Abstract

Despite extensive conservation and management efforts, American black duck (Anas rubripes) populations remain below desired population levels. Researchers have noted declines at a number of wintering areas, but indications are that wintering populations in the northern part of the range are increasing. Intermittently between 1970 and 1989, and annually since 1992, wildlife biologists have flown aerial surveys of the entire coast of Nova Scotia, Canada, to count wintering waterfowl. This survey counted the total number of ducks seen in predefined lengths of coastline. We analyzed those survey data using generalized linear mixed models, over the entire time period (1970–2015) and in the recent time period (1992–2015, when surveys were done every year), across five general regions of Nova Scotia. We fit models using Bayesian methods with uninformative priors; models with negative binomial response distributions performed well. Due to the large variation in mean numbers of black ducks across the predefined lengths of coastline, we treated these blocks of coastline as a fixed effect, while annual trend (slope) was modeled as a random effect to account for variation in annual trend across blocks of coastline. Results were similar between the entire time series (1970–2015) or the most recent and more complete time series (1992–2015). In general, numbers of wintering black ducks in Nova Scotia increased (1.0–16.0%/y) and increases were significant (Bayesian credible intervals did not bound 0) in four of five regions. Increasing numbers in Nova Scotia are consistent with other observations of increasing wintering numbers at the northern range of American black ducks and may indicate a shift in the wintering range that has been ongoing for decades. Future habitat management actions will benefit from consideration of regional trends and the distributional change of black duck.

Introduction

American black duck (Anas rubripes) remains a species of international management concern for a variety of reasons, including that the estimated population size remains below the North American Waterfowl Management Plan goal (Black Duck Joint Venture Management Board 2008). Declines in black ducks observed in traditional wintering sites may be explained in part by a decline in the quality or quantity of nonbreeding habitat (Conroy et al. 2002), and perhaps by a redistribution of birds wintering farther north (Brook et al. 2009). Christmas Bird Count (a volunteer-based bird survey conducted in late December) data indicated increases in the northeastern United States in winter (Link et al. 2006). Depending on ice severity, some black ducks have always wintered in Maritime Canada and observers in urban areas have noted local increases (Godfrey 1986; McCorquodale and Knapton 2003).

Biologists have collected winter aerial survey data on numbers and locations of observations of wintering black ducks around Nova Scotia, Canada, since 1970 and annually since 1992. These extensive surveys are based on aggregating data in predefined sections of coastline (coastal blocks; Lock et al. 1996; Allard et al. 2014). We assessed regional trends in numbers of wintering black ducks around Nova Scotia using generalized linear mixed models (Zuur et al. 2009, 2013) to examine whether increases observed at other parts of their northern wintering range extend to northeastern limit of the species' winter range.

Methods

Biologists conducted coastal surveys for waterfowl in Nova Scotia in winter 35 times between 1970 and 2015, which corresponded to the period after the waterfowl hunting season, and usually when freshwater wetlands, shallow bays, and waterways had frozen. The protocol was based on the U.S. Mid-winter Waterfowl Survey (MWS; U.S. Fish and Wildlife Service 2015). Wildlife managers developed the MWS to provide population estimates of waterfowl and monitor broad-scale changes in distribution on major wintering areas (Blohm et al. 2006). Although survey design and methods vary somewhat by region (Eggeman and Johnson 1989), the MWS is useful in describing long-term patterns and changes in distributions and habitats and potentially long-term trends in numbers. For our work, there was general consistency in observers (Nova Scotia Department of Natural Resources or Environment Canada staff) over the time of the study; new staff members were trained on identifications using online aerial identification websites, and by flying for several days with experienced observers prior to leading surveys. Consequently, there is annual consistency by participating agencies to reduce sources of error due to personnel turnover.

Surveyors used a variety of aircraft, typically small helicopters such as the Hughes 500 or Eurocopter 120, supporting a crew of two observers and the pilot, but occasionally one observer and the pilot. Each observer counted flocks independently, and used the intercom to report numbers to the lead surveyor. Surveyors flew between 0900 and 1600 hours, at altitudes of 100–150 m and only during good flight conditions (minimal rain, snow, fog or smoke; winds ≤ 40 km/h). Pilots flew survey aircraft at ground speeds varying from 30 to 150 km/h, and generally within 200 m of shore, depending on topography, land use, wind speed and direction, weather, and safety of the crew. The Nova Scotia coastline has a myriad of islands, so normally pilots flew the general coastline in one direction, rarely circling back over flocks. For small nearshore islands, the flight path bisected the island, with each observer counting an opposite side of the island. With larger islands, the pilot followed the shoreline. Observers estimated counts for large flocks in a variety of ways, often taking preconstructed “dot counts” with them as templates, but typically they estimated large flocks by first counting a small unit (∼ 50 birds), getting a visual image of the area involved, and then counting the number of areas this unit covered to estimate the number of total birds likely in the flock. In more recent years (since approximately 2005), surveyors took digital images of flocks and counted them after the survey.

We only considered surveys occurring between December and March in the analysis (range: 10 December to 30 March); most surveys occurred in January or February. Duplicate data entries were removed. If more than one survey was conducted in a year, we retained the survey occurring at a time when most of the coastline was surveyed in the data. We recorded these data summarized by coastal blocks, which we then grouped into five larger scale areas (Fundy Shore, Southern Shore, Eastern Shore, Cape Breton, and Northumberland Strait; Figure 1; Table S1, Supplemental Material). Data from 1970 to 2015 were available, but it was clear that data collection before 1992 was more sporadic, both across years and coastal blocks. To see whether estimated trends were reflective of the entire time period (1970–2015), or more reflected trends since data collection became more comprehensive in 1992, we also estimated a trend for the period between 1992 and 2015.

Figure 1.

Map of Nova Scotia, Canada, and the five regions analyzed to assess trends in numbers of wintering American black ducks (Anas rubripes) between 1970 and 2015. Counts of wintering American black ducks were conducted between December and March of most winters by rotary-wing aircraft.

Figure 1.

Map of Nova Scotia, Canada, and the five regions analyzed to assess trends in numbers of wintering American black ducks (Anas rubripes) between 1970 and 2015. Counts of wintering American black ducks were conducted between December and March of most winters by rotary-wing aircraft.

We employed standard techniques to analyze count data using generalized linear models (GLMs; Zuur et al. 2009) and generalized linear mixed models (GLMMs; Zuur et al. 2012, 2013) using R (R Core Team 2015). We considered data from each of five regions separately, and began each analysis with an exploratory phase using basic tabulations and graphical outputs. We removed coastal blocks that did not have sufficient data from the analysis (three or fewer positive counts, or counts restricted to one decade). For almost all regions, it was clear that coastal blocks varied considerably in their mean count of black ducks. Therefore, we considered coastal block in all models, first as a fixed effect, and then as a random effect in GLMMs. We first considered simple GLMs with Poisson distributions and year (trend) and coastal block as effects to examine overall patterns and levels of overdispersion. Not surprisingly, overdispersion was pervasive in these data so we then fitted GLMs with negative binomial distributions in an attempt to address the extra variance. Negative binomial models were able to fit these data (overdispersion ≤ 1.4), so we did not consider zero-inflation models further. We modeled coastal blocks as both random and fixed effects and for most regions, there was an interaction between year (trend) and coastal block, indicating trends varied across coastal blocks so we also fitted random-slope models (i.e., hierarchical analysis of the trend).

We fit basic GLMs using the package lme4 in R (Bates et al. 2015). We used a Bayesian hierarchical approach to fit GLMMs using JAGS (Plummer 2003), via the r2jags (Su and Yajima 2015) interface, to fit models with negative binomial distributions with fixed and random effects for coastal block and a random effect for annual trend (Text S1, Supplemental Material). In all cases, model selection (assessed by deviance information criteria, DIC) indicated models with fixed effects for coastal blocks performed similarly or better than those with random effects. This was due to the large differences in mean counts among the coastal blocks, which a single variance parameter appeared unable to adequately capture; this was particularly noticeable when examining residuals that showed a lot of heterogeneity among coastal blocks when treated as a random effect. We included an additive fixed effect for years 2005 to 2015, testing the assumption that counts after 2004 would be consistently larger due to the change from visual to photo counts in 2005. The effect of changing methods from visual to photo counts in 2005 was inconsistent, 95% credible intervals bound 0 for three regions, was positive in one region and negative in another. Given the inconsistent results, we did not include this effect in the final models.

The form of the final models that we used for estimation and inference were the following, where i is the coastal block (Block) and j is year (Year).

formula
formula
formula
formula

We used vague priors for all parameters. Regression parameters (β0, β1i, β2) had normal prior distributions with mean 0 and a variance of 10,000; the random effect for slope σ2 and κ had a prior based on a half (positive values only) Student's t distribution, with a mean of 0, a variance of 625 and four degrees of freedom. We ran models with three Markov chain Monte Carlo chains, each with 10,000 iterations, and a burn-in period of 5,000 iterations; we achieved good mixing of the Markov chain Monte Carlo chains in all models with this burn-in period and number of iterations. We have presented Bayesian 95% credible intervals, extracted from the posterior distributions of the Markov chain Monte Carlo chains for all parameter estimates. To assess model fit, we have presented Bayesian P values for each model, with values near 0.5 indicating good model fit and values near 0 or 1 indicating poor fit (Gelman et al. 2006).

Results

Negative binomial GLMMs, with coastal block as a fixed effect and annual trend across coastal blocks as a random effect fit the data well (in all cases the Bayesian P value was not close to 0 or 1; Table 1). Most trends indicated modest increases, except for the Fundy Shore (both time periods) and Eastern Shore (1992–2015), where the 95% credible intervals bound 1 (Table 1; Figure 1). The Northumberland Strait showed steep increases, but more variable trends among coastal blocks (σ2 = 0.109 and 0.161; Table 1; Figures S1 and S2, Supplemental Material). Recent trends (1992–2015) on the Fundy Shore were also notably variable (σ2 = 0.083). Although slight differences were apparent, trends in each region during the recent time period (1992–2015) were generally similar to the trend for the entire time series.

Table 1.

Annual trends in numbers of wintering American black ducks (Anas rubripes) in five general areas of coastal Nova Scotia, Canada, 1970–2015 and 1992–2015. Results are based on negative binomial generalized linear mixed models fit using Bayesian methods, where coastal block was treated as a fixed effect and annual trend across coastal blocks was considered a random effect. Kappa (κ) is the reciprocal of the negative binomial dispersion parameter (var = μ + μ2/κ). Bayesian 95% credible intervals are presented in parentheses. Bayesian P values near 0.5 indicate good model fit, while values near 0 or 1 suggest poor fit.

Annual trends in numbers of wintering American black ducks (Anas rubripes) in five general areas of coastal Nova Scotia, Canada, 1970–2015 and 1992–2015. Results are based on negative binomial generalized linear mixed models fit using Bayesian methods, where coastal block was treated as a fixed effect and annual trend across coastal blocks was considered a random effect. Kappa (κ) is the reciprocal of the negative binomial dispersion parameter (var = μ + μ2/κ). Bayesian 95% credible intervals are presented in parentheses. Bayesian P values near 0.5 indicate good model fit, while values near 0 or 1 suggest poor fit.
Annual trends in numbers of wintering American black ducks (Anas rubripes) in five general areas of coastal Nova Scotia, Canada, 1970–2015 and 1992–2015. Results are based on negative binomial generalized linear mixed models fit using Bayesian methods, where coastal block was treated as a fixed effect and annual trend across coastal blocks was considered a random effect. Kappa (κ) is the reciprocal of the negative binomial dispersion parameter (var = μ + μ2/κ). Bayesian 95% credible intervals are presented in parentheses. Bayesian P values near 0.5 indicate good model fit, while values near 0 or 1 suggest poor fit.

Discussion

Our results confirm previous analysis that suggested wintering American black ducks are stable or increasing in eastern Canada (McCorquodale and Knapton 2003; Link et al. 2006). The survey, developed in 1970, does not provide data to address issues such as interobserver variation and imperfect detections, so it is not without potential biases (Pearse et al. 2008). However, unlike previous analyses using local counts or general counts from the birding community, wildlife managers specifically designed these aerial surveys to count coastal wintering waterfowl and they are generally adequate for large-bodied and widespread species (Laursen et al. 2008). A methodological change from visual to photo counts in 2005 could explain the apparent increases. Our analysis did not indicate that counts showed a clear and consistent increase after 2004, but since time and the change in methods are confounded, the change in methods in 2005 cannot be entirely dismissed to explain the apparent increase. Increasing trends that include the early years of the survey (1970s and 1980s), a time when the survey was only conducted sporadically, may be the result of improved methods and more experienced observers in recent years. But because the trends were similar in the recent period (1992–2015) when the surveys were conducted annually by experienced crews, it suggests the increases observed are real. Link et al. (2006) reported a significant 3.1% (95% credible interval: 1.8–4.4) annual increase for American black ducks in the Atlantic Northern Forest Bird Conservation Region (BCR 14) from Christmas Bird Count data from 1966 to 2003. Nova Scotia is at the eastern edge of this BCR, and our results are generally consistent with those findings, with annual increases of 1.1–2.8% across all parts of Nova Scotia, except for the Northumberland Strait, between 1970 and 2015.

Northumberland Strait saw the largest (12–16%) annual increases, both through the entire time series (1970–2015), and in the recent period (1992–2015). This region is on the Gulf of St. Lawrence side of Nova Scotia, an area where sea ice regularly freezes, and which experiences colder winters and more continental-like weather compared to regions that border the Bay of Fundy or the Atlantic Ocean. Increases in this region may reflect a general amelioration of winter weather, and improving conditions for American black ducks at the northern parts of their wintering range. Consistent with that idea, the BCR that experienced the greatest increases (4.3%/y) in the Christmas Bird Count analysis by Link et al. (2006) was the Boreal Hardwood Transition BCR (BCR 12), which lies to the northwest of BCR 14 and Nova Scotia.

McCorquodale and Knapton (2003) noted that the number of wintering black ducks increased in the urbanized areas of Cape Breton (Sydney and environs) between 1992 and 1999–2002. Our results for Cape Breton suggest that this increase is continuing and spans the entire data series. Unlike other regions, the Fundy Shore did not show evidence of increases, as credible intervals bound 0 in both time periods. Strong tidal amplitudes in the Bay of Fundy mean that subtidal habitats and intertidal prey, which are important habitats (Ringelman et al. 2015) and food sources for black ducks, are available on a daily basis (Jorde and Owen 1990; English et al. 2017). The Bay of Fundy may have been a region that has always had significant wintering black duck populations, and so recent increases are not apparent.

Black ducks wintering in Nova Scotia largely comprise birds breeding in eastern Canada (English 2016; Robinson et al. 2016). Black duck numbers wintering in eastern Ontario were stable during 1986–1996, but increased sharply (20%/y) during 1997–2005, a time when breeding numbers in northern Ontario remained stable, suggesting breeding population increases were not leading to the increases seen in wintering areas in Ontario (Brook et al. 2009). Instead, black duck numbers wintering in eastern Ontario increased during years when numbers of black ducks counted in the Mississippi Flyway midwinter inventory were lower (Brook et al. 2009), suggesting a distributional change and more birds wintering farther north. A similar phenomenon may be occurring in Nova Scotia, and Atlantic Canada generally, with more birds wintering farther north. Trends from the core wintering area (New England/mid-Atlantic coasts) suggested a mild but insignificant decline over a similar (1996–2003) time period (Link et al. 2006), possibly indicating a redistribution of birds to more northern wintering areas. Based on surveys of breeding birds throughout their eastern range, black duck populations are stable or declining (Zimmerman et al. 2012), again suggesting that the increases seen in wintering birds in Nova Scotia are not the result of a general increase in black ducks, but rather are likely due to a redistribution of birds.

Reduced harvest pressure on locally breeding birds in Nova Scotia could lead to the increases seen, if it led to a largely nonmigratory resident population that has developed since the 1970s. However, several lines of evidence do not support this contention. First, harvest pressure on black ducks banded in the preseason in Nova Scotia is relatively high and most of those birds are harvested in Canada (Roy et al. 2015), limiting the opportunity for local population growth in Nova Scotia. Second, birds wintering in Nova Scotia (southeastern Canada) represent birds from a variety of regions, with most coming from northeastern Canadian breeding grounds (Robinson et al. 2016). The increases seen in the Nova Scotia wintering population appear to reflect a redistribution of the population to the north. Robinson et al. (2016) noted a significant movement of black ducks banded preseason in the eastern United States moving to southeast Canada during the hunting season, which would facilitate a redistribution of birds to the north if individuals decided to remain and winter in Canada.

Our methods using GLMMs appeared to successfully reflect the important properties of these data. Accelerating variances with the mean was captured by the negative binomial distribution, as was the abundance of zeroes in the data set. The dispersion parameter (1/κ) was relatively large, indicating the variance in the counts accelerated quickly with the mean of the counts. We expected this with these data, where occasional very large counts (thousands) are possible. Our hierarchical approach was able to incorporate the variation in the trends among coastal blocks. Introducing coastal block as a fixed effect (as opposed to a random effect) was costly in terms of adding more parameters to the model, but led to a better distribution of residuals across the coastal blocks compared to a random intercept model. Any analysis that has large differences in mean numbers across strata (in our case three orders of magnitude, from single digits to thousands) will be faced with how to address variation across strata and a single variance parameter may be inadequate to capture that variation.

Although at the northern edge of their wintering range, American black ducks in Nova Scotia are able to meet their energy demands from natural foods and anthropogenic subsidies (English et al. 2017). Our data indicate that wintering numbers are increasing in Nova Scotia, and may reflect a general shift in black duck nonbreeding distributions to the north. As climate warming continues, waterfowl at middle latitudes are likely to continue to further delay migration and eventually may not even migrate at all (Notaro et al. 2016), leading to further increases in northern areas. These results highlight that distribution and trends of black ducks vary across their range, and provide further support to efforts to understand and manage black ducks at smaller spatial scales (Roy et al. 2015; Robinson et al. 2016).

Supplemental Material

Please note: The Journal of Fish and Wildlife Management is not responsible for the content or functionality of any supplemental material. Queries should be directed to the corresponding author for the article.

Text S1. Sample JAGS code to fit a negative binomial model with fixed intercepts and random slopes. Sample code applies to increases in the number of American black ducks wintering in Nova Scotia, 1970-2015.

Found at DOI: http://dx.doi.org/10.3996/032017-JFWM-031.S1 (2 KB TXT).

Table S1. Number of wintering American black ducks (Anas rubripes) counted on coastal block aerial surveys in Nova Scotia, Canada, 1970–2015. Counts are summed across coastal blocks (Lock et al. 1996) in five coastal regions of Nova Scotia.

Found at DOI: http://dx.doi.org/10.3996/032017-JFWM-031.S2 (217 KB XLS).

Figure S1. Number of wintering American black ducks (Anas rubripes) counted on coastal block aerial surveys in Nova Scotia, Canada, 1970–2015. Lines represent trends for each coastal block, fit with negative binomial generalized linear mixed models (GLMMs). The size of the circle scales with the number of identical counts across coastal blocks in that year.

Found at DOI: http://dx.doi.org/10.3996/032017-JFWM-031.S3 (63,282 KB TIFF).

Figure S2. Number of wintering American black ducks (Anas rubripes) counted on coastal block aerial surveys in Nova Scotia, Canada, 1992–2015. Lines represent trends for each coastal block, fit with negative binomial generalized linear mixed models (GLMMs). The size of the circle scales with the number of identical counts across coastal blocks in that year.

Found at DOI: http://dx.doi.org/10.3996/032017-JFWM-031.S4 (63,282 KB TIFF).

Reference S1. Lock AR, Sircom JP, Gerriets SH. 1996. Coastal waterbirds in Atlantic Canada. Part 1: Aerial survey block descriptions. Dartmouth, Nova Scotia, Canada: Canadian Wildlife Service, Atlantic Region.

Found at DOI: http://dx.doi.org/10.3996/032017-JFWM-031.S5 (2,640 KB PDF).

Acknowledgments

Funding for this work was provided by Environment and Climate Change Canada and the Nova Scotia Department of Natural Resources. We thank the many personnel that have participated in the surveys, with special thanks to Keith McAloney, Scott Gilliland, Pamela Mills, Mike Boudreau, and the numerous pilots who got crews safely around the province, often in challenging conditions. Christian Roy, Nic McLellan, and Associate Editor David Haukos provided very helpful comments on an earlier draft of this 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.

References

Allard
K.
Hanson
A.
Mahoney
M.
2014
.
Important marine habitat areas for migratory birds in eastern Canada
.
Sackville, New Brunswick, Canada
:
Canadian Wildlife Service, Technical Report Series No. 530
. .
Bates
D.
Maechler
M.
Bolker
B.
Walker
S.
2015
.
Fitting linear mixed-effects models using lme4
.
Journal of Statistical Software
67
:
1
48
.
Black Duck Joint Venture Management Board
.
2008
.
Black Duck Joint Venture strategic plan 2008–2013
.
Laurel, Maryland: U.S. Fish and Wildlife Service and Ottawa, Ontario, Canada: Canadian Wildlife Service. Available: http://blackduck.cmi.vt.edu/docs/BDJV%20Strategic%20Plan%202008_2013.pdf (September 2017)
.
Blohm
RJ.
Sharp
DE.
Padding
PI.
Richkus
KD.
2006
.
Monitoring North America's waterfowl resource
.
Pages
448
452
in
Boere
GC.
Galbraith
CA.
Stroud
DA.
editors
.
Waterbirds around the world
.
Edinburgh, UK
:
The Stationery Office
.
Brook
RW.
Ross
RK.
Abraham
KF.
Fronczak
DL.
Davies
JC.
2009
.
Evidence for black duck winter distribution change
.
Journal of Wildlife Management
3
:
98
103
.
Conroy
MJ.
Miller
MW.
Hines
JE.
2002
.
Review of population factors and synthetic population model for American black ducks
.
Wildlife Monographs
150
:
1
64
.
Eggeman
DR.
Johnson
FA.
1989
.
Variation in effort and methodology for the Midwinter Waterfowl Inventory in the Atlantic Flyway
.
Wildlife Society Bulletin
17
:
227
233
.
English
MDB.
2016
.
An examination of the diet and body condition of American black ducks (Anas rubripes) overwintering in Atlantic Canada. Master's thesis
.
Wolfville, Nova Scotia, Canada
:
Acadia University
. .
English
MD.
Robertson
GJ.
Peck
LE.
Mallory
ML.
2017
.
Agricultural food resources and the foraging ecologies of American black ducks (Anas rubripes) and mallards (Anas platyrhynchos) at the northern limits of their winter ranges
. Urban Ecosystems doi:
Gelman
A.
Meng
XL.
Stern
H.
2006
.
Posterior predictive assessment of model fitness via realized discrepancies
.
Statistica Sinica
6
:
733
759
.
Godfrey
WE.
1986
.
The birds of Canada. Revised edition
.
Ottawa, Ontario, Canada
:
National Museum of Natural Sciences
.
Jorde
DG.
Owen
R.
1990
.
Foods of black ducks Anas rubripes wintering in marine habitats of Maine USA
.
Canadian Field Naturalist
104
:
300
302
.
Laursen
K.
Frikke
J.
Kahlert
J.
2008
.
Accuracy of ‘total counts' of waterbirds from aircraft in coastal waters
.
Wildlife Biology
14
:
165
175
.
Link
WA.
Sauer
JR.
Niven
DK.
2006
.
A hierarchical model for regional analysis of population change using Christmas Bird Count data, with application to the American black duck
.
Condor
108
:
13
24
.
Lock
AR.
Sircom
JP.
Gerriets
SH.
1996
.
Coastal waterbirds in Atlantic Canada. Part 1: Aerial survey block descriptions
.
Dartmouth, Nova Scotia, Canada
:
Canadian Wildlife Service, Atlantic Region
(see Supplemental Material, Reference S1, http://dx.doi.org/10.3996/032017-JFWM-031.S5)
.
McCorquodale
DB.
Knapton
RW.
2003
.
Changes in numbers of wintering American black ducks and mallards in urban Cape Breton Island, Nova Scotia
.
Northeastern Naturalist
10
:
297
304
.
Notaro
M.
Schummer
M.
Zhong
Y.
Vavrus
S.
Van Den Elsen
L.
Coluccy
J.
Hoving,
C.
2016
.
Projected influences of changes in weather severity on autumn–winter distributions of dabbling ducks in the Mississippi and Atlantic Flyways during the twenty-first century
.
PLoS ONE
11
:
e0167506
. doi:
Pearse
AT.
Gerard
PD.
Dinsmore
SJ.
Kaminski
RM.
Reinecke
KJ.
2008
.
Estimation and correction of visibility bias in aerial surveys of wintering ducks
.
Journal of Wildlife Management
72
:
808
813
.
Plummer
M.
2003
.
JAGS: a program for analysis of Bayesian graphical models using Gibbs sampling
.
In
Hornick
K.
Leisch
F.
Zeileia
A.
editors
.
Proceedings of the 3rd international workshop on distributed statistical computing (DSC 2003)
,
Vienna, Austria
:
Austrian Association for Statistical Computing and R Foundation for Statistical Computing
. .
Ringelman
KM.,
Williams
CK.
Devers
PK.
Coluccy
JM.
Castelli
PM.
Anderson
KA.
Bowman
JL.
Costanzo
GR.
Cramer
DM.
Dibona
MT.
Eichholz
MW.
Huang
M.
Lewis
B.
Plattner
DM.
Yerkes
T.
2015
.
A meta-analysis of American black duck winter habitat use along the Atlantic Coast: Atlantic Coast black duck telemetry
.
Journal of Wildlife Management
79
:
1298
1307
. doi
Robinson
OJ.
McGowan
CP.
Devers
PK.
2016
.
Updating movement estimates for American black ducks (Anas rubripes). PeerJ 4:e1787
. doi
Roy
C.
Cumming
SG.
McIntire
EJB.
2015
.
Spatial and temporal variation in harvest probabilities for American black duck
.
Ecology and Evolution
5
:
1992
2004
. doi
R Core Team
.
2015
.
R: a language and environment for statistical computing
.
Vienna, Austria
:
R Foundation for Statistical Computing
.
Available: https://www.R-project.org/ (September 2017)
.
Su
Y-S.
Yajima
M.
2015
.
R2jags: using R to Run ‘JAGS'. R package version 0.5-7
.
Available: https://CRAN.R-project.org/package=R2jags (September 2017)
.
U.S. Fish and Wildlife Service
.
2015
.
Mid-winter waterfowl survey
. .
Zimmerman
GS.
Sauer
JR.
Link
WA.
Otto
M.
2012
.
Composite analysis of black duck breeding population surveys in eastern North America
.
Journal of Wildlife Management
76
:
1165
1176
.
Zuur
AF.
Ieno
EN.
Walker
NJ.
Savaliev
AA.
Smith
GM.
2009
.
Mixed effects models and extensions in ecology in R
.
New York
:
Springer Science+Business Media
.
Zuur
AF.
Hilbe
JM.
Ieno
EN.
2013
.
A beginner's guide to GLM and GLMM with R
.
Newburgh, UK
:
Highland Statistics Ltd
.
Zuur
AF.
Savaliev
AA.
Ieno
EN.
2012
.
Zero-inflated models and generalized linear mixed models with R
.
Newburgh, UK
:
Highland Statistics Ltd
.

Author notes

Citation: Robertson GJ, Tomlik M, Milton GR, Parsons GJ, Mallory ML. 2017. Increases in the number of American black ducks wintering in Nova Scotia, 1970–2015. Journal of Fish and Wildlife Management 8(2):669-675; e1944-687X. doi: 10.3996/032017-JFWM-031

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.

Supplementary data