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American Woodcock Singing-Ground Survey: Comparison
of Four Models for Trend in Population Size
John R. Sauer,* William A. Link, Mark E. Seamans, Rebecca D. Rau

J.R. Sauer, W.A. Link
U.S. Geological Survey, Eastern Environmental Science Center, 12100 Beech Forest Road, Laurel, Maryland 20708
M.E. Seamans
U.S. Fish and Wildlife Service, Division of Migratory Bird Management, Lakewood, Colorado 80225

Abstract
Wildlife biologists monitor the status and trends of American woodcock Scolopax minor populations in the eastern and
central United States and Canada via a singing-ground survey, conducted just after sunset along roadsides in spring.
Annual analyses of the survey produce estimates of trend and annual indexes of abundance for 25 states and
provinces, management regions, and survey-wide. In recent years, researchers have used a log-linear hierarchical
model that defines year effects as random effects in the context of a slope parameter (the S model) to model
population change. Recently, researchers have proposed alternative models suitable for analysis of singing-ground
survey data. Analysis of a similar roadside survey, the North American Breeding Bird Survey, has indicated that
alternative models are preferable for almost all species analyzed in the Breeding Bird Survey. Here, we use leave-oneout cross-validation to compare model fit for the present singing-ground survey model to fits of three alternative
models, including a model that describes population change as the difference in expected counts between successive
years (the D model) and two models that include t-distributed extra-Poisson overdispersion effects (H models) as
opposed to normally distributed extra-Poisson overdispersion. Leave-one-out cross-validation results indicate that the
Bayesian predictive information criterion favored the D model, but a pairwise t-test indicated that the D model was not
significantly better-fitting to singing-ground survey data than the S model. The H models are not preferable to the
alternatives with normally distributed overdispersion. All models provided generally similar estimates of trend and
annual indexes suggesting that, within this model set, choice of model will not lead to alternative conclusions
regarding population change. However, as in Breeding Bird Survey analyses, we note a tendency for S model results to
provide slightly more extreme estimates of trend relative to D models. We recommend use of the D model for future
singing-ground survey analyses.
Keywords: birds; hierarchical models; singing-ground survey
Received: October 2020; Accepted: March 2021; Published Online Early: March 2021; Published: June 2021
Citation: Sauer JR, Link WA, Seamans ME, Rau RD. 2021. American woodcock singing-ground survey: comparison of
four models for trend in population size. Journal of Fish and Wildlife Management 12(1):83–97; e1944-687X. https://doi.
org/10.3996/JFWM-20-079
Copyright: All material appearing in the Journal of Fish and Wildlife Management is in the public domain and may be
reproduced or copied without permission unless specifically noted with the copyright symbol &. Citation of the
source, as given above, is requested.
The findings and conclusions in this article are those of the author(s) and do not necessarily represent the views of the
U.S. Fish and Wildlife Service.
* Corresponding author: [email protected]

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R.D. Rau
U.S. Fish and Wildlife Service, Division of Migratory Bird Management, Laurel, Maryland 20708

Estimating American Woodcock Trend

J.R. Sauer et al.

Introduction

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Figure 1. Observers have conducted roadside counts in spring
1968–2019 for a singing-ground survey that monitors the
American woodcock Scolopax minor within 25 states and
provinces that comprise most of the breeding range of American
woodcock in North America. Wildlife managers use the singingground survey to estimate annual indexes of abundance and
population trends for states, provinces, two management
regions, and survey-wide. The Eastern Management Region
consists of Connecticut, Delaware, Maine, Maryland, Massachusetts, New Brunswick, New Hampshire, New Jersey, New York,
Nova Scotia, Pennsylvania, Prince Edward Island, Quebec, Rhode
Island, Vermont, Virginia, and West Virginia, while the Central
Management Region contains Illinois, Indiana, Manitoba, Michigan, Minnesota, Ohio, Ontario, and Wisconsin.

In this paper, we apply the four models (S, D, SH, and
DH) to the SGS data. We compare estimated trends and
annual indexes based on these models to determine
whether the model results present conflicting views of
population change, and we use LOOCV to compare fit
among the four models.

Study Site
Wildlife biologists conduct the SGS in 25 states and
provinces in the eastern and central United States and
Canada, and define strata for analyses in terms of states
and provinces, and estimate population change for
Eastern and Central management regions (Seamans and
Rau 2019, Figure 1). Sample sizes vary greatly among
states, and researchers added Manitoba to the survey in
1992. Sauer et al. (2008) provides additional details on
regions surveyed by the SGS.

Methods
The American woodcock singing-ground survey
The SGS is composed of approximately 1,600
roadside survey routes located within randomly selectJune 2021 | Volume 12 | Issue 1 | 84

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In the 1930s Mendall and Aldous (1943) pioneered
roadside surveys for American woodcock Scolopax minor
in Maine. During the 1950s and 1960s, researchers
expanded surveys and modified survey design in various
ways to improve spatial sampling design and standardize
counting methods (e.g., Kozicky et al 1954). The singingground survey (SGS) currently used by the U.S. Fish and
Wildlife Service to assess population status and inform
harvest strategies was initiated in its current form in 1968
(Seamans and Rau 2019). Although researchers occasionally criticize the SGS due to the low encounter rates
of woodcock in southern states and limited samples from
the boreal forests in Ontario and Quebec, the SGS
provides information of much higher quality than the
much more geographically extensive North American
Breeding Bird Survey (BBS, Link et al. 2020) for the
species, as observers record few woodcock during the
morning samples collected using the BBS protocol (Sauer
et al. 2008). However, the BBS and SGS share similar
sample designs, and analyses of these roadside surveys
are challenging due to the need to control variation in
factors that influence counts, such as observer ability,
and limited data over the large geographic range of the
survey. Researchers analyze the SGS using methods
developed for BBS analyses. Link and Sauer (2002) and
Sauer et al. (2008) described the statistical model
currently used for analysis of SGS data.
Recently, Link et al. (2020) expanded the model set for
BBS analyses to include four alternative models. Researchers currently use one of these models for analysis
of the SGS. The current SGS model employs a log-linear
hierarchical model that defines year effects as random
effects having a linear regression on year (i.e., varying
randomly around a straight line across years, the S
model). The Link et al. (2020) model set also includes a
model that describes population change in terms of
conditionally independent differences between years
(the D model) and two models that use the S and D
population change structure but include t-distributed
extra-Poisson overdispersion effects as heavy-tailed
alternatives to normally distributed extra-Poisson overdispersion. These models are denoted as SH and DH.
Using leave-one-out cross-validation (LOOCV), Link et al.
(2020) compared model fit for the S model to fit of three
alternative models for 548 species of North American
breeding birds based on BBS data. Their comprehensive
analysis of BBS data indicated that the S model was the
least-preferred model of the set; model S was preferred
for only 4 of the 548 species they considered in their BBS
analyses. The BBS does include American woodcock, and
model selection based on the BBS data for American
woodcock suggested that model DH is strongly favored
over model S, and that model S was the least likely
model to fit the BBS American woodcock data. Link et al.
(2020) also noted that S models tended to produce
estimates of change that are more extreme than those
produced by D models, due to the presence of the slope
parameter in the model.

Estimating American Woodcock Trend

J.R. Sauer et al.

Hierarchical models for singing-ground survey
analysis
For the SGS and other roadside surveys such as the
BBS, analysts use log-linear hierarchical models fit using
Bayesian analysis methods to estimate aspects of
population change. In these models, they assume counts
(Yi) to be overdispersed Poisson random variables, and
model the log of the expected count as a function of
explanatory variables. Link et al. (2020) heuristically
denote the general modeling framework in Equation 1:
logðki Þ ¼ Ci þ Xi þ ei

ð1Þ

where Yijki ~ Poisson (ki), and Ci, Xi, and ei represent
year, observer, and overdispersion effects associated
with observation i. The model set consists of four models
that have alternative forms for year effects (S or D
models) and the distribution of overdispersion effects
(normal distributions or ‘‘heavy-tailed’’ t distributions).
For all models, observer effects are composed of x, a
mean zero normal random effect associated with
observer o(i) and a ‘‘start-up’’ effect g associated with
indicator variable f(i) to index first year of counting on a
route for an observer (i.e., Xi ¼ xo(i) þ g f(i)).
Year effects in both models, Ci ¼ cs(i),y(i) are parameters
describing relative abundance as a function of stratum
s(i) and year y(i). For S models, year effects are
conditionally independent and normally distributed with
means (expected values, denoted E()) defined by a
stratum and slope parameter, E(cs,y) ¼ Ss þ bs (y  y0), and
precision scs . The y0 is a baseline year. One can think of
the S model year effects as yearly deviations from a line
defined by the b (slope) parameter and an intercept. For
the D models, year effects cs,y are normally distributed
with mean cs,y1 and precision scs (i.e., the differences in
year effects are conditionally independent). Similarly to S
models, where the stratum effect Ss serves as an
intercept (baseline abundance), in D models a base year
is fixed and we set the year effect in the base year to Ss
(i.e., E(cs,y0) ¼ Ss). Stratum effects are normally distributed
with mean ls and precision ss. Extra-Poisson overdispersion effects ei take two possible forms: 1) they
can be assumed to be independent and normally
distributed with precision se, or 2) we can specify
Journal of Fish and Wildlife Management | www.fwspubs.org

independent and t-distributed ei that have scale parameter se and degrees-of-freedom parameter m. For the BBS,
we have found that extreme counts occur within the
data and that the t-distribution generally fits better than
the normal distribution (Link et al. 2020). We denote
models that use the t-distribution for overdispersion with
an H, due to their heavy tails.
The JAGS code (Plummer 2003) for our four candidate
models (S, SH, D, DH), along with specification of all
priors is included in Link et al. (2020; Data S1,
Supplemental Material). Briefly, we assign flat normal
priors (mean zero with standard deviation ¼ 1,000) and
vague gamma priors (shape parameter ¼ rate parameter
¼ 0.001) to mean parameters. We use a gamma
distribution with mean 20 and variance 200 as an
objective prior for m (Juárez and Steel 2010).
We describe population change using derived parameters (i.e., parameters that are functions of parameters in
the estimation models). We define annual indexes of
abundance for a stratum as a function of year effects,
ns,y¼ exp( cs,y þ 0.5r2eþ 0.5r2x ), where re and rx are the
standard deviations of the indicated random effects. In
the SGS analysis, states and province areas are the strata;
we present results for these strata as well as for Eastern
and Central management regions (Seamans and Rau
2019) and survey-wide. For multistratum regions, we
compute annual indexes as area-weighted averages of
state or provincial indexes. We define trend as the
geometric means of annual indexes, and estimate it as
the ratio of annual indexes for the last and first years in
the interval taken to the power 1/(yl  yf), where yf and yl
are the first and last years. The current harvest strategy
for woodcock uses 3-y moving averages of annual
indexes for Eastern and Central management regions
as a measure of population status in setting harvest
levels (U.S. Fish and Wildlife Service 2010).
Model selection
We used LOOCV for model selection. Link and Sauer
(2016a) and Link et al. (2020) described the motivation
for the approach and its application in the context of BBS
analyses. In LOOCV, we fit the model to a data set from
which we have omitted a single observation. We refer to
the Bayesian estimate of a distribution function (i.e.,
averaged over the posterior distribution of unknown
parameters) as the predictive distribution function. The
value of the predictive distribution function evaluated at
omitted data value i is termed the conditional predictive
ordinate (CPOi). We define the Bayesian predictive
information criterion (BPIC) as the sum of the logs of
CPOi over all observations. For model selection, we
compute BPIC for each of the four models and the
largest BPIC value indicates the model with best fit. Link
and Sauer (2016a) describe paired t-tests for evaluating
significance of differences in BPICs among models, in
which they use pairwise differences of CPOs between
models as the observations.
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ed 10-min degree blocks. Routes consist of 10 counting
stops along a 5.4-km-long survey route that observers
survey shortly after sunset. Observers conduct one
survey on a route each year, seasonally timed to
coincide with local peak of woodcock breeding activity
after migrants have moved through; the observer
records the number of woodcock heard vocalizing
(‘‘peenting’’) during a 2-min count period at each stop.
Sauer et al. (2008) and Seamans and Rau (2019) provide
additional details on the survey design, implementation, and data management. Managers and researchers
vet and analyze data yearly for presentation in status
reports and as input into harvest strategy analyses
(Seamans and Rau 2019).

Estimating American Woodcock Trend

J.R. Sauer et al.

Table 1. Population trend estimates and 95% credible intervals (2.5% and 97.5% percentiles from posterior distributions of trend
estimates) for American woodcock Scolopax minor estimated for 1968–2019 from the singing-ground survey based on four
alternative models: model S (a slope-year effect model), model SH (model S with t-distributed overdispersion), model D (year effects
based on differences), and model DH (model D with t-distributed overdispersion). The table presents results for states and provinces,
Eastern and Central management regions, and survey-wide. Note that observers conducted no surveys in Manitoba (MB) prior to
1992.
Model S
a

Model SH

Model D

Model DH

N

Trend

2.5% CI

97.5% CI

Trend

2.5% CI

97.5% CI

Trend

2.5% CI

97.5% CI

Trend

2.5% CI

97.5% CI

11
3
75
26
22
74
18
19
117
65
85
13
145
4
24
75
58
834
47
63
31
161
124
74
174
128
771
1605

2.53
2.77
1.21
3.66
2.58
0.97
1.26
5.94
0.79
0.78
1.04
1.45
0.91
5.81
1.01
5.10
2.18
1.09
1.38
3.96
0.03
1.01
0.47
1.48
1.31
0.27
0.88
0.99

4.14
5.86
1.68
5.03
3.51
1.70
2.23
7.35
1.22
1.45
1.75
2.61
1.71
9.52
1.86
6.12
3.00
1.36
3.44
5.08
1.39
1.35
0.06
2.17
1.74
0.73
1.10
1.17

0.87
0.14
0.71
2.36
1.61
0.30
0.31
4.52
0.35
0.15
0.32
0.28
0.16
2.67
0.14
4.06
1.38
0.83
0.95
2.85
1.44
0.66
1.03
0.79
0.86
0.19
0.67
0.82

2.50
2.78
1.30
3.59
2.55
0.94
1.28
5.91
0.79
0.75
1.05
1.41
0.95
5.72
1.03
5.12
2.20
1.11
1.61
3.88
0.11
1.02
0.40
1.36
1.30
0.30
0.89
1.00

4.06
5.71
1.80
5.00
3.52
1.63
2.29
7.25
1.23
1.42
1.72
2.57
1.76
9.01
1.85
6.14
3.04
1.38
3.19
4.93
1.46
1.36
0.10
2.05
1.74
0.77
1.10
1.18

1.02
0.17
0.81
2.16
1.54
0.29
0.30
4.53
0.33
0.12
0.34
0.23
0.17
2.78
0.20
4.14
1.36
0.84
0.03
2.87
1.25
0.67
0.97
0.66
0.87
0.15
0.68
0.83

2.16
1.54
1.27
2.89
2.50
1.43
1.26
5.44
0.75
0.84
0.98
1.23
0.39
5.31
0.97
4.61
1.90
1.11
1.34
3.70
0.17
0.96
0.96
1.40
1.20
0.12
0.69
0.91

3.83
5.47
1.76
4.55
3.54
2.06
2.31
7.13
1.19
1.54
1.69
2.39
1.26
10.83
1.90
6.09
2.79
1.40
3.38
5.03
2.69
1.30
0.41
2.08
1.64
0.57
0.90
1.09

0.56
0.84
0.78
1.40
1.45
0.83
0.28
3.91
0.32
0.21
0.28
0.06
0.47
1.67
0.03
3.24
1.06
0.83
0.95
2.47
2.37
0.61
1.52
0.71
0.76
0.32
0.48
0.72

2.13
1.30
1.35
2.76
2.51
1.47
1.31
5.55
0.73
0.83
0.93
1.25
0.39
4.66
0.98
4.63
1.94
1.12
1.40
3.72
0.28
0.97
0.90
1.24
1.22
0.14
0.70
0.92

3.93
5.01
1.84
4.23
3.51
2.09
2.36
7.30
1.16
1.51
1.59
2.46
1.24
9.51
1.91
6.33
2.85
1.41
3.59
5.20
2.71
1.32
0.34
2.01
1.64
0.59
0.91
1.11

0.58
1.11
0.88
1.38
1.42
0.86
0.36
3.97
0.29
0.18
0.28
0.10
0.47
1.45
0.06
3.29
1.05
0.85
0.60
2.41
2.14
0.63
1.47
0.57
0.77
0.30
0.49
0.74

a

CI ¼ credible interval; CT ¼ Connecticut; DE ¼ Delaware; IL ¼ Illinois; IN ¼ Indiana; ME ¼ Maine; MB ¼ Manitoba; MD ¼ Maryland; MA ¼ Massachusetts;
MI ¼ Michigan; MN ¼ Minnesota; NB ¼ New Brunswick; NH ¼ New Hampshire; NJ ¼ New Jersey; NY ¼ New York; NS ¼ Nova Scotia; OH ¼ Ohio; ON ¼
Ontario; PA ¼ Pennsylvania; PE ¼ Prince Edward Island; QC ¼ Quebec; RI ¼ Rhode Island; VT ¼ Vermont; VA ¼ Virginia; WV ¼ West Virginia; WI ¼
Wisconsin; CE ¼ Central Management Region; EA ¼ Eastern Management Region.

Model fitting
We used program JAGS called from program R for
model fitting and summary of posterior distributions
(Plummer 2003). We fit models with 3 chains, a thinning
of 5, and a burn-in of 1,000 iterations, and used 4,000
iterations to generate replicates for computation of
posterior distributions of parameters. We present medians of posterior distributions as parameter estimates,
and express uncertainty as 95% credible intervals (CI)
with lower boundaries as 2.5th percentiles and upper
boundaries of 97.5% of the posterior distributions as
computed from the 12,000 replicates (4,000 replicates
from each chain). For all parameters except moving
averages we present 95% CIs; for the moving averages
we present 70% CIs (15th and 85th percentiles of the
posterior distributions) to meet management needs
(USFWS 2010). Link et al. (2020) noted that LOOCV is
extremely time-consuming for BBS data sets, and they
reduced the computational time by randomly selecting a
balanced (by year) sample of observation for computing
Journal of Fish and Wildlife Management | www.fwspubs.org

BPICs. They selected two observation/year/species. The
SGS data set is large, (40,409 counts in the data from
1968 to 2019; Data S1, Supplemental Material), and we
also made a random, yearly balanced selection of 20
observations per year for the LOOCV analysis, computing
BPIC based on these 1,040 observations for the four
models. These observations represent 2.7% of the total
observations. Protocols for the cross-validation analyses
followed those used in Link et al. (2020).

Results
Comparative analysis of annual indexes and trends
for four models
When fit to SGS data, the four models produced very
similar estimates of trend (Tables 1–3). Overall for the
survey, estimates of change from 1968 to 2019 varied
from 0.91%/y (model D) to 1.00%/y (SH). Note that no
data exist for Manitoba for the early years of the survey,
and the 1968–2019 trend analyses do not include
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Region
CT
DE
ME
MD
MA
NB
NH
NJ
NY
NS
PA
PE
QC
RI
VT
VA
WV
EA
IL
IN
MB
MI
MN
OH
ON
WI
CE
ALL

Estimating American Woodcock Trend

J.R. Sauer et al.

Table 2. Population trend estimates and 95% credible intervals (2.5% and 97.5% percentiles from posterior distributions of trend
estimates) for American woodcock Scolopax minor estimated for 2009–2019 from the singing-ground survey based on four
alternative models: model S (a slope-year effect model), model SH (model S with t-distributed overdispersion), model D (year effects
based on differences), and model DH (model D with t-distributed overdispersion). The table presents results for states and provinces,
Eastern and Central management regions, and Survey-wide.
Model S
a

Model SH

Model D

Model DH

Trend

2.5% CI

97.5% CI

Trend

2.5% CI

97.5% CI

Trend

2.5% CI

97.5% CI

Trend

2.5% CI

97.5% CI

CT
DE
ME
MD
MA
NB
NH
NJ
NY
NS
PA
PE
QC
RI
VT
VA
WV
EA
IL
IN
MB
MI
MN
OH
ON
WI
CE
ALL

2.32
2.82
0.88
3.78
3.10
0.20
3.09
7.63
0.83
0.37
1.85
1.62
1.35
5.92
2.02
3.90
2.13
0.99
1.54
3.79
0.51
0.68
0.45
1.71
2.25
0.20
0.79
0.89

6.13
8.81
2.78
7.10
6.25
1.92
6.68
13.18
2.41
1.85
4.66
5.23
3.86
11.33
5.50
7.54
4.93
1.88
9.96
8.50
2.64
2.03
1.24
4.43
4.15
1.60
1.62
1.49

1.81
3.52
1.10
0.41
0.33
2.44
0.01
3.31
0.86
2.77
0.80
1.92
0.71
0.28
1.31
1.16
0.72
0.14
7.56
0.93
4.04
0.77
2.12
0.91
0.31
2.03
0.05
0.29

2.24
2.83
0.95
3.72
3.14
0.14
3.20
7.26
0.87
0.52
1.71
1.51
1.57
5.81
1.97
4.11
2.15
1.06
1.46
3.71
0.37
0.45
0.46
1.40
2.38
0.12
0.76
0.90

5.80
7.57
2.84
7.26
6.25
1.92
6.61
11.82
2.58
1.82
4.55
5.16
4.31
10.51
5.19
7.40
5.11
2.00
7.36
7.81
2.62
1.81
1.17
4.09
4.24
1.66
1.57
1.53

1.52
2.08
0.96
0.10
0.18
2.23
0.20
3.54
0.85
3.07
0.95
2.05
0.83
1.04
1.22
0.03
0.78
0.14
5.06
0.13
3.61
0.94
2.09
1.20
0.44
1.93
0.06
0.30

0.52
1.28
1.50
1.01
3.43
1.65
4.53
6.68
0.26
0.26
2.06
0.77
1.47
2.39
1.77
1.53
0.78
1.31
3.08
2.69
1.91
0.74
0.72
1.32
2.63
0.39
0.80
1.05

4.56
11.53
3.38
7.85
7.14
3.67
8.25
13.30
2.00
1.95
5.18
4.75
4.46
16.89
5.20
8.76
4.52
2.31
11.14
9.51
1.36
2.08
0.89
4.08
4.33
1.37
1.59
1.70

5.56
7.29
0.42
5.67
0.16
0.46
1.13
0.29
1.42
2.59
0.97
3.20
1.23
11.85
1.58
6.80
2.94
0.34
5.36
3.62
5.50
0.65
2.32
1.51
0.85
2.19
0.02
0.42

0.61
1.24
1.60
0.96
3.49
1.64
4.68
6.82
0.33
0.28
1.00
0.86
1.67
1.92
1.78
2.21
1.00
1.33
3.82
2.64
1.66
0.53
0.64
0.97
2.65
0.30
0.77
1.05

4.12
10.02
3.49
6.93
7.28
3.55
8.39
13.66
2.05
1.96
4.16
5.02
4.67
15.46
5.14
8.78
4.83
2.36
11.01
9.36
1.52
1.89
0.90
3.78
4.40
1.39
1.53
1.70

5.66
7.15
0.31
5.09
0.19
0.44
1.37
0.48
1.28
2.67
1.91
3.18
1.02
10.70
1.48
5.57
2.80
0.36
4.43
3.98
5.03
0.82
2.23
1.88
0.93
2.07
0.02
0.44

a

CI ¼ credible interval; CT ¼ Connecticut; DE ¼ Delaware; IL ¼ Illinois; IN ¼ Indiana; ME ¼ Maine; MB ¼ Manitoba; MD ¼ Maryland; MA ¼ Massachusetts;
MI ¼ Michigan; MN ¼ Minnesota; NB ¼ New Brunswick; NH ¼ New Hampshire; NJ ¼ New Jersey; NY ¼ New York; NS ¼ Nova Scotia; OH ¼ Ohio; ON ¼
Ontario; PA ¼ Pennsylvania; PE ¼ Prince Edward Island; QC ¼ Quebec; RI ¼ Rhode Island; VT ¼ Vermont; VA ¼ Virginia; WV ¼ West Virginia; WI ¼
Wisconsin; CE ¼ Central Management Region; EA ¼ Eastern Management Region.

Manitoba. Although none of the estimates from any
state, province, or management region differed among
models (as indicated by overlap in the 95% CIs),
comparison of differences in trend estimates by state
and provinces from S and D models indicated that S
models produced slightly more negative trend estimates
(average difference: 0.22%/y; 95% confidence interval:
0.35, 0.09). This mean difference includes results from
states and provinces with limited data and imprecise
results; trends from all regions combined indicate a
smaller difference (0.08%/y). For 10-y trend estimates,
the average differences in S  D model estimates among
states and provinces were negative (0.55%/y; 95%
confidence interval: 1.08, 0.02). Trends from a few
states and provinces with few routes appear to drive this
result; composite trends for the management regions
and all regions combined were slightly larger under the S
model results for 10-y trends. We could not discern any
consistent differences in 2-y trend estimates (average
difference in S  D estimates among states and provinces
¼ 0.97%/y; 95% confidence interval: 1.15, 3.09).
Journal of Fish and Wildlife Management | www.fwspubs.org

We compared half-widths of 95% CIs of trends among
the 25 states and provinces for the four models. For
trends computed over the 1968–2019 interval, model D
had larger 95% CIs than model S, but the mean
difference is small (the half-width is only 0.15 larger for
D models; Table 4). Generally, D models had slightly
larger 95% CIs than did S models, but no consistent
differences existed between D and DH or between S and
SH (Table 4). For 2009–2019 trends, D models had larger
95% CIs than S models, but H model results also tended
to have smaller 95% CIs than non-H models (i.e., SH
results had smaller 95% CIs than S results, DH results had
smaller 95% CIs than D results). Although all 95% CIs are
large for 2-y trends, S models tend to have larger 95% CIs
than D models among states and provinces and DH is
more precise than D (Table 4).
Annual indexes provide a great deal of insight into
relationships among models (Figure 2). Within many
states and provinces (e.g., Indiana, Maine, Michigan, New
Jersey, Nova Scotia, New York, Ohio, Ontario, Prince
Edward Island, Virginia, Vermont, Wisconsin, and West
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Region

Estimating American Woodcock Trend

J.R. Sauer et al.

Table 3. Population trend estimates and 95% credible intervals (2.5% and 97.5% percentiles from posterior distributions of trend
estimates) for American woodcock Scolopax minor estimated for 2018–2019 from the singing-ground survey based on four
alternative models: model S (a slope-year effect model), model SH (model S with t-distributed overdispersion), model D (year effects
based on differences), and model DH (model D with t-distributed overdispersion). The table presents results for states and provinces,
Eastern and Central management regions, and survey-wide.
Model S
a

Model SH

Model D

Model DH

Trend

2.5% CI

97.5% CI

Trend

2.5% CI

97.5% CI

Trend

2.5% CI

97.5% CI

Trend

2.5% CI

97.5% CI

6.51
2.24
13.83
3.01
0.63
27.53
4.33
10.89
4.78
6.16
1.86
3.34
3.32
5.53
15.49
1.41
1.53
5.60
3.10
11.89
5.11
12.50
6.33
8.94
3.07
11.63
3.61
4.55

39.76
45.08
5.79
29.73
25.07
3.42
31.94
48.52
9.87
14.56
25.59
32.90
22.23
41.51
40.06
32.77
20.81
2.85
63.89
47.29
21.34
0.91
19.82
14.59
17.20
5.05
3.63
1.01

33.47
75.36
38.41
36.33
35.46
58.49
31.04
46.28
22.98
33.36
27.49
37.39
18.02
52.17
16.11
64.71
34.88
14.46
145.42
34.72
43.22
27.98
9.45
43.31
13.22
31.51
11.40
10.36

6.56
2.80
14.32
2.84
0.29
26.52
4.90
9.26
4.76
7.58
1.76
2.91
4.05
5.63
14.94
0.12
2.17
5.38
1.56
9.24
4.90
12.98
6.87
7.65
4.42
13.36
3.47
4.37

36.19
36.65
5.26
30.33
25.86
3.64
30.66
41.78
10.58
13.56
25.58
32.40
24.65
36.42
38.62
30.14
23.25
3.37
48.74
41.07
20.18
0.36
20.09
15.32
18.46
3.02
3.52
1.15

30.99
48.63
38.69
36.64
36.30
54.31
30.79
37.82
21.99
34.90
28.59
36.87
19.82
42.54
15.47
49.86
38.69
14.92
86.54
32.03
38.58
27.98
8.23
38.57
11.34
32.87
11.20
10.48

3.37
0.62
5.90
0.84
1.09
12.01
5.26
7.31
0.55
2.17
1.05
2.68
3.49
0.50
8.93
5.95
0.65
1.26
0.85
4.45
0.05
4.38
6.94
3.71
4.88
4.01
0.58
0.33

27.75
27.73
7.58
23.87
19.72
3.72
24.63
37.62
10.65
11.65
17.00
23.11
18.31
39.43
29.14
22.08
15.68
4.77
41.07
31.26
17.47
5.96
18.11
11.52
15.71
8.30
6.07
3.82

26.00
34.85
23.32
28.64
21.94
32.18
15.91
32.93
11.27
19.60
16.83
21.34
10.67
63.77
13.70
50.90
21.33
7.40
70.73
29.26
21.90
16.65
5.69
24.74
7.49
18.65
5.43
4.58

3.91
0.24
6.21
0.35
1.11
12.72
4.98
6.43
0.58
2.66
0.93
2.65
4.23
0.42
8.97
4.93
0.60
1.20
0.33
3.35
0.12
4.82
7.74
2.85
5.83
4.23
0.81
0.19

27.21
25.18
7.42
23.18
20.42
3.09
23.79
37.05
11.11
11.29
16.24
23.87
18.97
36.93
28.92
22.43
15.84
4.77
38.84
30.25
17.61
5.48
18.80
11.59
16.87
7.71
6.26
3.89

23.94
32.64
23.31
28.95
22.29
32.95
17.42
33.67
11.54
20.44
15.99
22.21
9.92
53.58
13.13
46.58
21.11
7.14
60.46
30.48
21.51
16.96
4.81
22.81
6.34
18.56
5.07
4.37

a

CI ¼ credible interval; CT ¼ Connecticut; DE ¼ Delaware; IL ¼ Illinois; IN ¼ Indiana; ME ¼ Maine; MB ¼ Manitoba; MD ¼ Maryland; MA ¼ Massachusetts;
MI ¼ Michigan; MN ¼ Minnesota; NB ¼ New Brunswick; NH ¼ New Hampshire; NJ ¼ New Jersey; NY ¼ New York; NS ¼ Nova Scotia; OH ¼ Ohio; ON ¼
Ontario; PA ¼ Pennsylvania; PE ¼ Prince Edward Island; QC ¼ Quebec; RI ¼ Rhode Island; VT ¼ Vermont; VA ¼ Virginia; WV ¼ West Virginia; WI ¼
Wisconsin; CE ¼ Central Management Region; EA ¼ Eastern Management Region.

Virginia), annual indexes are very similar for all models.
For the other states and provinces, annual indexes based
on models S and SH provide virtually identical patterns
of population change over time. Results from models D
and DH are likewise very similar. As a general rule,
however, both sets of trajectories, even if varying over
several years, varied within the 95% CI bands, suggesting

that we can attribute any apparent differences in pattern
of change over time to chance. A few differences might
be meaningful. In Minnesota, trajectories were similar
except in the first 3 y. The larger populations indicated
by the S models in those early years are observable in the
regional (Central Management Region) results. In Que-

Table 4. Comparison of half-widths of 95% credible intervals of estimates of trends in American woodcock Scolopax minor from four
models fit to singing-ground survey data: model S (a slope-year effect model), model SH (model S with t-distributed overdispersion),
model D (year effects based on differences), and model DH (model D with t-distributed overdispersion). The table presents results as
mean differences by state and provinces and associated 2.5% and 97.5% confidence intervals computed for three time intervals:
1968–2019 (N ¼ 24 regions), 2009–2019 (N ¼ 25 regions), and 2018–2019 (N ¼ 25 regions).
Model
comparison
S–SH
S–D
S–DH
SH–D
SH–DH
D–DH

1968–2019

2009–2019

2018–2019

Difference

2.5%

97.5%

Difference

2.5%

97.5%

Difference

2.5%

97.5%

0.05
0.15
0.12
0.20
0.17
0.03

0.00
0.27
0.22
0.35
0.29
0.02

0.11
0.02
0.02
0.05
0.06
0.07

0.28
1.03
0.87
1.31
1.15
0.17

0.04
1.81
1.54
2.18
1.90
0.03

0.52
0.25
0.20
0.45
0.40
0.30

3.58
10.29
11.04
6.70
7.46
0.75

0.37
6.41
6.80
4.75
5.67
0.04

6.79
14.16
15.27
8.65
9.24
1.47

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Region
CT
DE
ME
MD
MA
NB
NH
NJ
NY
NS
PA
PE
QC
RI
VT
VA
WV
EA
IL
IN
MB
MI
MN
OH
ON
WI
CE
ALL

Estimating American Woodcock Trend

J.R. Sauer et al.

bec, trajectories were markedly different in the early
years, when researchers conducted very few surveys.
Results from regional moving averages are consistent
with patterns in annual indexes (Figure 3). Moving
Journal of Fish and Wildlife Management | www.fwspubs.org

averages smooth the annual indexes, and the 70% CIs
used for this analysis make the width of the CIs much
smaller. For both regions, the four models provided very
similar estimates and 70% CIs. Eastern Management
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Figure 2. Annual indexes of abundance for American woodcock Scolopax minor estimated from the singing-ground survey using four
alternative models for estimation of population change. We compared models using a leave-one-out-cross-validation model selection
procedure. The figure presents annual indexes and associated 95% credible intervals (CIs) from model D (the favored model, in which
year effects are based on differences) and annual indexes model DH (model D with t-distributed overdispersion) in red; solid dots for
model D and stars for model DH indicate yearly index values. Annual indexes and 95% credible intervals for model S (a slope-year
effect model) and annual indexes for model SH (model S with t-distributed overdispersion) are black; solid dots for model S and as
stars for model SH indicate yearly index values. We present results for states and provinces, Eastern and Central management regions,
and survey-wide. Results cover the years 1968–2019 for all regions except Manitoba (MB), where no surveys were conducted prior to
1992. CT ¼ Connecticut; DE ¼ Delaware; IL ¼ Illinois; IN ¼ Indiana; ME ¼ Maine; MB ¼ Manitoba; MD ¼ Maryland; MA ¼ Massachusetts; MI
¼ Michigan; MN ¼ Minnesota; NB ¼ New Brunswick; NH ¼ New Hampshire; NJ ¼ New Jersey; NY ¼ New York; NS ¼ Nova Scotia; OH ¼
Ohio; ON ¼ Ontario; PA ¼ Pennsylvania; PE ¼ Prince Edward Island; QC ¼ Quebec; RI ¼ Rhode Island; VT ¼ Vermont; VA ¼ Virginia; WV ¼
West Virginia; WI ¼ Wisconsin; CE ¼ Central Management Region; EA ¼ Eastern Management Region.

Estimating American Woodcock Trend

J.R. Sauer et al.

Region estimates for 2017–2019 ranged from 2.29
(model SH) to 2.38 (D) and the width of the CIs varied
from 0.20 (SH) to 0.22 (DH). Central Management Region
estimates for 2017–2019 ranged from 2.56 (model SH) to
2.60 (D) and the width of the CIs varied from 0.156 (SH)
to 0.164 (D).
Model selection results
We computed BPICs for each model based on 1,040
randomly selected observations. Model D had the largest
BPIC (2,665), followed by model S (2,670), model DH
(2,701) and model SH (2,702). Paired t-test results
comparing fit of models D and S indicated no significant
difference (t ¼ 1.07, P . 0.28). Models SH and DH also had
Journal of Fish and Wildlife Management | www.fwspubs.org

similar BPICs (t ¼ 0.18, P , 0.86), but all comparisons of H
models with non-H models were significant (all P , 0.01).

Discussion
American woodcock are difficult to survey and
observers encounter them at low frequencies on survey
routes in many of the states and provinces included in
the SGS. The slope-year effect parameterization of the S
model relies on the random effects to model deviations
from a consistent long-term trend. Researchers historically favored this parameterization for data sets such as
the SGS because data quality (in terms of number of
routes and consistency of coverage among routes) varies
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Figure 2. Continued.

Estimating American Woodcock Trend

J.R. Sauer et al.

greatly among states and provinces; the S model
effectively defaults to a slope-trend model for data sets
with very limited data. However, Link et al. (2020)
convincingly demonstrated that models D and DH better
fit most BBS species data sets than models S and SH did.
They also showed that there was a tendency for S
models to produce slightly more extreme trend estimates than D models for the BBS data. They attributed
this result to limited data in the early years of the BBS.
When this occurs, the S model has limited data for
estimation of the year effects, the yearly effects in that
case tend to be shrunk toward the slope component of
the S model, and the resulting annual indexes are
primarily governed by a slope parameter that may not be
an adequate representation of change in those years.
Journal of Fish and Wildlife Management | www.fwspubs.org

Year effects in D models are shrunk toward adjacent
year’s year effects, and do not use a long-term trend to
predict yearly estimates when data are limited. Our
comparative analyses and LOOCV model selection results
provide useful insights into how the alternative models
behave when applied to SGS data and allow us to make
recommendations for appropriate analyses to be used in
future SGS analyses.
Our LOOCV analysis found that model D had the largest
BPIC, suggesting that D is to be preferred, but the paired
t-test results comparing fit at individual observations did
not indicate a significantly better fit of the D model
relative to the S model. Our expectations based on BBS
model selection was that D models, and particularly
model DH, were likely to best fit SGS data. In the BBS
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Figure 2. Continued.

Estimating American Woodcock Trend

J.R. Sauer et al.

analysis, model D best fit 53 species while model DH best
fit 458 species (Link et al. 2020). The BBS surveys American
woodcock, although observers only rarely encounter the
species on early-morning stops along BBS routes that
temporally coincide with woodcock activity. The BBS has
average counts of 0.02 observations/route across their
range. Model selection of American woodcock from BBS
data indicated a clear superiority of model DH, and the
trend estimated using this model over 611 BBS routes
during 1966–2019 indicated a trend of 0.73%/y (95% CI:
1.52, 0.07) for the species.
Analysis of SGS data indicates that the S model does
appear to provide slightly more negative estimates of
trend than does the D model when applied to SGS data.
The size of these effects is small (0.08%/y at the surveywide level), and as with BBS results the pattern is likely
Journal of Fish and Wildlife Management | www.fwspubs.org

due to limited samples in a few states and provinces in
the early years of the survey. Inspection of annual
indexes only indicates meaningful differences in annual
indexes (as indicated by comparisons of CIs of indexes)
for Minnesota and Quebec in the early years of the SGS.
These results, along with the observations of more
extreme trends associated with S model results in BBS
analyses, are an argument in favor of use of the D model
for SGS analyses. Although D model results tended to be
less precise than S model results, the differences in CI
width are small, indicating that use of the D model
would not greatly limit our ability to detect meaningful
population changes in the SGS.
The SH and DH models fit less well than expected
based on the experience of BBS analyses. We expect H
models to be superior for species in which extreme
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Figure 2. Continued.

Estimating American Woodcock Trend

J.R. Sauer et al.

observations occasionally occur, leading to heavy-tailed
overdispersion. The SGS is primarily based on observers
hearing displaying male woodcock, and observers tend
to display considerable differences in ability to hear
woodcock. However, the models account for this aspect
of counting by incorporating observer and startup
effects; the SGS protocols, in which observers are
generally drawn from the population of professional
wildlife biologists and new observers conduct paired
counts with old observers when observers change on a
route, may lead to better training and more consistent
counting by observers during their tenure of counting
on routes. BBS observers are drawn from the larger
population of citizen scientists, and often have limited
tenures on survey routes (Link and Sauer 2016b), and this
Journal of Fish and Wildlife Management | www.fwspubs.org

large pool of observers may lead to greater variability
both within and among observers.
Implementing the D model for the SGS will lead to no
significant differences in trend results presently used in
woodcock status reports, and we can compute the
moving average population status metric used in
woodcock harvest management as derived statistics
from the D model year effects in exactly the same way as
presently implemented for the S model. Moving
averages of regional population change are virtually
identical in recent years in the Central Management
Region and very similar in the Eastern Management
Region, indicating that use of the D model for estimation
of population indexes will have little consequence for
management decisions based on SGS analyses.
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Figure 2. Continued.

Estimating American Woodcock Trend

J.R. Sauer et al.

Wildlife managers can also use derived statistics
develop predictions based on long-term population
trajectories as was required in 2020 when the SGS data
collection was disrupted due to concerns about deploying staff to conduct surveys during the coronavirus
pandemic (Seamans and Rau 2020). In this situation,
managers were interested in prediction of expected
population change in woodcock in 2020, given the
long-term declining trend in woodcock populations. The
S model readily produced these predictions, although
data from 2020 did not inform these results. Analysts
added an additional year node to the analysis and treated
it as missing data. The Bayesian analysis permitted
estimation of the ‘‘year effect’’ for 2020 (in this case, a
prediction based on the slope parameter), and analysts
Journal of Fish and Wildlife Management | www.fwspubs.org

produced posterior distributions of predicted annual
indexes and trends. Long-term trend information such
as that embedded in the slope parameter of the S model
would not have informed the D model, if analysts
employed it for such a prediction. However, analysts
could produce a similar prediction by defining a derived
slope statistic from the year effects estimated in the D
model and predicting the change in population status
between 2019 and 2020.

Supplemental Material
Please note: The Journal of Fish and Wildlife Management
is not responsible for the content or functionality of any
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Figure 2. Continued.

Estimating American Woodcock Trend

J.R. Sauer et al.

supplemental material. Queries should be directed to the
corresponding author for the article.

Found at DOI: https://doi.org/10.3996/JFWM-20-079.S1
(797 KB TXT).

Data S1. Singing-ground survey data collected by
observers along roadside survey routes in 25 states and
provinces for years 1968–2019. We have formatted data for
use with JAGS programs provided as supplemental
materials in Link et al. (2020). Variables are N of counts
(ncounts), N of route/observers (nobservers), N of years
(nyears), N of strata (nstrata), areas of strata (areaweight),
counts (count, vector of size N), year index for counts (year,
vector of length N with values indexing year of count),
route/observer index for counts (obser, vector of length N),
index of strata for counts (strat, vector of length N), and
index for first year of counting (firstyr, vector of length N).

Reference S1. Seamans ME, Rau RD. 2019. American
woodcock population status, 2019. Laurel, Maryland: U.S.
Fish and Wildlife Service.
Found at DOI: https://doi.org/10.3996/JFWM-20-079.S2
(2.38 MB PDF).

Journal of Fish and Wildlife Management | www.fwspubs.org

Reference S2. Seamans ME, Rau RD. 2020. American
woodcock population status, 2020. Laurel, Maryland: U.S.
Fish and Wildlife Service.
Found at DOI: https://doi.org/10.3996/JFWM-20-079.S3
(1.61 MB PDF).
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Figure 2. Continued.

Estimating American Woodcock Trend

J.R. Sauer et al.

Acknowledgments
The singing-ground survey is a cooperative effort
coordinated by state, provincial, Canadian Wildlife
Service, Birds Canada, and U.S. Fish and Wildlife Service
biologists. We thank the many biologists who organize
and conduct the survey. We also thank Guthrie Zimmerman, Tom Cooper, David E. Anderson, and the Associate
Editor for helpful comments that improved the manuscript.
Any use of trade, product, website, or firm names in
this publication is for descriptive purposes only and does
not imply endorsement by the U.S. Government.

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Journal of Fish and Wildlife Management | www.fwspubs.org

Link WA, Sauer JR. 2016a. Bayesian cross-validation for
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Figure 3. Moving averages of annual indexes of abundance for American woodcock Scolopax minor estimated from the singingground survey using four alternative models for estimation of population change. Moving averages are based on 3-y averages of
annual indexes, and are plotted by first year of the average (i.e., value for 1995 is average of annual indexes for 1993–1995). Moving
averages and associated 70% credible intervals from model D (the favored model, in which year effects are based on differences)
and moving averages for model DH (model D with t-distributed overdispersion) are presented in red; solid dots for model D and
stars for model DH indicate yearly values. Moving averages and 70% credible intervals for model S (a slope-year effect model) and
moving averages for model SH (model S with t-distributed overdispersion) are black; solid dots for model S and stars for model SH
indicate moving average values. The figure presents results for Eastern and Central management regions. Abbreviations: EA
indicates Eastern Management Region; CE, Central Management Region.

Estimating American Woodcock Trend

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population status, 2019. Laurel, Maryland: U.S. Fish
and Wildlife Service (see Supplemental Material,
Reference S1).
Seamans ME, Rau RD. 2020. American woodcock
population status, 2020. Laurel, Maryland: U.S. Fish
and Wildlife Service (see Supplemental Material,
Reference S2).

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American woodcock harvest strategy. Woodcock
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www.fws.gov/migratorybirds/pdf/surveys-and-data/
Webless%20Migratory%20Game%20Birds/American%
20Woodcock%20pdf%20files/Interim%20Woodcock%
20Harvest%20strategy%20-%20Feb%202,2010.pdf
(April 2021).

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