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 fallflight 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).
AHM for Eastern Mallards Page 5

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
AHM for Eastern Mallards Page 6

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.
AHM for Eastern Mallards Page 8

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; R2=0.20)

logistic: A = 1.5027/(1+e-(BBS-2.8608)/-0.649) (P=0.01; R2=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*e1.3534E-6(N) (P= 0.002; R2=0.85)

data

linear: BBS = -0.7234 + 3.136E-6(N) (P=0.003; R2=0.83)

exp. rise to max.: BBS = 11200.6(1-e-0.0002E-6(N)) (P=0.006; R2=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.
AHM for Eastern Mallards Page 11

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.
AHM for Eastern Mallards Page 12

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; R2=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

B reed ing 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 (A

M)

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
AHM for Eastern Mallards Page 15

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
AHM for Eastern Mallards Page 16

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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