alternate survey designs. Similarly, the MDNR began counting sandhill
cranes in 2005
; however, MDNR only estimated sandhill crane abundance from 2010 forward as

Statistica
l
A
nalysis

Alternate Visibility Correction Factors

As an alternative to

the
use of

long
-
term
mean
statewide species
-
specific VCF
s
, VCFs

calculated for shorter intervals (e.g., annual,
three
-
year average,
or
five
-
year average)
could be
used to correct fixed
-
wing counts.
If there are
temporal

changes to the system,
including
occasional changes in observers, then
alternate
VCFs may better represent waterfowl species
detection, thus more accurately estimating their populations.
Furthermore, VCFs could be
calculated for each stratum.

We considered s
even

alternate VCFs: yearly statewide,
three
-
year statewide,
five
-
year

statewid
e,

yearly stratum
-
specific,
three
-
year

stratum
-
specific,
five
-
year

stratum
-
specific, and
all
-
year stratum
-
specific (Table
1
). Comparing statewide to stratum
-
specific VCFs will
determine if there
are

significant difference
s

in visibility detection between t
he
f
arm

u
rban

stratum

and
n
orthern
f
orested stratum. The
n
orthern
f
orested stratum
has
a
higher composition of
vegetative

cover in the landscape compared to the

f
arm

u
rban which may lead to a difference in
waterfowl detection.
T
he number of years
included
in the estimation also likely

influence
s

the
VCF

and associated variance
.
Detection

may change over time

due to

observer error, change in
helicopter aircraft or pilots
, or
covariates on the VCF

(leaf
-
cover, weather, wind, etc.)
.
A

single
-
year
VCF
or
VCF calculated by
averaging
shorter time periods

may be significantly different
than the long
-
term average VCF.
We estimated eleven alternate VCFs to determine if the SOP
VCF is appropriate for estim
ating waterfowl abundance as stratum
-
specific VCFs would yield
two VCFs each year. We compared alternate farm urban, northern forested, and statewide VCFs
to their all
-
year average VCFs for Canada goose, mallard, and sandhill crane.
Analysis for
alternate

Canada goose

and mallard

VCFs used data from 2003,
2010, 2014, 2018, and 2019

Table 1.
Descriptions of methods to estimate Visibility Correction Factors (VCFs) for the
Michigan DNR spring waterfowl survey, including seven VCFs to compare against the
Standard
Operating Procedure (SOP) VCF
.

VCF Name

Definition

Equation

Yearly Statewide

The ratio of the total
helicopter observations to the
total fixed
-
wing observations
for each species annually.

(9)

Three
-
Year Statewide

The ratio of
the total
helicopter observations to the
total fixed
-
wing observations
from the past three VCF
years.

(10)

Five
-
Year Statewide

The ratio of the total
helicopter observations to the
total fixed
-
wing observations
from the past
five VCF years.

(11)

SOP

All
-
years statewide VCF. The
ratio of the total helicopter
observations to the total fixed
-
wing observations for each
species from all historic VCF
years to the current VCF year.

(2)

Yearly Stratum
-
Specific

The ratio of the total
helicopter observations to the
total fixed
-
wing observations
for each species in each
stratum annually.

(12)

Three
-
Year Stratum
-
Specific

The ratio of the total
helicopter
observations to the
total fixed
-
wing observations
for each species from the past
three VCF years for each
stratum.

(13)

VCF Name

Definition

Equation

Five
-
Year Stratum
-
Specific

The ratio of the total
helicopter
observations to the
total fixed
-
wing observations
for each species from the past
five VCF years for each
stratum.

(14)

All
-
Year Stratum
-
Specific

The ratio of the total
helicopter observations to the
total
fixed
-
wing observations
for each species from all
historic VCF years to the
current VCF year for each
stratum.

(15)

helicopter survey years. Analysis for alternate sandhill crane VCFs used data from 2010, 2014,
2018, and 2019
helicopter survey

years. To meet MDNR standards, any alternative VCFs that
produced a CV of less than 20% w
ere

considered potentially acceptable.

Alternate Aerial Survey Designs

We analyzed data from the spring waterfowl survey to compare the current SOP survey
design to a helicopter
-
only and modified SOP (Figure 2). A helicopter
-
only survey design was
similar to the SOP, but there was no VCF and we

derived population estimates only from
helicopter counts. Helicopter data from 2003, 2010, 2014, 2018, and 2019 were used to calculate
population estimates for the helicopter
-
only design for the given years. Comparable to the SOP,
we estimated waterfowl a
bundance and CV from the modified SOP aerial survey design using
fewer fixed
-
wing transects. Therefore, the modified SOP design used the same population
estimate and CV formulas as the SOP, but with modified survey effort. Fixed
-
wing data and
VCFs estimate
d for all years were used to calculate 2003, 2010, 2014, 2018, and 2019
population estimates for the modified SOP.

The population estimate for the helicopter
-
only survey design was calculated

(16)

where

is the unbiased estimator for the total population, L is the total number of strata,

is
the total number of segments that can be available in stratum h, and

is the sample mean in
stratum h (
Thompson 1992)
. The associated variance is then

(17)

Figure 2. Map
s

of aerial survey design
s

for

a)
Standard Operating Procedure (
SOP
),

b) helicopter
-
only, and c) modified SOP. East
-
west
survey transects (4
-
digit numbers) are
shown as solid lines, fixed
-
wing surveys are shown in the
red outlined box, helicopter surveys are shown in the yellow outlined box, and non
-
surveyable
areas are shown in light blu
e
.

Figure 2
(
cont'd
)

Figure 2 (cont'd)

where

is the sample size in stratum h, and

is the sample standard error in stratum h.

Population estimates for the helicopter survey design with a
ninety
-
five percent

confidence interval were calculated as

(1
8
)

w
here

is defined in equation
16

and

is defined in equation

17
.

The CV was calculated for each SOP population as

(
19
)

Helicopter Bootstrap

W
e

used

the
bootstrap method to determine how many helicopter segments are needed to
achieve a CV
of less than 20% with feasible costs. Bootstrapping

is used

when the

underlying
statistical distribution is
unknown
, so
t
he distribution of
values

found in random sample
s

from
the population is
a reasonable

guide to the d
istribution of the
population estimate

(Manly 1997).
To approximate the population, the sample is resampled
numerous times
with replacement.

We
bootstrapped
helicopter
data from the
2003, 2010, 2014, 2018, and 2019 VCF
years

for Canada
goose and mallard

with a random sample
of 10 to 90 segments with increments of 10.
We
randomly sampled with replacement from 27 segments in 2003, 29 segments in 2010, 28
segments in 2014, 40 segments in 2018, and 40 segments in 2019. To obtain confidence intervals
for each segm
ent sample size
,
we ran
1,000 iterations.
We bootstrapped s
andhill crane helicopter
data
from

2010, 2014, 2018, and 2019

and bootstrapped m
ute swan helicopter data

from

2018
and 2019.

To determine the cost for each helicopter segment interval, we used the average
2018
and
2019 helicopter costs per segment to compare among the other VCF years.

Fixed
-
wing Bootstrap

W
e used bootstrap methods to determine how many fixed
-
wing transects can be removed
to still achieve a CV of less than 20% with feasible costs. Savings in
fixed
-
wing cost
s

could
allow more VCF segments to be surveyed and may help to reduce the variance. Based on the
sampling scheme for the spring waterfowl survey, we decided to only bootstrap the
f
arm
u
rban
transects as there

w
ere

twice as many segments in t
his stratum as in

the northern forested
stratum
.

two

segments, and transect 5912 contains

one

segment.
We bootstrapped

data from the

2003, 2010,
2014, 2018, and 2019 VCF years
f
or Canada goose, mallard,
and
mute swan.
We bootstrapped
s
andhill crane fixed
-
wing data

from

2010, 2014, 2018, and 2019. We
randomly remov
ed

from
one

to 10 transects

with increments of
one
.
T
ransect length varied
among the 10

farm urban
transects used
for bootstrapping from

six

to 10 segments.
To obtain the confidence interval for
each transect
sample size
, we ran 1,000 iterations.
We used the average
2018 and
2019 fixed
-
wing cost per transect
to
compare among the other VCF years.

In order to make costs

more
comparable among years, we standardized the 2003, 2010, and 2014 costs to 2018 and 2019
costs.

Based on the number of transects that
w
as

removed,

created two modified SOP

survey
designs
.
We
systematically remove
d

even
-
numbered
transect
s

for the mo
dified SOP
,

and
systematically removed odd
-
numbered
transects

for the modified SOP
-
2.

For example, if
the
bootstrap method

results in removing
five

transects, we would remove every
even
-
numbered
transect in the
f
arm
u
rban stratum for the modified SOP
design

(Figure 2c)
, while the modified
SOP
-
2

design would remove every
odd
-
numbered

transect in the farm urban stratum
.

W
e calculated the cost for each aerial survey design

and
separated a
ircraft costs into three
categories: hourly rate, flight hours, and
overtime charges.
We estimated h
elicopter costs per
segment as
:

(
2
0
)

where C is the total cost, r is the hourly rate for the aircraft, h is the flight hours, o is the total
overtime charges, and n is the number of segments surveyed.

We est
imated f
ixed
-
wing costs per transect as
:

(
2
1
)

where t is the number of transects surveyed.

We calculated

t
otal costs for each survey type as:

(
22
)

where
C is the total cost,
i is day i of the aerial survey, D is
the total number of aerial survey
days
, and r, h, and o are defined in equation 20
.

RESULTS

Survey Timing and Sample Sizes

We initiated

fixed
-
wing waterfowl survey
s

on 26 April 2018 and on 24 April 2019 and
these dates were near the 1992
-
2017 average start date of 20 April with a range between 2 April
to 30 April. The fixed
-
wing waterfowl survey concluded on 23 May 2018 and on 14 May 2019
and these dates were later t
han the 1992
-
2017 average end date of 11 May with a range between
19 April to 24 May.

W
e flew a

total of 40 18
-
mile segments with helicopters in each of 2018 and
2019 in cooperation with Michigan State Police

and MDNR personnel
; these flights included
two

observers and
one

trainee in addition to the helicopter pilot and were completed between 27
April and May 25, 2018 and 25 April and 17 May, 2019. These helicopter dates were near the
average (1992
-
1996, 2003, 2010, 2014, and 20
18
-
2019) start date of 24 April with a range
between 14 April and 1 May. The 2019 helicopter survey end date was near the average (1992
-
1996, 2003, 2010, 2014, and 2018
-
2019) end date
of 16 May
while the 2018 helicopter end date
was later than the average
end date with a range between 4 May and 19 May.

We surveyed
40

helicopter segments in 2018 and 2019 and

this number of

segments
was
more than the 1992
-
201
4

average segments of 18 with a range
of

six

to 29 segments. The 2018
spring waterfowl survey had a
4.4
-
day difference between when the fixed
-
wing and helicopter
surveys of
the same segment
were conducted,
which was more than the average (1992
-
1996,
2003, 2010, 2014, and 2018
-
2019) time of 2.3 days with a range
of

one

to 13 days. The 2019
spring waterfow
l survey had a 1.4
-
day difference which was less than the average.

Helicopter
flight hours per segment w
as

on average 1.16 hours in 2018 and 0.96 hours in 2019. Fixed
-
wing
flight hours per segment was on average 0.4 hours in 2018 and 2019.
Total flight hou
rs
,
including commute time,

for the helicopter survey was 46.4 hours in 2018 and 38.4 hours in
29

2019. Total flight hours for the fixed
-
wing survey was 51.6 hours in 2018 and 52.9 hours in
2019.

We surveyed h
elicopter segments in 2018 and 2019 using the GRT
S methodology which
resulted in a higher proportion of segments being surveyed in the northern forested
stratum
than
in
previous years. An average
(1992
-
1996, 2003, 2010,
and
2014)
of 68% of the
helicopter
segments
were

located in the
farm urban
stratum compared to an average

(1992
-
1996, 2003,
2010, and 2014)

of 32%
in

t
he northern forested stratum. In 2018 and 2019, 52% of the
helicopter segments were located in the
farm urban stratum
compared to
48%

in the

northern
forest
ed
.

Canada goose VCFs
ranged from 1.46 to 4.95 (Table
2
a). Mallard VCFs ranged from
1.91 to 6.48 (Table
2
b). Sandhill crane VCFs ranged from 1
.00

to 16
.00

(Table
2
c).

Alternate Visibility Correction Factors

Ninety
-
two percent of alternate statewide VCFs for Canada goose showed

no significant
difference compared to the Canada goose SOP (all
-
year average statewide) VCF for the five
most recent VCF years since 95% confidence intervals overlapped (Figure 3). In 2003, the
Canada goose yearly statewide VCF was significantly lower tha
n the Canada goose SOP VCF.
On average, the alternate statewide Canada goose VCFs were 15% smaller than the Canada
goose SOP VCF. Similarly, ninety
-
two percent of alternate farm urban VCFs for Canada goose
showed no significant difference compared to the C
anada goose all
-
year farm urban VCF. In
2003, the Canada goose yearly farm urban VCF was significantly lower than the Canada goose
all
-
year farm urban VCF. On average, the alternate farm urban Canada goose VCFs were 17%
smaller than the all
-
year farm urban

VCF. All the alternate northern forested VCFs for Canada

Table
2
.
Annual Visibility Correction Factor (VCF) for a) Canada goose, b) mallard, and c)
sandhill crane, 1992
-
2019. A VCF with 1 and SE of 0 is an assumed value in table c before
sandhill cranes
were counted on VCF flights
.

Year

Number of
Segments

Fixed
-
wing
Indicated Birds

Helicopter
Indicated Birds

VCF

1992

201

2.96

0.34

1993

416

4.95

1.18

1994

438

4.92

1.16

1995

212

2.75

0.26

1996

115

343

2.98

0.72

2003

217

316

1.46

0.3

2010

229

665

2.9

0.38

2014

223

648

2.91

0.46

2018

406

891

2.19

0.35

2019

332

659

1.98

0.4

Year

Number of
Segments

Fixed
-
wing
Indicated Birds

Helicopter
Indicated Birds

VCF

1992

138

411

2.98

0.7

1993

283

961

3.4

0.56

1994

138

894

6.48

1.19

1995

139

410

2.95

0.75

1996

228

652

2.86

0.66

2003

212

404

1.91

0.43

2010

265

550

2.08

0.43

2014

204

625

3.06

0.5

2018

218

540

2.48

0.45

2019

235

525

2.23

0.37

Year

Number of
Segments

Fixed
-
wing
Indicated Birds

Helicopter
Indicated Birds

VCF

1992

1993

1994

1995

1996

2003

2010

3.5

1.77

2014

12.03

2018

3.11

1.19

2019

2.68

1.12

Figure 3. Comparison of Canada goose alternate Visibility Correction Factors (VCFs) using
fixed
-
wing and helicopter surveys over the state of Michigan for a) 2003, b)
2010, c) 2014, d)
2018, and e) 2019. The black bars represent ninety
-
five percent confidence intervals.

goose showed no significant difference compared to the Canada goose all
-
year
northern forested
VCF. On average, the alternate northern forested Canada goose VCFs were 7% smaller than the
all
-
year northern forested VCF. On average, alternate Canada goose VCFs were 11% smaller
compared to the Canada goose SOP VCF. Alternate Canada go
ose VCFs ranged from 1.18 to
3.45 and standard errors ranged from 0.17 to 2.00 for the five most recent VCF years. Variations
in trends occurred in the Canada goose VCFs. Canada goose five
-
year farm urban, five
-
year
statewide, all
-
year statewide, and SOP V
CFs decreased each year while the remaining alternate
VCFs showed no pattern in their respective VCF values. Canada goose northern forested VCFs
had noticeably larger variances than the Canada goose statewide and farm urban VCFs.

All the alternate statew
ide and farm urban VCFs for mallard showed no significant
difference compared to the mallard SOP VCF and the all
-
year farm urban VCF, respectively
(Figure 4). On average, alternate statewide mallard VCFs were 16% smaller and farm urban
VCFs were 15% smalle
r compared to their respective all
-
year averaged VCF. Ninety
-
two
percent of alternate northern forested VCFs for mallard showed no significant difference
compared to the mallard all
-
year northern forested VCF. On average, the alternate northern
forested ma
llard VCFs were 11% smaller than the all
-
year northern forested VCF. On average,
alternate mallard VCFs were 16% smaller compared to the mallard SOP VCF. Alternate mallard
VCFs ranged from 1.06 to 4.38 and standard errors ranged from 0.19 to 1.33 for the f
ive most
recent VCF years. Mallard five
-
year farm urban, five
-
year statewide, all
-
year statewide, and SOP
VCFs decreased each year while the other alternate VCFs showed no pattern in their respective
VCF values. Confidence intervals for the mallard norther
n forested VCFs were consistently
larger than the mallard statewide and farm urban VCFs.

Figure 4. Comparison of mallard alternate Visibility Correction Factors (VCFs) using fixed
-
wing
and helicopter surveys over the state of Michigan for a) 2003, b
) 2010, c) 2014, d) 2018, and e)
2019. The black bars represent ninety
-
five percent confidence intervals.

Alternate statewide, farm urban, and northern forested sandhill crane VCFs
showed no
significant difference compared to the
ir respective
sandhill crane SOP VCF, all
-
year farm urban
VCF, and all
-
year northern forested VCF (Figure 5).
On average, alternate statewide VCFs were
8% larger,
farm urban VCFs were 25% larger, and northern forested VCFs were 7% smaller
compared to their respective all
-
year averaged VCF.
On average, alternate sandhill crane VCFs
were 15% larger compared to the s
andhill crane SOP VCF.
Some sandhill crane alternate VCFs
were identical to each other because the
observers in a
helicopter did not survey for sandhill
crane until the 2010 VCF year. Smaller
fixed
-
wing observations on VCF segments

for sandhill
crane resul
ted in VCF
s

that ranged from
1
.00

to 32
.00

with

standard error
s ranging

from 0.52 to
24
.00

for the f
our

most recent VCF years.

Sandhill crane
three
-
year

northern forested and all
-
year northern forested VCFs decreased each year while the other alternate VCF
s and SOP VCF
showed no pattern in the
ir

respective
VCF value
s
.

In 2010 and 2018, confidence intervals for the
sandhill crane northern forested VCFs were greater than the sandhill crane statewide and farm
urban VCFs. In 2014, sandhill crane yearly farm urb
an and statewide VCFs were considerably
larger than the other sandhill crane VCFs.

Using the alternate VCFs, we then compared population estimates to the SOP
population estimate. Alternate Canada goose population estimates were not significantly
differe
nt from the Canada goose SOP population estimate except for the 2003 Canada goose
yearly statewide and stratum
-
specific VCF estimation methods which resulted in lower
population estimates than the 2003 Canada goose SOP population estimate (Figure 6). On
av
erage, population estimates from statewide VCFs were 19% smaller for yearly, 17% smaller
for three
-
year, 9% smaller for five
-
year compared to the Canada goose SOP. Stratum
-
specific
population estimates were on average 18% smaller for yearly, 16% smaller fo
r three
-
year, and

Figure 5. Comparison of sandhill crane alternate Visibility Correction Factors (VCFs) using
fixed
-
wing and helicopter surveys over the state of Michigan for a) 2010, b) 2014, c) 2018, d)
2019. The black bars represent
ninety
-
five percent confidence intervals.

Figure 6. Comparison of Canada goose population estimates for
alternate Visibility Correction
Factors (VCFs) using fixed
-
wing and helicopter surveys over the state of Michigan for a) 2003,
b) 2010, c) 2014, d) 2018, and e) 2019. The black bars represent ninety
-
five percent confidence
intervals and n represents the nu
mber of segments to calculate the VCF for each VCF estimation
method.

n = 50

n = 77

n = 84

n = 27

n =
79

n =
106

n =
113

n = 2
9

n =
107

n =
134

n =
141

n = 2
8

n =
147

n =
174

n =
181

n =
40

n =
187

n =
214

n =
221

n =

221

n =
40

9% smaller for five
-
year compared to the Canada goose SOP. Population estimates from
all
-
year
stratum
-
specific VCFs were on average less than 1% smaller compared to the SOP. Moreover,
the 2003 Canada goose yearly statewide and stratum
-
specific VCFs resulted in 50% smaller
population estimates than the 2003 Canada goose SOP population estim
ate. The 2003 Canada
goose three
-
year statewide and three
-
year stratum
-
specific population estimates were around
28% smaller than the 2003 Canada goose SOP population estimate. In 2010, the Canada goose
three
-
year statewide and three
-
year stratum
-
specific
population estimates were on average lower
than the Canada goose SOP by 20%. In 2014, the Canada goose three
-
year statewide, three
-
year
stratum
-
specific, five
-
year statewide, and five
-
year stratum
-
specific population estimates were
on average smaller than
the Canada goose SOP by 15%. In 2018, the Canada goose three
-
year
stratum
-
specific VCF had a similar population estimate compared to the Canada goose SOP
population estimate, while the remaining alternate VCF estimates were an average of 14%
smaller than t
heir respective SOP

population

estimates. In 2019, the Canada goose population
estimate for the all
-
year stratum
-
specific VCF
was similar to the SOP population estimate. The
rest of the VCF estimation methods estimated on average 16% smaller population est
imates
compared to the Canada goose SOP population estimate. For the five most recent VCF years,
Canada goose population estimates for the stratum
-
specific and statewide VCF estimation
methods showed marginal differences to each other per year. Variances f
or each alternate VCF
estimation methods were similar to the Canada goose variances based on the SOP.

Few alternate mallard population estimates were

significantly

different from the mallard
SOP

(Figure 7)
.

I
n 2003,
the
yearly statewide VCF estimation met
hod resulted in
a

significantly

lower population estimate than the SOP

population estimate
. On average,
mallard
population
estimates from
statewide VCFs were 23% smaller for yearly,
20
% smaller for three
-
year, 11%

Figure 7. Comparison of mallard population estimates for alternate Visibility Correction Factors
(VCFs) using fixed
-
wing and helicopter surveys over the state of Michigan for a) 2003, b) 2010,
c) 2014, d) 2018, and e) 2019. The
black bars represent ninety
-
five percent confidence intervals
and n represents the number of segments to calculate the VCF for each VCF estimation method.

n = 50

n = 77

n = 84

= 84

n = 27

Figure 7

n =
79

n =
106

n =
113

n = 2
9

n =
107

n =
134

n =
141

n = 2
8

n =
147

n =
174

n =
181

n =
40

n =
187

n =
214

n =
221

n =

221

n =
40

smaller for five
-
year compared to the mallard SOP. Stratum
-
specific population estimates were
on average 20% smaller for yearly, 17% smaller for three
-
year, 9% smaller for five
-
year, and 3%
smaller for all
-
year compared to the mallard SOP. In 2003, populat
ion estimates from mallard
yearly stratum
-
specific and yearly statewide VCFs were similar to each other and were around
44% smaller compared to the 2003 mallard SOP. Additionally, the 2003 mallard yearly stratum
-
specific VCF estimated about 11,000 fewer bi
rds than the 2003 mallard yearly statewide but had
a higher variance which resulted in no significant difference to the SOP. Similar patterns from
the Canada goose population estimates repeated in the mallard population estimates. In 2003 and
2010, mallard

three
-
year statewide and three
-
year stratum
-
specific population estimates were on
average 23% smaller than their respective mallard SOP population estimates. Mallard yearly
statewide and yearly stratum
-
specific population estimates were on average 31% sma
ller in 2010
than the 2010 SOP population estimate. In 2014, the mallard all
-
year stratum
-
specific, yearly
stratum
-
specific, and yearly statewide VCFs population estimates were nearly identical to the
mallard SOP population estimate, while the remaining VC
F estimation methods estimated an
average of 18% fewer birds. In 2018 and 2019, similar patterns occurred for the alternate mallard
VCF estimation methods. The mallard all
-
year stratum
-
specific VCF population estimate was
slightly higher than the mallard S
OP population estimate by 6% in 2018 and 3% in 2019. The
rest of the alternate VCF estimation methods were on average around 14% smaller in 2018 and
17% smaller in 2019. In 2003, 2010, and 2014, mallard population estimates were marginally
different betwee
n stratum
-
specific and statewide VCF estimation methods. In 2018 and 2019,
mallard population estimates had higher population estimate differences between stratum
-
specific and statewide VCF estimation methods. During 2018 and 2019, the mallard stratum
-
spec
ific VCF estimation methods had higher population estimates than the statewide VCF
51

estimation methods. Variances for each alternate VCF estimation methods were similar to the
mallard SOP variances in corresponding years.

Sandhill crane alternate VCF
estimation methods resulted in no significant difference
compared to the SOP sandhill crane population estimates (Figure 8).

On average,
the
population
estimate from yearly statewide VCF was 25% larger compared to the sandhill crane SOP.
Stratum
-
specific p
opulation estimates were on average 33% smaller for yearly, 5% smaller for
five
-
year, and 5% smaller for all
-
year compared to the sandhill crane SOP. Population estimates
from three
-
year statewide, five
-
year statewide, and three
-
year stratum
-
specific VCFs
were less
than 1% different than SOP population estimates. Sandhill crane population estimates were
similar to each other in 2010, but all the sandhill crane stratum
-
specific VCF estimation methods
resulted in higher variances compared to the sandhill cran
e statewide VCF estimation methods.
In 2014, sandhill crane yearly statewide and yearly stratum
-
specific VCF population estimates
were on average 170% more than the sandhill crane SOP and the rest of the alternate VCF

estimation methods. Conversely, 2018 s
andhill crane yearly statewide and yearly stratum
-
specific VCF population estimates were 34% smaller than the sandhill crane population
estimates from SOP and other VCF estimation methods. In 2019, sandhill crane yearly stratum
-
specific

and

three
-
year stratum
-
specific population estimates were 39% smaller
,

while the yearly
statewide population estimate was 23% smaller than the sandhill crane SOP population estimate.
The remaining VCF estimation methods had negligible population estimate diff
erences.
Variances for each 2018 and 2019 alternate VCF estimation methods were similar to the
variances for the sandhill crane SOP.

Figure 8. Comparison of sandhill crane
population estimates for alternate Visibility Correction
Factors (VCFs) using fixed
-
wing and helicopter surveys over the state of Michigan for a) 2003,
b) 2010, c) 2014, d) 2018, and e) 2019. The black bars represent ninety
-
five percent confidence
interval
s and n represents the number of segments to calculate the VCF for each VCF estimation
method.

n =
29

n =

n =
29

n = 2
9

n =
57

n = 2
8

n =
97

n =
40

n =
108

n =
137

n =

137

n =
40

Lastly, we looked at averaged CV on population estimates from 2003, 2010, 2014, 2018,
and 2019. Averaged alternate Canada goose and mallard CVs on population estimates were not
significantly different than their respective SOP averaged CV except for the si
gnificantly higher
yearly stratum
-
specific averaged CV for both species (Figures 9a and 9b). Furthermore, the
yearly stratum
-
specific averaged CV exceeded the criteria of 20% or less with CV values at 21.2
for Canada goose and 21.6 for mallard. Based on th
e
overlap with the
95% confidence interval
s
,
yearly statewide averaged CV
s

for Canada goose and mallard

may be expected to exceed 20% in
some years
. For Canada goose and mallard, the variances on the alternate VCF estimation
methods were similar to the SOP

variances
. Averaged alternate sandhill crane CVs were not
significantly different compared to their respective SOP averaged CV (Figure 9c). Sandhill crane
three
-
year statewide, five
-
year statewide estimation methods had nearly identical averaged CV
s

compa
red to the sandhill crane SOP
CV and
with comparable variances. The stratum
-
specific
methods for sandhill crane had comparable variances to each other but were exceedingly higher
than the other alternate sandhill crane VCFs and SOP

variances
. The SOP metho
d had the lowest
averaged CV for Canada goose, mallard, and sandhill crane at 13.4, 13.1, and 39.9, respectively.

Canada goose and mallard averaged CVs were less than 20% except for yearly stratum
-
specific.
Averaged CVs for sandhill crane were always above

20%.

Helicopter Bootstrap

Using the five most recent VCF years, the bootstrap method resulted in decreased
variance as the number of segments increased (Figure 10). Invariant population estimates were
produced for each VCF year, showing that performing 1,000 iterations was sufficie
nt for the
bootstrap method. Canada goose and mallard bootstrapped CV showed that helicopter surveys

Figure 9. Comparison of average Coefficient of Variation (CV) on population estimates for
alternate Visibility Correction Factors (VCFs) using fixed
-
wing and helicopter surveys over the
state of Michigan for a) Canada goose (2003, 2010, 2014, 2018, and 2019), b) mallard (2003,
2010, 2014, 2018, and 2019), and c) sandhill crane (2010, 2014, 2018, and 2019). CV

of 20%

is
shown as the red dashed line. T
he black bars represent ninety
-
five percent confidence interval
s
.

Figure 10. The bootstrap method population estimates for the helicopter
-
only aerial survey
design using helicopter surveys over the state of
Michigan for the five most recent VCF years for
a) Canada goose, b) mallard, c) sandhill crane, and d) mute swan. The black bars represent

ninety
-
five percent confidence interval
s
.

with more than 40 segments would result in a CV of 20% or less (Figures 11a and 11b). Sandhill
crane and mute swan bootstrapped CV needed more than 40 segments to produce a CV of 20%
or less (Figures 11c and 11d). For the five most recent VCF years, al
l averaged Canada goose
CVs were more than 20% if 10 helicopter segments were surveyed.
Three

VCF year
s

had more
than 20% averaged Canada goose CV for
2
0 helicopter segments surveyed, while
one

VCF year
had
more than 20%

averaged C
V for 30 helicopter segme
nts
. At 40 helicopter segments
surveyed, all the VCF years for Canada goose had an averaged CV of 20% or less. For averaged
mallard CV, three VCF years at 10 helicopter segments, two VCF years at 20 helicopter
segments, and one VCF year had averaged mallar
d CVs more than 20%. At 40 helicopter
segments surveyed, all the VCF years for mallard had an averaged CV of 20% or less. Averaged
sandhill crane needed more than 80 helicopter segments to produce a CV of 20% or less. At 90
helicopter segments surveyed, av
eraged mute swan CV was close to a 20% CV.

Fixed
-
wing Bootstrap

Similar to the helicopter bootstrap results, the bootstrap method resulted in decreased
variance as the number of transects increased (Figure 12). Invariant population estimates were
produced

for each VCF year, showing that performing 1,000 iterations was sufficient for the
bootstrap method. Canada goose and mallard bootstrapped CVs showed that no more than five
transects should be removed in the farm urban stratum to maintain a CV of 20% or l
ess (Figures
13a and 13b). Sandhill crane and mute swan bootstrapped CVs resulted in a CV of 20% or more
for all number of transects in the farm urban stratum (Figures 13c and 13d). For the five most
recent VCF years, all averaged Canada goose CVs were mor
e than 20% if more than eight
transects were removed in the farm urban stratum. One and two VCF years had averaged Canada
goose CVs below a CV of 20% or less if seven transects or six transects were removed,

Figure 11. The bootstrap method
Coefficient of Variation (CV) on population estimates from the
helicopter
-
only aerial survey design using helicopter surveys over the state of Michigan for the
five most recent VCF years for a) Canada goose, b) mallard, c) sandhill crane, and d) mute swan.

CV of 20% is shown as the red dashed line.

Figure 12. The bootstrap method population estimates for the modified SOP aerial survey design
using fixed
-
wing and helicopter
surveys over the state of Michigan for the five most recent VCF
years for a) Canada goose, b) mallard, c) sandhill crane, and d) mute swan. The black bars
represent ninety
-
five percent confidence intervals.

Figure 12

Figure 13. The bootstrap method Coefficient of Variation (CV) on population estimates from the
modified SOP aerial survey design using fixed
-
wing and helicopter surveys over the state of
Michigan
for
the five most recent VCF years f
or a) Canada goose, b) mallard, c) sandhill crane,
and d) mute swan.
C
V

of 20%

is shown as the red dashed line.

respectively. Once five transects or less were removed, all the
VCF years had averaged Canada
goose CVs below 20%. For the five most recent VCF years, all averaged mallard CVs were more
than 20% if more than eight transects were removed. Two and four averaged mallard CVs were
below a CV of 20% or less if seven transect
s or six transects were removed, respectively. At five
transects removed, all averaged mallard CVs were below 20%. Averaged sandhill crane and
mute swan CVs were always more than 20% CV.

Alternate Aerial Survey Designs

Although there was considerable vari
ation among estimates from alternate aerial survey
designs, there were no significant differences for Canada goose, sandhill crane, and mute swan
population estimates compared to their respective SOP population estimates (Figures 14a, 14c,
and 14d). Altern
ate mallard population estimates also showed no significant difference from the
SOP except for the 2003 helicopter
-
only method which was significantly lower than the SOP
population estimate (Figure 14b). The modified SOP population estimates were always hi
gher
than their respective SOP population estimates, while the modified SOP
-
2 population estimates
were always lower than their respective SOP population estimates for all four species. On
average, the modified SOP was 12% larger, 11% larger, 25% larger, 1
9% larger compared to the
SOP population estimate for Canada goose, mallard, sandhill crane, and mute swan, respectively.
On average, the modified SOP
-
2 was 16% smaller, 14% smaller, 13% smaller, and 24% smaller
compared to the SOP population estimate for
Canada goose, mallard, sandhill crane, and mute
swan, respectively.

For Canada goose, the helicopter
-
only

population estimates
were on average 7% smaller
than the SOP population estimate except for the 2014

helicopter
-
only population estimate

which
was 41%

than the SOP.
Only
the

Canada goose

helicopter
-
only population estimate was

Figure 14. Comparison of population estimates among alternate aerial survey designs using
fixed
-
wing and helicopter s
urveys over the state of Michigan for a) Canada goose, b) mallard, c)
sandhill crane, and d) mute swan. The black bars represent ninety
-
five percent confidence
intervals.

nearly identical to the SOP population estimate in 2018. For mallard, the helicopter
-
only
population estimates were on average 17% smaller than the SOP population estimate. For 2003,
2010, and 2018, mallard population estimates averaged 36% smaller compare
d to the mallard
SOP population estimate. In 2014, the mallard helicopter
-
only population estimate was 25%
larger than the SOP population estimate. In 2019, the mallard helicopter
-
only population
estimate was similar to the SOP estimate, but 4% smaller. Th
e sandhill crane helicopter
-
only
population estimates were

on average 9% larger

than the SOP

population estimate
. I
n 2010 and
2014
, the
sandhill crane
helicopter
-
only
population estimates averaged

64%
greater

than the SOP
population estimate
. In 2018 and 2
019, the sandhill crane
helicopter
-
only
population estimates
averaged
47%
smaller than

the SOP

population estimate
.
The

2018

mute swan helicopter
-
only
population estimate was similar to the SOP

population estimate, while

the 2019
mute swan
helicopter
-
only
population estimate was
193% larger at
around 15,000
mor
e

birds

than the SOP.

For each VCF year, variances on the Canada goose and mallard population estimates
were similar for each aerial survey design.
Variances on the populat
ion estimates for sandhill
crane were comparable to the SOP
variances
except for the modified SOP and modified SOP
-
2
in 2018 which were noticeably higher

and

the helicopter
-
only in 2019 which was lower.
Variances on the 2018
mute swan
modified SOP and the
2019
mute swan
helicopter
-
only
population estimates were higher compared to the
ir respective

2018 and 2019 variances for the
other three aerial survey designs.

Averaged CVs on population estimates for alternate aerial survey designs were not
significantl
y different than their respective SOP averaged CV for Canada goose, mallard,
sandhill crane, and mute swan (Figure 15).

The SOP was the lowest averaged CV for Canada
goose and mallard at 13.4 and 13.1, while the helicopter
-
only design was the lowest averag
ed

Figure 15. Comparison of average Coefficient of Variation (CV) on population estimates among
alternate aerial survey designs using fixed
-
wing and helicopter surveys over the state of
Michigan for a) Canada goose (2003, 2010, 2014, 2018, and 2019)
, b) mallard (2003, 2010,
2014, 2018, and 2019), and c) sandhill crane (2010, 2014, 2018, and 2019), and d) mute swan
(2018 and 2019). CV

of 20%

is shown as the red dashed line. The black bars represent

ninety
-
five percent confidence interval
s
.

CV for sandhill crane and mute swan at 24.0 and 31.9. Canada goose and mallard CVs averaged
over years were less than 20%, and averaged CVs for sandhill crane and mute swan were always
above 20%. Based on the 95% confidence interval, the averaged Canada go
ose SOP and
modified SOP CVs comprised of CV values less than 20%, while only the averaged mallard SOP
CV encompassed CV values less than 20%. For averaged sandhill crane CVs, the helicopter
-
only
design had 95% confidence intervals that consisted of CV val
ues less than 20%.
The Canada
goose modified SOP had comparable variances to the SOP while the helicopter
-
only and
modified SOP
-
2 variances were higher. The mallard modified SOP variance was higher than the
variances on the other aerial survey designs. The

sandhill crane helicopter
-
only variance was
smaller than the variances on the other aerial survey designs. Lastly, mute swan helicopter
-
only
and modified SOP had the smallest variances among the aerial survey designs.

Lastly, we calculated population est
imates, CVs, and costs associated with the
helicopter
-
only and modified SOP designs for Canada goose, mallard, sandhill crane, and mute
swan (Tables
3,
4, 5, 6, 7, 8, 9, 10, 11,
and
12).
Costs for each alternate aerial survey design were
based on the 2018
and 2019 spring waterfowl survey
s

which w
ere

$22,921 and $23,251

in 2018
and 2019, respectively
. The fixed
-
wing survey cost on average $260 per transect in 2018 and
$336 per transect in 2019.
The helicopter survey cost on average $436 per segment in 2018 and
$405 per segment in 2019.
The cost for the helicopter
-
only design would be between $4,048 (1
0
segments) to $39,294 (90 segments). The cost of the modified SOP design would range from
$19,554 to $22,242. Average costs to achieve a 20% CV on population estimates for the
helicopter
-
only design for Canada goose, mallard, sandhill crane, and mute swan

were
respectively $13,942, $12,238, $22,185, and $35,839. Average costs to achieve a 20% CV on
population estimates for the modified
SOP

design for Canada goose, mallard, sandhill crane, and

Table
3
.
P
opula
tion estimates,
Coefficient of Variations (CVs)
, and costs to evaluate the helicopter
-
only design for Canada goose and
mallard
, 2003
. Two costs were calculated based on the 2018 or 2019 helicopter survey costs to determine helicopter
-
only design costs.

200
3

Canada Goose

Mallard

Cost

Number of
Segments

Population
Estimate

% CV

Population
Estimate

% CV

2018

2019

124,562

164,330

$4,366

$4,048

123,923

163,408

$8,732

$8,097

124,253

164,376

$13,098

$12,145

124,080

163,570

$17,464

$16,194

123,897

164,376

$21,830

$20,242

123,653

163,446

$26,196

$24,290

123,392

163,821

$30,562

$28,339

123,562

163,939

$34,928

$32,387

122,829

163,907

$39,294

$36,436

Table
4
.
P
opulation estimates,
Coefficient of Variations (CVs)
, and costs to evaluate the helicopter
-
only design for Canada goose,
mallard, and sandhill crane
, 2010
. Two costs were calculated based on the
2018 or 2019 helicopter survey costs to determine
helicopter
-
only design costs.

2010

Canada Goose

Mallard

Sandhill Crane

Cost

Number of
Segments

Population
Estimate

% CV

Population
Estimate

% CV

Population
Estimate

% CV

2018

2019

245,930

216,920

19,910

$4,366

$4,048

245,347

218,734

20,075

$8,732

$8,097

245,196

218,924

19,961

$13,098

$12,145

244,123

218,149

19,971

$17,464

$16,194

244,574

218,995

19,619

$21,830

$20,242

245,412

218,599

19,893

$26,196

$24,290

245,456

218,872

19,584

$30,562

$28,339

245,790

217,883

19,638

$34,928

$32,387

244,999

217,988

19,890

$39,294

$36,436

Table
5
.
P
opulation estimates,
Coefficient of Variations (CVs)
, and costs to evaluate the helicopter
-
only design for Canada goose,
mallard, and sandhill crane
, 2014
. Two costs were calculated based on the 2018 or 2019 helicopter survey costs to determine
h
elicopter
-
only design costs.

2014

Canada Goose

Mallard

Sandhill Crane

Cost

Number of
Segments

Population
Estimate

% CV

Population
Estimate

% CV

Population
Estimate

% CV

2018

2019

276,84
7

268,710

29,172

$4,366

$4,048

274,275

268,286

28,878

$8,732

$8,097

271,981

269,460

28,906

$13,098

$12,145

272,113

269,000

28,848

$17,464

$16,194

273,750

268,940

28,635

$21,830

$20,242

272,001

268,602

28,568

$26,196

$24,290

271,160

269,281

28,497

$30,562

$28,339

272,060

269,852

28,518

$34,928

$32,387

273,073

270,087

29,141

$39,294

$36,436

Table
6
.
P
opulation estimates,
Coefficient of Variations (CVs)
, and costs to evaluate the helicopter
-
only design for Canada goose,
mallard, sandhill crane, and mute swan
, 2018
. Two costs were calculated based on the 2018 or 2019 helicopter survey costs to
determine helicopter
-
only design costs.

2018

Canada Goose

Mallard

Sandhill Crane

Mute Swan

Cost

Number of
Segments

Population
Estimate

%
CV

Population
Estimate

%
CV

Population
Estimate

%
CV

Population
Estimate

%
CV

2018

2019

276,693

177,032

18,542

12,107

$4,366

$4,048

281,330

172,298

18,468

12,059

$8,732

$8,097

281,538

174,273

18,430

12,044

$13,098

$12,145

275,425

171,808

18,431

11,889

$17,464

$16,194

280,217

171,823

18,499

11,798

$21,830

$20,242

279,130

173,442

18,458

11,907

$26,196

$24,290

278,395

172,918

18,476

11,701

$30,562

$28,339

279,816

173,660

18,430

11,924

$34,928

$32,387

277,738

172,477

18,542

11,916

$39,294

$36,436

Table
7
.
P
opulation estimates,
Coefficient of Variations (CVs)
, and costs to evaluate the
helicopter
-
only design for Canada goose,
mallard, sandhill crane, and mute swan
, 2019
. Two costs were calculated based on the 2018 or 2019 helicopter survey costs to
determine helicopter
-
only design costs.

2019

Canada Goose

Mallard

Sandhill Crane

Mute Swan

Cost

Number of
Segments

Population
Estimate

%
CV

Population
Estimate

%
CV

Population
Estimate

%
CV

Population
Estimate

%
CV

2018

2019

197,432

165,871

12,893

23,781

$4,366

$4,048

195,896

165,528

13,149

22,896

$8,732

$8,097

195,284

163,912

12,955

23,454

$13,098

$12,145

196,501

164,772

12,930

23,074

$17,464

$16,194

197,611

164,375

12,978

22,987

$21,830

$20,242

196,406

164,468

13,135

23,083

$26,196

$24,290

196,155

164,042

12,867

23,086

$30,562

$28,339

195,810

163,444

13,021

23,065

$34,928

$32,387

195,696

164,591

13,012

22,956

$39,294

$36,436

Table
8
.
P
opulation estimates,
Coefficient of Variations (CVs)
, and costs to evaluate the modified SOP design for Canada goose,
mallard, and mute swan
, 2003
. Two
costs were calculated based on the 2018 or 2019 MDNR spring waterfowl survey costs to
determine modified SOP design costs.

2003

Canada Goose

Mallard

Mute Swan

Cost

Number of
Transects

Population
Estimate

% CV

Population
Estimate

% CV

Population
Estimate

% CV

2018

2019

221,195

301,077

2,726

134

$19,803

$19,554

221,119

303,940

2,575

$20,063

$19,890

221,058

303,061

2,544

$20,322

$20,226

220,429

304,217

2,584

$20,582

$20,562

218,472

304,049

2,517

$20,842

$20,898

219,697

303,410

2,492

$21,102

$21,234

219,174

303,303

2,546

$21,362

$21,570

219,372

303,631

2,532

$21,622

$21,906

218,746

303,612

2,521

$21,881

$22,242

Table
9
.
P
opulation estimates,
Coefficient of Variations (CVs)
, and costs to evaluate the modified SOP design for Canada goose,
mallard, sandhill crane, and mute swan
, 2010
. Two costs were calculated based on the
2018 or 2019 MDNR spring waterfowl survey
costs to determine modified SOP design costs.

2010

Canada Goose

Mallard

Sandhill Crane

Mute Swan

Cost

Number of
Transects

Population
Estimate

%
CV

Population
Estimate

%
CV

Population
Estimate

%
CV

Population
Estimate

%
CV

2018

2019

316,843

342,077

10,983

129

2,301

130

$19,803

$19,554

312,727

342,113

10,884

2,348

$20,063

$19,890

309,824

343,770

10,932

2,351

$20,322

$20,226

312,859

347,501

10,909

2,355

$20,582

$20,562

312,565

345,349

10,904

2,345

$20,842

$20,898

313,089

344,511

10,837

2,380

$21,102

$21,234

312,492

343,368

10,795

2,368

$21,362

$21,570

312,071

344,038

10,835

2,381

$21,622

$21,906

312,561

344,900

10,773

2,379

$21,881

$22,242

Table 1
0
.
P
opulation estimates,
Coefficient of Variations (CVs)
, and costs to evaluate the
modified SOP design for Canada goose,
mallard, sandhill crane, and mute swan
, 2014
. Two costs were calculated based on the 2018 or 2019 MDNR spring waterfowl survey
costs to determine modified SOP design costs.

2014

Canada Goose

Mallard

Sandhill Crane

Mute Swan

Cost

Number of
Transects

Population
Estimate

%
CV

Population
Estimate

%
CV

Population
Estimate

%
CV

Population
Estimate

%
CV

2018

2019

197,440

218,262

21,918

121

7,468

120

$19,803

$19,554

195,714

217,733

21,035

7,641

$20,063

$19,890

196,597

217,253

21,005

7,884

$20,322

$20,226

195,757

221,602

21,054

7,537

$20,582

$20,562

194,398

219,268

20,826

7,922

$20,842

$20,898

195,302

220,242

20,672

7,742

$21,102

$21,234

195,654

220,628

20,563

7,817

$21,362

$21,570

195,613

220,930

20,568

7,818

$21,622

$21,906

195,594

220,880

20,623

7,721

$21,881

$22,242

Table 1
1
.
P
opulation estimates,
Coefficient of Variations (CVs)
, and costs to evaluate the modified SOP design for Canada goose,
mallard, sandhill crane, and mute swan
,
2018
. Two costs were calculated based on the 2018 or 2019 MDNR spring waterfowl survey
costs to determine modified SOP design costs.

2018

Canada Goose

Mallard

Sandhill Crane

Mute Swan

Cost

Number of
Transects

Population
Estimate

%
CV

Population
Estimate

%
CV

Population
Estimate

%
CV

Population
Estimate

%
CV

2018

2019

271,648

211,279

33,406

138

6,059

137

$19,803

$19,554

275,686

212,910

32,218

107

6,582

100

$20,063

$19,890

273,310

211,740

32,773

7,237

$20,322

$20,226

276,986

210,792

33,520

7,009

$20,582

$20,562

276,202

211,940

33,380

7,358

$20,842

$20,898

277,574

210,530

33,599

6,976

$21,102

$21,234

277,634

211,146

33,471

6,930

$21,362

$21,570

275,895

211,163

33,898

7,096

$21,622

$21,906

276,975

211,077

33,869

7,034

$21,881

$22,242

Table 1
2
.
P
opulation estimates,
Coefficient of Variations (CVs)
, and costs to evaluate the modified SOP design for Canada goose,
mallard, sandhill crane, and mute swan
, 2019
. Two costs were
calculated based on the 2018 or 2019 MDNR spring waterfowl survey
costs to determine modified SOP design costs.

2019

Canada Goose

Mallard

Sandhill Crane

Mute Swan

Cost

Number of
Transects

Population
Estimate

%
CV

Population
Estimate

%
CV

Population
Estimate

%
CV

Population
Estimate

%
CV

2018

2019

229,720

169,870

26,971

7,835

101

$19,803

$19,554

229,741

170,621

26,650

7,602

$20,063

$19,890

229,394

172,121

26,878

7,740

$20,322

$20,226

229,282

172,312

26,615

7,722

$20,582

$20,562

231,166

172,018

26,832

7,869

$20,842

$20,898

230,581

172,521

26,658

7,894

$21,102

$21,234

230,086

172,771

26,691

7,929

$21,362

$21,570

230,667

172,749

26,762

7,879

$21,622

$21,906

230,233

172,254

26,773

7,927

$21,881

$22,242

mute swan were respectively $20,807, $20,663, $24,410, and $24,188. The SOP design has
achieved a CV of less than 20% for the past five VCF years for Canada goose and mallard. On
average, the CVs
from SOP population estimates
were 13%, 13%, 40%, and 32% fo
r Canada
goose, mallard, sandhill crane, and mute swan, respectively.

DISCUSSION

Alternate Visibility Correction Factors

F
ew

of the alternate VCFs were significantly different than the SOP VCF for a given
year.

Although,

while

it should be noted
that VCFs precision is positively related to sample size,
we need
to be cautious of using older data when estimating an all
-
year avera
ge statewide VCF
s
.
Data from 1992 is now 27 years old. Changes in technology, aircraft, observers, and landscape
may alter waterfowl detection. Previously, VCF segments were
not
surveyed random
ly

and not
indicative of the representation of the state of Mic
higan,
potentially
violating the assumption that

samples were independent and identically distributed. In addition, 1992 and 1995 VCF years did
not survey the northern forested stratum. The 2003 survey added more VCF segments which
increased the spatial re
presentation
within

Michigan. A rolling average like a three or five
-
year
statewide VCF estimate would be a viable alternative to accurately predict how the detection
may change over time while also maintaining a CV of 20% or less on population estimates

f
or
Canada goose and mallards
.

Five
-
year and
three
-
year

averaged

VCFs were always within
the
95% confidence interval
of
the SOP VCF for all three species. When the alternate VCFs were applied to estimate
population size,
five
-
year

and
three
-
year

statewide a
nd stratum
-
specific VCF estimation methods
were comparable to
the
SOP

population estimates
. While the SOP had the lowest CV, the
five
-
year

and
three
-
year

statewide and stratum
-
specific VCF estimation methods were comparable.
Additionally, the CV for the
th
ree
-
year

statewide VCF estimation method was nearly identical to
the SOP CV for the three species.
With comparable population estimates and the lowest CV
among the alternate VCF estimation methods,
a
three
-
year

statewide VCF would be an
acceptable alternat
iv
e to the SOP.

Population estimates for the yearly statewide and stratum
-
specific VCF estimation
m
ethods were consistently below the SOP since the all
-
year average VCF was higher than the
yearly VCFs. In 2003, the yearly population estimates were considerably smaller than the SOP
since the yearly VCF estimate was at its lowest for each of the species.
As more years were
surveyed, the all
-
year average VCF started to decrease since the yearly VCFs were getting
smaller too, resulting in the population estimates
based
on the yearly VCF estimation methods

comparable to the SOP in
2010,
2014, 2018, and 2019.

Unexpectedly
,

the

2003 yearly statewide Canada goose and mallard population estimates
and VCFs were significantly lower than their respective SOP population estimate and VCF.

ds missed by
the helicopter survey in 2003 which contributed to a lower yearly statewide VCF and subsequent
smaller population estimate. They are unsure what caused this phenomenon
,

but some of the
2003 survey crew members recalled that the helicopter pilo
ts were
flying

the helicopters at
higher altitudes and speeds than the standard operating procedures. The 2003 survey
used
contracted pilots
, so the helicopter pilots were new to the survey. New pilots that are not familiar
with the SOP may

have

fl
own the
helicopter

faster and higher than other VCF years, impacting
the VCF. An increase in altitude and speed has a negative effect on detection (Caughley 1974).
As altitude increases, waterfowl are less prone to flush from their habitat and exhibit a response
t
o the noise (Calef et al. 1976, Shupe and Beasom 1987, Tracey and Fleming 2007). As speed
increases, observers have less time to detect and record birds (Caughley 1974).

More broadly, detection could change over time due to other factors. Improvements in
a
ircraft could impact how
observers in
both fixed
-
wing and helicopter surveys detect birds
(Clancy 1999, Soulliere and Chadwick 2003). Currently, the

spring waterfowl survey

uses Bell
93

407
, but Hughes 500
, Bell 430, and Bell 206

were used

prior to 2018
.
The
Bell
206 was used in
surveys before 2003, and the Bell 430
was used in 2010 and 2014.

The Hughes 500 was used
once in 2003.

The difference in the helicopter model can impact visibility for front and rear seat
observers (Tracey
and Fleming
200
7
). Front seat observers in a Hughes 500 have a bigger field
of view than the rear seat observer, while the inverse is evident in the Bell Jet Ranger. Changes
in
the
field of view could affect how many birds can be seen by an observer.
However, both rear
an
d front seat observers are used for the helicopter survey so total waterfowl observations should
remain the same.
The difference in helicopter models can
also
contribute to variation in sounds
produced by the aircraft. Tracey and Fleming (2007) found that
Hughes 500 helicopters had a
louder sound where more animals responded

to the helicopter noise

compared to Bell
models
.
In
2003, waterfowl may have been alerted to the Hughes 500 much earlier than the Bell 206,
resulting in waterfowl taking cover or flying

out of the transect boundaries before the observers
could count them.
Surveys before 2003 relied on county road maps
,

air photos
, and personal
experience of the transect

to follow the transect line and an imaginary line to delineate transect
width. Starti
ng in 2003, GPS technology was equipped to both the fixed
-
wing and helicopter
surveys. Since helicopters circle wetlands and deviate from the centerline,
the addition of

GPS
technology

helped to prevent overcounting outside of the designated transect line
(
Soulliere

and
Chadwick 2003). This may have led to fewer waterfowl observations on the helicopter than
previous VCF years.

Another
factor potentially impacting VCF estimates was

the MDNR switc
h

to a random
sampling of VCF segments in 2003, whereas before
the spring waterfowl survey sampled VCF
segments with high waterfowl density. In 2003, more VCF segments were randomly sampled in
the northern forested stratum which is more forested and has more variable
or lower
waterfowl
94

densities than the farm urban st
ratum. In 2018, the MDNR switched to a GRTS sampling to
achieve a better spatial representation of the population

than a simple random sampling design

(Gitzen et al. 2012).
A

slightly

larger proportion of segments
surveyed were
in the northern
forested str
atum. The proportion of segments in the northern forested surveyed increased from
43% to 48% in the GRTS sampling.

Since 2003, GRTS and random sampling have resulted in a
more accurate representation of the waterfowl density for the VCF segments than the p
revious
sampling design from 1992
-
1996.

Prior to 2003, fixed
-
wing densities on VCF segments were on
average 101% larger for Canada goose and 59% larger for mallard compared to their respective
fixed
-
wing densities on total segments.

In 2003, 2010, and 2014
, fixed
-
wing densities on VCF
segments
using random sampling

were on average 8% larger for Canada goose and 1% smaller
for mallard compared to their respective fixed
-
wing densities on total segments. In 2018 and
2019, fixed
-
wing densities on VCF segments u
sing GRTS sampling were on average 4% larger
for Canada goose and 4% smaller for mallard compared to their respective fixed
-
wing densities
on total segments.

Observer error may impact how the VCF is estimated. Observer error can result in
different visibil
ity from one person to another. Observers may lack consistency, accuracy, or bias
due to personal experience (Diem and Lu 1960). Untrained observers show high individual

had a
91% detection rate while untrained observers had a 79% detection rate for ground
-
based surveys.
For the spring waterfowl survey, each observer is trained on waterfowl identification and any
new observers are a trainee for a year. Different levels of
years observing could have slight
impacts on how a person detects a bird.
In addition, h
igh waterfowl densities can increase
observer error because observers have a more difficult time simultaneously recording
95

observations when new birds are being detected (Bart and Schoultz 1984, Nichols et al. 200
0
).
To maintain

a consistent observer error
throughout the years
, a consistent crew of observers
is
important

(Pearse et al. 20
08)
.
While standardized guidelines are in place to help

maintain
consistent data collection,
observer error

can still arise
.

Also, weather conditions such as cloud cover an
d wind speed might affect detection; for
example, bright sun can produce glare obscuring visibility of birds on water, depending on
viewing angle relative to the horizon and azimuth. Often, swimming waterfowl leave a visible
wake on the water surface under

calm conditions and these wave patterns help observers detect
birds except in windy conditions when wind
-
created waves obscure waterfowl movements
(Shirkey 2012).

Although the SOP had a higher number of segments surveyed to estimate the VCF, the
alternat
e VCF estimation methods had comparable CVs. The SOP had the lowest CV on the
population estimate, showing that more segments surveyed resulted in a lower CV and a more
precise population estimate. The variances on the alternate VCFs
, including yearly alte
rnate
VCFs (27 to 40 segments),

were similar to the SOP

variances
.

Thus, the variance on the
alternate
VCF
s

contributed less to the total variance on the population estimate.

Instead, variation in
indicated birds
and therefore bird density estimates on seg
ments

had a greater impact on the
variance
s on statewide population estimates
.

Since the alternate VCFs used the same fixed
-
wing
indicated birds for each year, the variances were comparable.
For example, the 2018 mallard CV
had the highest

mallard

CV for t
he past five VCF years. A
large
group of 150 mallards was
detected on
a segment during
the fixed
-
wing s
urvey

which resulted in higher variance and CV

on
the population estimate
.

Mallard indicated

birds in 2018 ranged from
0 to 26 without the group
96

of 150 m
allards.

When the
150
-
mallard

group was removed from the calculation, the 2018 CV
on the population estimate
dropped

from 17.57 to 12.13.

We found that the alternate VCF estimation methods for Canada goose and mallard
resulted in
comparable population estimates to the SOP since there were slight differences in the
VCF values for the five most recent VCF years. On average, the alternate Canada goose VCFs
were 11% smaller, and the alternate mallard VCFs were
16
% smaller than their re
spective SOP
VCFs. Alternate sandhill VCFs were on average 15% larger than their SOP VCFs due to high
northern forested VCFs

contributing to higher stratum
-
specific VCFs
. Since the number of fixed
-
wing observations for a species remains the same to calcula
te the population estimate, small
changes to the VCF
had

low

impact
on
population
estimates
. Additionally, changing the VCF
had
a
minimal

impact

the CV. On average, alternate CVs for Canada goose, mallard, and
sandhill crane were respectively 20%, 2
5
%
, and 19% higher than their SOP CV.

Survey Timing and Sample Sizes

Survey timing has varied throughout the years, as spring weather in Michigan can change
quickly.
T
he

MDNR attempted

to complete surveys during the

specific survey timeframe

(before
nests
from Canada geese hatched, half of the mallard females started nests, and when there was
at least 20% visibility)
,

but
it
is difficult for the MDNR to monitor or to know if this

survey

timeframe was achieved or not
.
However, t
he historic starting date of the survey was linearly
related to growing degree
-
days near the starting transect (MDNR, unpublished data), suggesting
that the criteria used to decide when to start the survey are strongly related to annual variation in
plant
phenology.
Warmer weather can bring leaf
-
out earlier than expected which impedes
visibility. Survey timing in 2018 and 2019 was variable but was not noticeably different than
previous years

based on the dates of the survey
. The 2018 survey had an unexpecte
d later end
97

date as wetlands and Lake Michigan in the upper peninsula were still frozen over, and a week of
rain delayed the surveys. The 2019 survey commenced earlier than the 2018 survey, but a week
of rain delayed the survey too. The delays in both year
s also led to a longer time between when
the fixed
-
wing and helicopter surveys were completed on the same segment. The spring
waterfowl survey does not operate on the weekends, so it is possible to have at least a three
-
day
difference in surveying the same

segment. Leaf
-
out did start to occur for the last two survey
years but did not hinder waterfowl detection as leaf
-
out was less than 20% on trees and shrubs.

Helicopter segments are dependent on funding as early helicopter flights were costly,
reducing th
e number of helicopter segments surveyed. In 2010, a partnership between the
MDNR and MSP developed, and helicopter survey costs became reduced. Helicopter surveys
were important to the spring waterfowl survey, as the observers in helicopter detected more
total
waterfowl observations on average compared to the inexpensive fixed
-
wing surveys.
Contributing to the expensive costs on the helicopter survey, flight hours per segment were
longer in the helicopter compared to the fixed
-
wing. Total flight hours on t
he fixed
-
wing were
more than the helicopter, but cheaper hourly rates contributed to a more inexpensive fixed
-
wing
survey.

Bootstrap
Met
hods

We found that the bootstrap method allowed us to estimate the variability of population
estimates and CVs for alt
ernate surveys, as well as creating 95% confidence intervals based on
the sample for each VCF year (Manly 1997). The bootstrap method for Canada goose and
mallard on the helicopter observations showed that 40
or more
segments on average would result
in a 2
0% or less CV on the population estimate for the helicopter
-
only design. If the budget or
time is constrained in a given year, 30 helicopter segments may be acceptable

since only
the
98

2018 VCF year resulted
in

an averaged CV higher than 20%

for Canada goose

and mallard
.

The
bootstrap method for Canada goose and mallard on the fixed
-
wing observations showed that
removing less than

five

transects on average would result in a 20% or less CV on the population
estimate for the modified SOP design. If the budget o
r time is constrained in a given year,
removing
six

or
seven

transects may be acceptable
. T
he
averaged CVs for removing
six

or
seven

transects in the farm urban stratum for Canada goose and mallard were 24% or less.

The
bootstrap method for sandhill crane
and mute swan resulted in undesirable CVs for both the
helicopter
-
only and modified SOP
. Higher CVs for sandhill crane and mute swan could be
attributed to f
ew
fixed
-
wing
observations
, resulting in
a
high variation o
n

population estimates.

The removal of transects would result in lower total flight hour
s

for the fixed
-
wing survey which
would result in a lower fixed
-
wing survey cost. However, the precision o
f

the population
estimate
may

be reduced
, causing inaccurate population estimates
.

Al
ternate Aerial Survey Designs

No alternate aerial survey design was better or worse than the SOP survey design since
the comparison of alternate aerial survey designs found no significant difference for the four
species
.

Thus
,

the current transect number
and configuration should remain the same
. While
the
2003 mallard population estimate for the helicopter
-
only design was significantly smaller than
the 2003 SOP population estimate, the other four VCF years found no significant differences to
their respecti
ve SOP population estimate.
Low

helicopter

observations

in 2003 resulted in a
lower yearly statewide VCF and helicopter population estimate.

For 2003 mallard VCF
segments, the helicopter survey counted 404 birds
. Additionally, the helicopter survey counted

192 more birds than the fixed
-
wing observation
which is less than the average
difference

of
302

birds. The 2003
mallard
SOP population estimate was 130,000 birds more than what the
99

helicopter
-
only method estimated.

Similarly, the 2003 Canada goose

SOP

population estimate
was about 90,000 birds
more

than the 2003
helicopter
-
only

population estimate.

In 2003, the
helicopter survey counted 99
more
Canada geese
on the helicopter than the fixed
-
wing
which is
lower than the average difference of 350 birds on

VCF segments.
Both the 2003 helicopter
-
only
population estimate for Canada goose and mallard could have been impacted by
a
change in
aircraft and pilot,
sampling design,

or observer error which also resulted in a smaller yearly
statewide VCF.

Averaged CV
s showed that none of the alternate aerial survey designs are better or worse
than the SOP. The SOP had the lowest averaged CV for Canada goose and mallard, showing that
using both fixed
-
wing and helicopter surveys
, including

all the transects in the farm
urban

stratum,

results in the most precise aerial survey method. Averaged CV
s

on sandhill crane

and
mute swan

w
ere

higher for the SOP

compared to the mallard and Canada goose CV on the SOP
,
but this may be attributed to low fixed
-
wing observations to estim
ate a precise population.

From
the historical data and the 2018
-
2019 surveys, at least 750 indicated birds
statewide on the fixed
-
wing survey
sh
ould result

in
a
CV of less than 20% (Figure 16). Most
VCF

years were able to
detect at least 750 indicated bird
s

on the fixed
-
wing survey

for Canada goose and mallard which
resulted in CVs on population estimates less than 20%. However, low indicated bird counts
from
the fixed
-
wing survey
on sandhill crane and mute swans resulted in high CVs.
On average

(2010,
2014
, 2018, and 2019)
, the fixed
-
wing survey counted 64

indicated

birds

for sandhill crane
,
while fixed
-
wing surveys for Canada goose and mallard detected over 700
indicated
birds

from
the 2003, 2010, 2014, 2018, and 2019 VCF years
. Mute swan averaged CV was similar for
helicopter
-
only and SOP, although a higher variance on the SOP could be because few mute

swans were detected on the fixed
-
wing survey. On average (2018 and 2019), t
he fixed
-
wing

100

Figure 16. Comparison of indicated birds

on the fixed
-
wing survey

to the Coefficient of
Variation (CV) on population estimates from the
Standard Operating Procedure (
SOP
)

aerial
survey design using

fixed
-
wing and helicopter surveys over

the state of Michigan

for a) Canada
goose (1992
-
2019), b) mallard (1992
-
2019), c) sandhill crane (2005
-
2019), and d) mute swan
(2007
-
2019).
C
V o
f 20%

is shown as the red dashed line.

101

c
)

102

103

survey detected 148 mute swans.

The helicopter
-
only design
produced

comparable population estimate
s

and CV
s

t
o the
SOP, especially for Canada goose and mallard.

This shows that the helicopter
-
only design would
be an acceptable alternate aerial survey desig
n.
Averaged CVs on the population estimate
s for
the helicopter
-
only design

were below 20% for Canada goose and mallard but were only slightly
higher than their respective averaged SOP CV.
Averaged
Canada goose CV increased by 31%
from the SOP
while
average
d
mallard CV increased by 11%
from the SOP
using the helicopter
-
only design.
We also noticed a pattern occurring for the helicopter population estimates.
Whenever the yearly statewide VCF was smaller than the SOP VCF, the helicopter population
estimate was

smaller than the SOP population estimate, and the inverse occurred when the yearly
statewide VCF was larger than the SOP population estimate.

Since the helicopter survey corrects

the fixed
-
wing counts, both the corrected fixed
-
wing and helicopter densities
should

be
similar

using a yearly statewide VCF

under a randomized or GRTS sampling framework
.

Thus, the
corrected fixed
-
wing density would be higher than the helicopter if the ye
arly statewide VCF
was lower than the SOP VCF for that given year
. Due to the variation of yearly statewide VCF,
the helicopter population estimate should randomly be above or below the SOP population
estimat
e
.

Based on the helicopter bootstrap, the surve
y would cost between $16,194 and $17,464 to
survey 40 segments. The helicopter
-
only design would cost between
$5,786 and
$6,726 less than
the SOP design. Labor costs would also be reduced for the MDNR since they would not have to
spend funds on the fixed
-
w
ing survey and take time away from their employees to conduct the
survey.
Savings and reduce
d

labor costs make the helicopter
-
only design an affordable option if
the MDNR chooses to modify the spring waterfowl survey.

104

We found that savings on removing fixed
-
wing transects in the farm urban
stratum
were
minimal. With each transect removed, the MDNR could save on average $300 per transect. By
removing
five

transects in the farm urban stratum, the modified SOP designed wou
ld save
$1,500 and still achieve a CV of 20% or less. The MDNR could then use these funds to allocate
for more helicopter segments. However, helicopter surveys cost on average $420 per segment
which equates to

adding

three

more helicopter segments. Based o
n the helicopter bootstrap,
three

additional helicopter segments would not gain enough precision to warrant the need for more
helicopter segments surveyed. While the modified SOP aerial survey design is an acceptable
alternate aerial survey design, there a
re not enough benefits gained to change from the SOP
aerial survey design.
Both the modified SOP and modified SOP
-
2 gave comparable results
.
R
emov
al of

only odd or even transects does not
change outcomes
, although the modified SOP
had a higher
population e
stimate t
han the SOP
, and the modified SOP
-
2 had a lower population
estimate than the SOP
.
The difference between population estimates on modified SOP and
modified SOP
-
2 may be related to differences in wetland habitat conditions
,

resulting in slightly
mor
e birds on average in the odd
-
numbered transects.
Averaged Canada goose and mallard CV
increased by 17% and
14% from the SOP

using the modified SOP
, respectively. Averaged
Canada goose and mallard CV increased by 9%

and
13% from the SOP
using the
modified SOP
-
2
.
However, the MDNR may
believe

that a saving of $1,500 could be worthwhile. In addition to
saving money, MDNR employees conducting the fixed
-
wing survey would have fewer days in
the field and could
utilize
their time performing other
activit
ies
. On average,
observers

complete
the
fixed
-
wing
farm urban stratum in
five

days, so reducing the number of transects in half could
complete the farm urban stratum in
two

or
three

days.

105

We also noticed that costs for fixed
-
wing and helicopter surveys ca
n be dependent on

MDNR overtime hours expense whenever the pilots go over their allotted work hours. This is

e changes daily, and the MSP
oversees

schedul
ing

a pilot
for
each survey day. For the fixed
-
wing survey, $658 and $867 were defined
as overtime charges in 2018 and 2019, respectively. For the helicopter survey, $2,057 and $1,716
were charged as overtime ex
penses in 2018 and 2019, respectively.
If future changes are to be
made, the MDNR should be prudent that estimated costs could go slightly over based on
overtime charges occurring.

106

MANAGEMENT IMPLICATIONS

Aerial surveys with precise estimates o
f abundance provide important information used
in setting annual hunting regulations for waterfowl and other birds. The MDNR depends on
recreational waterfowl hunting as a source of funding for wildlife and habitat management, as
well as providing informat
ion about waterfowl movement patterns, survival rates from band
reporting, and management of overabundant species like Canada geese (Miller and Vaske 2003,
Garrettson et al. 2014). Each year, the MDNR reports the waterfowl population estimates from
the spr
ing waterfowl survey to the USFWS. For waterfowl management, Michigan is part of the
Mississippi flyway which consists of representatives from U.S. state and Canadian provincial
wildlife management agencies within the region. Together, the USFWS and the Mi
ssissippi
flyway set frameworks for harvest regulations based on the Adaptive Harvest Management
program (AHM) which regulates daily bag limit, season length, and opening and closing dates
(Williams et al. 1996, USFWS 2018).
Although harvest of mallard pop
ulations is managed at the
f
lyway scale and larger, the state of Michigan can make decisions to help manage mallards more
locally. For example, t
he MDNR
can

propose their own specific waterfowl hunting season
regulations for Michigan that cannot be more liberal than the federal framework but can be more
conservative. With recommendations from the Citizens Waterfowl Advisory Committee
(CWAC) and other public i
nput, the MDNR will recommend Michigan waterfowl hunting
season regulations to the Natural Resources Commission. The CWAC is a group of dedicated
civilians that provides feedback on proposed Michigan waterfowl regulations for the next year,
as well as any
waterfowl hunting issues (MDNR 2017). Finally, the MDNR presents
recommendations to the Natural Resources Commission to make the final decision for waterfowl
hunting regulations in Michigan.

107

Considerable evaluation should be
considered

when choosing the t
ype of monitoring
technique

depending on the species and management questions

(Lancia et al. 2005). Monitoring
programs like the spring waterfowl survey need to have specific objectives in place that estimate
abundance with high precisions while also minim
izing
the
cost

(Reynolds et al. 2011). Alternate
aerial survey designs would be considered acceptable if
the
estimation of waterfowl abundances
is

precise by meeting a CV of less than 20% without increasing the
cost
s
. We believe that the
current transect n
umber and survey configuration

is still the best waterfowl monitoring program
for the state of Michigan as alternative options did not produce enough benefits to outweigh the
disadvantages. The modified SOP
design

was slightly cheaper than the SOP method b
ut resulted
in a higher CV

for both the modified SOP and modified SOP
-
2
. The helicopter
-
only method is
about $6,000 cheaper than the SOP method but also resulted in
slightly

higher CV
s
. If helicopter
survey costs continue to decline, the helicopter
-
only de
sign could be a viable alternative aerial
survey design

as more helicopter segments could be surveyed, reducing the CV
. A trade
-
off
occurs between the fixed
-
wing and helicopter. Fixed
-
wing aircraft are cheaper but observers in a
fixed
-
wing aircraft detect
fewer birds. Helicopter surveys are more expensive and take longer
than a fixed
-
wing survey, but observers in helicopters detect more birds. We believe it is
important to combine the benefits of both aerial surveys
by using the SOP aerial survey design
in
estimating waterfowl abundance.

We recommend t
hat

the MDNR
maintain the current transect number and configuration
for the spring waterfowl survey,
but

we caution
continued use of
older data. Many factors (e.g.,
weather, observers, population demographics,

and survey cost) could change detection annually
(Cowardin and Blohm 1992, Tracey

et al.

2008, Mills 2012, Ransom 2012, Schummer et al.
2018). Thus,
we recommend
incorporat
ing

a
three
-
year average statewide VCF

as this VCF
108

estimation method better capture
s annual variation than the SOP

VCF
.

A
three
-
year average
statewide VCF would
also
be preferable as the CV is nearly identical to the SOP
CV
and lines up
with decision frameworks for some species like Canada geese that use
three
-
year cycles.
On
average, th
e
three
-
year statewide VCF estimate
d

1
7
% and
20
%

fewer

birds

than the SOP

population estimate
for Canada goose and mallard, respectively
.
If the MDNR
is

concerned
about
incorporating a shorter time interval averaged VCF

in the population estimates for Canada
goose and mallard, then a
five
-
year

statewide would be more appropriate.
The five
-
year
statewide population estimate
s were on
average
9% and 11% smaller

than the SOP population
estimate for Canada goose and mallard,
respectively.
We would
also
advise

the MDNR
to
conduct the helicopter survey
every year if possible, to continuously update the VCF for each
species
, as year
-
to
-
year variability occurs
.
However, we understand that annual helicopter
surveys are still expens
ive, so we would recommend conducting helicopter surveys every other
year or once every three years.

We recommend that a minimum of 40 VCF segments should be
conducted every VCF
year
and to continue using the GRTS sampling.
I
f the MDNR
considers

the altern
ate aerial survey designs, then we recommend the helicopter
-
only design to be surveyed
with 40

or more

helicopter segments and the modified SOP design to be surveyed by removing
no more than
five

transects in the farm urban stratum.
The spring waterfowl su
rvey may be
reexamined if helicopter survey costs continue to reduce and become similar to fixed
-
wing
survey costs, as the helicopter
-
only design may be reconsidered.
No matter what aerial survey
design the MDNR chooses, the same observers should be used
in

each survey platform

helped to inform the MDNR that modifications to the existing methodology
should be
incorporated
.

109

APPENDIX

110

APPENDIX

The MDNR spring waterfowl survey is a statewide survey that involves flying a series of
21 fixed
-
width transects using fixed
-
wing aircraft (Figure 1
7
; CWS and USFWS 1987, Smith
1995). To get consistent results, the MDNR follow an accomplishment di
rective to create
standard operating procedures (SOP) for the spring waterfowl survey (CWS and USFWS 1987,
B. Avers, MDNR, unpublished report). The SOP survey methodology has fixed
-
width transects
that are 0.4 km (1/4 mi) wide. Surveys are flown along an e
ast
-
west orientation to avoid visibility
error from the sun. Each transect is divided into segments that are 29 km (18 mi) long. The total
number of historic segments have ranged from 139 to 152. Due to differences in terrain and
feasibility of conducting
fixed
-
wing surveys, the aircraft is flown at an altitude between 0.03
-
0.05 km (100
-
150 feet) and speed between 144.8
-
169.0 kph (90
-
105 mph) throughout the survey.
Using a Cessna 172, 180, or 260 plane, fixed
-
wing surveys travel along the segment line and
c
onsist of a pilot with a front and rear seat observer. Surveys were not flown when beginning
wind speeds exceeded 25 kph (15 mph) or when wind speeds reached 40 kph (25 mph) during
the day.

Both observers identify all waterfowl species from 0.2 km (1/8 mi
) on their side of the
segment line. They also record the wetland type for each waterfowl observation and the segment
number. To determine in a fixed
-
wing aircraft if the wetland is within 0.2 km from the segment
line, a clinometer is used to measure this
appropriate angle. The tape is placed on the wing struts
to help guide observers on the segment edge location. Any bird above the tape line is out and not
recorded. In addition to recording waterfowl observations, rear
-
seat observers record every
wetland t
hat they see within the segment even if there are no waterfowl observations for an
estimate of total statewide wetlands.

111

For each segment surveyed, a front and rear seat observer record waterfowl observation
and assign them to one of six grouping categori
es: singles, flocked drakes, pairs, nesting pairs,
nesting singles, and groups (Table 1
3
). For both fixed
-
winged and helicopter surveys,
the
total

breeding biology. Drakes, flocked drakes, and pairs are adjusted by a
multiplier of
two

while groups are not adjusted. To reduce misidentification bias, each crew
member is trained in waterfowl identification.

Since not all birds are seen by observers in
the fixed
-
wing aircraft (i.e., detection
probability is <1), estimation of waterfowl abundance through the SOP survey design requires
surveying a sample of segments with helicopters to establish species
-
specific visibility correction
factors (VCF; Caughley

1974). Helicopter surveys follow the same protocols as the fixed
-
wing
surveys with slight variations. Segments are surveyed in a quadratic grid that is 0.2 km (1/8 mi)
from either side of the segment line and wetlands within the segment are circled, allo
wing for
more complete counts of waterfowl. To be accurate, the pilot uses Global Positioning Systems
(GPS) to determine how far off the transect centerline is to the helicopter. Using Hughs 500 or
Bell Jet Ranger, helicopter surveys are not flown every ye
ar because they are expensive and
require additional personnel time. Historically eight VCF flights were conducted, in 1992
-
1996,
2003, 2010, and 2014, with 2018 and 2019 survey years conducted during this thesis. The ratio
of the helicopter to fixed
-
wing
counts create
s

a visibility correction factor that is applied to
correct the fixed
-
wing counts. The SOP averages statewide species
-

years. Corrected fixed
-
wing density estimates from each segment are then expanded for the area
of

Michigan to compute population estimates.

112

Figure
1
7
. Fixed
-
wing
S
tandard
O
perating
P
rocedure
(SOP)
for conducting the Michigan
DNR
spring waterfowl survey.

113

Table
1
3
. Waterfowl grouping types for the M
ichigan DNR

spring waterfowl survey.

Grouping Type

Species

Definition

Singles

All

Record the number of lone
males with the absence of a
female.

Flocked Drakes

Ducks

Record the total number of
males observed together with
the absence of females. Only
record for
two to four drakes.

Pairs

All

Record the number of pairs
(males and females close
together and can be separated).

Nesting Pairs

Geese, swans, and cranes

Record the number of pairs that
are near or flushed from their
nest.

Nesting Singles

Geese,
swans, and cranes

Record the number of singles
that are near or flushed from
their nest.

Groups

All

Record the number of birds in
mixed
-
sex groupings that
cannot be differentiated into
pairs. More than four flocked
drakes become a group.

114

LITERATURE CITED

115

LITERATURE CITED

Anteau
,

M. J. 2012. Do interactions of land use and climate affect productivity of waterbirds and
prairie
-
pothole wetlands? Wetlands 32:1

9
.

Ankney, C. D. 1996. An embarrassment of riches: too many geese. Journal of Wildlife
Management 60:217

223.

Austin, J. E.,
T. K. Buhl, G. R. Guntenspergen, W. Norling, and H.

T. Sklebar
.

2001. Duck
populations as indicators of landscape condition in the Prairie Pothole Region.
Environmental Management and Assessment 69:29

47.

Avers, B., B. Luukkonen, and K. Fisher. 2017. Sandh
ill crane status in Michigan. Michigan
Department of Natural Resources Wildlife Division Report 3631, Lansing, MI, USA.

Bart, J., and J. D. Schoultz. 1984. Reliability of singing bird surveys:

c
hanges in observer
efficiency with avian density. Auk 101:307

318.

Bartzen, B., K. W. Dufour, M. T. Bidwell, M. D. Watmough, and R. G. Clark. 2017.
Relationships between abundances of breeding ducks and attributes of Canadian prairie
wetlands. Wildlife Society Bulletin 41:416
-
423.

Bellrose, F. C., and D. J. Holm. 1994. Ecology and
m
anagement of the
w
ood
d
uck. Stackpole
Books, Mechanicsburg, PA, USA.

Calef, G. W.,
E. A.
DeBock, and
G. M.
Lortie
.

1976. The reaction of barren
-
ground caribou to
aircraft. Arctic 29:201

212.

Canadian Wild
life Service
,

and U.S. Fish and Wildlife Service. 1987. Standard operating
procedures for aerial waterfowl breeding ground population and habitat surveys in North
America, unpublished manual as revised. U.S. Fish and Wildlife Service, Laurel
Maryland, USA.

Caughley, G. R. 1974. Bias in aerial survey. Journal of Wildlife Management 38:921
-
933.

Caughley, G., R. Sinclair, and D. Scott
-
Kemmis. 1976. Experiments in aerial survey. Journal of
Wildlife Management 40:290
-
300.

Caughley, G. R. 1977. Analysis of verteb
rate populations. John Wiley and Sons, New York,
New York, USA.

Ciaranca, M. 1990. Interactions between mute swans (
Cygnus olor
) and native waterfowl in
southeastern Massachusetts on freshwater ponds. Thesis, Northeastern University,
Boston,
Massachusetts, USA.

116

Clancy, T. F. 1999. Choice of survey platforms and technique for broadscale monitoring of
kangaroo populations. Australian Zoologist 31:267

274.

Cleveland, K. T. 1994. Predictive models for the fall flight of selected waterfowl species
in
Michigan. Thesis, Michigan State University, East Lansing, USA.

Cochran, W. G. 1977. Sampling techniques. Third edition. John Wiley and Sons, New York,
New York, USA.

Conroy, M. J., J. R. Goldsberry, J. E. Hines, and D. B. Stotts. 1988. Evaluation of a
erial transect
surveys for wintering American black ducks. Journal of Wildlife Management 52:694
-
703.

Cordts, S. D., G. G. Zenner, and R. R. Koford. 2002. Comparison of helicopter and ground
counts for waterfowl in Iowa. Wildlife Society Bulletin 30:317
-
32
6.

Cowardin, L. M., and R. J. Blohm. 1992. Breeding population inventories and measurements of
recruitment. Pages 423

445 in B. D. J. Batt, A. D. Afton, M. G. Anderson, C. D. Ankney,
D. H. Johnson, J. A. Kadlec, and G. L. Krapu, editors. Ecology and manage
ment of
breeding waterfowl. University of Minnesota Press, Minneapolis, USA.

Cowardin, L. M., T. L., Shaffer, and P. M. Arnold. 1995. Evaluations of duck habitat and
estimation of duck population sizes with a remote
-
sensing
-
based system. National
Biologica
l Service, Biological Science Report 2. Washington, D.C., USA.

Diem, K. L., and K. H. Lu. 1960. Factors influencing waterfowl censuses in the parklands,
Alberta, Canada. Journal of Wildlife Management 24:113
-
133.

Dzubin, A. 1969. Assessing breeding populat
ions of ducks by ground counts. Saskatoon
Wetlands Seminar. Canadian Wildlife Service Report Series 6:178

237.

Fleming, P. J. S.
,

and

J. P. Tracey. 2008. Some human, aircraft and animal factors affecting
aerial surveys: how to enumerate animals from the ai
r. Wildlife Research 35:258
-
267.

Garrettson, P. R., R. V. Raftovich, J. E. Hines, G. S. Zimmerman. 2014. Band reporting
probabilities of mallards, American black ducks, and wood ducks in eastern North
America. Journal of Wildlife Management 78:50
-
57
.

Gitze
n, R. A., J. J. Millspaugh, A. B. Cooper, and D. S. Licht. 2012. Design and analysis of long
-
term ecological monitoring studies. Cambridge University Press, publishers, New York.

Grado, S. C., K. M. Hunt, C. P. Hutt, X. T. Santos, and R. M. Kaminski. 2011.

Economic
impacts of waterfowl hunting in Mississippi derived from a state
-
based mail survey.
Human Dimensions of Wildlife 16:100

113.

117

Green, M. C., M. C. Luent, T. C. Michot, C. W. Jeske and P. L. Leberg. 2008. Comparison and
assessment of aerial and grou
nd estimates of waterbird colonies. Journal of Wildlife
Management 72:697

706.

Hagy, H. M., C. S. Hine, M. M. Horath, A. P. Yetter, R. V. Smith, and J. D. Stafford. 2016.
Waterbird response indicates floodplain wetland restoration. Hydrobiologia 1

19.

John
son, W. C., B. V. Millett, T. Gilmanov, R. A. Voldseth, G. R. Guntenspergen, and D. E.
Naugle. 2005. Vulnerability of northern prairie wetlands to climate change. Bioscience
55:863

872.

Krapu, G. L.
, and

K. J. Reinecke.

1992. Ecology and management of bree
ding waterfowl
.

University of Minnesota Press, Minneapolis, USA.

Lancia, R. A., W. L. Kendall, K. H. Pollock, and J. D. Nichols. 2005. Estimating the
n
umbers of
a
nimals in
w
ildlife
p
opulations in C. E. Braun, ed. Techniques for wildlife investigations
and
management. The Wildlife Society, Bethesda, Maryland.

Luukkonen, D. R., H. H. Prince, and R. C. Mykut. 2008. Movements and survival of molt
migrant Canada geese from southern Michigan. Journal of Wildlife Management 72:449

462.

Manly, B. F. J. 1997. Random
ization, bootstrap, and Monte Carlo methods in biology. Chapman
& Hall, London, UK.

Meine, C. D., and G. W. Archibald. 1996. The
c
ranes: status survey and conservation action
plan. IUCN, Gland, Switzerland, and Cambridge, UK.

Martin, F. W., R. S.
Pospahala, and J. D. Nichols. 1979. Assessment and population management
of North American migratory birds. Pages 187
-
239 in J. Cairns, Jr., G. P. Patil, and W. E.
Waters, editors. Environmental biomonitoring, assessment, prediction, and
management

certain

case studies and related quantitative issues. International Co
-
operative Publication House, Burtonsville, Maryland, USA.

Michigan Department of Natural Resources. 2012. Mute swan management and control program
policy and procedures.
<https://www.michigan.gov/documents/dnr/2012_Mute_Swan_Policy_378701_7.pdf>.
Accessed 27 Sept 2018.

waterfowl advisory committee.

<https://www.michigan.gov/documents/dnr
/CWAC
_
Information_04242013_420795_7.p

df>. Accessed 29 Oct 2018.

Michigan Department of Natural Resources.

2019. Migratory
g
ame
b
ird
h
unting
s
easons
w
ildlife
c
onservation
o
rder
a
me
ndment No. 3 of 2019.
118

<https://www.michigan.gov/documents/dnr/03WCO2019_Migratory_Game_Bird_64541
1_7.pdf>. Accessed 18 June 2019.

Miller, C., and
J. J.
Vaske
.

2003. Individual and situational influences on declining hunter effort
in Illinois. Human Dimensi
ons of Wildlife 8:263

276.

Mills, S. L. 2012. Conservation of wildlife populations: demography, genetics, and management,
second edition. Wiley Blackwell, Hoboken, New Jersey, USA.

Nichols, J. D., J. E. Hines, J. R. Sauer, F. W. Fallon, J. E. Fallon, and P
. J. Heglund. 2000. A
double
-
observer approach for estimating detection probability and abundance from point
counts. Auk 117:393

408.

Norton
-
Griffiths, M. 1975. Counting animals. Serengeti Ecological Monitoring Programme,
African Wildlife Leadership Founda
tion, Nairobi, Kenya.

Pagano, A. M.
,

and T. W. Arnold. 2009. Detection probabilities for ground
-
based breeding
waterfowl surveys. Journal of Wildlife Management 73:392
-
398.

Pearse, A. T., S. J. Dinsmore, R. M. Kaminski, and K. J. Reinecke. 2008. Evaluatio
n of an
a
erial
s
urvey to
e
stimate
a
bundance of
w
intering
d
ucks in Mississippi. Journal of Wildlife
Management 72:1413
-
1419.

Ransom, J. I.
2012. Probability in aerial surveys of feral horses. Journal of Wildlife Management
76:299
-
307.

Reynolds, J. H., W. L.

Thompson, and B. Russell. 2011. Planning for success: identifying
effective and efficient survey designs for monitoring. Biological Conservation 144:1278

1284.

Ross, R. K. 1985. Helicopter vs. ground surveys of waterfowl in the boreal forest.
Wildlife
Society Bulletin 13:153
-
157.

Sauer, J. R., G. S. Zimmerman, J. D. Klimstra, and W. A. Link. 2014. Hierarchical model
analysis of the Atlantic flyway breeding waterfowl survey. Journal of Wildlife
Management 78:1050
-
1059.

Schummer, M. L., A. D. Aft
on, S. S. Badzinski, G. H. Olsen, and M. A. Mitchell. 2018.
Evaluating the waterfowl breeding population and habitat survey for scaup. Journal of
Wildlife Management 82:1252
-
1262.

Shirkey, B. T. 2012. Diving duck abundance and distribution on Lake St. Clai
r and western Lake
Erie. Thesis, Michigan State University, East Lansing, USA.

Shupe, T. E., and S. L. Beasom. 1987. Speed and altitude influences on helicopter surveys of
mammals in brushland. Wildlife Society Bulletin 15:552

555.

119

Singer, H. V., D. R. Luu
kkonen, L. M. Armstrong, and S. R. Winterstein. 2016. Influence of
weather, wetland availability, and mallard abundance on productivity of Great Lakes
mallards (
Anas platyrhynchos
). Wetlands 36:969
-
978.

Smith, G. W. 1995. A critical review of the aerial an
d ground surveys of breeding waterfowl in
North America. Biological Science Report 5, National Biological Service, Washington,
D.C., USA.

Soulliere, G. J., and S. B. Chadwick. 2003. Using helicopter sampling to estimate visibility bias
on the Michigan spri
ng waterfowl survey. Wildlife Division Report 3408, Michigan
Department of Natural Resources, Lansing, MI.

Stone, W. B., and A. D. Marsters. 1970. Aggression among captive mute swans. New York Fish
and Game Journal 17:51
-
53.

Thompson, S. K. 1992. Sampling
. John Wiley and Sons, New York, New York, USA.

Tracey, J. P., and
P. J. S.
Fleming
.

2007. Behavioural responses of feral goats (
Capra hircus
) to
helicopters. Applied Animal Behaviour Science 108:114

128.

Tracey, J. P., P. J. S. Fleming, and G. J. Melville
. 2008. Accuracy of some aerial survey
estimators
-

contrasts with known numbers. Wildlife Research 35:377
-
384.

United States Department of the Interior. 2005. Final environmental impact statement: resident
Canada goose management. U.S. Fish and Wildlife S
ervice, Washington, D.C., USA.

United States Fish and Wildlife Service. 2018. Waterfowl population status, 2018. U.S.
Department of Interior, Washington D.C., USA.

United States Fish and Wildlife Service. 2018. Adaptive harvest management: 2019
hunting
season. U.S. Department of Interior, Washington D.C., USA.

Williams, B. K., F. A. Johnson, and K. Wilkins. 1996. Uncertainty and the adaptive management
of waterfowl harvests. Journal of Wildlife Management 60:223

232.

Yerkes, T., R. Paige, R. Macl
eod, L. Armstrong, G. Soulliere, and R. Gatti. 2007. Predicted
distribution and characteristics of wetlands used by mallard pairs in five
G
reat
L
akes
states. The American Midland Naturalist 157:356
-
364.

Zimmerman, G. S., J. R. Sauer, W. A. Link, and M. Ott
o. 2012. Composite analysis of black
duck breeding population surveys in eastern North America. Journal of Wildlife
Management 76:1165
-
1176.