Adaptive harvest management for eastern mallards progress report January 13, 2000

              U. S. Fish & Wildlife Service
Adaptive
Harvest Management
for Eastern Mallards
Progress Report
January 13, 2000
Adaptive Harvest Management for Eastern Mallards
Progress Report - January 13, 2000
Fred A. Johnson Diane R. Eggeman
Office of Migratory Bird Management Waterfowl Section
U.S. Fish & Wildlife Service Florida Fish & Wildlife Conservation Commission
Laurel, Maryland Tallahassee, Florida
James Dubovsky Mary Moore
Office of Migratory Bird Management Office of Migratory Bird Management
U.S. Fish & Wildlife Service U.S. Fish & Wildlife Service
Laurel, Maryland Laurel, Maryland
Introduction
The biology of eastern mallards appears to differ from that of midcontinent mallards (Fig. 1) in several
important ways. The size of the midcontinent population has been fairly stable over time, and numerically
is much larger than the eastern population. However, the eastern population appears to be more productive
than the midcontinent population, and apparently has been growing in size at least since the mid-1960's.
These biological differences suggest possible differences in allowable harvest pressure. Based on recent
analyses, the optimal regulatory strategy for eastern mallards is more liberal than that for the midcontinent
population, even in the face of regulation-specific harvest rates that are higher in eastern North America.
midcontinent
eastern
Mallard population:
Fig. 1. Survey areas currently assigned to the midcontinent and
eastern populations of mallards for purposes of harvest management.
AHM for Eastern Mallards Page 3
Because of these biological differences and their management implications, there has been considerable
interest in modifying the current AHM protocol to account for the status and dynamics of eastern mallards.
This modification involves:
(1) revision of the objective function to account for harvest-management goals for eastern mallards;
(2) augmentation of the decision criteria to include population and environmental variables relevant to
eastern mallards; and
(3) modification of the decision rules to allow Flyway-specific regulatory choices.
This report summarizes our efforts since August 1999 to address these issues. This report is intended
primarily as a synopsis of major findings and policy implications and, therefore, we have omitted a great
deal of technical detail. We hope to have a more comprehensive report available prior to the Flyway
Council technical meetings in February.
Modification of Decision Rules
The current AHM protocol permits one regulatory decision for all four Flyways based on the predicted fall-flight
of midcontinent mallards. Our goal is to allow Flyway-specific regulatory choices, which are
determined by each Flyway’s unique derivation of mallards (assuming, of course, that there is sufficient
differences in derivation among Flyways). This modification of the decision rules greatly complicates the
optimization procedure, however. Instead of five possible regulatory decisions (C, VR, R, M, and L), we
have to evaluate 54 = 625 decisions for every possible combination of each breeding population’s size and
associated environmental condition(s). In our effort to include eastern mallards in the AHM protocol, we
investigated the expected gain in management performance associated with moving from one nationwide
regulatory decision to Flyway-specific decisions for the Atlantic, Mississippi, and Central/Pacific Flyways.
Our intent was to determine the number of regulatory decisions that provided a reasonable balance between
management performance and regulatory complexity.
This exercise was based on an objective to maximize the harvest of eastern mallards, the “working model”
of eastern mallard population dynamics, and current models and management objective for midcontinent
mallards (U.S. Fish and Wildlife Service, 1999, Adaptive Harvest Management: 1999 Duck Hunting
Season, Dept. Inter., Washington, D.C., 37pp.). We evaluated a full range of possible harvest rates, rather
than discrete regulatory alternatives, and assumed perfect controllability of harvest. We derived optimal
harvest strategies using dynamic programming, and then simulated application of the strategies to derive
three measures of expected performance: (1) average population size of midcontinent mallards (Nm); (2)
average population size of eastern mallards (Ne); and (3) average aggregate harvest (H). We also
calculated the mean harvest rate (h) for each harvest area (i.e., each Flyway or combination of Flyways).
There were moderate gains in performance when comparing a 2-dimensional decision (i.e., Atlantic Flyway
vs. the remainder of the country) with a nationwide decision (Table 1). The 2-dimensional decision resulted
in an average midcontinent population size closer to the NAWMP goal, higher aggregate harvest, and
optimal harvest rates that were higher for the Atlantic Flyway. The additional gain in performance with a
3-dimensional decision was negligible.
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Table 1. Expected performance of optimal harvest strategies, conditioned on the number of harvest areas
for which regulatory decisions are made. (Definitions of metrics are provided in the report narrative.)
Performance metric
Decision space Nm* Ne* H* hAF hMF hremainder
(1) nationwide 7.85 1.36 1.55 0.14 0.14 0.14
(2) AF, remainder 8.21 0.88 1.66 0.29 0.12 0.12
(3) AF, MF, remainder 8.14 0.86 1.67 0.29 0.14 0.09
* in millions.
Based on this exercise, we used current harvest models (U.S. Fish and Wildlife Service, 1999:28-31,
Adaptive Harvest Management: 1999 Duck Hunting Season, Dept. Inter., Washington, D.C., 37pp.) to
predict population-specific harvest rates for the 25 combinations of regulatory alternatives in the Atlantic
Flyway and the remainder of the country. Harvest rates of midcontinent mallards are affected little by the
regulatory choice in the Atlantic Flyway because of the small proportion (2%) of midcontinent mallards
migrating to that Flyway (Table 2). However, harvest rates of eastern mallards are affected to a fair degree
by regulations in the western three Flyways because of the relatively high proportion (13%) of eastern
mallards that migrate there (Table 3).
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Table 2. Predicted harvest rates of midcontinent mallards for current regulatory alternatives, allowing for different
regulatory choices between the Atlantic Flyway and the remaining Flyways.
Proposed
Regulatory
Alternative for MF,
CF, and PF
Proposed
Regulatory
Alternative for
AF
Predicted MC
Mallard
Harvest Rate
(%)
Standard Error
Closed Closed 0.0 0.0
Closed Very Restrictive 1.9343 0.52116
Closed Restrictive 1.9722 0.52222
Closed Moderate 2.0326 0.52414
Closed Liberal 2.0681 0.52598
Very Restrictive Closed 5.2087 1.02560
Very Restrictive Very Restrictive 5.2644 1.06198
Very Restrictive Restrictive 5.3046 1.06890
Very Restrictive Moderate 5.3602 1.08056
Very Restrictive Liberal 5.4029 1.08706
Restrictive Closed 6.5760 1.36330
Restrictive Very Restrictive 6.6222 1.41532
Restrictive Restrictive 6.6530 1.42327
Restrictive Moderate 6.7240 1.43431
Restrictive Liberal 6.7595 1.44138
Moderate Closed 10.9442 2.50067
Moderate Very Restrictive 11.0389 2.63703
Moderate Restrictive 11.0792 2.64459
Moderate Moderate 11.1407 2.65685
Moderate Liberal 11.1774 2.66372
Liberal Closed 12.8217 3.04241
Liberal Very Restrictive 12.9129 3.20371
Liberal Restrictive 12.9520 3.21152
Liberal Moderate 13.0147 3.22356
Liberal Liberal 13.0514 3.23040
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Table 3. Predicted harvest rates of eastern mallards for current regulatory alternatives, allowing for different
regulatory choices between the Atlantic Flyway and the remaining Flyways.
Proposed
Regulatory
Alternative for AF
Proposed
Regulatory
Alternative for
MF, CF and PF
Predicted Eastern
Mallard Harvest
Rate (%)
Standard
Error
Closed Closed 0.0 0.0
Closed Very Restrictive 9.2678 1.41717
Closed Restrictive 9.5930 1.38131
Closed Moderate 10.6237 1.31170
Closed Liberal 11.0953 1.30447
Very Restrictive Closed 11.2990 2.10816
Very Restrictive Very Restrictive 12.1225 2.04704
Very Restrictive Restrictive 12.4476 2.03105
Very Restrictive Moderate 13.4784 2.01257
Very Restrictive Liberal 13.9482 2.02033
Restrictive Closed 12.3726 2.24807
Restrictive Very Restrictive 13.1961 2.19813
Restrictive Restrictive 13.5213 2.18646
Restrictive Moderate 14.5520 2.17861
Restrictive Liberal 15.0236 2.19051
Moderate Closed 14.0733 2.56853
Moderate Very Restrictive 14.7289 2.52117
Moderate Restrictive 15.2219 2.52950
Moderate Moderate 16.2527 2.53612
Moderate Liberal 16.7243 2.55214
Liberal Closed 15.0611 2.81626
Liberal Very Restrictive 15.8847 2.79176
Liberal Restrictive 16.2098 2.78818
Liberal Moderate 17.2405 2.80076
Liberal Liberal 17.7104 2.81849
AHM for Eastern Mallards Page 7
Harvest Management Objectives
The preliminary 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. The objective for midcontinent mallards is to
maximize long-term cumulative harvest, subject to a population goal of 8.7 million breeding birds. One of
the difficulties in modifying the current AHM protocol involves combining the population-specific
objectives into one objective function so that an aggregate harvest strategy can be derived. We initially
explored three possible forms for the aggregate objective function:
OF1: "Hm + He, which uses the actual harvest of eastern mallards (He) added to the harvest utility of
midcontinent mallards ("Hm , i.e., actual harvest [Hm] devalued ["] when populations are expected to be
lower than NAWMP goal). In this case, the value of the objective function is influenced heavily by the
harvest of midcontinent mallards because of the difference in size of the two populations.
OF2: "(Hm + He), which uses the actual harvest of eastern mallards added to the actual harvest of
midcontinent mallards, and then the sum is devalued when midcontinent mallard populations are expected
to be lower than NAWMP goal. For this objective function, a primary management concern would be the
NAWMP goal for midcontinent mallards. This objective likely would reduce harvest opportunity in the
Atlantic Flyway when midcontinent mallards were below the NAWMP goal.
OF3: weighting the actual harvest of eastern mallards and the harvest utility of midcontinent mallards to
account for the discrepancy in magnitude of the two populations:
OF3A: 0.2"Hm + 0.8He, which uses population-specific weights based on the relative magnitude of
each population’s predicted mean harvest. These are model-based weights, conditional on the
“working model” for eastern mallards and current models for midcontinent mallards.
OF3B: "Hm + 8.9He, which uses weights based on the difference in size of the two breeding
populations. We used the average ratio of breeding population estimates of midcontinent to eastern
mallards during 1992-99.
The expected performance of optimal harvest strategies was not sensitive to the form of the objective
function (Table 4), principally because there is a high degree of spatial separation of the two populations
during the hunting season.
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Table 4. Expected performance of optimal harvest strategies, conditioned on alternative objective functions. Nm =
average midcontinent population size, Ne = average eastern population size, H = average annual harvest utility, hAF
= average annual harvest rate in the Atlantic Flyway, Hremainder = average annual harvest rate in the remainder of the
country.
Performance metric
Objective Nm Ne H hAF hremainder
OF1: "Hm + He 8.21e6 0.88e6 1.66e6 0.289 0.121
OF2: "(Hm + He) 8.35e6 0.89e6 1.64e6 0.288 0.117
OF3A: 0.2"Hm + 0.8He 8.21e6 0.88e6 1.66e6 0.289 0.121
OF3B: "Hm + 8.9He 8.13e6 0.89e6 1.66e6 0.286 0.123
Models of Eastern Mallard Population Dynamics
The population dynamics of eastern mallards were studied extensively by Sheaffer and Malecki (1996, Quantitative
Models for Adaptive Harvest Management of Mallards in Eastern North America, New York Coop. Fish and
Wildl. Res. Unit, Ithaca, N.Y., 116pp.), 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 used to help managers understand the potential biological impacts of the current AHM process on eastern
mallards (U.S. Fish and Wildlife Service, 1999:21-24, Adaptive Harvest Management: 1999 Duck Hunting Season,
Dept. Inter., Washington, D.C., 37pp.).
We examined all structural components of the “working model,” updated relevant databases, tested various
hypotheses, and identified what we believed to be key sources of uncertainty in the population dynamics of eastern
mallards. We developed a set of eight alternative models based on differences in the functional form of the
relationship between dependent and independent variables of interest. This differs from our previous approach to
construction of alternative models that was based on parametric uncertainty after specifying a unique functional
form. Through extensive investigations, we have discovered that the functional forms used to express population
processes can have profound effects on optimal harvest strategies, even when alternative forms fit existing data
equally well (M.C. Runge, F. A. Johnson, J. D. Nichols, and W. L. Kendall, The importance of functional form in
optimal control solutions of population dynamics, unpubl. ms.).
Reproductive models: We made the decision to use fall age ratios of males rather than females to index production
of young. Using male-based age-ratios has two important advantages. First, there is evidence for eastern mallards
that natural mortality of females is high and variable, relative to males. Because we do not fully understand the
nature of the temporal variability, it is difficult to interpret female age ratios (e.g., high age ratios could mean good
production of young, poor summer survival of adults, or both). Although we recognize that males do not lay eggs,
we do believe that male age ratios should be a better index of production because natural mortality of males is
lower and less variable than that of females. Secondly, we found that the best predictor of male age-ratios is simply
breeding population size (i.e., the BBS index). Both spring precipitation and breeding population size are needed
in a model predicting female age-ratios, resulting in a model that is more complex, but that has no greater
explanatory power than the single-variable model for males. Our goal is model parsimony because model
complexity carries a high cost in terms of computing optimal harvest strategies.
AHM for Eastern Mallards Page 9
BBS
0 1 2 3 4 5
Male age ratio (A)
0.0
1.0
2.0
data
neg. exponential: A = 1.7330*e
-0.2036(BBS)
(P=0.007; R
2
=0.20)
logistic: A = 1.5027/(1+e
-(BBS-2.8608)/-0.649
) (P=0.01; R
2
=0.23)
linear: A = 1.6934-0.2717(BBS) (P=0.005; R2=0.22)
Fig. 2. Models relating the fall age ratio of eastern mallard males to a Breeding Bird Survey index in the
northeastern U.S.
We expressed fall age ratios of males as a function of a Breeding Bird Survey (BBS) index, which
represented a weighted average of stratum-specific indices in the northeastern U.S. (Fig. 2). We considered
three functional forms for this relationship: (1) negative exponential; (2) logistic; and (3) linear. The
logistic model expresses a dampening of density-dependent effects at small densities, while the negative
exponential model does not. These two models also differ in the degree which density dependence is
operative at high population levels. The linear model expresses the same degree of density dependence at
all population sizes. All three models fit the data equally well. From a biological perspective, we believed
the negative exponential and logistic to be most plausible and, therefore, retained them in the final model
set.
AHM for Eastern Mallards Page 10
N
0.0 5.0e+5 1.0e+6 1.5e+6 2.0e+6 2.5e+6 3.0e+6
BBS
0
2
4
6
8
10
12
14
16
18
20
logarithmic: BBS = 0.6184*e
1.3534E-6(N)
(P= 0.002; R
2
=0.85)
data
linear: BBS = -0.7234 + 3.136E-6(N) (P=0.003; R
2
=0.83)
exp. rise to max.: BBS = 11200.6(1-e
-0.0002E-6(N)
) (P=0.006; R
2
=0.77)
Fig. 3. The relationship between population size of eastern mallards (N) and the Breeding Bird Survey
index in the northeastern U.S.
We expressed the BBS index as a function of the combined population size of mallards in fixed-wing strata
(51-54, 56) and northeastern plot surveys (Fig. 3). This was necessary to enable managers to use current
estimates of population size, rather than the BBS index, as the criterion for regulatory decisions. We
considered three forms of the relationship: (1) logarithmic; (2) linear; and (3) exponential rise to a
maximum. All models fit the data equally well. We retained the logarithmic and exponential forms to
characterize possible extremes in the relationship. The logarithmic model tends to predict large changes in
the BBS index with small changes in population size. This might be the case if populations in areas
surveyed by the BBS were growing at a faster rate than in the population as a whole. The model specifying
an exponential rise to a maximum suggests that only small changes in the BBS index associated with large
changes in population size, which might be the case where BBS routes had become “saturated” with
mallards.
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Survival models: We compiled preseason banding and recovery records of mallards banded in reference
areas 8 (eastern Ontario, western Quebec), 15 and 16 (northeastern U.S.) for the period 1979-95. We
adjusted hunter recoveries for non-reporting of bands (Nichols et al., 1995, Geographic variation in band
reporting rates for mallards based on reward banding., J. Wildl. Manage. 59:697-708, and C. Moore, J.
Dubovsky and W. Kendall, unpubl. data) and for crippling loss, and then investigated spatial, temporal,
and demographic sources of variability in harvest and natural mortality rates. The most general model took
the form:
Sasry = 2asry ( 1 - Kasry),
where S = annual survival, 2 = survival from natural causes, K = rate of hunter kill, a = adult or young,
s = male or female, r = reference area, and y = year. Likelihood-ratio tests confirmed that all four sources
of variation were significant (P = 0.00), but even the most general model fit the data poorly (variance
inflation factor = 9.1). Although specification of adequate survival models has always been a problem for
eastern mallards, our models (general model above, as well as its reduced forms) nonetheless provide
relatively unbiased estimates of survival (although the estimated variances are biased low).
In all subsequent investigations, we used reduced models which ignored reference-area effects. While the
reference-area effects were substantial in some cases (particularly for kill rates), we did not have a
sufficient time-series of population estimates with which to weight reference-area specific estimates.
Therefore, our survival estimates reflect pooling of banding and recovery data across the three reference
areas. We also assumed no age effects in survival after the hunting season (i.e., differences in annual
survival of young and adults are attributable to differences in harvest pressure), and that sex-specific
differences in natural mortality are confined to the breeding season. Finally, we assumed that survival
during February-April was a constant 90%, and then calculated summer survival rates for males and
females (Fig. 4).
For females, we considered two alternative models for summer survival: (1) a mean model, with random
variation in summer survival; and (2) a logistic model in which variation in summer survival was a function
of the BBS index. The latter model reflects density-dependence in the mortality process, and provides a
mechanism to partially compensate for harvest during the previous hunting season. Summer survival of
males was higher on average than that for females, and was not related to the BBS index. Therefore, we
combined a single mean model with randomly varying summer survival for males with the two alternative
models for female survival.
Optimal Harvest Strategies
We first examined model behavior and optimal harvest strategies associated with the eight alternative
models (2 reproduction models × 2 BBS models × 2 survival models) of eastern mallard population
dynamics. In deriving optimal harvest strategies, we used an objective to maximize long-term cumulative
harvest, and assumed perfect controllability of harvest rates. Population sizes expected in the absence of
harvest, and when exposed to optimal harvest rates, varied among models (Table 5). However, there were
minimal differences among models in average optimal harvest rates. Optimal harvest rates tend to increase
with increasing population size, although the increase is not monotonic for all models (Fig. 5). For recent
population sizes (i.e., >1 million), seven of the eight models prescribe optimal harvest rates that are higher
than those attained with the current liberal regulatory alternative.
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BBS
0 1 2 3 4 5
Summer survival (S)
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
females
females - mean
males
males - mean
females: logit(S)=1.6746-0.5422(BBS) (P=0.007; R
2
=0.37)
Fig. 4. Estimated summer survival rates of male and female eastern mallards in relation to the Breeding Bird Survey
index in the northeastern U.S.
AHM for Eastern Mallards Page 13
Breeding population size
0.0 5.0e+5 1.0e+6 1.5e+6 2.0e+6 2.5e+6
0.0 5.0e+5 1.0e+6 1.5e+6 2.0e+6 2.5e+6
Harvest rate (AM)
0.0
0.1
0.2
0.3
0.4
0.5
0.0
0.1
0.2
0.3
0.4
0.5
r1b1s1
r1b1s2
r1b2s1
r1b2s2
r2b1s1
r2b1s2
r2b2s1
r2b2s2
Fig. 5. Optimal harvest rates (adult males) for eight alternative models of eastern mallard population
dynamics. Model designations refer to models described in Table 4.
Table 5. Expected population sizes of mallards in the absence of harvest and when exposed to optimal harvest
rates, for eight alternative models of population dynamics. Ph=0 = average population size expected in the absence
of harvest, P* = average population size expected under an optimal harvest regime, and h* = average optimal
harvest rate of adult males.
Model
Reproduction BBS Summer
survival
Designation Ph=0 P* h*
negative exponential logarithmic constant r1b1s1 1.95e6 0.91e6 0.20
negative exponential logarithmic f(BBS) r1b1s2 1.49e6 0.82e6 0.21
negative exponential expmax constant r1b2s1 3.49e6 1.20e6 0.18
negative exponential expmax f(BBS) r1b2s2 2.20e6 0.96e6 0.20
logistic logarithmic constant r2b1s1 1.41e6 0.77e6 0.22
logistic logarithmic f(BBS) r2b1s2 1.23e6 0.74e6 0.23
logistic expmax constant r2b2s1 1.68e6 0.83e6 0.22
logistic expmax f(BBS) r2b2s2 1.48e6 0.79e6 0.22
AHM for Eastern Mallards Page 14
We next examined optimal harvest strategies in which we integrated eastern and midcontinent mallards.
We specified the following conditions to derive an optimal strategy:
(1) an objective function that maximizes the long-term cumulative sum of eastern mallard harvest and
midcontinent mallard harvest utility (OF1: "Hm + He);
(2) all possible combinations of current regulatory alternatives in the Atlantic Flyway and the remainder of
the country (Tables 2 and 3), and an assumption of perfect controllability (i.e., deterministic harvest rates);
and
(3) current population models and associated weights for midcontinent mallards, and eight models of
eastern mallards, equally weighted.
The optimal regulatory choice for the Atlantic Flyway rarely diverges from the liberal alternative, even
when the status of midcontinent mallards is poor (Table 6). The status of eastern mallards has somewhat
more effect on the optimal regulatory choice in the remainder of the country, but the effect is minimal and
observed only under extreme conditions. These results are consistent with the high degree of spatial
discrimination between the two populations during the hunting season. We recognize that it is most
appropriate to develop the optimal strategy using: (1) smaller increments for population sizes and ponds
than we used here; and (2) harvest rates that incorporate stochastic variation. However, such a solution
likely will take approximately over three weeks on a dual-300mhz Pentium II processor. While we do not
expect any major changes in the patterns of optimal regulations presented here, we intend to make the more
comprehensive solution available prior to the winter Flyway meetings.
Table 6. Optimal regulatory choices for midcontinent and eastern mallards. The objective function,
models of population dynamics, and harvest rates associated with each regulatory alternative are provided
in text.
Midcontinent Mallard
Breeding Pop. (millions)
Prairie Ponds
(millions)
Eastern Mallard
Breeding Pop. (millions)
PF/CF/MF
Regulation
AF
Regulation
3 1-5 0.5-1.5 C L
3 6 0.5 C M
3 6 0.6-1.5 C L
3 7 0.5 C M
3 7 0.6-1.5 C L
4 1-6 0.5-1.5 C L
4 7 0.5 C M
4 7 0.6-1.5 C L
5 1-5 0.5-1.5 C L
5 6 0.5 C L
5 6 0.6-1.5 VR L
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5 7 0.5-0.6 VR L
5 7 0.7-1.5 R L
6 1-2 0.5-1.5 C L
6 3 0.5-1.5 VR L
6 4 0.5-0.6 VR L
6 4 0.7-1.5 R L
6 5 0.5-0.9 R L
6 5 1.0-1.5 R L
6 6 0.5 M M
6 6 0.6-1.5 M L
6 7 0.5 M M
6 7 0.6-1.5 M L
7 1 0.5-0.7 VR L
7 1 0.8-1.5 R L
7 2 0.5-1.5 R L
7 3 0.5-0.7 R L
7 3 0.8-1.5 M L
7 4 0.5 M M
7 4 0.6-1.5 M L
7 5 0.5 L M
7 5 0.6-1.5 L L
7 6-7 0.5-1.5 L L
8 1 0.5-1.5 M L
8 2 0.5-1.0 M L
8 2 1.1-1.3 L L
8 2 1.4-1.5 M L
8 3 0.5 M L
8 3 0.6-1.5 L L
8 4-7 0.5-1.5 L L
9 1 0.5 L M
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9 1 0.6-1.5 L L
9 2 0.5 L M
9 2 0.6-1.5 L L
9 3-7 0.5-1.5 L L
10 1 0.5 L M
10 1 0.6-1.5 L L
10 2-7 0.5-1.5 L L
11-12 1-7 0.5-1.5 L L
Conclusions
Modifying the AHM protocol to account for multiple duck populations is perhaps the most challenging
technical issue facing harvest managers. Never before have we tried to consider the status of multiple
populations in such a formal way, nor have we attempted to give Flyways the ability to choose regulations
that are predicated on their particular derivation of birds. We expect the effort with eastern mallards to be
precedent setting and, thus, must be done carefully and in a way that provides a sound conceptual
framework for considering additional populations in the future. In that regard, the approach described
herein provides an objective basis for determining the additional benefit derived from stratifying breeding
populations and harvest areas into more homogeneous units. However, the utility of this approach could be
greatly enhanced by incorporating the additional monitoring and assessment costs, and possibly
administrative costs, associated with these higher-level stratifications. Only then can we make sound and
effective decisions regarding the extent to which our harvest management protocol should account for
sources of spatial, temporal, and bio-organizational variation in the biological systems of interest.
With respect to our effort to account for both midcontinent and eastern mallards, we make the following
observations:
(1) Based on our investigation of the potential levels of stratification for harvest areas (i.e., the number of
Flyway-specific regulatory choices), we believe there is sufficient justification for allowing a regulatory
choice in the Atlantic Flyway that can differ from that in the remainder of the country. However, there
seems to be little additional benefit (in terms of harvest) from allowing different rates of harvest in the
Atlantic Flyway, Mississippi Flyway, and the remainder of the country, in spite of the considerable
difference in the proportion of eastern mallards migrating to the Mississippi Flyway and the western two
Flyways (13% vs. 0.05%, respectively). Moreover, when we permitted different harvest rates in the
Mississippi and Central/Pacific Flyways, the pattern of differences in Flyway-specific harvest rates was not
always intuitive and, consequently, raised questions regarding the most appropriate allocation of harvest
opportunity between the Mississippi Flyway and the remainder of the country. The allocation of
sustainable harvests (within that allowed by biological constraints) is a value judgement, and would require
considerable inter-Flyway dialogue before a broadly accepted harvest strategy could be derived.
(2) The patterns in predicted harvest rates associated with the 25 combinations of regulations in the
Atlantic Flyway and the remainder of the country are consistent with what we know about the wintering
distributions of midcontinent and eastern mallards. However, we emphasize that these predictions
AHM for Eastern Mallards Page 17
represent extrapolation beyond our range of experience. Moreover, the estimation procedure relies heavily on
statistical and conceptual models that must meet certain assumptions. We have no way to verify these
assumptions, nor can we gauge their effects should they not be met. Therefore, the use of this procedure for
predicting mallard harvest rates warrants considerable caution and underscores the need to accumulate experience
with a stable set of regulatory alternatives.
(3) Initially, we were surprised that management performance (in terms of expected population sizes and harvest)
was not sensitive to the form of the aggregate objective function. However, the result seems to follow from the
high degree of spatial segregation of the two mallard populations during the hunting season. Therefore, an
unweighted sum of population-specific harvest utilities seems to us a reasonable choice. However, we emphasize
that in many, if not most, cases of managing multiple stocks the form of the aggregate objective function will be
critical. Difficult value judgements will be necessary where populations vary markedly in abundance and capacity
to support harvest, and where there is limited ability to regulate population-specific harvest rates.
(4) We constructed alternative population models based on plausible functional forms of biological relationships,
rather than on the variance of parameter estimates from a given functional form. This decision was influenced
heavily by recent theoretical work, which suggests that the choice of functional form can greatly influence optimal
harvest strategies, and that this influence can exceed that associated with alternative parameter values for a given
statistical model. Our approach also has the advantage of providing alternative models that fit the data equally
well, which is not the case with models based on alternative parameter values. Finally, we believe that our
approach forces managers and researchers to think more critically about the nature of biological relationships,
particularly those system responses that might be observed beyond the range of experience.
(5) Our technical efforts to account for eastern mallards in the current AHM protocol appear to have substantial
policy implications. In particular, there seems to be no influence of midcontinent mallard status on Atlantic
Flyway regulatory prescriptions, nor does there seem to be any significant impact of eastern mallard status on
regulations in the remainder of the country (at least within the range of population sizes we examined). Therefore,
the additional benefit (in terms of harvest opportunity and the NAWMP goal for midcontinent mallards) of
integration appears to be negligible. However, the computational costs associated with derivation of the optimal
harvest strategy for midcontinent and eastern mallards is considerable. We experienced severe limitations in our
ability to fully explore the implications of all sources of uncertainty, for all possible system states, even when using
state-of-the-art Pentium workstations. We also are concerned about the implications of the integrated harvest
strategy for the Atlantic Flyway, which suggests liberal regulations under almost all conditions. Clearly, the
absence of any formal consideration for other key species in the Flyway (e.g., wood ducks, scaup) limits the utility
of this management strategy. Therefore, we suggest that it may be more productive to integrate the harvests of
eastern mallards with those of other key species in the Atlantic Flyway, rather than with midcontinent mallards. In
effect, we suggest that the management community consider allowing the regulatory decision in the western three
Flyways to be determined solely by the status of midcontinent mallards. For the Atlantic Flyway, we suggest that
managers may want to moderate the regulatory strategy designed to maximize the harvest of eastern mallards by:
(1) explicitly modeling the impacts of regulations on other species of concern; (2) decreasing the season length and
bag limits associated with the liberal regulatory alternative; or (3) using a population goal for eastern mallards that
was sufficiently high to introduce regulatory conservatism. The latter alternative would be the most practical in the
short term if a constraint were deemed necessary, but we believe a long-term solution involves explicit
consideration of the dynamics of other duck populations breeding in the Atlantic Flyway.
AHM for Eastern Mallards Page 18
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Tables 2 (page 5) and 3 (page 6) indicate 0.0% harvest rates for closed seasons in the United Sates. These
predictions are probably not correct, in that they do not account for the possibility that seasons in Canada
would remain open. While we don’t believe correction of this error will markedly change the results in this
report, we currently are attempting to derive more reliable predictions under the closed-season scenario.
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