Adaptive harvest management 2010 duck hunting season

              U.S. Fish and Wildlife Service
Adaptive Harvest
Management
2010 Hunting Season
Adaptive
Harvest
Management
2010 Hunting Season
PREFACE
The process of setting waterfowl hunting regulations is conducted annually in the United States (Blohm 1989).
This process involves a number of meetings where the status of waterfowl is reviewed by the agencies respon-
sible for setting hunting regulations. In addition, the U. S. Fish and Wildlife Service (USFWS) publishes
proposed regulations in the Federal Register to allow public comment. This document is part of a series of
reports intended to support development of harvest regulations for the 2010 hunting season. Speci cally, this
report is intended to provide waterfowl managers and the public with information about the use of adaptive
harvest management (AHM) for setting waterfowl hunting regulations in the United States. This report
provides the most current data, analyses, and decision-making protocols. However, adaptive management is
a dynamic process and some information presented in this report will di er from that in previous reports.
Citation: U. S. Fish and Wildlife Service. 2010. Adaptive Harvest Management: 2010 Hunting Sea-
son. U. S. Department of Interior, Washington, D. C. 59 pp. Available online at http://www.fws.gov/
migratorybirds/mgmt/AHM/AHM-intro.htm
ACKNOWLEDGMENTS
A working group comprised of representatives from the USFWS, the U. S. Geological Survey (USGS), the
Canadian Wildlife Service (CWS), and the four Flyway Councils (Appendix A) was established in 1992 to
review the scienti c basis for managing waterfowl harvests. The working group, supported by technical
experts from the waterfowl management and research communities, subsequently proposed a framework for
adaptive harvest management, which was  rst implemented in 1995. The USFWS expresses its gratitude
to the AHM Working Group and to the many other individuals, organizations, and agencies that have
contributed to the development and implementation of AHM.
This report was prepared by the USFWS Division of Migratory Bird Management. G. S. Boomer and
T. A. Sanders were the principal authors. Individuals that provided essential information or otherwise as-
sisted with report preparation were G. Zimmerman (USFWS), N. Zimpfer (USFWS), M. Kone  (USFWS),
K. Richkus (USFWS), J. Klimstra (USFWS), E. Silverman (USFWS), K. Magruder (USFWS) and P. Gar-
rettson (USFWS). Comments regarding this document should be sent to the Chief, Division of Migratory
Bird Management-USFWS, 4401 North Fairfax Drive, MS MSP-4107, Arlington, VA 22203.
We are grateful for the continuing technical support from F. A. Johnson, M. C. Runge, and J. A. Royle
(USGS), and acknowledge that information provided by USGS in this report has not received the Director's
approval and, as such, is provisional and subject to revision.
Cover art: 2010 Federal Duck stamp artist Robert Bealle's painting of an American Wigeon (Anas ameri-
cana).
2
TABLE OF CONTENTS
1 EXECUTIVE SUMMARY 6
2 BACKGROUND 7
3 MALLARD STOCKS AND FLYWAY MANAGEMENT 8
4 MALLARD POPULATION DYNAMICS 9
4.1 Mid-Continent Stock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
4.2 Eastern Stock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
4.3 Western Stock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
5 HARVEST-MANAGEMENT OBJECTIVES 14
6 REGULATORY ALTERNATIVES 14
6.1 Evolution of Alternatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
6.2 Regulation-Speci c Harvest Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
7 OPTIMAL REGULATORY STRATEGIES 18
8 APPLICATION OF AHM CONCEPTS TO OTHER STOCKS 19
8.1 Northern Pintails . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
8.2 Scaup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
9 EMERGING ISSUES IN AHM 24
LITERATURE CITED 25
A AHM WORKING GROUP 28
B MID-CONTINENT MALLARD MODELS 32
C EASTERN MALLARD MODELS 36
D WESTERN MALLARD MODELS 40
E MODELING MALLARD HARVEST RATES 46
F NORTHERN PINTAIL MODELS 51
G SCAUP MODEL 55
3
LIST OF FIGURES
1 Survey areas currently assigned to the mid-continent, eastern, and western stocks of mallards
for the purposes of AHM. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2 Population estimates of mid-continent mallards observed in the WBPHS and the Great Lakes
region. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3 Top panel: population estimates of mid-continent mallards observed in the WBPHS com-
pared to mid-continent mallard model set predictions from 1996 to 2010. Bottom panel: mid-
continent mallard model weights (SaRw = additive mortality and weakly density-dependent
reproduction, ScRw = compensatory mortality and weakly density-dependent reproduction,
SaRs = additive mortality and strongly density-dependent reproduction,ScRs = compensatory
mortality and strongly density-dependent reproduction). . . . . . . . . . . . . . . . . . . . . . 10
4 Population estimates of eastern mallards observed in the northeastern states (AFBWS) and
in southern Ontario and Quebec. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
5 Top panel: observed population estimates of eastern mallards compared to eastern mallard
model set predictions from 1997 to 2010. Bottom panel: eastern mallard model weights
(RsR = strong density-dependent reproduction and biased reproductive rates, RwR = weak
density-dependent reproduction and biased reproductive rates, RsS = strong density-dependent
reproduction and biased survival rates, RwS = weak density-dependent reproduction and bi-
ased survival rates, and Rs0 = strong-dependent reproduction and no model bias, Rw0 = weak
density-dependent reproduction and no model bias). . . . . . . . . . . . . . . . . . . . . . . . 12
6 Population estimates of western mallards observed in Alaska, California and Oregon (state
surveys) combined. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
F.1 Harvest yield curves resulting from an equilibrium analysis of the northern pintail model set
based on 2010 model weights. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4
LIST OF TABLES
1 Regulatory alternatives for the 2010 duck-hunting season. . . . . . . . . . . . . . . . . . . . . 15
2 Predictions of harvest rates of adult-male mid-continent mallards expected with application of
the 2010 regulatory alternatives in the Mississippi and Central Flyways. . . . . . . . . . . . . 16
3 Predictions of harvest rates of adult-male eastern mallards expected with application of the
2010 regulatory alternatives in the Atlantic Flyway. . . . . . . . . . . . . . . . . . . . . . . . . 17
4 Predictions of harvest rates of adult-male western mallards expected with application of the
2010 regulatory alternatives in the Paci c Flyway. . . . . . . . . . . . . . . . . . . . . . . . . 18
5 Optimal regulatory strategy for the Mississippi and Central Flyways for the 2010 hunting
season. This strategy is based on current regulatory alternatives (including the closed-season
constraint), mid-continent mallard models and weights, and the dual objectives of maximizing
long-term cumulative harvest and achieving a population goal of 8.5 million mallards. . . . . 19
6 Optimal regulatory strategy for the Atlantic Flyway for the 2010 hunting season. This strat-
egy is based on current regulatory alternatives, eastern mallard models and weights, and an
objective to maximize long-term cumulative harvest. . . . . . . . . . . . . . . . . . . . . . . . 19
7 Optimal regulatory strategy for the Paci c Flyway during the 2010 hunting season. This strat-
egy is based on the 2010 regulatory alternatives, current (1990{2009) western mallard popu-
lation models and parameter estimates, and an objective to maximize long-term cumulative
harvest subject to a constraint intended to prevent extreme changes in regulations associated
with relatively small changes in population sizes. . . . . . . . . . . . . . . . . . . . . . . . . . 20
8 Total pintail harvest expected from the set of regulatory alternatives speci ed for each Flyway
under the northern pintail adaptive harvest management protocol. . . . . . . . . . . . . . . . 21
9 Substitution rules in the Central and Mississippi Flyways for joint implementation of northern
pintail and mallard harvest strategies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
10 Northern pintail optimal regulatory strategy for all 4 Flyways for the 2010 hunting season. This
strategy is based on current regulatory alternatives (including the closed-season constraint),
northern pintail models and weights, and the objective of maximizing long-term cumulative
harvest. The shaded cell indicates the regulatory prescription for 2010. . . . . . . . . . . . . . 22
11 Optimal scaup harvest levels and corresponding breeding population sizes. This strategy is
based on the current scaup population model, and an objective to achieve 95% of long-term
cumulative harvest. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
B.1 Estimates (N) and associated standard errors (SE) of mid-continent mallards observed in the
WBPHS and the Great Lakes region. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
C.1 Estimates (N) and associated standard errors (SE) of eastern mallards observed in the north-
eastern U.S. (AFBWS) and southern Ontario and Quebec. . . . . . . . . . . . . . . . . . . . . 36
D.1 Estimates (N) and associated standard errors (SE) of mallards observed in Alaska and Cali-
fornia and Oregon (state surveys) combined. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
D.2 Estimates of model parameters resulting from  tting a discrete logistic model with MCMC to
a time series of estimated population sizes and harvest rates of mallards breeding in Alaska,
1990{2009. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
D.3 Estimates of model parameters resulting from  tting a discrete logistic model with MCMC to
a time-series of estimated population sizes and harvest rates of mallards breeding in California
and Oregon, 1992{2009. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
E.1 Parameter estimates for predicting mid-continent mallard harvest rates resulting from a hier-
archical, Bayesian analysis of mid-continent mallard banding and recovery information from
1998{2009. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
E.2 Parameter estimates for predicting eastern mallard harvest rates resulting from a hierarchical,
Bayesian analysis of eastern mallard banding and recovery information from 2002{2009. . . . 49
E.3 Parameter estimates for predicting western mallard harvest rates resulting from a hierarchical,
Bayesian analysis of western mallard banding and recovery information from 2008{2009. . . . 50
G.1 Model parameter estimates resulting from a Bayesian analysis of scaup breeding population,
harvest, and banding information from 1974{2009. . . . . . . . . . . . . . . . . . . . . . . . . 58
5
1 EXECUTIVE SUMMARY
In 1995 the U.S. Fish and Wildlife Service (USFWS) implemented the Adaptive Harvest Management (AHM)
program for setting duck hunting regulations in the United States. The AHM approach provides a framework
for making objective decisions in the face of incomplete knowledge concerning waterfowl population dynamics
and regulatory impacts.
The AHM protocol is based on the population dynamics and status of three mallard (Anas platyrhynchos)
stocks. Mid-continent mallards are de ned as those breeding in the Waterfowl Breeding Population and
Habitat Survey (WBPHS) strata 13{18, 20{50, and 75{77 plus mallards breeding in the states of Michigan,
Minnesota, and Wisconsin (state surveys). The prescribed regulatory alternative for the Mississippi and
Central Flyways depends exclusively on the status of these mallards. Eastern mallards are de ned as those
breeding in WBPHS strata 51{54 and 56 and breeding in the states of Virginia northward into New Hampshire
(Atlantic Flyway Breeding Waterfowl Survey [AFBWS]). The regulatory choice for the Atlantic Flyway
depends exclusively on the status of these mallards. Western mallards are de ned as those birds breeding in
WBPHS strata 1{12 (hereafter Alaska) and those birds breeding in the states of California and Oregon (state
surveys). The regulatory choice for the Paci c Flyway depends exclusively on the status of these mallards.
Mallard population models are based on the best available information and account for uncertainty in popula-
tion dynamics and the impact of harvest. Model-speci c weights re
ect the relative con dence in alternative
hypotheses and are updated annually using comparisons of predicted and observed population sizes. For
mid-continent mallards, current model weights favor the weakly density-dependent reproductive hypothesis
(89%) and suggest some preference for the additive-mortality hypothesis (62%). For eastern mallards, vir-
tually all of the weight is on models that have corrections for bias in estimates of survival or reproductive
rates. Current model weights provide some support for the weakly density-dependent reproductive hypothesis
(65%). By consensus, hunting mortality is assumed to be additive in eastern mallards. Unlike mid-continent
and eastern mallards, we consider a single functional form to predict western mallard population dynamics
but consider a wide range of parameter values each weighted relative to the support from the data.
For the 2010 hunting season, the USFWS is considering the same regulatory alternatives as last year. The
nature of the restrictive, moderate, and liberal alternatives has remained essentially unchanged since 1997,
except that extended framework dates have been o ered in the moderate and liberal alternatives since 2002.
Harvest rates associated with each of the regulatory alternatives have been updated based on band-reporting
rate studies conducted since 1998. The expected harvest rates of adult males under liberal hunting seasons
are 0.117 (SD = 0.020), 0.148 (SD = 0.042), and 0.115 (SD = 0.031) for mid-continent, eastern, and western
mallards, respectively.
Optimal regulatory strategies for the 2010 hunting season were calculated using: (1) harvest-management
objectives speci c to each mallard stock; (2) the 2010 regulatory alternatives; and (3) current population
models. Based on this year's survey results of 8.60 million mid-continent mallards, 3.73 million ponds in
Prairie Canada, 0.763 million eastern mallards, and 1.05 million western mallards in Alaska (0.606 million) and
California-Oregon (0.443 million), the optimal choice for all four 
yways is the liberal regulatory alternative.
AHM concepts and tools are also being applied to help improve harvest management for several other water-
fowl stocks. In the last year, signi cant progress has been made to adopt an adaptive management protocol
to inform northern pintail (Anas acuta) harvest decisions for 2010. In addition, we continue to update our
understanding of the harvest potential of scaup (Aythya a nis, A. marila) as this decision making framework
continues to evolve with feedback from annual monitoring information.
6
2 BACKGROUND
The annual process of setting duck-hunting regulations in the United States is based on a system of resource
monitoring, data analyses, and rule-making (Blohm 1989). Each year, monitoring activities such as aerial
surveys and hunter questionnaires provide information on population size, habitat conditions, and harvest
levels. Data collected from this monitoring program are analyzed each year, and proposals for duck-hunting
regulations are developed by the Flyway Councils, States, and USFWS. After extensive public review, the
USFWS announces regulatory guidelines within which States can set their hunting seasons.
In 1995, the USFWS adopted the concept of adaptive resource management (Walters 1986) for regulating
duck harvests in the United States. This approach explicitly recognizes that the consequences of hunting
regulations cannot be predicted with certainty and provides a framework for making objective decisions in
the face of that uncertainty (Williams and Johnson 1995). Inherent in the adaptive approach is an awareness
that management performance can be maximized only if regulatory e ects can be predicted reliably. Thus,
adaptive management relies on an iterative cycle of monitoring, assessment, and decision-making to clarify
the relationships among hunting regulations, harvests, and waterfowl abundance.
In regulating waterfowl harvests, managers face four fundamental sources of uncertainty (Nichols et al. 1995a,
Johnson et al. 1996, Williams et al. 1996):
(1) environmental variation { the temporal and spatial variation in weather conditions and other key
features of waterfowl habitat; an example is the annual change in the number of ponds in the Prairie
Pothole Region, where water conditions in
uence duck reproductive success;
(2) partial controllability { the ability of managers to control harvest only within limits; the harvest resulting
from a particular set of hunting regulations cannot be predicted with certainty because of variation in
weather conditions, timing of migration, hunter e ort, and other factors;
(3) partial observability { the ability to estimate key population attributes (e.g., population size, reproduc-
tive rate, harvest) only within the precision a orded by extant monitoring programs; and
(4) structural uncertainty { an incomplete understanding of biological processes; a familiar example is
the long-standing debate about whether harvest is additive to other sources of mortality or whether
populations compensate for hunting losses through reduced natural mortality. Structural uncertainty
increases contentiousness in the decision-making process and decreases the extent to which managers
can meet long-term conservation goals.
AHM was developed as a systematic process for dealing objectively with these uncertainties. The key com-
ponents of AHM include (Johnson et al. 1993, Williams and Johnson 1995):
(1) a limited number of regulatory alternatives, which describe Flyway-speci c season lengths, bag limits,
and framework dates;
(2) a set of population models describing various hypotheses about the e ects of harvest and environmental
factors on waterfowl abundance;
(3) a measure of reliability (probability or \weight") for each population model; and
(4) a mathematical description of the objective(s) of harvest management (i.e., an \objective function"),
by which alternative regulatory strategies can be compared.
These components are used in a stochastic optimization procedure to derive a regulatory strategy. A regula-
tory strategy speci es the optimal regulatory choice, with respect to the stated management objectives, for
each possible combination of breeding population size, environmental conditions, and model weights (Johnson
et al. 1997). The setting of annual hunting regulations then involves an iterative process:
7
(1) each year, an optimal regulatory choice is identi ed based on resource and environmental conditions,
and on current model weights;
(2) after the regulatory decision is made, model-speci c predictions for subsequent breeding population size
are determined;
(3) when monitoring data become available, model weights are increased to the extent that observations of
population size agree with predictions, and decreased to the extent that they disagree; and
(4) the new model weights are used to start another iteration of the process.
By iteratively updating model weights and optimizing regulatory choices, the process should eventually
identify which model is the best overall predictor of changes in population abundance. The process is optimal
in the sense that it provides the regulatory choice each year necessary to maximize management performance.
It is adaptive in the sense that the harvest strategy evolves to account for new knowledge generated by a
comparison of predicted and observed population sizes.
3 MALLARD STOCKS AND FLYWAY MANAGEMENT
Since its inception AHM has focused on the population dynamics and harvest potential of mallards, especially
those breeding in mid-continent North America. Mallards constitute a large portion of the total U.S. duck
harvest, and traditionally have been a reliable indicator of the status of many other species. As management
capabilities have grown, there has been increasing interest in the ecology and management of breeding mallards
that occur outside the mid-continent region. Geographic di erences in the reproduction, mortality, and
migrations of mallard stocks suggest that there may be corresponding di erences in optimal levels of sport
harvest. The ability to regulate harvests of mallards originating from various breeding areas is complicated,
however, by the fact that a large degree of mixing occurs during the hunting season. The challenge for
managers, then, is to vary hunting regulations among Flyways in a manner that recognizes each Flyway's
unique breeding-ground derivation of mallards. Of course, no Flyway receives mallards exclusively from one
breeding area; therefore, Flyway-speci c harvest strategies ideally should account for multiple breeding stocks
that are exposed to a common harvest.
The optimization procedures used in AHM can account for breeding populations of mallards beyond the
mid-continent region, and for the manner in which these ducks distribute themselves among the Flyways
during the hunting season. An optimal approach would allow for Flyway-speci c regulatory strategies, which
represent an average of the optimal harvest strategies for each contributing breeding stock weighted by the
relative size of each stock in the fall 
ight. This joint optimization of multiple mallard stocks requires:
(1) models of population dynamics for all recognized stocks of mallards; (2) an objective function that
accounts for harvest-management goals for all mallard stocks in the aggregate; and (3) decision rules allowing
Flyway-speci c regulatory choices.
Currently, three stocks of mallards are o cially recognized for the purposes of AHM (Figure 1). We use a
constrained approach to the optimization of these stocks' harvest, in which the Atlantic Flyway regulatory
strategy is based exclusively on the status of eastern mallards, the regulatory strategy for the Mississippi
and Central Flyways is based exclusively on the status of mid-continent mallards, and the Paci c Flyway
regulatory strategy is based exclusively on the status of western mallards. This approach has been determined
to perform nearly as well as a joint-optimization because mixing of the three stocks during the hunting season
is limited and because of the constraints imposed by management objectives and regulatory alternatives.
8
Figure 1 { Survey areas currently assigned to the mid-continent, eastern, and western stocks of mallards for the
purposes of AHM.
4 MALLARD POPULATION DYNAMICS
4.1 Mid-Continent Stock
Mid-continent mallards are de ned as those breeding in WBPHS strata 13{18, 20{50, and 75{77, and in
the Great Lakes region (Michigan, Minnesota, and Wisconsin; see Figure 1). Estimates of the size of
this population are available since 1992, and have varied from 6.4 to 11.2 million (Table B.1, Figure 2).
Estimated breeding-population size in 2010 was 8.60 million (SE = 0.29 million), including 7.82 million
(SE = 0.28 million) from the WBPHS and 0.780 million (SE = 0.059 million) from the Great Lakes region.
Details describing the set of population models for mid-continent mallards are provided in Appendix B. The
set consists of four alternatives, formed by the combination of two survival hypotheses (additive vs. compen-
satory hunting mortality) and two reproductive hypotheses (strongly vs. weakly density dependent). Relative
weights for the alternative models of mid-continent mallards changed little until all models under-predicted
the change in population size from 1998 to 1999, perhaps indicating there is a signi cant factor a ecting
population dynamics that is absent from all four models (Figure 3). Updated model weights suggest some
preference for the additive-mortality models (62%) over those describing hunting mortality as compensatory
(38%). For most of the time frame, model weights have strongly favored the weakly density-dependent re-
productive models over the strongly density-dependent ones, with current model weights of 89% and 11%,
respectively. The reader is cautioned, however, that models can sometimes make reliable predictions of pop-
ulation size for reasons having little to do with the biological hypotheses expressed therein (Johnson et al.
2002b).
9
1995 2000 2005 2010
0 2 4 6 8 10 12
Year
Population Size (millions)
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
Total
WBPHS Survey
Great Lakes
Figure 2 { Population estimates of mid-continent mallards observed in the WBPHS (strata: 13{18, 20{50, and
75{77) and the Great Lakes region (Michigan, Minnesota, and Wisconsin). Error bars represent one standard
error.
6 7 8 9 10
Year
Population Size (millions)
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l l
l
l
l
l
l
l
Observed
Predicted
1995 2000 2005 2010
0.0 0.2 0.4 0.6
Year
Model Weights
l l l l
l l l l
l l l l l l
l l
l
SaRw
ScRw
SaRs
ScRs
Year
Figure 3 { Top panel: population estimates of mid-continent mallards observed in the WBPHS compared to
mid-continent mallard model set predictions (weighted average based on 2010 model weights) from 1996 to 2010.
Error bars represent 95% con dence intervals. Bottom panel: mid-continent mallard model weights (SaRw =
additive mortality and weakly density-dependent reproduction, ScRw = compensatory mortality and weakly
density-dependent reproduction, SaRs = additive mortality and strongly density-dependent reproduction,ScRs
= compensatory mortality and strongly density-dependent reproduction). Model weights were assumed to be
equal in 1995.
10
4.2 Eastern Stock
Eastern mallards are de ned as those breeding in southern Ontario and Quebec (WBPHS strata 51{54 and
56) and in the northeastern U.S. (AFBWS; Heusmann and Sauer 2000, see Figure 1). Estimates of population
size have varied from 0.76 to 1.1 million since 1990, with the majority of the population accounted for in
the northeastern U.S. (Table C.1, Figure 4). For 2010, the estimated breeding-population size of eastern
mallards was 0.763 million (SE = 0.053 million), including 0.653 million (SE = 0.049 million) from the
northeastern U.S. and 0.110 million (SE = 0.021 million) from the WBPHS. The reader is cautioned that these
estimates di er from those reported in the USFWS annual waterfowl trend and status reports, which include
composite estimates based on more  xed-wing strata in eastern Canada and helicopter surveys conducted by
the Canadian Wildlife Service (CWS).
Details concerning the set of population models for eastern mallards are provided in Appendix C. The set
consists of six alternatives, formed by the combination of two reproductive hypotheses (strongly vs. weakly
density dependent) and three hypotheses concerning bias in estimates of survival and reproductive rates (no
bias vs. biased survival rates vs. biased reproductive rates). With respect to model weights, there is no single
model that is clearly favored over the others at the current time. Collectively, current model weights provide
some support for the weakly density-dependent reproductive hypotheses 65% compared to the strongly density
dependent reproductive hypotheses 35% (Figure 5). In addition, there is overwhelming evidence of bias in
extant estimates of survival or reproductive rates, assuming that survey estimates are unbiased.
1990 1995 2000 2005 2010 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
Year Population Size (millions)
l
l
l
l
l
l
l
l
l
l
l
l l
l l l
l
l
l
l
l
l
Total
AFBWS
WBPHS
Figure 4 { Population estimates of eastern mallards observed in the northeastern states (AFBWS) and in
southern Ontario and Quebec (WBPHS strata 51{54 and 56). Error bars represent one standard error.
11
0.6 0.8 1.0 1.2 1.4
Year
Population Size (millions)
l
l
l
l
l
l l l
l
l
l l
l
l
l
l
l l
l
l
l
l
l
l
l
l
l
l
l
l
Observed
Predicted
1996 1998 2000 2002 2004 2006 2008 2010
0.0 0.1 0.2 0.3 0.4
Year
Model Weights
l
l l
l
l
l l
l
l l
l
l
l l
l
l l l
l l l l l l l l l l l
l
l
RsR
RwR
RsS
RwS
Rs0
Rw0
Year
Figure 5 { Top panel: observed population estimates of eastern mallards compared to eastern mallard model
set predictions (weighted average based on 2010 model weights) from 1997 to 2010. Error bars represent 95%
con dence intervals. Bottom panel: eastern mallard model weights (RsR = strong density-dependent reproduc-
tion and biased reproductive rates, RwR = weak density-dependent reproduction and biased reproductive rates,
RsS = strong density-dependent reproduction and biased survival rates, RwS = weak density-dependent repro-
duction and biased survival rates, and Rs0 = strong-dependent reproduction and no model bias, Rw0 = weak
density-dependent reproduction and no model bias). Model weights were assumed to be equal in 1996.
4.3 Western Stock
Western mallards consist of 2 substocks and are de ned as those birds breeding in Alaska (WBPHS strata
1{12) and those birds breeding in California and Oregon (state surveys; see Figure 1). Estimates of the size of
these subpopulations have varied from 0.283 to 0.843 million in Alaska since 1990 and 0.355 to 0.694 million
in California and Oregon since 1992 (Table D.1, Figure 6). The total population size of western mallards has
ranged from 0.748 to 1.407 million. For 2010, the estimated breeding-population size of western mallards was
1.049 million (SE = 0.077 million), including 0.443 million (SE = 0.056 million) from California and Oregon
and 0.606 million (SE = 0.053 million) from Alaska.
Ideally, the western mallard stock assessment would account for mallards breeding in the states of the Paci c
Flyway (including Alaska), British Columbia, and the Yukon Territory. However, we have had continuing
concerns about our ability to determine changes in population size based on the collection of surveys con-
ducted independently by Paci c Flyway States and the CWS in British Columbia. These surveys tend to
vary in design and intensity, and in some cases lack measures of precision. We reviewed extant surveys to de-
termine their adequacy for supporting a western-mallard AHM protocol and selected Alaska, California, and
Oregon for modeling purposes. These three states likely harbor about 75% of the western-mallard breeding
population. Nonetheless, this geographic delineation is considered temporary until surveys in other areas can
be brought up to similar standards and an adequate record of population estimates is available for analysis.
Details concerning the set of population models for western mallards are provided in Appendix D. To pre-
dict changes in abundance we relied on a discrete logistic model, which combines reproduction and natural
mortality into a single parameter, r, the intrinsic rate of growth. This model assumes density-dependent
growth, which is regulated by the ratio of population size, N, to the carrying capacity of the environment,
12
1995 2000 2005 2010
0.0 0.5 1.0 1.5
Year
Population Size (millions)
l
l
l
l l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
Total
AK
CA−OR
Figure 6 { Population estimates of western mallards observed in Alaska (WBPHS strata 1{12), California and
Oregon (state surveys) combined. Error bars represent one standard error.
K (i.e., equilibrium population size in the absence of harvest). In the traditional formulation of the logistic
model, harvest mortality is completely additive and any compensation for hunting losses occurs as a result
of density-dependent responses beginning in the subsequent breeding season. To increase the model's gener-
ality we included a scaling parameter for harvest that allows for the possibility of compensation prior to the
breeding season. It is important to note, however, that this parameterization does not incorporate any hy-
pothesized mechanism for harvest compensation and, therefore, must be interpreted cautiously. We modeled
Alaska mallards independently of those in California and Oregon because of di ering population trajectories
(see Figure 6) and substantial di erences in the distribution of band recoveries.
We used Bayesian estimation methods in combination with a state-space model that accounts explicitly for
both process and observation error in breeding population size (Meyer and Millar 1999). Breeding population
estimates of mallards in Alaska are available since 1955, but we had to limit the time series to 1990{2009
because of changes in survey methodology and insu cient band-recovery data. The logistic model and
associated posterior parameter estimates provided a reasonable  t to the observed time series of Alaska
population estimates. The estimated mean carrying capacity was 1.13 million, the intrinsic rate of growth
was 0.31, while the scaling parameter estimate suggests that harvest mortality may be additive. Breeding
population and harvest-rate data were available for California and Oregon mallards for the period 1992{2008.
The logistic model also provided a reasonable  t to these data, suggesting a mean carrying capacity of
0.64 million, an intrinsic rate of growth of 0.33, while the scaling parameter estimate suggests that harvest
mortality may be only partially additive.
Ideally, the development of AHM protocols for mallards would consider how di erent breeding stocks dis-
tribute themselves among the four Flyways so that Flyway-speci c harvest strategies could account for the
mixing of birds during the hunting season. At present, however, a joint optimization of western, mid-continent,
and eastern stocks is not feasible due to computational hurdles. However, our preliminary analyses suggest
that the lack of a joint optimization does not result in a signi cant decrease in performance. Therefore, the
AHM protocol for western mallards is structured similarly to that used for eastern mallards, in which an
optimal harvest strategy is based on the status of a single breeding stock and harvest regulations in a single

yway. Although the contribution of mid-continent mallards to the Paci c Flyway harvest is signi cant, we
13
believe an independent harvest strategy for western mallards poses little risk to the mid-continent stock.
Further analyses will be needed to con rm this conclusion, and to better understand the potential e ect of
mid-continent mallard status on sustainable hunting opportunities in the Paci c Flyway.
5 HARVEST-MANAGEMENT OBJECTIVES
The basic harvest-management objective for mid-continent mallards is to maximize cumulative harvest over
the long term, which inherently requires perpetuation of a viable population. Moreover, this objective is
constrained to avoid regulations that could be expected to result in a subsequent population size below the
goal of the North American Waterfowl Management Plan (NAWMP). According to this constraint, the value
of harvest decreases proportionally as the di erence between the goal and expected population size increases.
This balance of harvest and population objectives results in a regulatory strategy that is more conservative
than that for maximizing long-term harvest, but more liberal than a strategy to attain the NAWMP goal
(regardless of e ects on hunting opportunity). The current objective for mid-continent mallards uses a
population goal of 8.5 million birds, which consists of 7.9 million mallards from the WBPHS (strata 13{18,
20{50, and 75{77) corresponding to the mallard population goal in the 1998 update of the NAWMP (less the
portion of the mallard goal comprised of birds breeding in Alaska) and a goal of 0.6 million for the combined
states of Michigan, Minnesota, and Wisconsin.
For eastern and western mallards, there is no NAWMP goal or other established target for desired population
size. Accordingly, the management objective for eastern and western mallards is simply to maximize long-term
cumulative (i.e., sustainable) harvest. Additionally for western mallards, maximum long-term cumulative
harvest is subject to a constraint intended to prevent extreme changes in regulations associated with relatively
small changes in population sizes.
6 REGULATORY ALTERNATIVES
6.1 Evolution of Alternatives
When AHM was  rst implemented in 1995, three regulatory alternatives characterized as liberal, moderate,
and restrictive were de ned based on regulations used during 1979{84, 1985{87, and 1988{93, respectively.
These regulatory alternatives also were considered for the 1996 hunting season. In 1997, the regulatory
alternatives were modi ed to include: (1) the addition of a very-restrictive alternative; (2) additional days
and a higher duck bag limit in the moderate and liberal alternatives; and (3) an increase in the bag limit of
hen mallards in the moderate and liberal alternatives. In 2002, the USFWS further modi ed the moderate
and liberal alternatives to include extensions of approximately one week in both the opening and closing
framework dates.
In 2003, the very-restrictive alternative was eliminated at the request of the Flyway Councils. Expected
harvest rates under the very-restrictive alternative did not di er signi cantly from those under the restrictive
alternative, and the very-restrictive alternative was expected to be prescribed for <5% of all hunting seasons.
Also in 2003, at the request of the Flyway Councils the USFWS agreed to exclude closed duck-hunting seasons
from the AHM protocol when the population size of mid-continent mallards was  5.5 million (WBPHS
strata 1{18, 20{50, and 75{77 plus the Great Lakes region). Based on our original assessment, closed hunting
seasons did not appear to be necessary from the perspective of sustainable harvesting when the mid-continent
mallard population exceeded this level. The impact of maintaining open seasons above this level also appeared
negligible for other mid-continent duck species, as based on population models developed by Johnson (2003).
In 2008, because of the re-de nition of the mid-continent mallard stock that excludes mallards breeding in
Alaska, we re-scaled the closed-season constraint. Initially, we attempted to adjust the original 5.5 million
14
Table 1 { Regulatory alternatives for the 2010 duck-hunting season.
Flyway
Regulation Atlantica Mississippi Centralb Paci cc
Shooting Hours one-half hour before sunrise to sunset
Framework Dates
Restrictive Oct 1{Jan 20 Saturday nearest Oct 1 to the Sunday nearest Jan 20
Moderate
Saturday nearest September 24 to the last Sunday in January
Liberal
Season Length (days)
Restrictive 30 60 39 60
Moderate 45 45 60 86
Liberal 60 60 74 107
Bag Limit (total / mallard / hen mallard)
Restrictive 3 / 3 / 1 3 / 2 / 1 3 / 3 / 1 4 / 3 / 1
Moderate 6 / 4 / 2 6 / 4 / 1 6 / 5 / 1 7 / 5 / 2
Liberal 6 / 4 / 2 6 / 4 / 2 6 / 5 / 2 7 / 7 / 2
a The states of Maine, Massachusetts, Connecticut, Pennsylvania, New Jersey, Maryland, Delaware, West
Virginia, Virginia, and North Carolina are permitted to exclude Sundays, which are closed to hunting, from
their total allotment of season days.
b The High Plains Mallard Management Unit is allowed 12, 23, and 23 extra days in the restrictive, moderate,
and liberal alternatives, respectively.
c The Columbia Basin Mallard Management Unit is allowed seven extra days in the restrictive and moderate
alternatives.
closure threshold by subtracting out the 1985 Alaska breeding population estimate, which was the year upon
which the original closed season constraint was based. Our initial re-scaling resulted in a new threshold equal
to 5.25 million. Simulations based on optimal policies using this revised closed season constraint suggested
that the Mississippi and Central Flyways would experience a 70% increase in the frequency of closed seasons.
At this time, we agreed to consider alternative re-scalings in order to minimize the e ects on the mid-continent
mallard strategy and account for the increase in mean breeding population sizes in Alaska over the past several
decades. Based on this assessment, we recommended a revised closed season constraint of 4.75 million which
resulted in a strategy performance equivalent to the performance expected prior to the re-de nition of the
mid-continent mallard stock. Because the performance of the revised strategy is essentially unchanged from
the original strategy, we believe it will have no greater impact on other duck stocks in the Mississippi and
Central Flyways. However, complete- or partial-season closures for particular species or populations could
still be deemed necessary in some situations regardless of the status of mid-continent mallards. Details of
the regulatory alternatives for each Flyway are provided in Table 1.
6.2 Regulation-Specific Harvest Rates
Harvest rates of mallards associated with each of the open-season regulatory alternatives were initially pre-
dicted using harvest-rate estimates from 1979{84, which were adjusted to re
ect current hunter numbers and
contemporary speci cations of season lengths and bag limits. In the case of closed seasons in the U.S., we
assumed rates of harvest would be similar to those observed in Canada during 1988{93, which was a period
of restrictive regulations both in Canada and the U.S. All harvest-rate predictions were based only in part on
15
band-recovery data, and relied heavily on models of hunting e ort and success derived from hunter surveys
(Appendix C in U. S. Fish and Wildlife Service 2002). As such, these predictions had large sampling variances
and their accuracy was uncertain.
In 2002, we began relying on Bayesian statistical methods for improving regulation-speci c predictions of
harvest rates, including predictions of the e ects of framework-date extensions. Essentially, the idea is to
use existing (prior) information to develop initial harvest-rate predictions (as above), to make regulatory
decisions based on those predictions, and then to observe realized harvest rates. Those observed harvest
rates, in turn, are treated as new sources of information for calculating updated (posterior) predictions.
Bayesian methods are attractive because they provide a quantitative, formal, and an intuitive approach to
adaptive management.
For mid-continent mallards, we have empirical estimates of harvest rate from the recent period of liberal hunt-
ing regulations (1998{2009). The Bayesian methods thus allow us to combine these estimates with our prior
predictions to provide updated estimates of harvest rates expected under the liberal regulatory alternative.
Moreover, in the absence of experience (so far) with the restrictive and moderate regulatory alternatives, we
reasoned that our initial predictions of harvest rates associated with those alternatives should be re-scaled
based on a comparison of predicted and observed harvest rates under the liberal regulatory alternative. In
other words, if observed harvest rates under the liberal alternative were 10% less than predicted, then we
might also expect that the mean harvest rate under the moderate alternative would be 10% less than pre-
dicted. The appropriate scaling factors currently are based exclusively on prior beliefs about di erences in
mean harvest rate among regulatory alternatives, but they will be updated once we have experience with
something other than the liberal alternative. A detailed description of the analytical framework for modeling
mallard harvest rates is provided in Appendix E.
Our models of regulation-speci c harvest rates also allow for the marginal e ect of framework-date extensions
in the moderate and liberal alternatives. A previous analysis by the U. S. Fish and Wildlife Service (2001)
suggested that implementation of framework-date extensions might be expected to increase the harvest rate of
mid-continent mallards by about 15%, or in absolute terms by about 0.02 (SD = 0.01). Based on the observed
harvest rates during the 2002{2009 hunting seasons, the updated (posterior) estimate of the marginal change
in harvest rate attributable to the framework-date extension is 0.007 (SD = 0.007). The estimated e ect of
the framework-date extension has been to increase harvest rate of mid-continent mallards by about 6% over
what would otherwise be expected in the liberal alternative. However, the reader is strongly cautioned that
reliable inference about the marginal e ect of framework-date extensions ultimately depends on a rigorous
experimental design (including controls and random application of treatments).
Current predictions of harvest rates of adult-male mid-continent mallards associated with each of the regu-
latory alternatives are provided in Table 2. Predictions of harvest rates for the other age and sex cohorts are
based on the historical ratios of cohort-speci c harvest rates to adult-male rates (Runge et al. 2002). These
ratios are considered  xed at their long-term averages and are 1.5407, 0.7191, and 1.1175 for young males,
adult females, and young females, respectively. We make the simplifying assumption that the harvest rates
of mid-continent mallards depend solely on the regulatory choice in the Mississippi and Central Flyways.
The predicted harvest rates of eastern mallards are updated in the same fashion as that for mid-continent
Table 2 { Predictions of harvest rates of adult-male mid-continent mallards expected with application of the
2010 regulatory alternatives in the Mississippi and Central Flyways.
Regulatory alternative Mean SD
Closed (U.S.) 0.0088 0.0019
Restrictive 0.0562 0.0129
Moderate 0.1002 0.0216
Liberal 0.1165 0.0197
16
mallards based on reward banding conducted in eastern Canada and the northeastern U.S. (Appendix E).
Like mid-continent mallards, harvest rates of age and sex cohorts other than adult male mallards are based
on constant rates of di erential vulnerability as derived from band-recovery data. For eastern mallards,
these constants are 1.153, 1.331, and 1.509 for adult females, young males, and young females, respectively
(Johnson et al. 2002a). Regulation-speci c predictions of harvest rates of adult-male eastern mallards are
provided in Table 3.
Table 3 { Predictions of harvest rates of adult-male eastern mallards expected with application of the 2010
regulatory alternatives in the Atlantic Flyway.
Regulatory alternative Mean SD
Closed (U.S.) 0.0805 0.0232
Restrictive 0.1103 0.0392
Moderate 0.1361 0.0475
Liberal 0.1476 0.0418
In contrast to mid-continent mallards, framework-date extensions were expected to increase the harvest rate
of eastern mallards by only about 5% (U. S. Fish and Wildlife Service 2001), or in absolute terms by about
0.01 (SD = 0.01). Based on the observed harvest rates during the 2002{2009 hunting seasons, the updated
(posterior) estimate of the marginal change in harvest rate attributable to the framework-date extension is
0.003 (SD = 0.009). The estimated e ect of the framework-date extension has been to increase harvest rate
of eastern mallards by about 2% over what would otherwise be expected in the liberal alternative.
Based on available estimates of harvest rates of mallards banded in California and Oregon during 1990{1995
and 2002{2007, there was no apparent relationship between harvest rate and regulatory changes in the Paci c
Flyway. This is unusual given our ability to document such a relationship in other mallard stocks and in other
species. We note, however, that the period 2002{2007 was comprised of both stable and liberal regulations
and harvest rate estimates were based solely on reward bands. Regulations were relatively restrictive during
most of the earlier period and harvest rates were estimated based on standard bands using reporting rates
estimated from reward banding during 1987{1988. Additionally, 1993{1995 were transition years in which
full-address and toll-free bands were being introduced and information to assess their reporting rates (and
their e ects on reporting rates of standard bands) is limited. Thus, the two periods in which we wish to
compare harvest rates are characterized not only by changes in regulations, but also in estimation methods.
Consequently, we lack a sound empirical basis for predicting harvest rates of western mallards associated with
current regulatory alternatives in the Paci c Flyway. In 2009, we applied Bayesian statistical methods for
improving regulation-speci c predictions of harvest rates (see Appendix E). The methodology is analogous
to that currently in use for mid-continent and eastern mallards except that the marginal e ect of framework
date extensions in moderate and liberal alternatives is inestimable because there are no data prior to imple-
mentation of extensions. In 2008, we speci ed prior regulation-speci c harvest rates of 0.01, 0.06, 0.09, and
0.11 with associated standard deviations of 0.003, 0.02, 0.03, and 0.03 for the closed, restrictive, moderate,
and liberal alternatives, respectively. The harvest rates for the liberal alternative were based on empirical
estimates realized under the current liberal alternative during 2002{2007 and determined from adult-male
mallards banded with reward bands in California and Oregon. Harvest rates for the moderate and restrictive
alternatives were based on the proportional (0.85 and 0.51) di erence in harvest rates expected for mid-
continent mallards under the respective alternatives. And  nally, harvest rate for the closed alternative was
based on what we might realize with a closed season in the U.S. (including Alaska) and a very restrictive sea-
son in Canada, similar to that for mid-continent mallards. A relatively large standard deviation (CV = 0.3)
was chosen to re
ect greater uncertainty about the means than that for mid-continent mallards (CV = 0.2).
Current predictions (2010) of harvest rates of adult-male western mallards associated with each regulatory
alternative are provided in Table 4.
17
Table 4 { Predictions of harvest rates of adult-male western mallards expected with application of the 2010
regulatory alternatives in the Paci c Flyway.
Regulatory alternative Mean SD
Closed (U.S.) 0.0097 0.0182
Restrictive 0.0592 0.0163
Moderate 0.0984 0.0271
Liberal 0.1149 0.0306
7 OPTIMAL REGULATORY STRATEGIES
We calculated optimal regulatory strategies using stochastic dynamic programming (Lubow 1995, Johnson
and Williams 1999). For the Mississippi and Central Flyways, we based this optimization on: (1) the 2010
regulatory alternatives, including the closed-season constraint; (2) current population models and associated
weights for mid-continent mallards; and (3) the dual objectives of maximizing long-term cumulative harvest
and achieving a population goal of 8.5 million mid-continent mallards. The resulting regulatory strategy
(Table 5) is similar to that used last year. Note that prescriptions for closed seasons in this strategy represent
resource conditions that are insu cient to support one of the current regulatory alternatives, given current
harvest-management objectives and constraints. However, closed seasons under all of these conditions are not
necessarily required for long-term resource protection, and simply re
ect the NAWMP population goal and
the nature of the current regulatory alternatives. Assuming that regulatory choices adhered to this strategy
(and that current model weights accurately re
ect population dynamics), breeding-population size would be
expected to average 6.87 million (SD = 1.86 million). Based on an estimated population size of 8.60 million
mid-continent mallards and 3.73 million ponds in Prairie Canada, the optimal choice for the Mississippi and
Central Flyways in 2010 is the liberal regulatory alternative.
We calculated an optimal regulatory strategy for the Atlantic Flyway based on: (1) the 2010 regulatory
alternatives; (2) current population models and associated weights for eastern mallards; and (3) an objective
to maximize long-term cumulative harvest. The resulting strategy suggests liberal regulations for all popu-
lation sizes of record, and is characterized by a lack of intermediate regulations (Table 6). We simulated the
use of this regulatory strategy to determine expected performance characteristics. Assuming that harvest
management adhered to this strategy (and that current model weights accurately re
ect population dynam-
ics), breeding-population size would be expected to average 0.904 million (SD = 0.184 million). Based on an
estimated breeding population size of 0.763 million mallards, the optimal choice for the Atlantic Flyway in
2010 is the liberal regulatory alternative.
We calculated an optimal regulatory strategy for the Paci c Flyway based on: (1) the 2010 regulatory al-
ternatives, (2) current (1990{2009) population models and parameter estimates, and (3) an objective to
maximize long-term cumulative harvest subject to a constraint intended to prevent extreme changes in reg-
ulations associated with relatively small changes in population sizes (Table 7). We simulated the use of
this regulatory strategy to determine expected performance characteristics. Assuming that harvest man-
agement adhered to this strategy (and that current model parameters accurately re
ect population dynam-
ics), breeding-population size would be expected to average 1.05 million (SD = 0.18 million) in Alaska and
0.45 million (SD = 0.01 million) in California and Oregon. Based on an estimated breeding population size
of 0.606 million mallards in Alaska and 0.443 million in California and Oregon, the optimal choice for the
Paci c Flyway in 2010 is the liberal regulatory alternative (see Table 7).
18
Table 5 { Optimal regulatory strategya for the Mississippi and Central Flyways for the 2010 hunting season.
This strategy is based on current regulatory alternatives (including the closed-season constraint), mid-continent
mallard models and weights, and the dual objectives of maximizing long-term cumulative harvest and achieving
a population goal of 8.5 million mallards. The shaded cell indicates the regulatory prescription for 2010.
Pondsc
Bpopb 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0
 4.5 C C C C C C C C C C
4.75{5.75 R R R R R R R R R R
6 R R R R R R R R M M
6.25 R R R R R R M M M L
6.5 R R R R M M M L L L
6.75 R R R M L L L L L L
7 R M M M L L L L L L
7.25 M L L L L L L L L L
7.5 L L L L L L L L L L
 7.75 L L L L L L L L L L
a C = closed season, R = restrictive, M = moderate, L = liberal.
b Mallard breeding population size (in millions) in the WBPHS (strata 13{18, 20{50, 75{77) and Michigan, Minnesota, and
Wisconsin.
c Ponds (in millions) in Prairie Canada in May.
Table 6 { Optimal regulatory strategya for the Atlantic Flyway for the 2010 hunting season. This strategy
is based on current regulatory alternatives, eastern mallard models and weights, and an objective to maximize
long-term cumulative harvest. The shaded cell indicates the regulatory prescription for 2010.
Mallardsb Regulation
 0.350 C
0.375 R
 0.400 L
a C = closed season, R = restrictive, M = moderate, L = liberal.
b Estimated number of mallards (in millions) in eastern Canada (WBPHS strata 51{54, 56) and the northeastern
U.S. (AFBWS).
8 APPLICATION OF AHM CONCEPTS TO OTHER STOCKS
The USFWS is striving to apply the principles and tools of AHM to improve decision-making for several
other stocks of waterfowl. Over the last year, some progress has been made to develop AHM frameworks for
American black ducks (Anas rubripes) and the Atlantic Population of Canada geese (Branta canadensis),
but these results are not yet  nalized for inclusion in this year's report. As these frameworks are developed
further, we will continue to describe this work in subsequent reports. Below, we provide the 2010 updates
for two decision-making frameworks that are currently informing harvest management.
19
Table 7 { Optimal regulatory strategya for the Paci c Flyway during the 2010 hunting season. This strategy is
based on the 2010 regulatory alternatives, current (1990{2009) western mallard population models and parameter
estimates, and an objective to maximize long-term cumulative harvest subject to a constraint intended to prevent
extreme changes in regulations associated with relatively small changes in population sizes. The shaded cell
indicates the regulatory prescription for 2010.
Alaska BPOPb
CA{OR BPOPb 0 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50  0.55
0 C C L L L L L L L L L L
0.05 C C R R R M M M M L L L
0.10 C R R M M L L L L L L L
0.15 R R M M L L L L L L L L
0.20 M R M L L L L L L L L L
0.25 L R L L L L L L L L L L
0.30 L M L L L L L L L L L L
0.35 L M L L L L L L L L L L
0.40 L M L L L L L L L L L L
 0.45 L M L L L L L L L L L L
a C = closed season, R = restrictive, M = moderate, L = liberal.
b Estimated number of mallards (in millions) for Alaska (WBPHS strata 1{12) and in California and Oregon.
8.1 Northern Pintails
Over the past two years, scientists from the U.S. Geological Survey (USGS) and the USFWS, in consultation
with the Flyway Councils, have collaborated on the development of an adaptive management framework
to inform northern pintail (Anas acuta) harvest management. The proposed framework has been revised a
number of times in response to comments and feedback from the Flyways. For 2010, the Flyway Councils and
the USFWS agreed that the adaptive framework be adopted to inform pintail harvest management decisions.
The current, adaptive protocol is based on: (1) an explicit harvest management objective; (2) regulatory
alternatives that do not admit partial seasons or 3-bird daily bag limits; (3) a formal optimization process
using stochastic dynamic programming (Lubow 1995, Johnson and Williams 1999); (4) harvest allocation on
a national rather than Flyway-by-Flyway basis, with no explicit attempt to achieve a particular allocation
of harvest among Flyways; and (5) the same system models as the previous prescribed strategy. Details
describing the historical development of the technical and policy elements of the 2010 northern pintail harvest
strategy can be found in the northern pintail harvest strategy document (U. S. Fish and Wildlife Service
2010).
The harvest-management objective for the northern pintail population is to maximize long term cumulative
harvest, which inherently requires perpetuation of a viable population. This objective is speci ed under
a constraint that provides for an open hunting season when the observed breeding population is above
1.75 million birds (based on the lowest observed breeding population size since 1985 of 1.79 million birds in
2002).
The single objective and constraint, in conjunction with the regulatory options (see next section) were de-
termined after an intensive elicitation process with the waterfowl management community. The resulting
management objective serves to integrate and balance multiple competing objectives for pintail harvest man-
agement, including minimizing closed seasons, eliminating partial seasons (shorter pintail season within the
general duck season), maximizing seasons with liberal season length and greater than 1-bird daily bag limit,
20
and minimizing large changes in regulations. These multiple, competing objectives relate directly or indirectly
to more fundamental objectives that stakeholders have for pintail harvest management, which may include
the following (1) conserve pintail populations inde nitely (a legal requirement under the Migratory Bird
Treaty Act); (2) provide harvest opportunity; (3) minimize regulatory burden on the public; (4) encourage
hunter participation; and (5) provide for other non-consumptive uses.
The adaptive management protocol considers a range of regulatory alternatives for pintail harvest manage-
ment that includes a closed season, 1-bird daily bag limit, or 2-bird daily bag limit. The maximum pintail
season length depends on the general duck season framework (characterized as liberal, moderate, or restric-
tive and varying by Flyway) speci ed by mallard AHM. Each regulatory combination of bag limit and season
length has an associated predicted pintail harvest (Table 8). Technical details that describe the models used
to predict harvest can be found in Appendix F.
Table 8 { Total pintail harvest expected from the set of regulatory alternatives speci ed for each Flyway under
the northern pintail adaptive harvest management protocol.
Paci c Central Total
Atlantic Mississippi Harvest
Closed Closed 67,000
Liberal 1 Closed 278,000
Liberal 1 Restrictive 3 410,000
Liberal 1 Moderate 3 523,000
Liberal 1 Liberal 1 569,000
Liberal 2 Closed 357,000
Liberal 2 Restrictive 3 490,000
Liberal 2 Moderate 3 603,000
Liberal 2 Liberal 2 672,000
An optimal pintail regulation is calculated under the assumption of a liberal mallard season length in all
Flyways. However, if the season length of the general duck season determined by mallard AHM is less than
liberal in any of the Flyways, then an appropriate pintail daily bag limit would be substituted for that
Flyway. Thus, a shorter season length dictated by mallard AHM would result in an equivalent season length
for pintails, but with increased bag limit if the expected harvest remained within allowable limits.
Regulatory substitution rules have been developed for the Central and Mississippi Flyways, where the general
duck season length is driven by the mid-continent mallard AHM protocol (Table 9). These substitutions were
determined by  nding a pintail daily bag limit whose expected harvest was less than or equal to that called for
under the national recommendation. Thus, if the national pintail harvest strategy called for a liberal 2-bird
bag limit, but the mid-continent mallard season length was moderate, the recommended pintail regulation
for the Central and Mississippi Flyways would be moderate in length with a 3-bird bag limit. Because
season lengths more restrictive than liberal are expected infrequently in the Atlantic and Paci c Flyways
under current eastern and western mallard AHM strategies, substitution rules have not yet been developed
for these Flyways. If shorter season lengths were called for in the Paci c or Atlantic Flyway, then similar
rules would be speci ed for these 
yways and used to identify the appropriate substitution. In all cases, a
substitution produces a lower expected harvest than the harvest allowed under the pintail strategy .
The current adaptive protocol considers two population models. Each model represents an alternative hy-
pothesis about the e ect of harvest on population dynamics: one in which harvest is additive to natural
mortality, and another in which harvest is compensatory to natural mortality. The compensatory model as-
sumes that the mechanism for compensation is density-dependent post-harvest (winter) survival. The models
21
Table 9 { Substitution rules in the Central and Mississippi Flyways for joint implementation of northern pintail
and mallard harvest strategies. The mid-continent mallard AHM strategy stipulates the maximum season length
for pintails in the Central and Mississippi Flyways. The substitutions are used when the mid-continent mallard
season length is less than liberal. For example, if the pintail strategy calls for a liberal season length with a
2-bird bag, but the mid-continent mallard strategy calls for a restrictive season length, the recommended pintail
regulation for the Central and Mississippi Flyways would be restrictive in length with a 3-bird bag limit.
Pintail Mid-continent mallard AHM season length
Regulation Closed Restrictive Moderate Liberal
Closed Closed Closed Closed Closed
Liberal 1 Closed Restrictive 3 Moderate 3 Liberal 1
Liberal 2 Closed Restrictive 3 Moderate 3 Liberal 2
di er only in how they incorporate the winter survival rate. In the additive model, winter survival rate is a
constant, whereas winter survival is density-dependent in the compensatory model. A complete description
of the model set used to predict pintail population change can be found in Appendix F. Model weights for
the pintail model set have been updated annually since 2007 by comparing model predictions with observed
survey results. As of 2010, current model weights favor the hypothesis that harvest mortality is additive
(60%).
Northern pintail optimal regulatory strategies for the 2010 hunting season were calculated using: (1) pintail
harvest-management objectives; (2) the 2010 regulatory alternatives; and (3) current population models and
model weights. Based on this year's survey results of 3.51 million birds observed at a mean latitude of 54.4
degrees, the optimal regulatory choice for all four 
yways is the liberal regulatory alternative with a 2 bird
bag (Table 10).
Table 10 { Northern pintail optimal regulatory strategya for all 4 Flyways for the 2010 hunting season. This
strategy is based on current regulatory alternatives (including the closed-season constraint), northern pintail
models and weights, and the objective of maximizing long-term cumulative harvest. The shaded cell indicates
the regulatory prescription for 2010.
Mean Latitudec
Bpopb 53.0 53.5 54.0 54.5 55.0 55.5 56.0 56.5 57.0
  1.75 C C C C C C C C C
1.75{2.5 L1 L1 L1 L1 L1 L1 L1 L1 L1
  2.5 L2 L2 L2 L2 L2 L2 L2 L2 L2
a C = closed season, L1 = liberal season with 1 bird bag, L2 = liberal season with 2 bird bag.
b Observed northern pintail breeding population size (in millions) from the WBPHS (strata 1{50, 75{77)
c Mean Latitude (in degrees).
8.2 Scaup
In 2008, the USFWS implemented a decision-making framework for establishing scaup harvest regulations
that was initially proposed in 2007 (Boomer and Johnson 2007). In addition, the USFWS committed to
22
working with the Flyways to develop an alternative scaup population model for inclusion in the current
decision-making framework. This model will capture the belief that the scaup population will decline to and
stabilize at some lower equilibrium level in response to a declining carrying capacity and that harvest at
current levels is completely compensatory. We plan to report on our e orts to develop an alternative model
at the 2010 AHM Working Group meeting.
In 2007, the USFWS also outlined methods to facilitate the speci cation of regulatory alternatives for scaup
harvest management (Boomer et al. 2007). We proposed harvest thresholds to be considered under regulatory
alternatives based on a simulation of an optimal policy that was derived under an objective to achieve 95%
of the long-term cumulative harvest. We used this objective because it results in a strategy less sensitive
to small change in population size as compared to a strategy derived under an objective to achieve 100%
of long-term cumulative harvest. In addition, the 95% objective allows for some harvest opportunity at
relatively low population sizes. We have worked with the Flyways to determine what regulations would
achieve the allowable harvest thresholds set forth in Boomer et al. (2007). In 2008 during deliberations over
scaup regulatory alternatives, the USFWS also agreed to consider a \hybrid season" option that would be
available to all Flyways for the restrictive and moderate alternatives. In 2008, initial Restrictive, Moderate,
and Liberal scaup regulatory alternatives were de ned and implemented in all four Flyways. Subsequent
concerns and dialogue led the USFWS to further clarify criteria associated with the establishment of \hybrid
seasons" and to allow additional modi cations of the alternatives for each Flyway in 2009. Final scaup
regulatory alternatives were adopted for each Flyway in 2009. These alternatives will remain in place for a
period of three years and then revisited as the latest harvest information is evaluated.
The USFWS will continue to work with the Flyways to determine acceptable harvest-management objectives
and evaluate regulatory alternatives to be used in the evolving decision-making framework for scaup harvest
management. Presently, the scaup harvest strategy prescribes optimal harvest levels, not optimal regulatory
alternatives. It is important to note that we currently have limited ability to predict expected scaup harvest
under the newly-established, Flyway-speci c scaup regulatory alternatives. The initial regulatory alternatives
adopted for each Flyway were based on relatively crude predictions from harvest models developed in Boomer
et al. (2007) or alternative harvest models proposed by the Flyways. As we gain experience with scaup
regulatory alternatives, we will re ne predicted harvest distributions associated with the Flyway-speci c
alternatives with the ultimate goal being to use regulatory alternatives, as opposed to harvest, as the control
variable in deriving future scaup harvest policies.
The lack of scaup demographic information over a su cient timeframe and at a continental scale precludes
the use of a traditional balance equation to represent scaup population and harvest dynamics. As a result, we
used a discrete-time, stochastic, logistic-growth population model to represent changes in scaup abundance,
while explicitly accounting for scaling issues associated with the monitoring data. Details describing the
modeling and assessment framework that has been developed for scaup can be found in Appendix G and in
Boomer and Johnson (2007).
We updated the scaup assessment based on the current model formulation and data extending from 1974
through 2009. As in past analyses, the state space formulation and Bayesian analysis framework provided
reasonable  ts to the observed breeding population and total harvest estimates with realistic measures of
variation. The posterior mean estimate of the intrinsic rate of increase (r ) is 0.122 while the posterior mean
estimate of the carrying capacity (K) is 8.17 million birds. The posterior mean estimate of the scaling
parameter (q) is 0.556, ranging between 0.484 and 0.634 with 95% probability.
We calculated an optimal harvest policy for scaup based on: (1) a control variable of total harvest (U.S. and
Canada combined), (2) current population model and updated parameter estimates, and (3) an objective to
achieve 95% of the long-term cumulative harvest. We simulated the use of this regulatory strategy to de-
termine expected performance characteristics. Assuming that harvest management adhered to this strategy
(and that current model parameters accurately re
ect population dynamics), breeding-population size would
be expected to average 4.56 million (SD = 0.81 million). With an estimated breeding population size of
4.2 million scaup, the optimal harvest level for scaup is 0.35 million (Table 11). Based on the harvest thresh-
olds speci ed in Boomer et al. (2007), this year's optimal harvest corresponds to the moderate regulatory
alternative.
23
Table 11 { Optimal scaup harvest levels (observed scale in millions) and corresponding breeding population sizes
(in millions). This strategy is based on the current scaup population model, and an objective to maximize 95%
of long-term cumulative harvest. The shaded cell indicates the optimal harvest level for 2010 which corresponds
to the moderate regulatory alternative.
BPOP Optimal Harvest
0.0{1.8 0
2.0{2.2 0.05
2.4{2.6 0.10
2.8{3.0 0.15
3.2{3.4 0.20
3.6{3.8 0.25
4.0 0.30
4.2 0.35
4.4 0.40
4.6{4.8 0.45
5.0{5.2 0.50
5.4 0.55
9 EMERGING ISSUES IN AHM
Learning occurs passively with the current AHM protocol as annual comparisons of model predictions to
observations from monitoring programs are used to update model weights and relative beliefs about system
responses to management (Johnson et al. 2002b) or as model parameters are updated based on an assessment
of the most recent monitoring data (Boomer and Johnson 2007, Johnson et al. 2007). However, learning
can also occur as decision-making frameworks are evaluated to determine if objectives are being achieved,
have changed, or if other aspects of the decision problem are adequately being addressed. Often the feedback
resulting from this process results in a form of \double loop" learning (Lee 1993) that o ers the opportunity to
adapt decision-making frameworks in response to a shifting decision context, novel or emerging management
alternatives, or a need to revise models that may perform poorly or need to account for new information.
Adaptive management depends on this iterative process to ensure that decision-making protocols remain
relevant in evolving biological and social systems.
As a byproduct of the adaptive management process, it is natural to think about when or how decision-
making protocols should be revised to incorporate new information or to accommodate changes in the overall
management context. Recent outcomes from the 2008 Future of Waterfowl Management Workshop and
evaluations of waterfowl harvest and habitat management programs (e.g., Anderson et al. 2007) suggest
compelling reasons for a re-evaluation of the objectives of waterfowl management as well as the technical
and institutional frameworks through which harvest and habitat management decisions are made. The AHM
working group recognizes the need to better integrate harvest and habitat management objectives (sensu
Runge et al. 2005, Anderson et al. 2007) as an ongoing e ort to continue to make informed decisions while
attempting to maximize management e ciency. Within the last year, the waterfowl management community
has engaged in an broad-scale e ort to determine the fundamental objectives of waterfowl management as
part of a structured process to inform the North American Waterfowl Management Plan Revision (North
American Waterfowl Management Plan Revision Steering Committee 2009). The results of this consultation
and the content of the NAWMP Revision may have signi cant implications for all of the policy elements
currently de ned in existing AHM protocols. We view such introspection as completely consistent with the
principles underlying AHM, and, in fact, critical to its long-term utility as a decision framework for waterfowl
24
harvest regulation.
The AHM Working Group has also begun discussing the technical challenges involved with dealing with
large-scale habitat and environmental change on the decision-making frameworks used to inform waterfowl
harvest management. We anticipate that large-scale system change will exacerbate all forms of uncertainty
that a ect waterfowl AHM, but we believe that the elements of the current AHM framework provide the
necessary structure for coping with these changing systems. In addition, the AHM Working Group continues
to explore questions related to the appropriate taxonomic, spatial, and temporal resolution of waterfowl
harvest management. These, and other issues, are also being considered in the course of ongoing deliberations
over the draft 2010 Supplemental Environmental Impact Statement on the Issuance of Annual Regulations
Permitting the Hunting of Migratory Birds (U. S. Department of the Interior 2010). In light of these issues, we
remain committed to the continued reassessment of AHM decision frameworks through the adaptive process
of \double loop" learning. Ultimately, we will need to prioritize the scope of work required to revisit AHM
protocols in the face of limited resources, shifting priorities, and in response to rapidly changing biological
and social systems. We look forward to working with the Flyways as we continue to re ne the adaptive
harvest management framework.
LITERATURE CITED
Anderson, D. R., and K. P. Burnham, 1976. Populatin ecology of the mallard. VI. The e ect of exploitation
on survival. U. S. Fish and Wildlife Service Resource Publication. 128. 66pp.
Anderson, M. G., D. Casewell, J. M. Eadie, J. T. Herbert, M. Huang, D. D. Humberg, F. A. Johnson, M. D.
Kone , S. E. Mott, T. D. Nudds, E. T. Reed, J. K. Ringleman, M. C. Runge, and B. C. Wilson, 2007.
Unpublished Report from the Joint Task Group for clarifying North American waterfowl management plan
population objectives and their use in harvest management.
Blohm, R. J. 1989. Introduction to harvest { understanding surveys and season setting. Proceedings of the
International Waterfowl Symposium 6:118{133.
Blohm, R. J., R. E. Reynolds, J. P. Bladen, J. D. Nichols, J. E. Hines, K. P. Pollock, and R. T. Eberhardt.
1987. Mallard mortality rates on key breeding and wintering areas. Transactions of the North American
Wildilfe and Resources Conference 52:246{263.
Boomer, G. S., and F. A. Johnson, 2007. A proposed assessment and decision-making framework to
inform scaup harvest management. Unpublished Report. U. S. Fish and Wildlife Service, Laurel,
MD. 26pp., URL http://www.fws.gov/migratorybirds/NewReportsPublications/SpecialTopics/BySpecies/
SCAUP2007Report.pdf.
Boomer, G. S., F. A. Johnson, M. D. Kone , T. A. Sanders, and R. E. Trost, 2007. A process to determine
scaup regulatory alternatives. Unpublished Scoping Document. U. S. Fish and Wildlife Service, Laurel,
MD. 20pp., URL http://www.fws.gov/migratorybirds/NewReportsPublications/SpecialTopics/BySpecies/
scaup_regs_scoping_draftVI.pdf.
Brooks, S. P., and A. Gelman. 1998. Alternative methods for monitoring convergence of iterative simulations.
Journal of Computational and Graphical Statistics 7:434{455.
Burnham, K. P., G. C. White, and D. R. Anderson. 1984. Estimating the e ect of hunting on annual survival
rates of adult mallards. Journal of Wildlife Management 48:350{361.
Henny, C. J., and K. P. Burnham. 1976. A reward band study of mallards to estimate reporting rates.
Journal of Wildlife Management 40:1{14.
Heusmann, H. W., and J. R. Sauer. 2000. The northeastern states' waterfowl breeding population survey.
Wildlife Society Bulletin 28:355{364.
25
Hodges, J. L., J. G. King, B. Conant, and H. A. Hanson. 1996. Aerial surveys of waterbirds in Alaska
1975{94: population trends and observer variability. National Biological Service, U.S. Department of the
Interior Information and Technology Report 4, Washington, D. C.
Johnson, F. A., 2003. Population dynamics of ducks other than mallards in mid-continent North America.
Draft. U. S. Fish and Wildlife Service, U. S. Department of the Interior, Washington, D. C. 15pp.
Johnson, F. A., G. S. Boomer, and T. A. Sanders, 2007. A proposed protocol for the adaptive harvest
management of mallards breeding in Western North America. Unpublished Report. U. S. Fish and Wildlife
Service, Laurel, MD. 33pp.
Johnson, F. A., J. A. Dubovsky, M. C. Runge, and D. R. Eggeman. 2002a. A revised protocol for the adaptive
harvest management of eastern mallards. Fish and Wildlife Service, U. S. Department of the Interior
Technical report, Washington, D. C. URL http://www.fws.gov/migratorybirds/NewReportsPublications/
AHM/Year2002/emal-ahm-2002.pdf.
Johnson, F. A., W. L. Kendall, and J. A. Dubovsky. 2002b. Conditions and limitations on learning in the
adaptive management of mallard harvests. Wildlife Society Bulletin 30:176{185.
Johnson, F. A., C. T. Moore, W. L. Kendall, J. A. Dubovsky, D. F. Caithamer, J. Kelley, J. R., and B. K.
Williams. 1997. Uncertainty and the management of mallard harvests. Journal of Wildlife Management
61:202{216.
Johnson, F. A., and B. K. Williams. 1999. Protocol and practice in the adaptive management of waterfowl
harvests. Conservation Ecology 3:8. URL http://www.consecol.org/vol3/iss1/art8.
Johnson, F. A., B. K. Williams, J. D. Nichols, J. E. Hines, W. L. Kendall, G. W. Smith, and D. F. Caithamer.
1993. Developing an adaptive management strategy for harvesting waterfowl in North America. Transac-
tions of the North American Wildlife and Natural Resources Conference 58:565{583.
Johnson, F. A., B. K. Williams, and P. R. Schmidt. 1996. Adaptive decision-making in waterfowl harvest
and habitat management. Proceedings of the International Waterfowl Symposium 7:26{33.
Lee, K. N. 1993. Compass and Gyroscope: Integrating Science and Politics for the Environment. Island
Press, Washington, D.C.
Lubow, B. C. 1995. SDP: Generalized software for solving stochastic dynamic optimization problems. Wildlife
Society Bulletin 23:738{742.
Meyer, R., and R. B. Millar. 1999. BUGS in Bayesian stock assessments. Canadian Journal of Fisheries and
Aquatic Sciences 56:10078{1086.
Millar, R. B., and R. Meyer. 2000. Non-linear state space modeling of  sheries biomass dynamics by using
Metropolis-Hastings within Gibbs sampling. Applied Statistics 49:327{342.
Nichols, J. D., F. A. Johnson, and B. K. Williams. 1995a. Managing North American waterfowl in the face
of uncertainty. Annual Review of Ecology and Systematics 26:177{199.
Nichols, J. D., R. E. Reynolds, R. J. Blohm, R. E. Trost, J. E. Hines, and J. P. Bladen. 1995b. Geographic
variation in band reporting rates for mallards based on reward banding. Journal of Wildlife Management
59:697{708.
North American Waterfowl Management Plan Revision Steering Committee, 2009. North American Wa-
terfowl Management Plan Revision Communiqu e. URL http://nawmprevision.org/sites/default/files/
Plan_Revision_Communique.pdf.
Runge, M. C., 2007. Northern pintail harvest strategy: development of a compensatory model. Unpublished
Report. U. S. Geological Survey, Patuxent Wildlife Research Center, Laurel, MD.
26
Runge, M. C., and G. S. Boomer, 2005. Population dynamics and harvest management of the continental
northern pintail population. Unpublished Report. U. S. Geological Survey, Patuxent Wildlife Research Cen-
ter, Laurel, MD. 42pp., URL http://www.fws.gov/migratorybirds/NewReportsPublications/AHM/Year2005/
NOPI%202005%20Report%202.pdf.
Runge, M. C., F. A. Johnson, M. G. Anderson, M. D. Kone , E. T. Reed, and S. E. Mott. 2005. The need
for coherence between waterfowl harvest and habitat management. Wildlife Society Bulletin 34:1231{1237.
Runge, M. C., F. A. Johnson, J. A. Dubovsky, W. L. Kendall, J. Lawrence, and J. Gammonley. 2002.
A revised protocol for the adaptive harvest management of mid-continent mallards. Fish and Wildlife
Service, U. S. Department of the Interior Technical report, Washington, D. C. URL http://www.fws.gov/
migratorybirds/NewReportsPublications/AHM/Year2002/MCMrevise2002.pdf.
Schaefer, M. B. 1954. Some aspects of the dynamics of populations important to the management of
commercial marine  sheries. Bulletin of the Inter-American Tropical Tuna Commission 1:25{56.
Smith, G. W. 1995. A critical review of the aerial and ground surveys of breeding waterfowl in North America.
National Biological Service, U. S. Department of the Interior Biological Science Report 5,Washington, D. C.
Spiegelhalter, D. J., A. Thomas, N. Best, and D. Lunn. 2003. WinBUGS 1.4 User manual. MRC Biostatistics
Unit, Institues of Public Health, Cambridge, UK.
U. S. Department of the Interior, 2010. Draft Supplemental Environmental Impact Statement: Issuance of
Annual Regulations Permitting the Hunting of Migratory Birds. U. S. Fish and Wildlife Service, Washing-
ton, D. C. 305pp., URL http://www.fws.gov/migratorybirds/NewReportsPublications/Hunting/SEIS%207%
20June%20b%202010.pdf.
U. S. Fish and Wildlife Service, 2000. Adaptive harvest management: 2000 duck hunting season.
U. S. Department of Interior, Washington, D. C. 43pp., URL http://www.fws.gov/migratorybirds/
NewReportsPublications/AHM/Year2000/ahm2000.pdf.
U. S. Fish and Wildlife Service, 2001. Framework-date extensions for duck hunting in the United States:
projected impacts & coping with uncertainty. U. S. Department of Interior, Washington, D. C. 8pp., URL
http://www.fws.gov/migratorybirds/NewReportsPublications/AHM/Year2001/ahm2001.pdf.
U. S. Fish and Wildlife Service, 2002. Adaptive harvest management: 2002 duck hunting season.
U. S. Department of Interior, Washington, D. C. 34pp., URL http://www.fws.gov/migratorybirds/
NewReportsPublications/AHM/Year2002/2002-AHM-report.pdf.
U. S. Fish and Wildlife Service, 2010. Northern Pintail Harvest Strategy. U. S. Department of Interior,
Washington, D. C. 20pp., URL http://www.fws.gov/migratorybirds/NewsPublicationsReports.html.
Walters, C. 1986. Adaptive Management of Renewable Resources. Macmillian, New York.
Williams, B. K., and F. A. Johnson. 1995. Adaptive management and the regulation of waterfowl harvests.
Wildlife Society Bulletin 23:430{436.
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.
27
A AHM WORKING GROUP
(Note: This list includes only permanent members of the AHM Working Group. Not listed here are numerous
persons from federal and state agencies that assist the Working Group on an ad-hoc basis.)
Coordinator:
Scott Boomer
U. S. Fish & Wildlife Service
11510 American Holly Drive
Laurel, Maryland 20708-4017
phone: 301-497-5684
fax: 301-497-5871
e-mail: scott boomer@fws.gov
USFWS Representatives:
Brad Bortner (Region 1) Jim Kelley (Region 9)
U. S. Fish & Wildlife Service U. S. Fish & Wildlife Service
911 NE 11th Ave. 1 Federal Drive
Portland, OR 97232-4181 Fort Snelling, MN 55111-0458
phone: 503-231-6164 phone: 612-713-5409
fax: 503-231-2364 fax: 612-713-5393
e-mail: brad bortner@fws.gov e-mail: james r kelley@fws.gov
Dave Case (contractor) Sean Kelly (Region 3)
D. J. Case & Associates U. S. Fish & Wildlife Service
607 Lincolnway West 1 Federal Drive
Mishawaka, IN 46544 Fort Snelling, MN 55111-4056
phone: 574-258-0100 phone: 612-713-5470
fax: 574-258-0189 fax: 612-713-5393
e-mail: dave@djcase.com e-mail: sean kelly@fws.gov
Jim Dubovsky (Region 6) Mark Kone  (Region 9)
U. S. Fish & Wildlife Service U. S. Fish & Wildlife Service
P.O. Box 25486-DFC 11510 American Holly Drive
Denver, CO 80225-0486 Laurel, Maryland 20708-4017
phone: 303-236-4403 phone: 301-497-5648
fax: 303-236-8680 fax: 301-497-5871
e-mail: james dubovsky@fws.gov e-mail: mark kone @fws.gov
28
Je  Haskins (Region 2) Paul Padding (Region 9)
U. S. Fish & Wildlife Service U. S. Fish & Wildlife Service
P.O. Box 1306 11510 American Holly Drive
Albuquerque, NM 87103 Laurel, MD 20708
phone: 505-248-6827 (ext 30) phone: 301-497-5851
fax: 505-248-7885 fax: 301-497-5885
e-mail: je  haskins@fws.gov e-mail: paul padding@fws.gov
Diane Pence (Region 5) Bob Trost (Region 9)
U. S. Fish & Wildlife Service U. S. Fish & Wildlife Service
300 Westgate Center Drive 911 NE 11th Ave.
Hadley, MA 01035-9589 Portland, OR 97232-4181
phone: 413-253-8577 phone: 503-231-6162
fax: 413-253-8424 fax: 503-231-6228
e-mail: diane pence@fws.gov e-mail: robert trost@fws.gov
Russ Oates (Region 7) David Viker (Region 4)
U. S. Fish & Wildlife Service U. S. Fish & Wildlife Service
1011 East Tudor Road 1875 Century Blvd., Suite 345
Anchorage, AK 99503-6119 Atlanta, GA 30345
phone: 907-786-3446 phone: 404-679-7188
fax: 907-786-3641 fax: 404-679-7285
e-mail: russ oates@fws.gov e-mail: david viker@fws.gov
Dave Sharp (Region 9)
U. S. Fish & Wildlife Service
P.O. Box 25486, DFC
Denver, CO 80225-0486
phone: 303-275-2386
fax: 303-275-2384
e-mail: dave sharp@fws.gov
Canadian Wildlife Service Representatives:
Eric Reed
Canadian Wildlife Service
351 St. Joseph Boulevard
Hull, QC K1A OH3, Canada
phone: 819-953-0294
fax: 819-953-6283
e-mail: eric.reed@ec.gc.ca
29
Flyway Council Representatives:
Min Huang (Atlantic Flyway) Larry Reynolds (Mississippi Flyway)
CT Dept. of Environmental Protection LA Dept. of Wildlife & Fisheries
Franklin Wildlife Mgmt. Area P.O. Box 98000
391 Route 32 Baton Rouge, LA 70898-9000, USA
North Franklin, CT 06254, USA Phone: 225-765-0456
Phone: 860-642-6528 Fax: 225-763-5456
fax: 860-642-7964 e-mail: lreynolds@wlf.state.la.us
e-mail: min.huang@po.state.ct.us
Mike Johnson (Central Flyway) Jon Runge (Paci c Flyway)
North Dakota Game and Fish Department Colorado Division of Wildlife
100 North Bismarck Expressway 317 West Prospect
Bismarck, ND 58501-5095 Fort Collins, CO 80526
phone: 701-328-6319 Phone: 970-472-4365
fax: 701-328-6352 e-mail: Jon.Runge@state.co.us
e-mail: mjohnson@state.nd.us
Bryan Swift (Atlantic Flyway) Dan Yparraguirre (Paci c Flyway)
NY Dept. Environmental Conservation California Dept. of Fish and Game
625 Broadway 1812 Ninth Street
Albany, NY 12233-4754 Sacramento, CA 95814
phone: 518-402-8866 phone: 916-445-3685
fax: 518-402-9027 or 402-8925 e-mail: dyparraguirre@dfg.ca.gov
e-mail: blswift@gw.dec.state.ny.us
Mark Vrtiska (Central Flyway) Guy Zenner (Mississippi Flyway)
Nebraska Game and Parks Commission Iowa Dept. of Natural Resources
P.O. Box 30370 1203 North Shore Drive
2200 North 33rd Street Clear Lake, IA 50428
Lincoln, NE 68503-1417 phone: 515-357-3517, ext. 23
phone: 402-471-5437 fax: 515-357-5523
fax: 402-471-5528 e-mail: gzenner@netins.net
email: mvrtiska@ngpc.state.ne.us
30
USGS Technical Consultants:
Fred Johnson Andy Royle
Florida Integrated Science Center Patuxent Wildlife Research Center
U. S. Geological Survey U. S. Geological Survey
P.O. Box 110485 12100 Beech Forest Rd.
Gainesville, FL 32611 Laurel, MD 20708
phone: 352-392-5075 phone: 301-497-5846
fax: 352-846-0841 fax: 301-497-5545
e-mail: fjohnson@usgs.gov e-mail: aroyle@usgs.gov
Mike Runge Patuxent Wildlife Research Center
U. S. Geological Survey
12100 Beech Forest Rd.
Laurel, MD 20708
phone: 301-497-5748
fax: 301-497-5545
e-mail: mrunge@usgs.gov
31
B MID-CONTINENT MALLARD MODELS
In 1995, we developed population models to predict changes in mid-continent mallards based on the traditional
survey area which includes individuals from Alaska (Johnson et al. 1997). In 1997, we added mallards from
the Great Lakes region (Michigan, Minnesota, and Wisconsin) to the mid-continent mallard stock, assuming
their population dynamics were equivalent. In 2002, we made extensive revisions to the set of alternative
models describing the population dynamics of mid-continent mallards (Runge et al. 2002, U. S. Fish and
Wildlife Service 2002). In 2008, we rede ned the population of mid-continent mallards (Table 1) to account
for the removal of Alaskan birds (WBPHS strata 1{12) that are now considered to be in the western mallard
stock and have subsequently rescaled the model set appropriately.
Mid-continent Mallard Breeding Population Estimates
Table B.1 { Estimates (N) and associated standard errors (SE) of mid-continent mallards (in millions) ob-
served in the WBPHS (strata 13{18, 20{50, and 75{77) and the Great Lakes region (Michigan, Minnesota, and
Wisconsin).
WBPHS area Great Lakes region Total
Year N SE N SE N SE
1992 5.6304 0.2379 0.9946 0.1597 6.6249 0.2865
1993 5.4253 0.2068 0.9347 0.1457 6.3600 0.2529
1994 6.6292 0.2803 1.1505 0.1163 7.7797 0.3035
1995 7.7452 0.2793 1.1214 0.1965 8.8666 0.3415
1996 7.4193 0.2593 1.0251 0.1443 8.4444 0.2967
1997 9.3554 0.3041 1.0777 0.1445 10.4331 0.3367
1998 8.8041 0.294 1.1224 0.1792 9.9266 0.3443
1999 10.0926 0.3374 1.0591 0.2122 11.1518 0.3986
2000 8.6999 0.2855 1.2350 0.1761 9.9348 0.3354
2001 7.1857 0.2204 0.8622 0.1086 8.0479 0.2457
2002 6.8364 0.2412 1.0820 0.1152 7.9184 0.2673
2003 7.1062 0.2589 0.8360 0.0734 7.9422 0.2691
2004 6.6142 0.2746 0.9333 0.0748 7.5474 0.2847
2005 6.0521 0.2754 0.7862 0.0650 6.8383 0.2830
2006 6.7607 0.2187 0.5881 0.0465 7.3488 0.2236
2007 7.7258 0.2805 0.7677 0.0584 8.4935 0.2865
2008 7.1914 0.2525 0.6750 0.0478 7.8664 0.2570
2009 8.0094 0.2442 0.6958 0.0564 8.7052 0.2506
2010 7.8246 0.2799 0.7800 0.0588 8.6046 0.2860
32
Model Structure
Collectively, the models express uncertainty (or disagreement) about whether harvest is an additive or com-
pensatory form of mortality (Burnham et al. 1984), and whether the reproductive process is weakly or strongly
density-dependent (i.e., the degree to which reproductive rates decline with increasing population size).
All population models for mid-continent mallards share a common \balance equation" to predict changes in
breeding-population size as a function of annual survival and reproductive rates:
Nt+1 = Nt (mSt;AM + (1 􀀀 m)(St;AF + Rt(St;JF + St;JM sum
F = sum
M )))
where:
N=breeding population size,
m = proportion of males in the breeding population,
SAM, SAF , SJF , and SJM = survival rates of adult males, adult females, young females, and young
males, respectively,
R = reproductive rate, de ned as the fall age ratio of females,
 sum
F = sum
M = the ratio of female (F) to male (M) summer survival, and t = year.
We assumed that m and  sum
F = sum
M are  xed and known. We also assumed, based in part on information
provided by Blohm et al. (1987), the ratio of female to male summer survival was equivalent to the ratio of
annual survival rates in the absence of harvest. Based on this assumption, we estimated  sum
F = sum
M = 0.897.
To estimate m we expressed the balance equation in matrix form:
"
Nt+1;AM
Nt+1;AF
#
=
"
SAM RSJM sum
F = sum
M
0 SAF + RJF
# "
Nt;AM
Nt;AF
#
and substituted the constant ratio of summer survival and means of estimated survival and reproductive
rates. The right eigenvector of the transition matrix is the stable sex structure that the breeding population
eventually would attain with these constant demographic rates. This eigenvector yielded an estimate of
m = 0.5246.
Using estimates of annual survival and reproductive rates, the balance equation for mid-continent mallards
over-predicted observed population sizes by 11.0% on average. The source of the bias is unknown, so we
modi ed the balance equation to eliminate the bias by adjusting both survival and reproductive rates:
Nt+1 = 
SNt (mSt;am + (1 􀀀 m) (St;AF + 
RRt (St;JF + St;JM sum
F = sum
M )))
where 
 denotes the bias-correction factors for survival (S), and reproduction (R). We used a least squares
approach to estimate 
S = 0:9407 and 
R = 0:8647.
Survival Process
We considered two alternative hypotheses for the relationship between annual survival and harvest rates. For
both models, we assumed that survival in the absence of harvest was the same for adults and young of the
same sex. In the model where harvest mortality is additive to natural mortality:
St;sex;age = SA
0;sex(1 􀀀 Kt;sex;age)
33
and in the model where changes in natural mortality compensate for harvest losses (up to some threshold):
St;sex;age =
(
sC 0;sex if Kt;sex;age   1 􀀀 sC 0;sex
1 􀀀 Kt;sex;age if Kt;sex;age > 1 􀀀 sC 0;sex
where s0 = survival in the absence of harvest under the additive (A) or compensatory (C) model, and K =
harvest rate adjusted for crippling loss (20%, Anderson and Burnham 1976). We averaged estimates of s0
across banding reference areas by weighting by breeding-population size. For the additive model, s0 = 0:7896
and 0.6886 for males and females, respectively. For the compensatory model, s0 = 0:6467 and 0.5965 for
males and females, respectively. These estimates may seem counterintuitive because survival in the absence
of harvest should be the same for both models. However, estimating a common (but still sex-speci c) s0
for both models leads to alternative models that do not  t available band-recovery data equally well. More
importantly, it suggests that the greatest uncertainty about survival rates is when harvest rate is within the
realm of experience. By allowing s0 to di er between additive and compensatory models, we acknowledge
that the greatest uncertainty about survival rate is its value in the absence of harvest (i.e., where we have no
experience).
Reproductive Process
Annual reproductive rates were estimated from age ratios in the harvest of females, corrected using a constant
estimate of di erential vulnerability. Predictor variables were the number of ponds in May in Prairie Canada
(P, in millions) and the size of the breeding population (N, in millions). We estimated the best- tting linear
model, and then calculated the 80% con dence ellipsoid for all model parameters. We chose the two points
on this ellipsoid with the largest and smallest values for the e ect of breeding-population size, and generated
a weakly density-dependent model:
Rt = 0:7166 + 0:1083Pt 􀀀 0:0373Nt
and a strongly density-dependent model:
Rt = 1:1390 + 0:1376Pt 􀀀 0:1131Nt
Predicted recruitment was then rescaled to re
ect the current de nition of mid-continent mallards which now
excludes birds from Alaska but includes mallards observed in the Great Lakes region.
Pond Dynamics
We modeled annual variation in Canadian pond numbers as a  rst-order autoregressive process. The estimated
model was:
Pt+1 = 2:2127 + 0:3420Pt + "t
where ponds are in millions and "t is normally distributed with mean = 0 and variance = 1.2567.
34
Variance of Prediction Errors
Using the balance equation and sub-models described above, predictions of breeding-population size in year
t+1 depend only on speci cation of population size, pond numbers, and harvest rate in year t. For the period
in which comparisons were possible, we compared these predictions with observed population sizes.
We estimated the prediction-error variance by setting:
et = ln
􀀀
Nobs
t
 
􀀀 ln (Npre
t )
et   N
􀀀
0;  2
 
 ^2 =
P
t
 
ln
􀀀
Nobs
t
 
􀀀 ln (Npre
t )
 2
=(n 􀀀 1)
where Nobs and Npre are observed and predicted population sizes (in millions), respectively, and n = the
number of years being compared. We were concerned about a variance estimate that was too small, either
by chance or because the number of years in which comparisons were possible was small. Therefore, we
calculated the upper 80% con dence limit for  2 based on a Chi-squared distribution for each combination
of the alternative survival and reproductive sub-models, and then averaged them. The  nal estimate of  2
was 0.0280, equivalent to a coe cient of variation of about 18%.
Model Implications
The population model with additive hunting mortality and weakly density-dependent recruitment (SaRw)
leads to the most conservative harvest strategy, whereas the model with compensatory hunting mortality
and strongly density-dependent recruitment (ScRs) leads to the most liberal strategy. The other two models
(SaRs and ScRw) lead to strategies that are intermediate between these extremes. Under the models with
compensatory hunting mortality (ScRs and ScRw), the optimal strategy is to have a liberal regulation re-
gardless of population size or number of ponds because at harvest rates achieved under the liberal alternative,
harvest has no e ect on population size. Under the strongly density-dependent model (ScRs), the density
dependence regulates the population and keeps it within narrow bounds. Under the weakly density dependent
model (ScRw), the density-dependence does not exert as strong a regulatory e ect, and the population size

uctuates more.
Model Weights
Model weights are calculated as Bayesian probabilities, re
ecting the relative ability of the individual alter-
native models to predict observed changes in population size. The Bayesian probability for each model is a
function of the models previous (or prior) weight and the likelihood of the observed population size under
that model. We used Bayes' theorem to calculate model weights from a comparison of predicted and observed
population sizes for the years 1996{2010, starting with equal model weights in 1995.
35
C EASTERN MALLARD MODELS
We also revised the population models for eastern mallards in 2002 (Johnson et al. 2002a, U. S. Fish and
Wildlife Service 2002). The current set of six models: (1) relies solely on federal and state waterfowl surveys
(rather than the Breeding Bird Survey) to estimate abundance; (2) allows for the possibility of a positive
bias in estimates of survival or reproductive rates; (3) incorporates competing hypotheses of strongly and
weakly density-dependent reproduction; and (4) assumes that hunting mortality is additive to other sources
of mortality.
Eastern Mallard Breeding Population Estimates
Table C.1 { Estimates (N) and associated standard errors (SE) of eastern mallards (in millions) observed in the
northeastern U.S. (AFBWS) and southern Ontario and Quebec (WBPHS strata 51{54 and 56).
Northeastern U.S. WBPHS Total
Year N SE N SE N SE
1990 0.6651 0.0783 0.1907 0.0472 0.8558 0.0914
1991 0.7792 0.0883 0.1528 0.0337 0.9320 0.0945
1992 0.5622 0.0479 0.3203 0.0530 0.8825 0.0715
1993 0.6866 0.0499 0.2921 0.0482 0.9786 0.0694
1994 0.8563 0.0628 0.2195 0.0282 1.0758 0.0688
1995 0.8641 0.0704 0.1844 0.0400 1.0486 0.0810
1996 0.8486 0.0611 0.2831 0.0557 1.1317 0.0826
1997 0.7952 0.0496 0.2121 0.0396 1.0073 0.0634
1998 0.7752 0.0497 0.2638 0.0672 1.0390 0.0836
1999 0.8800 0.0602 0.2125 0.0369 1.0924 0.0706
2000 0.7626 0.0487 0.1323 0.0264 0.8948 0.0554
2001 0.8094 0.0516 0.2002 0.0356 1.0097 0.0627
2002 0.8335 0.0562 0.1915 0.0319 1.0250 0.0647
2003 0.7319 0.0470 0.3083 0.0554 1.0402 0.0726
2004 0.8066 0.0517 0.3015 0.0533 1.1081 0.0743
2005 0.7536 0.0536 0.2934 0.0531 1.0470 0.0755
2006 0.7214 0.0476 0.1740 0.0284 0.8954 0.0555
2007 0.6876 0.0467 0.2193 0.0336 0.9069 0.0576
2008 0.6191 0.0407 0.1960 0.0300 0.8151 0.0505
2009 0.6668 0.0457 0.2411 0.0434 0.9078 0.0630
2010 0.6526 0.0492 0.1100 0.0205 0.7626 0.0533
36
Model Structure
As with mid-continent mallards, all population models for eastern mallards share a common balance equation
to predict changes in breeding-population size as a function of annual survival and reproductive rates:
Nt+1 = Nt
 
(pSam
t ) +
 
(1 􀀀 p) Saf
t
 
+ (p (Amt
=d) Sym
t ) +
 
p (Amt
=d)  Syf
t
  
where:
N = breeding-population size,
p = proportion of males in the breeding population,
Sam; Saf ; Sym, and Syf = survival rates of adult males, adult females, young males, and young
females, respectively,
Am = ratio of young males to adult males in the harvest,
d = ratio of young male to adult male direct recovery rates,
  = the ratio of male to female summer survival, and t = year.
In this balance equation, we assume that p, d, and   are  xed and known. The parameter   is necessary to
account for the di erence in anniversary date between the breeding-population survey (May) and the survival
and reproductive rate estimates (August). This model also assumes that the sex ratio of 
edged young is
1:1; hence Am=d appears twice in the balance equation. We estimated d = 1:043 as the median ratio of
young:adult male band-recovery rates in those states from which wing receipts were obtained. We estimated
  = 1:216 by regressing through the origin estimates of male survival against female survival in the absence
of harvest, assuming that di erences in natural mortality between males and females occur principally in
summer. To estimate p, we used a population projection matrix of the form:
"
Mt+1
Ft+1
#
=
"
Sam + (Am=d) Sym 0
(Am=d)  Syf Saf
# "
Mt
Ft
#
where M and F are the relative number of males and females in the breeding populations, respectively. To
parameterize the projection matrix we used average annual survival rate and age ratio estimates, and the
estimates of d and   provided above. The right eigenvector of the projection matrix is the stable proportion
of males and females the breeding population eventually would attain in the face of constant demographic
rates. This eigenvector yielded an estimate of p = 0:544.
We also attempted to determine whether estimates of survival and reproductive rates were unbiased. We
relied on the balance equation provided above, except that we included additional parameters to correct for
any bias that might exist. Because we were unsure of the source(s) of potential bias, we alternatively assumed
that any bias resided solely in survival rates:
Nt+1 = Nt!
 
pSam
t +
 
(1 􀀀 p) Saf
t
 
+ (p (Amt
=d) Sym
t ) +
 
p (Amt
=d)  Syf
t
  
(where ! is the bias-correction factor for survival rates), or solely in reproductive rates:
Nt+1 = Nt
 
pSam
t +
 
(1 􀀀 p) Saf
t
 
+ (p  (Amt
=d) Sym
t ) +
 
p  (Amt
=d)  Syf
t
  
(where   is the bias-correction factor for reproductive rates). We estimated ! and   by determining the
values of these parameters that minimized the sum of squared di erences between observed and predicted
37
population sizes. Based on this analysis, ! = 0:836 and   = 0:701, suggesting a positive bias in survival
or reproductive rates. However, because of the limited number of years available for comparing observed
and predicted population sizes, we also retained the balance equation that assumes estimates of survival and
reproductive rates are unbiased.
Survival Process
For purposes of AHM, annual survival rates must be predicted based on the speci cation of regulation-speci c
harvest rates (and perhaps on other uncontrolled factors). Annual survival for each age (i) and sex (j) class
under a given regulatory alternative is:
Si;j
t =   j
 
1 􀀀
ham
t  i;j
1 􀀀 c
 
where:
S = annual survival,
  j= mean survival from natural causes,
ham = harvest rate of adult males,
  = harvest vulnerability relative to adult males, and
c = rate of crippling (unretrieved harvest).
This model assumes that annual variation in survival is due solely to variation in harvest rates, that relative
harvest vulnerability of the di erent age and sex classes is  xed and known, and that survival from natural
causes is  xed at its sample mean. We estimated   j = 0:7307 and 0.5950 for males and females, respectively.
Reproductive process
As with survival, annual reproductive rates must be predicted in advance of setting regulations. We relied
on the apparent relationship between breeding-population size and reproductive rates:
Rt = aebNt
where Rt is the reproductive rate (i.e., Amt
=d), Nt is breeding-population size in millions, and a and b are
model parameters. The least-squares parameter estimates were a = 2:508 and b = 􀀀0:875. Because of both
the importance and uncertainty of the relationship between population size and reproduction, we speci ed
two alternative models in which the slope (b) was  xed at the least-squares estimate   one standard error,
and in which the intercepts (a) were subsequently re-estimated. This provided alternative hypotheses of
strongly density-dependent (a = 4:154, b = 􀀀1:377) and weakly density-dependent reproduction (a = 1:518,
b = 􀀀0:373).
Variance of Prediction Errors
Using the balance equations and sub-models provided above, predictions of breeding-population size in year
t+1 depend only on the speci cation of a regulatory alternative and on an estimate of population size in
year t. For the period in which comparisons were possible (1991{96), we were interested in how well these
38
predictions corresponded with observed population sizes. In making these comparisons, we were primarily
concerned with how well the bias-corrected balance equations and reproductive and survival sub-models
performed. Therefore, we relied on estimates of harvest rates rather than regulations as model inputs.
We estimated the prediction-error variance by setting:
et = ln
􀀀
Nobs
t
 
􀀀 ln (Npre
t )
then assuming et   N
􀀀
0;  2
 
and estimating ^ 2 =
P
t
 
ln
���
Nobs
t
 
􀀀 ln (Npre
t )
 2
=n
where Nobs and Npre are observed and predicted population sizes (in millions), respectively, and n = 6.
Variance estimates were similar regardless of whether we assumed that the bias was in reproductive rates
or in survival, or whether we assumed that reproduction was strongly or weakly density-dependent. Thus,
we averaged variance estimates to provide a  nal estimate of  2 = 0:006, which is equivalent to a coe cient
of variation (CV ) of 8.0%. We were concerned, however, about the small number of years available for
estimating this variance. Therefore, we estimated an 80% con dence interval for  2 based on a Chi-squared
distribution and used the upper limit for  2 = 0.018 (i.e., CV = 14.5%) to express the additional uncertainty
about the magnitude of prediction errors attributable to potentially important environmental e ects not
expressed by the models.
Model Implications
Model-speci c regulatory strategies based on the hypothesis of weakly density-dependent reproduction are
considerably more conservative than those based on the hypothesis of strongly density-dependent reproduc-
tion. The three models with weakly density-dependent reproduction suggest a carrying capacity (i.e., average
population size in the absence of harvest) >2.0 million mallards, and prescribe extremely restrictive regu-
lations for population size <1.0 million. The three models with strongly density-dependent reproduction
suggest a carrying capacity of about 1.5 million mallards, and prescribe liberal regulations for population
sizes >300 thousand. Optimal regulatory strategies are relatively insensitive to whether models include a bias
correction or not. All model-speci c regulatory strategies are \knife-edged", meaning that large di erences
in the optimal regulatory choice can be precipitated by only small changes in breeding-population size. This
result is at least partially due to the small di erences in predicted harvest rates among the current regulatory
alternatives (see the section on Regulatory Alternatives).
Model Weights
We used Bayes' theorem to calculate model weights from a comparison of predicted and observed population
sizes for the years 1997{2010. We calculated weights for the alternative models based on an assumption
of equal model weights in 1996 (the last year data was used to develop most model components) and on
estimates of year-speci c harvest rates (Appendix E).
39
D WESTERN MALLARD MODELS
In contrast to mid-continent and eastern mallards, we did not model changes in population size for both the
Alaska and California-Oregon stocks of western mallards as an explicit function of survival and reproductive
rate estimates (which in turn may be functions of harvest and environmental covariates). We believed this
so-called \balance-equation approach" was not viable for western mallards because of insu cient banding in
Alaska to estimate survival rates, and because of the di culty in estimating stock-speci c fall age ratios from
a sample of wings derived from a mix of breeding stocks.
Western Mallard Breeding Population Estimates
Table D.1 { Estimates (N) and associated standard errors (SE) of mallards (in millions) observed in Alaska
(WBPHS strata 1{12) and California and Oregon (state surveys) combined.
Alaska California Oregon Total
Year N SE N SE N SE
1990 0.3669 0.0370
1991 0.3853 0.0363
1992 0.3457 0.0387 0.4835 0.0605 0.8292 0.0718
1993 0.2830 0.0295 0.4654 0.0510 0.7484 0.0589
1994 0.3509 0.0371 0.4367 0.0426 0.7876 0.0565
1995 0.5242 0.0680 0.4541 0.0428 0.9783 0.0803
1996 0.5220 0.0436 0.6451 0.0802 1.1671 0.0912
1997 0.5842 0.0520 0.6390 0.1043 1.2232 0.1166
1998 0.8362 0.0673 0.4868 0.0489 1.3230 0.0832
1999 0.7131 0.0696 0.6937 0.1066 1.4068 0.1273
2000 0.7703 0.0522 0.4639 0.0532 1.2342 0.0745
2001 0.7183 0.0541 0.4044 0.0451 1.1227 0.0705
2002 0.6673 0.0507 0.3775 0.0327 1.0449 0.0603
2003 0.8435 0.0668 0.4340 0.0501 1.2775 0.0835
2004 0.8111 0.0639 0.3547 0.0352 1.1658 0.0729
2005 0.7031 0.0547 0.4014 0.0474 1.1045 0.0724
2006 0.5158 0.0469 0.4879 0.0576 1.0037 0.0743
2007 0.5815 0.0551 0.4900 0.0546 1.0715 0.0775
2008 0.5324 0.0468 0.3814 0.0478 0.9138 0.0669
2009 0.5030 0.0449 0.3815 0.0639 0.8844 0.0781
2010 0.6056 0.0531 0.4430 0.0557 1.0485 0.0769
40
Model Structure
To evaluate western mallard population dynamics, we used a discrete logistic model (Schaefer 1954), which
combines reproduction and natural mortality into a single parameter r, the intrinsic rate of growth. The
model assumes density-dependent growth, which is regulated by the ratio of population size, N, to the
carrying capacity of the environment, K (i.e., equilibrium population size in the absence of harvest). In
the traditional formulation, harvest mortality is additive to other sources of mortality, but compensation for
hunting losses can occur through subsequent increases in production. However, we parameterized the model
in a way that also allows for compensation of harvest mortality between the hunting and breeding seasons.
It is important to note that compensation modeled in this way is purely phenomenological, in the sense
that there is no explicit ecological mechanism for compensation (e.g., density-dependent mortality after the
hunting season). The basic model for both the Alaska and California-Oregon stocks has the form:
Nt+1 =
 
Nt + Ntr
 
1 􀀀
Nt
K
  
(1 􀀀  t)
where,
 t = dhAM
t
and where t = year, hAM = the harvest rate of adult males, and d = a scaling factor. The scaling factor is
used to account for a combination of unobservable e ects, including un-retrieved harvest (i.e., crippling loss),
di erential harvest mortality of cohorts other than adult males, and for the possibility that some harvest
mortality may not a ect subsequent breeding-population size (i.e., the compensatory mortality hypothesis).
Estimation Framework
We used Bayesian estimation methods in combination with a state-space model that accounts explicitly for
both process and observation error in breeding population size. This combination of methods is becoming
widely used in natural resource modeling, in part because it facilitates the  tting of non-linear models that
may have non-normal errors (Meyer and Millar 1999). The Bayesian approach also provides a natural and
intuitive way to portray uncertainty, allows one to incorporate prior information about model parameters,
and permits the updating of parameter estimates as further information becomes available.
We  rst scaled N by K as recommended by Meyer and Millar (1999), and assumed that process errors et
were log-normally distributed with mean 0 and variance  2. Thus, the process model had the form:
Pt = Nt=Kt
log(Pt) = log
􀀀
[Pt􀀀1 + Pt􀀀1r (1 􀀀 Pt􀀀1)]
􀀀
1 􀀀 dhAM
t􀀀1
  
+ et
where,
et   N(0;  2)
The observation model related the unknown population sizes (PtK) to the population sizes (Nt) estimated
from the breeding-population surveys in Alaska and California-Oregon. We assumed that the observation
process yielded additive, normally distributed errors, which were represented by:
41
Nt = PtK + "BPOP
t ;
where,
"BPOP
t   N(0;  2B
POP ):
permitting us to estimate the process error, which re
ects the inability of the model to completely describe
changes in population size. The process error re
ects the combined e ect of misspeci cation of an appropriate
model form, as well as any un-modeled environmental drivers. We initially examined a number of possible
environmental covariates, including the Palmer Drought Index in California and Oregon, spring temperature
in Alaska, and the El Ni~no Southern Oscillation Index (http://www.cdc.noaa.gov/people/klaus.wolter/MEI/
mei.html). While the estimated e ects of these covariates on r or K were generally what one would expect,
they were never of su cient magnitude to have a meaningful e ect on optimal harvest strategies. We therefore
chose not to further pursue an investigation of environmental covariates, and posited that the process error
was a su cient surrogate for these un-modeled e ects. Parameterization of the models also required measures
of harvest rate. Beginning in 2002, harvest rates of adult males were estimated directly from the recovery of
reward bands. Prior to 1993, we used direct recoveries of standard bands, corrected for band-reporting rates
provided by Nichols et al. (1995b). We also used the band-reporting rates provided by Nichols et al. (1995b)
for estimating harvest rates in 1994 and 1995, except that we in
ated the reporting rates of full-address
and toll-free bands based on an unpublished analysis by Clint Moore and Jim Nichols (Patuxent Wildlife
Research Center). We were unwilling to estimate harvest rates for the years 1996{2001 because of suspected,
but unknown, increases in the reporting rates of all bands. For simplicity, harvest rate estimates were treated
as known values in our analysis, although future analyses might bene t from an appropriate observation
model for these data.
In a Bayesian analysis, one is interested in making probabilistic statements about the model parameters
( ), conditioned on the observed data. Thus, we are interested in evaluating P( jdata), which requires
the speci cation of prior distributions for all model parameters and unobserved system states ( ) and the
sampling distribution (likelihood) of the observed data P(dataj ). Using Bayes theorem, we can represent
the posterior probability distribution of model parameters, conditioned on the data, as:
P( jdata) / P( )   P(dataj )
Accordingly, we speci ed prior distributions for model parameters r, K, d, and P0, which is the initial
population size relative to carrying capacity. For both stocks, we speci ed the following prior distributions
for r, d, and  2:
r   Lognormal(􀀀1:0397; 1:4427)
d   Uniform(0; 2)
 2   Inverse 􀀀 gamma(0:001; 0:001)
The prior distribution for r is centered at 0.35, which we believe to be a reasonable value for mallards based on
life-history characteristics and estimates for other avian species. Yet the distribution also admits considerable
uncertainty as to the value of r within what we believe to be realistic biological bounds. As for the harvest-rate
scalar, we would expect d   1 under the additive hypothesis and d < 1 under the compensatory hypothesis.
As we had no data to specify an informative prior distribution, we speci ed a vague prior in which d could
take on a wide range of values with equal probability. We used a traditional, uninformative prior distribution
for  2. Prior distributions for K and P0 were stock-speci c and are described in the following sections.
42
We used the public-domain software WinBUGS (http://www.mrc-bsu.cam.ac.uk/bugs/) to derive samples from
the joint posterior distribution of model parameters via Markov-Chain Monte Carlo (MCMC) simulations. We
obtained 510,000 samples from the joint posterior distribution, discarded the  rst 10,000, and then thinned
the remainder by 50, resulting in a  nal sample of 10,000.
Alaska mallards
Data selection|Breeding population estimates of mallards in Alaska (and the Old Crow Flats in Yukon)
are available since 1955 in WBPHS strata 1{12 (Smith 1995). However, a change in survey aircraft in 1977
instantaneously increased the detectability of waterfowl, and thus population estimates (Hodges et al. 1996).
Moreover, there was a rapid increase in average annual temperature in Alaska at the same time, apparently
tied to changes in the frequency and intensity of El Ni~no events (http://www.cdc.noaa.gov/people/klaus.
wolter/MEI/mei.html). This confounding of changes in climate and survey methods led us to truncate the
years 1955{1977 from the time series of population estimates.
Modeling of the Alaska stock also depended on the availability of harvest-rate estimates derived from band-
recovery data. Unfortunately, su cient numbers of mallards were not banded in Alaska prior to 1990. A
search for covariates that would have allowed us to make harvest-rate predictions for years in which band-
recovery data were not available was not fruitful, and we were thus forced to further restrict the time series
to 1990 and later. Even so, harvest rate estimates were not available for the years 1996{2001 because of
unknown changes in band-reporting rates. Because available estimates of harvest rate showed no apparent
variation over time, we simply used the mean and standard deviation of the available estimates and generated
independent samples of predictions for the missing years based on a logit transformation and an assumption
of normality:
ln
 
ht
1 􀀀 ht
 
  Normal(􀀀2:3434; 0:0778) for t = 1996{2001
Prior distributions for K and P0|We believed that su cient information was available to use mildly informa-
tive priors for K and P0. In recent years the Alaska stock has contained approximately 0.8 million mallards.
If harvest rates have been comparable to that necessary to achieve maximum sustained yield (MSY) under
the logistic model (i.e., r /2), then we would expect K   1:6 million. On the other hand, if harvest rates
have been less than those associated with MSY, then we would expect K < 1:6 million. Because we believed
it was not likely that harvest rates were > r=2, we believed the likely range of K to be 0.8{1.6 million. We
therefore speci ed a prior distribution that had a mean of 1.4 million, but had a su ciently large variance
to admit a wide range of possible values:
K   Lognormal(0:13035; 0:41224)
Extending this line of reasoning, we speci ed a prior distribution that assumed the estimated population size
of approximately 0.4 million at the start of the time-series (i.e., 1990) was 20{60% of K. Thus on a log scale:
Po   Uniform(􀀀1:6094;􀀀0:5108)
Parameter estimates|The logistic model and associated posterior parameter estimates provided a reasonable
 t to the observed time-series of population estimates. The posterior means of K and r were similar to their
priors, although their variances were considerably smaller (Table 1). However, the posterior distribution of
d was essentially the same as its prior, re
ecting the absence of information in the data necessary to reliably
estimate this parameter.
43
Table D.2 { Estimates of model parameters resulting from  tting a discrete logistic model with MCMC to a
time series of estimated population sizes and harvest rates of mallards breeding in Alaska, 1990{2009.
Parameter Mean SD 95% credibility interval
K 1.129 0.319 0.658{1.869
P0 0.341 0.095 0.207{0.556
d 1.072 0.537 0.098{1.949
r 0.310 0.131 0.096{0.600
 2 0.023 0.013 0.007{0.056
California-Oregon mallards
Data selection|Breeding-population estimates of mallards in California are available starting in 1992, but
not until 1994 in Oregon. Also, Oregon did not conduct a survey in 2001. To avoid truncating the time series,
we used the admittedly weak relationship (P = 0.07) between California and Oregon population estimates
to predict population sizes in Oregon in 1992, 1993, and 2001. The  tted linear model was:
NOR
t = 68937 + 0:0961(NCA
t )
To derive realistic standard errors, we assumed that the predictions had the same mean coe cient of variation
as the years when surveys were conducted (n = 15, CV = 0.082). The estimated sizes and variances of the
CaliforniaOregon stock were calculated by simply summing the state-speci c estimates.
We pooled banding and recovery data for California and Oregon and estimated harvest rates in the same
manner as that for Alaska mallards. Although banded sample sizes were su cient in all years, harvest rates
could not be estimated for the years 1996{2001 because of unknown changes in band-reporting rates. As
with Alaska, available estimates of harvest rate showed no apparent trend over time, and we simply used the
mean and standard deviation of the available estimates and generated independent samples of predictions for
the missing years based on a logit transformation and an assumption of normality:
ln
 
ht
1 􀀀 ht
 
  Normal(􀀀2:2485; 0:1811) for t = 1996{2001
Prior distributions for K and P0|Unlike the Alaska stock, the California-Oregon population has been rela-
tively stable with a mean of 0.48 million mallards. We believed K should be in the range 0.48{0.96 million,
assuming the logistic model and that harvest rates were   r=2. We therefore speci ed a prior distribution
on K that had a mean of 0.7 million, but with a variance su ciently large to admit a wide range of possible
values:
K   Lognormal(􀀀0:5628; 0:41224)
The estimated size of the California-Oregon stock was 0.48 million at the start of the time-series (i.e., 1992).
We used a similar line of reasoning as that for Alaska for specifying a prior distribution P0, positing that
initial population size was 40-100% of K. Thus on a log scale:
Po   Uniform(􀀀0:9163; 0:0)
44
Table D.3 { Estimates of model parameters resulting from  tting a discrete logistic model with MCMC to
a time-series of estimated population sizes and harvest rates of mallards breeding in California and Oregon,
1992{2009.
Parameter Mean SD 95% credibility interval
K 0.636 0.172 0.440{1.095
P0 0.757 0.158 0.436{0.988
d 0.585 0.404 0.033{1.577
r 0.331 0.227 0.064{0.916
 2 0.013 0.012 0.001{0.043
Parameter estimates|The logistic model and associated posterior parameter estimates provided a reasonable
 t to the observed time series of population estimates. The posterior means of K and r were similar to their
priors, although the variances were considerably smaller (Table 2). Interestingly, the posterior mean of d was
< 1, suggestive of a compensatory response to harvest; however the standard deviation of the estimate was
large, with the upper 95% credibility limit > 1.
For each western mallard substock, we further summarized the simulation results for r, K, and the scaling
factor d to admit parametric uncertainty with a formal correlation structure within the optimization procedure
used to calculate the harvest strategy. We  rst de ned a joint distribution for 3 discrete outcomes for each of
the 3 population parameters. We used the 30 and 70 percent quantiles for each parameter as the cut points
to de ne three bins for which to discretize 3 values of each posterior distribution. We then determined the
frequency of occurrence of each of the 27 possible combinations of each parameter value falling within the 3
bins from the MCMC simulation results. These frequencies were then assigned parameter values based on
the midpoint of bin ranges (15, 50, 85 percent quantiles) to specify the joint distribution of the population
parameter values used in the optimization.
45
E MODELING MALLARD HARVEST RATES
Mid-continent
We modeled harvest rates of mid-continent mallards within a Bayesian hierarchical framework. We developed
a set of models to predict harvest rates under each regulatory alternative as a function of the harvest rates
observed under the liberal alternative, using historical information. We modeled the probability of regulation-
speci c harvest rates (h) based on normal distributions with the following parameterizations:
Closed: p(hC)   N( C;  2C
)
Restrictive: p(hR)   N( R;  2R
)
Moderate: p(hM)   N( M;  2M
)
Liberal: