Adaptive harvest management considerations for the 1998 duck hunting season

              1
Adaptive Harvest Management
Considerations for the
1998 Duck Hunting Season
PREFACE
The process of setting waterfowl hunting regulations is conducted annually in the United States. This process
involves a number of meetings where the status of waterfowl is reviewed by the agencies responsible for setting
hunting regulations. In addition, the U.S. Fish and Wildlife Service (USFWS) holds public hearings and
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 1998 hunting season.
Specifically, this report is intended to provide waterfowl managers and the public with information about the
use of adaptive harvest management for setting duck-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 information presented herein may differ from that published previously. Moreover,
the set of regulatory alternatives has not yet been finalized for the 1998 hunting season and, therefore, harvest
strategies presented in this report should be considered preliminary.
ACKNOWLEDGEMENTS
A working group comprised of technical representatives from the USFWS and the four Flyway Councils
(Appendix A) was established in 1992 to review the scientific basis for managing waterfowl harvests. The
working group subsequently proposed a framework of adaptive harvest management (AHM), which was first
implemented in 1995. The USFWS expresses its gratitude to the working group and other individuals,
organizations, and agencies that have contributed to the development and implementation of AHM. We
especially thank D. J. Case and Associates for help with information and education efforts.
This report was prepared by the USFWS Adaptive Management & Assessment Team, which is administered
by the Office of Migratory Bird Management and the North American Waterfowl and Wetlands Office. Fred
A. Johnson was the principal author. J. P. Bladen, R. J. Blohm, D. F. Caithamer, D. J. Case, J. A. Dubovsky,
K. Gamble, J. R. Kelley, W. L. Kendall, E. M. Martin, M. T. Moore, M. C. Otto, P. I. Padding, A. Romer,
S. E. Sheaffer, G. W. Smith, and K. A. Wilkins provided information or otherwise assisted with report
preparation. Comments regarding this document should be sent to Paul R. Schmidt, Chief, Office of Migratory
Bird Management - USFWS, Arlington Square, Room 634, 4401 North Fairfax Drive, Arlington, VA 22203.
Cover art: the 1935 duck stamp with a pen and ink drawing of canvasbacks
by Frank W. Benson, who has been called the dean of American duck etchers.
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Annual reports on adaptive harvest management are available on the Internet at:
http://www.fws.gov/r9mbmo/reports/reports.html
TABLE OF CONTENTS
EXECUTIVE SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
BACKGROUND . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
MALLARD STOCKS AND FLYWAY MANAGEMENT . . . . . . . . . . . . . . . . . . . . . . . . . 5
MALLARD POPULATION DYNAMICS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
HARVEST MANAGEMENT OBJECTIVES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
REGULATORY ALTERNATIVES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
OPTIMAL HARVEST STRATEGIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
FUTURE CHALLENGES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
LITERATURE CITED . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
APPENDIX A: AHM Working Group . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
APPENDIX B: Eastern Mallard Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
APPENDIX C: Past Regulations and Harvest Strategies . . . . . . . . . . . . . . . . . . . . . 26
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EXECUTIVE SUMMARY
In 1995, the U.S. Fish and Wildlife Service (USFWS) embraced the concept of adaptive resource
management for regulating duck harvests in the United States. The adaptive 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. Moreover,
adaptive harvest management (AHM) relies on the iterative cycle of monitoring, assessment, and
decision making to clarify relationships among hunting regulations, harvests, and waterfowl
abundance.
To date, AHM has focused primarily on midcontinent mallards, but progress is being made on
extending the process to account for mallards breeding eastward and westward of the midcontinent
region. The ultimate goal is to develop Flyway-specific harvest strategies, which represent an average
of optimal strategies for each mallard breeding population, weighted by the relative contribution of
each population to the respective Flyways. Geographic boundaries used to define midcontinent and
eastern mallards have been established, and mathematical models of population dynamics are available
for predicting regulatory impacts. Investigations regarding the geographic bounds and population
dynamics of western mallards are ongoing.
A critical need for successful implementation of AHM is a set of regulatory alternatives that remain
fixed for an extended period. When AHM was first implemented in 1995, three regulatory
alternatives characterized as liberal, moderate, and restrictive were defined based on recent regulatory
experience. The 1995 regulatory alternatives also were considered for the 1996 hunting season. In
1997, the regulatory alternatives were modified in response to requests from the Flyway Councils.
Changes included provisions for additional hunting opportunity under the moderate and liberal
alternatives, as well as the addition of a very restrictive alternative. For the 1998 season, the USFWS
wishes to maintain the same regulatory alternatives as those considered in 1997, although a final
decision is pending.
Preliminary harvest strategies were derived for midcontinent and eastern mallards, but they do not
yet allow for Flyway-specific regulatory choices. The strategy for midcontinent mallards was based
on: (1) an objective to maximize long-term harvest and achieve a population goal of 8.7 million; (2)
an assumption that regulatory alternatives will remain the same as in 1997; and (3) current
understanding of regulatory impacts. Based on a breeding population size of 10.6 million mallards
and 2.5 million ponds in Prairie Canada, the optimal regulatory choice for midcontinent mallards in
1998 is the liberal alternative. The strategy for eastern mallards was based on: (1) an objective to
maximize long-term harvest; (2) the regulatory alternatives for 1997; and (3) a “working model” of
population dynamics. Based on a breeding population size of 1.0 million mallards and spring
precipitation of 11.6 inches, the optimal regulatory choice for eastern mallards in 1998 also is the
liberal alternative.
Future challenges include: (1) stabilization of regulatory alternatives for an extended period; (2)
development of large-scale habitat monitoring programs; (3) further refinement of mallard population
models; and (4) agreement on the appropriate scales of adaptive harvest management.
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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 harvest levels, population
size, and habitat conditions. This monitoring program represents the most comprehensive of its kind
for any widely distributed group of wildlife species. Data collected from this monitoring program are
analyzed each year, and proposals for duck-hunting regulations are developed by the Flyway
Councils, States, and U.S. Fish and Wildlife Service (USFWS). After extensive public review, the
USFWS announces a regulatory framework within which States can set their hunting seasons.
In 1995, the USFWS embraced the concept of adaptive resource management (Walters 1986) for
regulating duck harvests in the United States. The adaptive 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, in terms of sustainable
hunting opportunities, can be maximized only if regulatory effects can be predicted reliably. Thus,
adaptive management relies on the iterative cycle of monitoring, assessment, and decision making
described above 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 - 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 influence 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 effort, and other factors;
(3) 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;
(4) partial observability - the ability to estimate key population variables (e.g., population size,
reproductive rate, harvest) only within the precision afforded by existing monitoring programs.
Adaptive harvest management (AHM) was developed as a systematic process for dealing effectively
with these uncertainties. The key components of AHM (Johnson et al. 1993, Williams and Johnson
1995) include:
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(1) a limited number of regulatory alternatives, which contain Flyway-specific season lengths, bag
limits, and framework dates;
(2) a set of population models describing various hypotheses about the effects of harvest and the
environment 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 harvest strategies can be evaluated.
These components are used in an optimization procedure to derive a harvest strategy, which specifies
the appropriate regulatory choice 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:
(1) each year, an optimal regulatory alternative is identified based on resource and environmental
conditions, and on current model weights;
(2) after the regulatory decision is made, model-specific 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 most appropriate to describe the dynamics of the managed
population. 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.
MALLARD STOCKS AND FLYWAY MANAGEMENT
Since 1995, the AHM process has focused on midcontinent mallards, which are defined as those
breeding in federal survey strata 1-18, 20-50, and 75-77, and in Minnesota, Wisconsin, and Michigan
(Fig. 1). An optimal regulatory alternative for midcontinent mallards is based on breeding population
size and prairie water conditions, and on the weights assigned to the alternative models of population
dynamics. The same regulatory alternative is applied in all four Flyways, although season lengths and
bag limits are Flyway-specific.
Efforts are underway to extend the AHM process to account for mallards breeding westward and
eastward of the midcontinent survey area. These mallard stocks make significant contributions to the
total mallard harvest, particularly in the Atlantic and Pacific Flyways (Munro and Kimball 1982).
Extension of the current process to account for multiple mallard stocks and Flyway-specific
regulatory choices involves:
midcontinent
eastern
Mallard population:
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(1) augmentation of the decision criteria to include population and environmental variables
relevant to eastern and western mallards;
(2) revision of the objective function to account for harvest management objectives for mallards
outside the midcontinent region; and
(3) modification of the decision rules to allow independent regulatory choices in the Flyways.
An optimal harvest strategy for each Flyway then can be derived, which in effect would represent an
average of the optimal strategies for each breeding stock, weighted by the relative contribution of
each stock to the respective Flyways.
For the purposes of this report, eastern mallards are defined as those breeding in survey strata 51-54
and 56, and in New Hampshire, Vermont, Massachusetts, Connecticut, Rhode Island, New York,
Pennsylvania, New Jersey, Delaware, Maryland, and Virginia (Fig. 1). Managers are in the process
of establishing the geographic bounds of western mallards (see page 10).
Fig. 1. Survey areas currently assigned to the midcontinent and eastern populations of mallards for purposes of harvest
management.
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MALLARD POPULATION DYNAMICS
Midcontinent Mallards
Estimates of the entire midcontinent population (as defined above) are available only since 1992.
Since then, the number of midcontinent mallards has grown by an average of 8.9 percent (SE = 1.0)
per annum (Table 1).
Table 1. Estimatesa of midcontinent mallards breeding in the federal survey area (strata 1-18, 20-50, and 75-77) and
the states of Minnesota, Wisconsin, and Michigan.
Federal surveys State surveys Total
Year N SE N SE N SE
1992 5976.1 241.0 977.9 118.7 6954.0 268.6
1993 5708.3 208.9 863.5 100.5 6571.8 231.8
1994 6980.1 282.8 1103.0 138.8 8083.1 315.0
1995 8269.4 287.5 1052.2 130.6 9321.6 304.5
1996 7941.3 262.9 945.7 81.0 8887.0 275.1
1997 9939.7 308.5 1026.1 91.2 10965.8 321.7
1998 9640.4 301.6 979.6 88.4 10620.0 314.3
a In thousands.
ly, the dynamics of midcontinent mallards are described by four alternative models, whic
result fr s
e nt) about whether harvest is an additive or compensatory form of
m nd whether the reproductive process is weakly or strongly density
d lability limits reproductive success). The model with
ad hunting mortality and weakly density-dependent recruitment (S R t A W
conservative harvest strategy, whereas the model with compensatory hunting mortality and strongly
density-dependent recruitment leads to the most liberal strategy (S R ). The other two models (S R C S A S
and S R ) lead to strategies that are intermediate between these extremes. C W
Two other sources of uncertainty in mallard harvest management are acknowledged. Unpredictability
in environmental conditions is characterized by random variation in annual precipitation, which affects
the number of ponds available during May in Canada. There is also an accounting for partial
controllability, in which the link between regulations and harvest rates is imperfect due to
uncontrollable factors (e.g., weather, access to hunting areas) that affect mallard harvest. A detailed
description of the population dynamics of midcontinent mallards and associated sources of uncertainty
are provided by Johnson et al. (1997).
A key component of the AHM process for midcontinent mallards is the updating of model weights.
1996 1997 1998
Year
8
9
10
11
12
13
14
Population size (millions)
8
9
10
11
12
13
14
SaRs
SaRw
ScRs
ScRw
observed
8
These weights describe the relative ability of the alternative models to mimic changes in population
size, and they ultimately influence the nature of the optimal harvest strategy. Model weights are
based on a comparison of predicted and observed population sizes, with the updating leading to
higher weights for models that prove to be good predictors (i.e., models with relatively small
differences between predicted and observed population sizes) (Fig. 2). These comparisons must
account for sampling error (i.e., partial observability) in population size and pond counts, as well as
for partial controllability of harvest rates.
When the AHM process was initiated in 1995, the four alternative models of population dynamics
were considered equally likely, reflecting a high degree of uncertainty about harvest and
environmental impacts on mallard abundance. Model weights changed markedly in 1996, and have
remained relatively stable since (Table 2). On the whole, comparisons of observed and predicted
population sizes provide some evidence of strongly density-dependent reproduction, but little
indication of a compensatory response to hunting mortality.
Fig. 2. Estimates of observed mallard population size (solid bar) compared with predictions from four alternative models
of population dynamics (SaRs = additive mortality and strongly density-dependent reproduction; SaRw = additive
mortality and weakly density-dependent reproduction; ScRs = compensatory mortality and strongly density-dependent
reproduction; ScRw = compensatory mortality and weakly density-dependent reproduction).
Eastern Mallards
Midwinter counts and the Breeding Bird Survey provide evidence of exponential growth in the eastern
mallard population since the mid-1970s. This pattern of growth also is apparent in the more recent
fixed-wing (strata 51-54 and 56) and northeastern plot (New Hampshire south through Virginia)
surveys (Table 3), although population growth seems to have slowed in more recent years.
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Table 2. Temporal changes in probabilities ("weights") for alternative hypotheses of midcontinent mallard population
dynamics.
Model weights
Mortality
hypothesis Reproductive hypothesis 1995 1996 1997 1998
Additive Strong density dependence 0.2500 0.6417 0.5668 0.6462
Additive Weak density dependence 0.2500 0.3576 0.4235 0.3537
Compensatory Strong density dependence 0.2500 0.0005 0.0082 0.0001
Compensatory Weak density dependence 0.2500 0.0002 0.0015 0.0000
Table 3. Estimatesa of mallards breeding in the northeastern U.S. (plot survey from New Hampshire to Virginia) and
eastern Canada (fixed-wing survey strata 51-54 and 56).
Plot survey Fixed-wing survey Total
Year N SE N SE N SE
1990 665.1 78.3 190.7 47.2 855.8 91.4
1991 779.2 88.3 152.8 33.7 932.0 94.5
1992 562.2 47.9 320.3 53.0 882.5 71.5
1993 683.1 49.7 292.1 48.2 975.2 69.3
1994 853.1 62.7 219.5 28.2 1072.5 68.7
1995 862.8 70.2 184.4 40.0 1047.2 80.9
1996 848.4 61.1 283.1 55.7 1131.5 82.6
1997 795.1 49.6 212.1 39.6 1007.2 63.4
1998 775.1 49.7 263.8 67.2 1038.9 83.6
a In thousands.
The population dynamics of eastern mallards were studied extensively by Sheaffer and Malecki
(1996), but managers have not yet established a set of alternative models that characterize key
uncertainties about the mortality and reproductive processes. In the interim, a “working model” has
been developed to help managers understand the potential biological impacts of the current AHM
process on eastern mallards.
The working model of eastern mallards incorporates natural mortality rates that are similar to those
of midcontinent mallards and an assumption of completely additive hunting mortality. Reproductive
rates are predicted based on the size of the population and regional precipitation during March-May
of the current year. The reproductive process is characterized as strongly density dependent,
predicting the highest reproductive rates during years in which population size is relatively low and
spring precipitation is high. Mathematical details of the working model for eastern mallards are
provided in Appendix B.
0 1 2 3 4 5 6 7 8 9 10
Harvest value (%)
100
80
60
40
20
0
Expected population size next year (in millions)
population
goal = 8.7
10
Western Mallards
The analyses necessary to incorporate western mallards into the AHM process are ongoing. Initial
work has focused on delineating population boundaries by examining the geographic distribution of
recoveries from birds banded in various breeding areas. Mallards banded in the Pacific Flyway states,
British Columbia, the Yukon Territories, and southern Alberta have similar band-recovery
distributions, suggesting they share breeding, migration, and wintering areas. This analysis has
prompted concern over whether mallards in southern Alberta should be reassigned from the
midcontinent to the western population. Recent analyses of banding and harvest data suggest that
survival and productivity of breeding mallards in southern Alberta are similar to those in southern
Saskatchewan, implying that southern Alberta is correctly aligned with the midcontinent population.
In the next phase of investigation, efforts will be made to estimate reproductive and survival rates of
mallards breeding in the Pacific Flyway states (including Alaska), the Yukon Territories, and British
Columbia, and to identify important environmental factors influencing those rates.
HARVEST MANAGEMENT OBJECTIVES
Midcontinent Mallards
The basic harvest management objective for midcontinent mallards is to maximize cumulative harvest
over the long term, which inherently requires conservation of population size. Moreover, the
objective devalues harvest decisions that could be expected to result in a subsequent population size
below the goal of the North American Waterfowl Management Plan (NAWMP) (Fig. 3). The value
of harvest opportunity decreases proportionally as the difference between the goal and expected
population size increases. This balance of harvest and population objectives results in a harvest
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 losses in hunting opportunity. The current
objective uses a population goal of 8.7 million mallards, which is based on the NAWMP goal of 8.1
million for the federal survey area and a goal 0.6 million for the combined states of Minnesota,
Wisconsin, and Michigan.
Fig. 3. The relative value of mallard harvest, expressed as a function of breeding-population size expected in the
subsequent year.
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Eastern Mallards
For the purposes of this report, the management objective for eastern mallards is to maximize long-term
cumulative harvest. This objective is subject to change once the implications for average
population size, variability in annual regulations, and other performance characteristics are better
understood.
REGULATORY ALTERNATIVES
Evolution of Alternatives
When AHM was first implemented in 1995, three regulatory alternatives characterized as liberal,
moderate, and restrictive were defined based on regulations used during 1979-84, 1985-87, and 1988-
93, respectively (Appendix C, Table C-1). These regulatory alternatives also were considered for the
1996 hunting season. In 1997, the regulatory alternatives were modified 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. For the 1998 season, the USFWS wishes to maintain the same regulatory alternatives
as those used in 1997 (Table 4), although a final decision is pending (Federal Register 63:38705).
Mallard Harvest Rates
The most recent empirical estimates of mallard harvest rates are based on band-recovery data from
1979-93. Since 1995, harvest rates associated with the AHM regulatory alternatives have been
predicted using these estimates, which have been adjusted to reflect differences in season length and
bag limit, and for contemporary trends in hunter numbers (Table 5). These adjustments are not based
on band-recovery data, but rather on estimates of hunting effort and success from hunter surveys.
The reliability of these adjustments rests on the assumption that the ratio of total harvests achieved
under any two regulatory alternatives is equal to the ratio of harvest rates obtained under the same
two alternatives. The resulting predictions of harvest rates have large sampling variances, and their
accuracy is uncertain.
Harvest rates for each of the 1998 regulatory alternatives were predicted assuming no change in the
regulatory alternatives from 1997. However, expected harvest rates have changed due to revised
analytical procedures, which more reliably account for current framework dates, and for the fall and
winter distribution of mallards. The harvest-rate predictions changed most noticeably for eastern
mallards, primarily due to an increase in the estimated proportion of eastern mallards harvested in the
Atlantic Flyway.
Adult female mallards tend to be less vulnerable to harvest than adult males, while young are more
vulnerable (Table 6). Estimates of the relative vulnerability of adult females and young in the eastern
mallard population tend to be higher and more variable than in the midcontinent population.
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Table 4. Regulatory alternatives being considered for the 1998 duck-hunting season.
Flyway
Regulation Atlantica Mississippib Centralc Pacificd
Shooting hours one-half hour before sunrise to sunset for all Flyways
Framework dates Oct 1 - Jan 20 Saturday closest to October 1 and Sunday closest to January 20
Season length (days)
Very restrictive 20 20 25 38
Restrictive 30 30 39 60
Moderate 45 45 60 86
Liberal 60 60 74 107
Bag limit (total / mallard / female mallard)
Very restrictive 3 / 3 / 1 3 / 2 / 1 3 / 3 / 1 4 / 3 / 1
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 In the states of Alabama, Arkansas, Kentucky, Louisiana, Mississippi, and Tennessee, the season length and
framework closing date under the moderate and liberal alternatives have not been finalized.
c The High Plains Mallard Management Unit is allowed 8, 12, 23, and 23 extra days under the very restrictive, restrictive,
moderate, and liberal alternatives, respectively.
d The Columbia Basin Mallard Management Unit is allowed seven extra days under the very restrictive, restrictive, and
moderate alternatives.
Table 5. Expected harvest rates (SE) of adult male midcontinent and eastern mallards under different regulatory
alternatives, based on contemporary trends in hunter numbers. The predictions for 1998 are preliminary.
Mallard
Population
Regulatory alternatives considered for:
Alternative 1995 and 1996 1997 1998
Midcontinent Very restrictive N/A 0.060 (0.015) 0.067 (0.014)
Restrictive 0.084 (0.022) 0.084 (0.022) 0.869 (0.020)
Moderate 0.103 (0.027) 0.112 (0.029) 0.111 (0.026)
Liberal 0.123 (0.032) 0.139 (0.036) 0.133 (0.032)
Eastern Very restrictive N/A 0.084 (0.012) 0.130 (0.022)
Restrictive 0.112 (0.016) 0.118 (0.017) 0.148 (0.024)
Moderate 0.149 (0.021) 0.166 (0.023) 0.178 (0.027)
Liberal 0.151 (0.031) 0.200 (0.028) 0.197 (0.030)
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Table 6. Mean harvest vulnerability (SE) of female and young mallards, relative to adult males, based on band-recovery
data, 1979-95.
Age and sex
Mallard population Adult females Young females Young males
Midcontinent 0.748 (0.108) 1.188 (0.138) 1.361 (0.144)
Eastern 0.985 (0.145) 1.320 (0.264) 1.449 (0.211)
OPTIMAL HARVEST STRATEGIES
Midcontinent Mallards
The preliminary 1998 AHM strategy for midcontinent mallards was based on: (1) an assumption that
regulatory alternatives are unchanged from 1997; (2) model weights for 1998; and (3) the dual
objectives to maximize long-term cumulative harvest and achieve a population goal of 8.7 million
(Table 7). This strategy provides optimal regulatory choices for midcontinent mallards assuming that
all four Flyways would use the prescribed regulation. Ultimately, regulatory choices will be Flyway-specific
by accounting for the relative contribution of the three mallard breeding populations to each
Flyway. Overall, the 1998 harvest strategy is slightly more liberal than that for 1997, reflecting more
confidence in the strongly density-dependent reproductive hypothesis (Table 2). The optimal harvest
strategies for the 1995-97 seasons are provided in Appendix C (Tables C-2 to C-4) so that the reader
can see how the strategy for midcontinent mallards has “evolved” over time.
Table 7. Optimal regulatory choicesa for midcontinent mallards during the 1998 hunting season. This strategy is based
on the assumption that regulatory alternatives are unchanged from 1997, current model weights (Table 2), and on the
dual objectives of maximizing long-term cumulative harvest and achieving a population goal of 8.7 million.
Pondsb
Mallardsc 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0
<5.0
5.5 VR VR VR VR
6.0 VR VR VR VR VR R R R
6.5 VR VR VR VR VR R R M M L
7.0 VR R R R R M M L L L
7.5 R R M M M L L L L L
8.0 M M M L L L L L L L
8.5 M L L L L L L L L L
>9.0 L L L L L L L L L L
a VR = very restrictive, R = restrictive, M = moderate, and L = liberal.
b Estimated number of ponds in Prairie Canada in May, in millions.
c Estimated number of midcontinent mallards during May, in millions.
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Blank cells in Table 7 (and in other strategies in this report) represent combinations of population size
and environmental conditions that are insufficient to support an open season, given current regulatory
alternatives. In the case of midcontinent mallards, the prescriptions for closed seasons largely are a
result of the harvest management objective, which emphasizes population growth at the expense of
hunting opportunity when mallard numbers are below the NAWMP goal. However, limited harvests
at low population levels would not be expected to impact long-term population viability. Therefore,
the decision to actually close the hunting season would depend on both biological and sociological
considerations.
We simulated the use of the harvest strategy in Table 7 with the four population models and current
weights to determine expected performance characteristics. Assuming that harvest management
adhered to this strategy, the annual harvest and breeding population size would average 1.3 (SE =
0.5) million and 8.1 (SE = 0.8) million, respectively.
Based on a breeding population size of 10.6 million mallards and 2.5 million ponds in Prairie Canada
(and assuming regulatory alternatives remain the same as in 1997), the optimal regulatory choice for
midcontinent mallards in 1998 is the liberal alternative.
Eastern Mallards
The preliminary 1998 AHM strategy for eastern mallards was based on: (1) an assumption that
regulatory alternatives are unchanged from 1997; (2) the working model of population dynamics; and
(3) an objective to maximize long-term cumulative harvest (Table 8). The strategy is slightly more
conservative than that used last year, reflecting the increases in predicted harvest rates. Currently,
this strategy only provides optimal regulations for eastern mallards under the condition that all
Flyways would use the prescribed regulation. Ultimately, regulatory choices will be Flyway-specific
by accounting for the relative contribution of eastern and midcontinent mallards to each Flyway.
We simulated the use of this harvest strategy with the working model of population dynamics to
determine expected performance characteristics. Assuming that harvest management adhered to this
strategy, the annual harvest and breeding population size would average 354 (SE = 74) thousand and
999 (SE = 95) thousand, respectively.
Based on a breeding population size of 1.04 million mallards and spring precipitation of 11.6 inches
(and assuming that regulatory alternatives remain the same as in 1997), the optimal regulatory choice
for eastern mallards in 1998 is the liberal alternative.
FUTURE CHALLENGES
Fixed Regulatory Alternatives
A critical need for successful implementation of AHM is a set of regulatory alternatives that remain
fixed for an extended period. Frequent changes to the alternatives erode managers’ ability to learn
15
Table 8. Optimal regulatory choicesa for eastern mallards during the 1998 hunting season. This strategy is based on
the assumption that regulatory alternatives are unchanged from 1997, the working model of population dynamics, and
on an objective to maximize long-term cumulative harvest.
Spring precipitationb
Mallardsc 6 7 8 9 10 11 12 13 14 15
500 VR VR VR VR
550 VR VR VR VR R R
600 VR VR VR VR R M M L
650 VR VR VR VR R M M L L L
700 VR VR R M M L L L L L
750 R R M L L L L L L L
800 M M L L L L L L L L
850 M L L L L L L L L L
>900 L L L L L L L L L L
a VR = very restrictive, R = restrictive, M = moderate, and L = liberal.
b March to May precipitation in the northeastern U.S., in inches.
c Estimated number of eastern mallards in the combined fixed-wing and northeastern plot surveys, in thousands.
how regulations affect harvest and population size, and ultimately impact the ability to achieve
management objectives. Recognizing the need to stabilize the set of alternatives, the USFWS and
Flyway Councils expended considerable effort over the last two years to address concerns with the
original set of regulatory alternatives. Based on comments received to date, the regulatory
alternatives first considered for the 1997 hunting season appear to address most of those concerns.
During the last year, however, the USFWS came under increasing pressure to extend framework dates
(the outside dates within which States must set their hunting season) beyond those specified in the
current regulatory alternatives (Federal Register 63:29519-29520). In the interest of resolving the
issue, the USFWS encourages the Flyway Councils to discuss framework dates from a national
perspective. The USFWS believes that the National Flyway Council is the appropriate venue for this
dialogue because the issue inherently involves perceptions regarding the fair and equitable distribution
of hunting opportunity.
Large-scale Monitoring and Assessment of Waterfowl Habitat
Key to effective decision making within the AHM framework is at least some understanding of the
linkage between population abundance (and other demographic variables) and sport harvest, habitat
conditions, and other environmental features. This understanding is constructed from biological
monitoring and assessment programs, and is codified in mathematical models that help predict the
consequences of management actions. The monitoring and assessment programs used to guide
waterfowl management in North America are among the best such programs in the world.
Population-monitoring activities in particular are extensive and well focused, providing annual
estimates of breeding-population size, hunter activity and harvest, and reproductive and survival rates.
Si
' S0(1&$Ki)
16
However, mechanisms to monitor environmental conditions, and the effects of landscape changes,
are not well developed. Beyond an aerial survey of water conditions in the Prairie Pothole Region,
there are no systematic, large-scale programs to monitor important breeding or wintering habitats for
waterfowl.
The migratory nature of waterfowl will necessitate large-scale, coordinated approaches to
environmental monitoring, which can provide needed information at a variety of spatial and temporal
scales (Johnson et al. 1996). Large-scale monitoring programs are expensive, however, and managers
will need to rely on cost-effective remote sensing and GIS technologies. There have been some
recent successes in using low-level videography and satellite imagery to monitor spatial and temporal
variability in duck (Cowardin et al. 1995) and goose (Strong and Trost 1994) breeding habitat. To
date, however, the USFWS has been unable to mobilize the expertise needed to explore various air
and space-borne imaging platforms, data-management systems, habitat-recognition protocols, and
methods for integrating physiographic and biological information. Therefore, the USFWS recently
asked the National Aeronautics and Space Administration, through its Earth Science Strategic
Enterprise, to support the application of remote-sensing programs for monitoring migratory-bird
habitat changes on large geographic scales. If support is forthcoming, the effort would be
coordinated by the new USFWS Adaptive Management and Assessment Team, which is housed at
Patuxent Wildlife Research Center in Maryland.
Modeling Reproduction and Survival of Midcontinent Mallards
Reproduction--Current models used to predict reproductive success of midcontinent mallards include
as independent variables only the number of ponds and the size of the breeding population. Although
relationships between the number of duck broods and certain land-use variables (e.g., acreage of
crops) have been identified at small (i.e., stratum-level) scales, detection of similar relationships
between mallard age ratios and land-use variables measured at large scales has been elusive (M. W.
Miller, unpublished data). These results suggest that the large-scale spatial context of landscape
features may be important for predicting reproductive success. A recently-discovered relationship
between the mallard age ratio and the mean latitude of the breeding population also supports this
conclusion. Although landscape features other than pond numbers clearly could be useful for
predicting mallard reproductive success, additional work is needed to identify relevant landscape
features, as well as their appropriate spatial scale.
Survival--The current model set for midcontinent mallards includes two extreme forms of the
following model:
where S is annual survival, S is annual survival in the absence of hunting, $ is a compensation i 0
coefficient ($ = 0 implies total compensation and $ = 1 implies total additivity of hunting mortality),
and K = annual kill rate (Burnham et al. 1984). This model is useful in that it can be used to frame i
the debate over compensatory mortality (i.e., the model set for AHM includes $ = 0 and $ = 1). The
disadvantages are that: (1) the appropriate value for S under the two extreme models is unclear; and 0
(2) there is some evidence that $ changes over time, making it less useful for predictive purposes.
17
Current work is focusing on a more mechanistic model of survival, in which compensation for harvest
is allowed as a function of density-dependent mortality during the non-hunting season (Johnson et
al. 1993). A complicating factor in these investigations is that band-reporting rate, which is required
to convert band-recovery rates to kill rates, varies geographically (Nichols et al. 1995b). Recognition
of this variation has increased the number of model parameters that must be estimated, while making
band-recovery data more sparse. This situation, in turn, has caused difficulties in producing estimates
via existing computer programs. When these problems are resolved, the focus of the investigation
will turn to the identification of appropriately scaled environmental variables that influence annual
survival.
Modeling Reproduction and Survival of Eastern Mallards
Reproduction.--Among eastern mallards, there is a strong negative relationship between fall age ratios
and indices of breeding-population size, suggesting a high degree of density dependence in
reproduction. The nature of this relationship is important because the presence of strong density-dependence
in population growth can lead to very liberal harvest strategies. Therefore, further
investigations are needed to help understand whether the observed relationship actually represents
cause and effect. Also, questions remain about the influence of environmental conditions on
reproduction. To date, no weather variables have explained much of the variation in fall age ratios,
and it is unclear whether these results reflect an insensitivity to weather conditions or a failure to
identify the appropriate weather variable(s).
Survival.--There is some evidence that female mallards in the eastern population are more vulnerable
to harvest than their midcontinent counterparts. However, it has been difficult to understand the
spatial and temporal patterns (if any) of harvest vulnerability because band-reporting rates for female
mallards in eastern North America are unknown. Until estimates of band-reporting rate are available,
managers perhaps should consider sex-specific harvest vulnerability as a key source of uncertainty
in population models for eastern mallards.
Ecological Variation and the Question of Management Scale
All ecological systems exhibit variability on a broad range of temporal, spatial, and organizational (or
taxonomic) scales as a function of how individuals respond to their environment. The scale at which
individuals are aggregated for harvest-management purposes is an arbitrary decision, but one that can
strongly influence both the benefits and costs of management. Harvest management systems defined
at scales that account explicitly for large amounts of biological variation will produce relatively high
benefits, but also are characterized by high monitoring and assessment costs.
Determining the optimal scale for harvest management depends critically on the availability of explicit
performance criteria (i.e., management goals, objectives, and constraints, including how harvest
should be allocated among users) and on descriptions of how biological attributes vary among
different scales. The description of biological patterns, in turn, involves the use of data to explore
variation as a function of scale and to elucidate underlying causal mechanisms. The history of
waterfowl harvest management has been characterized by persistent efforts to account for increasingly
18
more spatial and organizational variation in waterfowl biology, but serious questions remain about
the cost-effectiveness of this approach. Based on both technical and social considerations, the AHM
framework may not be extended much beyond the three mallard stocks now under consideration.
Passive Versus Active Adaptive Management
The current protocol for AHM is passively adaptive, in the sense that any new knowledge about the
impacts of hunting regulations is an unplanned by-product of the process. The recognition that some
regulatory choices are more informative than others has led managers to consider more actively
adaptive strategies (Nichols et al. 1995a, Williams and Johnson 1995). Actively adaptive strategies
explicitly recognize that a reduction in management uncertainty is crucial to long-term success. Thus,
development of such strategies involves a tradeoff between short-term management performance and
the long-term value of knowing which alternative model of system dynamics is most appropriate.
Actively adaptive strategies are expected to perform better than passive strategies when the
management objective is based on an extended time frame (as in natural resource management).
Recent advances in theory and software have overcome some of the limitations in computing actively
adaptive strategies, and the AHM working group has begun to explore differences between passive
and active strategies for midcontinent mallards. In analyses to date, there appears to be a fairly broad
range of abundance in both midcontinent mallards and Canadian ponds where there is little or no
difference in passive and active policies. Under some conditions, however, the actively adaptive
policy is either more liberal or more restrictive than the corresponding passive policy. For the 1998
hunting season, there is no difference in the optimal regulatory choice between a passively adaptive
and an actively adaptive strategy. Further work is needed, however, to clarify the differences between
passive and active policies as a function of model weights, management objectives, planning horizons,
and other AHM features.
LITERATURE CITED
Blohm, R. J. 1989. Introduction to harvest - understanding surveys and season setting. Proc. Inter.
Waterfowl Symp. 6:118-133.
Burnham, K. P., G. C. White, and D. R. Anderson. 1984. Estimating the effect of hunting on annual
survival rates of adult mallards. J. Wildl. Manage. 48:350-361.
Cowardin, L. M., T. L. Shaffer, and P. M. Arnold. 1995. Evaluations of duck habitat and estimation
of duck population sizes with a remote-sensing-based system. Natl. Bio. Ser. Sci. Rep. 2.
26pp.
Johnson, F.A., C. T. Moore, W. L. Kendall, J. A. Dubovsky, D. F. Caithamer, J. R. Kelley, Jr., and
B. K. Williams. 1997. Uncertainty and the management of mallard harvests. J. Wildl.
Manage. 61:202-216.
19
_____, 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. Trans. North Am. Wildl. Nat. Resour. Conf. 58:565-583.
_____, _____, and P. R. Schmidt. 1996. Adaptive decision-making in waterfowl harvest and habitat
management. Proc. Inter. Waterfowl Symp. 7:26-33.
Munro, R. E., and C. F. Kimball. 1982. Population ecology of the mallard. VII. Distribution and
derivation of the harvest. U.S. Fish and Wildl. Serv. Resour. Pub. 147. 127pp.
Nichols, J. D., F. A. Johnson, and B. K. Williams. 1995a. Managing North American waterfowl
in the face of uncertainty. Ann. Rev. Ecol. Syst. 26:177-199.
_____, 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. J. Wildl. Manage.
59:697-708.
Sheaffer, S. E., and R. A. Malecki. 1996. Quantitative models for adaptive harvest management of
mallards in eastern North America. New York Coop. Fish and Wildl. Res. Unit, Cornell
Univ., Ithaca, unpubl. rep. 116pp.
Strong, L.L., and R.E. Trost. 1994. Forecasting production of Arctic nesting geese by monitoring
snow cover with Advanced Very High Resolution Radiometer data. Pages 425-430 in Proc.
PECORA 12 Symposium, Land Information from Space-Based Systems, Amer. Soc.
Photogrammetry, Bethesda, Md.
Walters, C. J. 1986. Adaptive management of renewable resources. MacMillan Publ. Co., New
York, N.Y. 374pp.
Williams, B. K., and F. A. Johnson. 1995. Adaptive management and the regulation of waterfowl
harvests. Wildl. Soc. Bull. 23:430-436.
_____, _____, and K. Wilkins. 1996. Uncertainty and the adaptive management of waterfowl
harvests. J. Wildl. Manage. 60:223-232.
20
APPENDIX A: AHM Working Group
Bob Blohm
U.S. Fish and Wildlife Service fax: 703-358-2272
Arlington Square, Room 634 e-mail: robert_blohm@fws.gov
4401 North Fairfax DriveArlington, VA 22203
phone: 703-358-1966
Brad Bortner
U.S. Fish and Wildlife Service fax: 503-231-2364
911 NE 11th Ave. e-mail: brad_bortner@fws.gov
Portland, OR 97232-4181
phone: 503-231-6164
Frank Bowers
U.S. Fish and Wildlife Service fax: 404-679-7285
1875 Century Blvd., Suite 345 e-mail: frank_bowers@fws.gov
Atlanta, GA 30345
phone: 404-679-7188
Don Brazil
Dept. of Wildlife, Fisheries, & Parks fax: 601-364-2008
P.O. Box 451 e-mail: janice@mdwfp.state.ms.us
Jackson, MS 39205
phone: 601-364-2211
Dave Caithamer
U.S. Fish & Wildlife Service fax: 301-497-5871
11500 American Holly Drive e-mail: dave_caithamer@fws.gov
Laurel, MD 20708-4016
phone: 301-497-5865
Dave Case
D.J. Case & Associates fax: 219-258-0189
607 Lincolnway West e-mail: djcase@csi.com
Mishawaka, IN 46544
phone: 219-258-0100
Dale Caswell
Canadian Wildlife Service fax: 204-983-5248
123 Main St. Suite 150 e-mail: dale.caswell@ec.gc.ca
Winnepeg, Manitoba, CANADA R3C 4W2
phone: 204-983-5260
21
John Cornely
U.S. Fish and Wildlife Service fax: 303-236-8680
P.O. Box 25486, DFC e-mail: john_cornely@fws.gov
Denver, CO 80225
phone: 303-236-8676
Gary Costanzo
Dept. of Game and Inland Fisheries fax: 757-253-4182
5806 Mooretown Road e-mail: gcostanzo@dgif.state.va.us
Williamsburg, VA 23188
phone: 757-253-4180
Jim Dubovsky
U.S. Fish & Wildlife Service fax: 301-497-5706
11510 American Holly Drive e-mail: james_dubovsky@fws.gov
Laurel, MD 20708-4017
phone: 301-497-5870
Joe Gabig
Game & Parks Commission fax: 402-471-5528
P.O. Box 30370 e-mail: jgabig@ngpsun.ngpc.state.ne.us
Lincoln, NE 68503-1417
phone: 402-471-5437
Ken Gamble
U.S. Fish and Wildlife Service fax: 573-876-1917
608 Cherry Street, Room 119 e-mail: ken_gamble@fws.gov
Columbia, MO 65201
phone: 573-876-1915
George Haas
U.S. Fish and Wildlife Service fax: 413-253-8480
300 Westgate Center Drive e-mail: george_haas@fws.gov
Hadley, MA 01035-9589
phone: 413-253-8576
Jeff Haskins
U.S. Fish and Wildlife Service fax: 505-248-7885
P.O. Box 1306 e-mail: jeff_haskins@fws.gov
Albuquerque, NM 87103
phone: 505-248-6827 ext 30
Jeff Herbert
Dept. of Fish, Wildlife and Parks fax: 406-444-4952
1420 East 6th Avenue e-mail: jherbert@mt.gov
Helena, MT 59620
phone: 406-444-2612
22
Dale Humburg
Dept. of Conservation fax: 573-882-4567
Fish & Wildlife Research Center e-mail: humbud@mail.conservation.state.mo.us
1110 South College Ave.
Columbia, MO 65201
phone: 573-882-9880 ext 3246
Fred Johnson
U.S. Fish & Wildlife Service fax: 301-497-5706
11510 American Holly Drive e-mail: fred_a_johnson@fws.gov
Laurel, MD 20708-4017
phone: 301-497-5861
Mike Johnson
Game and Fish Department fax: 701-328-6352
100 North Bismarck Expressway e-mail: mjohnson@state.nd.us
Bismarck, ND 58501-5095
phone: 701-328-6319
Jim Kelley
U.S. Fish & Wildlife Service fax: 301-497-5871
11500 American Holly Drive e-mail: james_r_kelley@fws.gov
Laurel, MD 20708-4016
phone: 301-497-5862
Bill Kendall
Patuxent Wildlife Research Center fax: 301-497-5666
11510 American Holly Drive e-mail: william_kendall@nbs.gov
Laurel, MD 20708-4017
phone: 301-497-5868
Bob Leedy
U.S. Fish and Wildlife Service fax: 907-786-3641
1011 East Tudor Road e-mail: robert_leedy@fws.gov
Anchorage, AK 99503-6119
phone: 907-786-3446
Mary Moore
U.S. Fish & Wildlife Service fax: 706-769-2359
206 Concord Drive e-mail: mary_moore@fws.gov
Watkinsville, GA 30677
phone: 706-769-2359
Jim Nichols
Patuxent Wildlife Research Center fax: 301-497-5666
11510 American Holly Drive e-mail: jim_nichols@usgs.gov
Laurel, MD 20708-4017
phone: 301-497-5660
23
Mark Otto
U.S. Fish & Wildlife Service fax: 301-497-5871
11500 American Holly Drive e-mail: mark_otto@fws.gov
Laurel, MD 20708-4016
phone: 301-497-5872
Paul Padding
U.S. Fish & Wildlife Service fax: 301-497-5981
10815 Loblolly Pine Drive e-mail: paul_padding@fws.gov
Laurel, MD 20708-4028
phone: 301-497-5980
Jerry Serie
U.S. Fish & Wildlife Service fax: 301-497-5885
12100 Beech Forest Road e-mail: jerry_serie@fws.gov
Laurel, MD 20708-4038
phone: 301-497-5851
Dave Sharp
U.S. Fish and Wildlife Service fax: 303-275-2384
P.O. Box 25486, DFC e-mail: dave_sharp@fws.gov
Denver, CO 80225-0486
phone: 303-275-2385
Sue Sheaffer
Coop. Fish & Wildl. Research Unit fax: 607-255-1895
Fernow Hall, Cornell University e-mail: ses11@cornell.edu
Ithaca, NY 14853
phone: 607-255-2837
Graham Smith
U.S. Fish & Wildlife Service fax: 301-497-5871
11500 American Holly Drive e-mail: graham_smith@fws.gov
Laurel, MD 20708-4016
phone: 301-497-5860
Bryan Swift
Dept.of Environmental Conservation fax: 518-478-0142
108 Game Farm Road, Building 9 e-mail: bryan.swift@dec.mailnet.state.ny.us
Delmar, NY 12054-9767
phone: 518-439-8083
Bob Trost
U.S. Fish and Wildlife Service fax: 503-231-6228
911 NE 11th Ave. e-mail: robert_trost@fws.gov
Portland, OR 97232-4181
phone: 503-231-6162
24
Khristi Wilkins
U.S. Fish & Wildlife Service fax: 301-497-5971
11500 American Holly Drive e-mail: khristi_a_wilkins@fws.gov
Laurel, MD 20708-4016
phone: 301-497-5557
Dan Yparraguirre
Dept. of Fish & Game fax: 916-653-1019
1416 Ninth Street e-mail: dyparrag@hq.dfg.ca.gov
Sacramento, CA 94244
phone: 916-653-8709
25
APPENDIX B: Eastern Mallard Model
The working model for eastern mallards predicts population size (N) as measured in the combined
federal and state waterfowl surveys in eastern Canada and the northeastern U.S. However, these
surveys have not been operational long enough to permit estimation of the relationship between
abundance and reproductive rate. Therefore, the model relies on a Breeding Bird Survey (BBS)
index, and its empirical relationship to N, to predict annual reproduction:
A(t) = 1.164646 - 0.200989 * BBS(t) + 0.085330 * SPRPPT(t) ,
where
t = year,
A(t) = predicted fall age ratio of females (young/adult),
BBS(t) = 0.000004656 * N(t), and
SPRPPT(t) = total precipitation (in inches) during March-May in the northeastern states.
SPRPPT is described as an independent, normally distributed random variable with mean = 10.7 and
standard deviation = 4.0.
The model assumes complete additivity of hunting mortality, and predicts changes in population size
using:
N(t+1) = N(t) * f(t) ,
where
f(t) = ((1 - sex) * ssf * (SHAF(t) + A(t) * (SHYF(t) + SHYM(t))) + sex * ssm * SHAM(t)) * sw ,
and where
sex = 0.55 = mean proportion of males in the breeding population,
ssf = 0.71 = summer survival of females,
ssm = 0.90 = summer survival of males,
sw = 0.90 = winter survival,
SHAF(t) = hunting-season survival of adult females,
SHYF(t) = hunting-season survival of young females,
SHYM(t) = hunting-season survival of young males, and
SHAM(t) = hunting-season survival of adult males.
Hunting-season survival rates are calculated using harvest rates predicted for each regulatory
alternative, which are adjusted to account for a crippling loss of 20 percent.
26
APPENDIX C: Past Regulations and Harvest Strategies
Table C-1. Regulatory alternatives considered for the 1995 and 1996 duck-hunting seasons.
Flyway
Regulation Atlantic Mississippi Centrala Pacificb
Shooting hours one-half hour before sunrise to sunset for all Flyways
Framework dates Oct 1 - Jan 20 Saturday closest to October 1 and Sunday closest to January 20
Season length (days)
Restrictive 30 30 39 59
Moderate 40 40 51 79
Liberal 50 50 60 93
Bag limit (total / mallard / female mallard)
Restrictive 3 / 3 / 1 3 / 2 / 1 3 / 3 / 1 4 / 3 / 1
Moderate 4 / 4 / 1 4 / 3 / 1 4 / 4 / 1 5 / 4 / 1
Liberal 5 / 5 / 1 5 / 4 / 1 5 / 5 / 1 6-7c / 6-7c / 1
a The High Plains Mallard Management Unit was allowed 12, 16, and 23 extra days under the restrictive, moderate,
and liberal alternatives, respectively.
b The Columbia Basin Mallard Management Unit was allowed seven extra days under all three alternatives.
c The limits were 6 in 1995 and 7 in 1996.
27
Table C-2. Optimal regulatory choicesa for midcontinent mallards during the 1995 hunting season. This strategy is
based on the regulatory alternatives for 1995, equal weights for four alternative models of population dynamics, and
the dual objectives of maximizing long-term cumulative harvest and achieving a population goal of 8.7 million.
Pondsb
Mallardsc 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0
4.5 R R M M M M L L L L
5.0 M M L L L L L L L L
5.5 L L L L L L L L L L
6.0 L L L L L L L L L L
6.5 L L L L L L L L L L
7.0 L L L L L L L L L L
7.5 L L L L L L L L L L
8.0 L L L L L L L L L L
8.5 L L L L L L L L L L
9.0 L L L L L L L L L L
9.5 L L L L L L L L L L
10.0 L L L L L L L L L L
10.5 L L L L L L L L L L
11.0 L L L L L L L L L L
a R = restrictive, M = moderate, and L = liberal.
b Estimated number of ponds in Prairie Canada in May, in millions.
c Estimated number of midcontinent mallards during May, in millions.
28
Table C-3. Optimal regulatory choicesa for midcontinent mallards during the 1996 hunting season. This strategy is
based on the regulatory alternatives and model weights for 1996, and the dual objectives of maximizing long-term
cumulative harvest and achieving a population goal of 8.7 million.
Pondsb
Mallardsc 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0
4.5
5.0
5.5 R R R R
6.0 R R R R R M M
6.5 R R R R R M M L L L
7.0 R R R M M L L L L L
7.5 R M M L L L L L L L
8.0 M L L L L L L L L L
8.5 L L L L L L L L L L
9.0 L L L L L L L L L L
9.5 L L L L L L L L L L
10.0 L L L L L L L L L L
10.5 L L L L L L L L L L
11.0 L L L L L L L L L L
a R = restrictive, M = moderate, and L = liberal.
b Estimated number of ponds in Prairie Canada in May, in millions.
c Estimated number of midcontinent mallards during May, in millions.
29
Table C-4. Optimal regulatory choicesa for midcontinent mallards during the 1997 hunting season. This strategy is
based on regulatory alternatives and model weights for 1997, and on the dual objectives of maximizing long-term
cumulative harvest and achieving a population goal of 8.7 million.
Pondsb
Mallardsc 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0
4.5
5.0
5.5 VR VR VR
6.0 VR VR VR VR VR VR R R
6.5 VR VR VR VR VR R R R M M
7.0 VR VR R R R R M M L L
7.5 R R R M M M L L L L
8.0 M M M M L L L L L L
8.5 M M M L L L L L L L
9.0 L L L L L L L L L L
9.5 L L L L L L L L L L
10.0 L L L L L L L L L L
10.5 L L L L L L L L L L
11.0 L L L L L L L L L L
a VR = very restrictive, R = restrictive, M = moderate, and L = liberal.
b Estimated number of ponds in Prairie Canada in May, in millions.
c Estimated number of mid-continent mallards during May, in
millions.