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This is to certify that the
thesis entitled

HOW MANY FISH ARE THERE AND HOW MANY CAN WE KILL?
IMPROVING CATCH PER EFFORT INDICES OF ABUNDANCE
AND EVALUATING HARVEST CONTROL RULES FOR LAKE
WHITEFISH IN THE GREAT LAKES

presented by

Jonathan J. Deroba

has been accepted towards fulfillment
of the requirements for the

 

 

PhD. degree in Fisheries and Wildlife, and
Ecology, Evolutionary Biology, and
Behavior
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HOW MANY FISH ARE THERE AND HOW MANY CAN WE KILL? IMPROVING-
CATCH PER EFFORT INDICES OF ABUNDANCE AND EVALUATING HARVEST
CONTROL RULES FOR LAKE WHITEFISH IN THE GREAT LAKES
By

Jonathan J. Deroba

A DISSERTATION ‘

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY
Fisheries and Wildlife, and Ecology, Evolutionary Biology, and Behavior

2009

ABSTRACT

HOW MANY FISH ARE THERE AND HOW MANY CAN WE KILL? IMPROVING
CATCH PER EFFORT INDICES OF ABUNDANCE AND EVALUATING HARVEST

CONTROL RULES FOR LAKE WHITEFISH IN THE GREAT LAKES

By
Jonathan J. Deroba

My dissertation has two main objectives: 1) to explore alternative ways to use
commercial lake Whitefish fishery catch per effort (CPE) data as an index of abundance
in 1836 Treaty-ceded waters of the Great Lakes, and 2) to evaluate alternative harvest
control rules for lake Whitefish. Chapter 1 was directed at exploring alternative ways to
use commercial lake Whitefish fishery CPE data, while Chapters 2 and 3 covered topics
related to harvest control rules.

Fishery CPE data is often used to assess relative fish abundance, and assessments
used in 1836 Treaty-ceded waters of the Great Lakes assume that commercial CPE (i.e.,
ratio of aggregate catch to aggregate effort in each year) from gill-net and trap-net
fisheries is proportional to abundance. However, CPE may change due to factors other
than abundance. In Chapter 1, I developed general linear mixed models (GLMMS) to
account for sources of variation in CPE unrelated to abundance, and used the least-
squares means (LSMs) for each year as an alternative to the current index of abundance.
Effects such as license holder, boat Size, and month accounted for much of the variation
in CPE. LSMs and the current CPE index displayed different temporal trends among

years in some areas, suggesting the importance of adjusting fishery CPE for effects like

boat Size, season, and license holder.

Harvest policies use control rules to dictate how fishing mortality or catch and
yield levels are determined. Common control rules include constant catch, constant
fishing mortality rate, and constant escapement. The “best” control rules for meeting
common fishery objectives (e.g., maximizing yield) is a source of controversy in the
literature, and results are seemingly contradictory. In Chapter 2, I conducted a detailed
review of the relevant harvest control rule literature to compare control rules for their
ability to meet widely used fishery objectives and identify potential causes for
contradictory results. The relative performance of control rules at meeting common
fishery objectives was affected by: fishery objectives, whether uncertainty in estimated
stock sizes was included in analyses, whether the maximum recruitment level was varied
in an autocorrelated fashion over time, how policy parameters were chosen, and the
amount of compensation in the stock—recruit relationship. More research is needed to
compare control rules while considering these and related factors.

In Chapter 3, I used an age-structured simulation model that incorporated
stochasticity in life history traits and multiple uncertainties to compare the current harvest
control rule for lake Whitefish (constant fishing rate; CF) with a range of alternative
control rules, including conditional constant catch (CCC), biomass-based (BB), and CF
and BB rules with a 15% limit on the interannual change in the target catch. The CF and
BB rules Simultaneously attained higher average yield and spawning stock biomass than
other control rules, while the CCC rule and limiting the target catch changes by 15% had
the lowest yearly variability in yield. The low yearly variability in yield provided by
limiting target catch changes to 15% comes at the cost of frequently reducing biomass to

low levels, so that in many situations other control rules would be preferred.

ACKNOWLEDGEMENTS

I am grateful to many people for helping me throughout my doctoral program. I
especially want to thank my advisor, Dr. James Bence, for not only teaching me about
quantitative fisheries analyses, but for also making the process fun. Jim was always
available and helpful whenever I had questions, and I am honored to have studied with
him and call him my fi'iend. I thank the other members of my graduate committee, Dr.
William Taylor, Dr. Jean Tsao, and Dr. Michael Jones for greatly improving my research.
The Modeling Sub—Committee of the 1836 Treaty Waters partially guided my research
and answered many questions about the Great Lakes. In particular, Mark Ebener
provided data, discussion, and entertainment. The Michigan Department of Natural
Resources and US. Fish and Wildlife Service provided funding. A scholarship from the
International Association of Great Lakes Research and a fellowship from the Department
of Fisheries and Wildlife also made my life much easier. Several staff members of the
Department of Fisheries and Wildlife also ensured that my degree progressed smoothly.

Lastly, I would like to thank my family and friends. My parents, Bill and Judy
Deroba, have supported me in countless ways and no amount of thanks could adequately
express my gratitude for their hard work and sacrifices. My brother, Aaron, provided me
with countless hours of fun and laughter. My grandparents, Bill and Judy Hoyer and
Irene Deroba, were always available to listen and provide anything I needed. Julie
Nieland helped maintain my sanity and made me a better person. My many friends from
the QFC, Bence/Jones lab, M.I.R.T.H. lab, F W Department, related Departments, and
MSU provided many necessary distractions. Thank you all.

iv

TABLE OF CONTENTS

LIST OF TABLES .......................................................................................................... vii

LIST OF FIGURES ......................................................................................................... ix

INTRODUCTION AND SUMMARY ............................................................................. 1

Indices of Abundance .......................................................................................... 1

Chapter 1: Improving indices of abundance for lake Whitefish ................ 2

Harvest Control Rules ........................................................................................... 4

Chapter 2: A review of harvest control rules ............................................ 4

Chapter 3: Evaluating harvest control rules for lake Whitefish ................. 5

Overall Conclusions and Future Directions .......................................................... 8

References ........................................................................................................... 10
CHAPTER 1

DEVELOPING MODEL-BASED INDICES OF LAKE WHITEFISH ABUNDANCE
USING COMMERCIAL FISHERY CATCH AND EFFORT DATA IN LAKES

HURON, MICHIGAN AND SUPERIOR ...................................................................... 12
Abstract ............................................................................................................... 13
Introduction ......................................................................................................... 14
Methods ............................................................................................................... 17

Study area ................................................................................................ 17
Data and analyses .................................................................................... 18
Results ................................................................................................................. 24
Gill-Net Fishery ...................................................................................... 24
Trap-Net Fishery ..................................................................................... 25
Discussion ........................................................................................................... 26
Acknowledgements ............................................................................................. 34
References ........................................................................................................... 36

CHAPTER 2

A REVIEW OF HARVEST POLICIES: UNDERSTANDING RELATIVE

PERFORMANCE OF CONTROL RULES ................................................................... 5 3
Abstract ............................................................................................................... 54
Introduction ......................................................................................................... 55
Common control rules ......................................................................................... 59
Common fishery objectives ................................................................................ 61
Relative performance with “perfect” information .............................................. 64

Comparing control rules ......................................................................... 64
Effect of the stock-recruit relationship ................................................... 70
Relative performance with “imperfect” information .......................................... 71
Policy parameters unadjusted for uncertainty ......................................... 72

V

Uncertainty adjusted policy parameters .................................................. 74

Selecting catch, fishing mortality, and threshold levels ..................................... 76
Available options —Simulations or biological reference points ............... 76
Constant catch levels ............................................................................... 77
Constant fishing mortality rate F levels .................................................. 78
Threshold levels ...................................................................................... 80
Summary and conclusions .................................................................................. 82
Acknowledgements ............................................................................................. 87
References ........................................................................................................... 89
CHAPTER 3
EVALUATING HARVEST CONTROL RULES FOR LAKE WHITEFISH IN THE
GREAT LAKES: ACCOUNTING FOR VARIABLE LIFE-HISTORY TRAITS ...... 108
Abstract ............................................................................................................. 108
Introduction ....................................................................................................... 109
Harvest control rules ............................................................................. 109
Lake Whitefish Fishery History and Management ............................... 109
Methods ............................................................................................................. 112
Stocks in 1836 Treaty waters ................................................................ 112
Overview of simulations ....................................................................... 112
Growth sub-models ............................................................................... 114
Stock-recruitment sub-model ................................................................ 116
Maturity sub-model ............................................................................... 118
Population abundance sub-model ......................................................... 119
Assessment and implementation error .................................................. 120
Control rules .......................................................................................... 121
Performance metrics ............................................................................. 124
Results ............................................................................................................... 126
Overview of results ............................................................................... 126
Rank-order performance of control rules .............................................. 127
Sensitivity to future growth uncertainty ............................................... 128
Sensitivity to assessment error parameters ........................................... 131
Discussion...............; ......................................................................................... 132
References ......................................................................................................... 1 3 7
APPENDIX A ............................................................................................................... 157
Classifying management units as fast or slow .................................................. 157
Growth sub-models ........................................................................................... 158
Stock-recruitment sub-model ............................................................................ 159
Maturity sub-model ........................................................................................... 161
Maximum sustainable yield and unfished SSB ................................................ 162
APPENDIX B ............................................................................................................... 166
COMPREHENSIVE LIST OF REFERENCES ........................................................... 183

Vi

LIST OF TABLES

CHAPTER 1

Table 1. Years of lake Whitefish catch and effort data analyzed from gill-net and trap-net
fisheries conducted in 1836 Treaty of Washington-ceded waters of Lakes Superior
(management units designated as WFS), Huron (WFH), and Michigan (WF M). .......... 49

Table 2. Difference (A) in the corrected Akaike’s information criterion (AICc) between
the final lake Whitefish abundance model and a means model (i.e., a model with only a
year effect; AAICc = means model AICc - final model AICc) for gill-net and trap-net
fisheries conducted in 1836 Treaty-ceded waters of Lakes Superior (management units
designated as WFS), Huron (WFH), and Michigan (WF M). ......................................... 50

Table 3. Average variance component (0' 2) estimates for a model Of lake Whitefish

catch per effort (CPE) in the gill-net fishery (residual error = 0'5”" b g, ; license holder =

of ; month x year = 030,) and for a model of trap-net fishery CPE (residual error =
Grim]; year x license holder = ail ; month x year = 0,30,; month x year x license holder

= 0' in”) for 1836 Treaty-ceded waters of Lakes Superior, Huron, and Michigan.

Variance component estimates were averaged across management units. ..................... 51

Table 4. Average coefficient estimates for three boat size categories (small: <20 ft;
medium: 20—30 R; large: >30 ft) in a model of lake Whitefish catch per effort for the gill-
net fishery in 1836 Treaty-ceded waters of Lakes Superior, Huron, and Michigan.
Coefficients were averaged across management units within each lake. ....................... 52

CHAPTER 2

Table 1. The rank order performance of control rules for meeting each of several
different fishery objectives. Results given in columns of the table correspond to cases
assuming no error in estimates of stock size, with the inclusion of error in estimates of
stock size, with and without policy parameters adjusted for uncertainty, and with and
without autocorrelation in the maximum level of recruitment (see text). When errors in
stock size estimates were incorporated, studies that compared performance for control
rules using the policy parameters that were optimal without these errors are “unadjusted”;
studies that sought policy parameters that were optimal over the uncertainty are
“uncertainty adjusted.” When uncertainty in stock assessments was incorporated, rank
order reflects finding for the highest levels of assessment error that were evaluated.

vii

When for a given table column there are no studies that evaluated relative performance of
a control rule, these policies are missing (-). ................................................................ 101

Table 2. Papers that compared harvest policies for meeting common fishery objectives
assuming no error in estimates of stock Size, with the inclusion of error in estimates of
stock size, and with or without autocorrelation in the maximum level of recruitment (i.e.,
asymptote of a Beverton-Holt stock-recruit function). Specific control rules and

characteristics included in each paper are indicated with a X. ..................................... 104
Table 3. Studies that evaluated various biological reference points (BRP) ................. 105
CHAPTER 3

Table 1. The different assessment and implementation error parameter values
evaluated. ...................................................................................................................... 155

Table 2. The performance of optimal policy parameters (see text) chosen assuming the
incorrect future about lake Whitefish growth (autocorrelated versus recent) for each of
four trade-offs in performance metrics and for fast and slow growing stocks in 1836
Treaty-ceded waters. The pairs of values under each grth scenario sub-heading are the
performance of the policy parameters chosen assuming the wrong future lake Whitefish
growth, and are in the same respective order as the performance metrics defined by the
trade-off plot for each row. The values in parentheses are the percent change from the
optimal set of policy parameters chosen assuming the correct future lake Whitefish
growth. Spawning stock biomass values are reported as a fraction of the unfished

level. .............................................................................................................................. 156

APPENDIX A

Table A1. Growth category and the range of years for which a random sample of
commercial trap-net data were available from lake Whitefish management units in the
1836 Treaty-ceded waters of Michigan used in pararneterizing growth and maturity sub-

models. .......................................................................................................................... l 63

Table A2. Expected mean length (mm) at age of lake Whitefish for four growth models
(see text for details). ...................................................................................................... 164

Table A3. Upper and lower caps placed on simulated length (mm) at age-3 lake
Whitefish for fast and slow growth category Simulations. ............................................ 165

viii

LIST OF FIGURES

CHAPTER 1

Figure 1. Map of 1836 Treaty—ceded waters and lake Whitefish management units in
Lakes Superior (units designated as WF S), Huron (WFH), and Michigan (WF M; Ebener
et al. 2005). ..................................................................................................................... 39

Figure 2. Average coefficient estimates (iSE representing uncertainty resulting from
variability among management units shown in Figure 1) for the month effect from a
general linear mixed model standardizing lake Whitefish catch per effort (catch =
aggregate round mass of fish) for the gill-net fishery (top panel; effort = aggregate net
length in thousands of feet) and trap-net fishery (bottom panel; effort = number of lifts) in
1836 Treaty-ceded waters of Lakes Superior, Huron, and Michigan. Coefficient estimates
were averaged across various years (generally 1981—2001) and management units ...... 40

Figure 3. Annual (generally 1981—2001) proportional difference between an index of
lake Whitefish abundance from a general linear mixed mode] (i.e., least-squares mean)
and catch per effort (ratio of fish round mass to aggregate net length) from the gill-net
fishery in 1836 Treaty-ceded waters of Lakes Superior (management units designated as
WFS), Huron (WFH), and Michigan (WFM). ................................................................ 44

Figure 4. Annual (generally 1981—2001) proportional difference between an index of
lake Whitefish abundance from a general linear mixed model (i.e., least-squares mean)
and catch per effort (ratio of fish round mass to aggregate number of lifts) from the trap-
net fishery in 1836 Treaty—ceded waters of Lakes Superior (management units designated
as WFS), Huron (WFH), and Michigan (WFM) ............................................................. 48
CHAPTER 2

Figure 1. Basic control rules and how fishing mortality generally changes with biomass
or abundance for each type. .......................................................................................... 106

Figure 2. VaIiants of basic control rules and how fishing mortality generally changes
with biomass or abundance for each type. .................................................................... 107

CHAPTER 3

Figure l. 1836 Treaty-ceded waters and lake Whitefish management units in Lakes
Superior, Huron, and Michigan (Ebener et a1. 2005) .................................................... 141

ix

Figure 2. Example of the biomass based control rule used in this analysis (solid line).
Dashed lines are provided as a reference for defining the policy parameters. ............. 142

Figure 3. Median spawning stock biomass versus yield (left column) and interannual
variability in yield versus the proportion of years with spawning stock biomass less than
20% of the unfished level (right column) for baseline levels of assessment and
implementation error parameters and fast growth similar to recent levels (see text for
details), for the conditional constant catch control rule (top row), constant-F (black dots,
middle row), constant-F with a 15% limit on the interannual change in target catch (grey
dots, middle row), biomass based (black dots, bottom row), and biomass based with a
15% limit on the interannual change in target catch (grey dots, bottom row). Each dot
corresponds to 1000 simulations for one combination of policy parameters for the given
control rule. ................................................................................................................... 144

Figure 4. AS in figure 3, except for median yield versus interannual variability in yield
(left column) and yield versus the proportion of years with spawning stock biomass less
than 20% of the unfished level (right column). ............................................................ 146

Figure 5. Median Interannual variability in yield versus the proportion of years with
spawning stock biomass less than 20% of the unfished level for baseline assessment and
implementation error variance, the extent of autocorrelation in assessment error set equal
to 0.0 or 0.9, and fast grth similar to recent levels (see text for details). Control rules
are displayed as in Figure 3. ......................................................................................... 148

Figure 6. As in Figure 5, except with the extent of autocorrelation in assessment error set
equal to the baseline level (0.7), and for assessment error variance equal to 0.01
or 0.20. .......................................................................................................................... 150

Figure 7. As in Figure 5, except with yield versus the interannual variability in
yield ............................................................................................................................... 152

Figure 8. As in Figure 5, except with the extent of autocorrelation in assessment error
equal to the baseline level (0.7), for assessment error variance equal to 0.01 or 0.20, and
for yield versus the interannual variability in yield. ..................................................... 154

APPENDIX E

Figure Bl. Median spawning stock biomass versus yield for baseline assessment and
implementation error variance, the extent of autocorrelation in assessment error set equal
to 0.0 or 0.9, and fast growth similar to recent levels (see text for details), for the
conditional constant catch control rule (top row), constant-F (black dots, middle row),
constant-F with a 15% limit on the interannual change in target catch (grey dots, middle
row), biomass based (black dots, bottom row), and biomass based with a 15% limit on the
interannual change in target catch (grey dots, bottom row) .......................................... 168

X

Figure B2. As in Figure 1B, except with the extent of autocorrelation in assessment error
set equal to the baseline level (0.7), and for assessment error variance equal to 0.01 or
0.20 ................................................................................................................................ 170

Figure B3. As in Figure 1B, except for median yield versus the proportion of years with
spawning stock biomass less than 20% of the unfished level. ...................................... 172

Figure B4. Median yield versus the pIOportion of years with spawning stock biomass
less than 20% of the unfished level with the extent of autocorrelation in assessment error
set equal to the baseline level (0.7), for assessment error variance equal to 0.01 or 0.20,
and fast growth similar to recent levels (see text for details). Control rules are displayed
as in Figure 1B. ............................................................................................................. 174

Figure B5. Median yield versus spawning stock biomass for baseline levels of
assessment and implementation error parameters and for autocorrelated fast growth,
autocorrelated slow growth, and slow growth similar to more recent levels. Control rules

are displayed as in Figure 1B. ....................................................................................... 176
Figure B6. As in Figure B5, except for variability in yield versus risk. ...................... 178
Figure B7. As in Figure B5, except for yield versus variability in yield. .................... 180

Figure B8. As in Figure BS, except for yield versus the proportion of years with
spawning stock biomass less than 20% of the unfished level ....................................... 182

xi

INTRODUCTION AND SUMMARY

Many fisheries are managed by using estimates of abundance and other
parameters from model-based stock assessments (e.g., fitted statistical catch at age
models) for setting annual fishery harvest quotas. Stock assessments are often fit to an
index of abundance, and so the estimates from the stock assessments can critically rely on
the accuracy of both the index and a measure of uncertainty for the index (Maunder and
Starr, 2003). Harvest control rules are often used to set a quota as a function of the
current estimate of the system state (e. g., an abundance estimate from an assessment).
These topics, indices of abundance and harvest control rules, were the main foci of my
research.

1. Indices of Abundance

Catch per effort (CPE) is usually used as the index of abundance for most
fisheries, and the common assumption is that CPE changes in proportion to abundance,
which is also referred to as “constant catchability” (Quinn and Deriso, 1999). Violations
of this assumption can lead to inaccurate estimates of abundance from stock assessments,
and consequently ineffective management, which sometimes results in fishery collapse
(Rose and Kulka, 1999; Harley et al., 2001). To avoid violations of this assumption, CPE
indices of abundance are ideally based on fishery independent survey data (e.g., Helser et
al., 2004). Such surveys are not available for many fisheries and so many indices of
abundance used in assessments are based on fishery dependent data. Fishery dependent
data is more likely to violate the constant catchability assumption due to things such as

systematic changes in characteristics of the fishing fleet (e. g., technological

1

advancements, entrance and exit of individual vessels), non-random search effort, and the
spatial distribution of the fish stock (Rose and Kulka, 1999; Harley et al., 2001; Maynou
et al., 2003; Battaile and Quinn, 2004; Bishop et al., 2004; Campbell, 2004). Even stock
assessment models that allow for some temporal changes in catchability will tend to work
better when such temporal variation is lower (Wilberg and Bence, 2006; Wilberg et al.,
2008)

To account for some of the variation in CPE not attributable to changes in
abundance, and provide a more accurate index, CPE data can be “standardized” by fitting
statistical models to the catch and effort data, and then using “year-effect” estimates as
the index of abundance (Maunder and Punt, 2004; Venables and Dichmont, 2004). Year-
effect estimates are commonly used because detecting trends in abundance over time is
usually the objective (Maunder and Punt, 2004). Frequently, some form of general or
generalized linear model is used to standardize the CPE data (Maunder and Punt 2004).
1.1. Chapter I : Improving indices of abundance for lake Whitefish

My main objective in Chapter 1 was to produce standardized indices of
abundance for lake Whitefish in 1836 Treaty-ceded waters of Lakes Huron, Michigan,
and Superior, but this work also allowed me to develop expertise in statistical techniques
(e.g., mixed models) that I used to parameterize the simulation model of chapter 3.
Currently, statistical catch at age assessments are fit in each of 18 management units, and
a quota is also set for each unit. The assessments are fit using two separate CPE indices
of abundance from gill-nets and trap-nets, with CPE estimated as the ratio of sum of
aggregate catch to sum of aggregate effort in each year. I developed general linear mixed
models (GLMM) for each gear type to standardize the fishery CPE data. Factors

2

included in the GLMMS were fixed effects of year, month, and boatsize (gill-net fishery
only), and random effects of license holder (i.e., analogous to boat captain), grid (i.e.,
location), and all two and three way interactions. The effect of the standardization by
using the GLMM method was evaluated by examining the temporal trends in the
proportional difference (PD) between the least squares means for each year (LSM) and
CPE (i.e., aggregate catch divided by aggregate effort for each year). Since both the
LSMS and CPE are relative indices, changes in PD over time were of interest and not
whether average PD differed from 1.0. Factors that were particularly influential in the
GLMM models were month, boat size, and license holder, which was similar to factors
important for marine commercial fisheries where standardization is more widely applied
than in freshwater systems. The proportional difference between the LSMS and CPE
trended through time in some management units, suggesting that adjusting fishery CPE
for effects such as boat size, season, and license holder was important. So, I concluded
that model-based indices of abundance should replace non-standardized CPE in some
lake Whitefish stock assessment models, especially those management units where the
proportional difference trended through time. In management units where the
proportional difference did not trend through time, using a model-based index of
abundance may still be beneficial. Accounting for variability due to random effects led
to year specific estimates of uncertainty (e. g., the standard errors for the LSMS) that were
not available when using non-standardized CPE. Using improved years-specific
estimates of uncertainty to weight the influence of indices of abundance can increase the

accuracy of stock assessment estimates (Helser et al., 2004; Maunder and Starr, 2003).

2. Harvest Control Rules

Harvest control rules are guidelines that specify an amount of catch, fishing effort,
or fishing mortality as a specific, and usually simple, function of a current estimate of the
system state (e.g, spawning biomass; Deroba and Bence, 2008). Common control rules
include constant catch, constant fishing mortality rate, constant escapement, or a few
variations of these. Each control rule is also defined by a number of policy parameters.
For example, the constant fishing mortality rate control rule is defined by one policy
parameter, the target level of fishing mortality. Ideally, a harvest control rule is chosen
because it meets fishery objectives (e. g., maximize yield, minimize interannual variability
in yield). However, which rules are best at meeting certain fishery objectives is a source
of controversy in the literature. Furthermore, the relative performance of control rules
depends on Specific characteristics of the fishery and underlying population dynamics
that are incorporated into an evaluation. Consequently, selecting a harvest control rule
and policy parameters can be a difficult task.
2.]. Chapter 2: A review of harvest control rules

In Chapter 2 I reviewed the harvest control rule literature with two Objectives: 1)
to compare and contrast the relative performance of various control rules at meeting
common fishery objectives, and 2) to identify reasons for what seem to be contradictory
results. The findings were also relevant for designing the harvest control rule evaluation
of Chapter 3 (see below). I found that the relative performance of control rules at
meeting common fishery objectives was affected by: the given fishery objective, whether
uncertainty in estimated stock sizes was included in analyses (i.e., assessment error),

whether the maximum recruitment level (e.g., the asymptote of a Beverton—Holt stock—

4

recruit fiInction) varied in an autocorrelated fashion over time, and the amount of
compensation in the stock—recruit relationship. Also, few studies have compared control
rules using optimal parameters (e.g., those that maximize some objective function) that
were found while including assessment error. More commonly, parameters that are
optimal without assessment error are used in a comparison of control rules that includes
assessment error. This approach can produce misleading results. Lastly, more research is
needed to compare control rules when accounting for uncertainty in key population
parameters, when stock—recruitment or other population dynamic parameters vary over
time, and for fisheries with non-yield-based or competing objectives.
2.2. Chapter 3: Evaluating harvest control rules for lake Whitefish

Chapter 3 addressed some of the harvest control rule research needs identified in
Chapter 2, and was based on a simulation analysis with the objective of evaluating the
ability of alternative control rules to meet fishery objectives for lake Whitefish in 1836
Treaty-ceded waters. Currently, a quota is set for each management unit so that total
annual mortality rate equals 65% for ages experiencing the highest levels of fishing
mortality. Because assessments in these waters assume a constant natural mortality rate
across ages and time (Ebener et al., 2005), this is equivalent to a constant fishing
mortality rate (constant-F) control rule. The constant-F control rule and the parameter
for the control rule (i.e., 65% total annual mortality rate) are based on analyses conducted
over 30 years ago (Healey, 1975), and so may not be optimal for meeting fishery
objectives.

Lake Whitefish stocks in 1836 Treaty-ceded waters are characterized by temporal

and Spatial variation in various population parameters. For example, lake Whitefish

5

growth in some areas of the Great Lakes declined during the 19905 and 20003, coincident
with declines in an important prey source, Diporeia (Hoyle et al., 1999; Pothoven et al.,
2001; Mohr and Nalepa, 2005), but similar declines have not occurred everywhere
despite Similar ecosystem changes (e.g., Cook et al., 2005; Lumb et al., 2007). Growth
rates, maturity ogives, natural mortality, and stock-recruit relationships also likely differ
spatially among some of the management units (e.g., Wang et al., 2008).

Drawing from my experiences with GLMMS from Chapter 1 and partially based
on the results of Chapter 2, I developed a stochastic age-structured simulation model that
incorporated stochasticity in life history traits, uncertainty in future lake Whitefish
growth, and other sources of uncertainty to compare the current harvest control rule with
a range of alternative control rules, including conditional constant catch (CCC), constant-
F, biomass-based (BB), and constant-F and BB rules with a 15% limit on the interannual
change in the target catch. Separate sets of growth parameters were estimated for fast
and slow growth stocks, and separate sets of simulations were done for these two
categories of individual stocks. Furthermore, I developed two variants of a growth model
to represent alternative hypotheses about future lake Whitefish growth; one with
temporally autocorrelated changes in growth and another where growth remained similar
to more recent patterns. Uncertainty in the stock-recruitment relationship was
incorporated by drawing stock-recruit parameters for each simulation from a set of
possible values, which were based on data from each management unit and estimated
using a GLMM (i.e., similar statistical model used in Chapter 1). The simulations also
included assessment and implementation error. Some of the model features mentioned

above were included because the results of Chapter 2 indicated that these can affect

6

relative control rule performance, in particular, accounting for uncertainty in the stock-
recruit relationship and assessment error. Each control rule was evaluated over a range of
the policy parameters that define the control rules. The performance of the control rules
was evaluated by examining trade-off plots of spawning stock biomass (SSB) versus yield
(Y), interannual variability in yield (Yvar) versus the proportion of years that SSB fell
below 20% of the unfished level (SSBF=0), Y versus Yvar, and Y versus the proportion of
years that SSB fell below 20% of SSBF=0.

While treating future growth as known, the rank order performance of the control
rules for each of the performance metrics was generally robust to sources of uncertainty.
For example, the constant-F and BB rules simultaneously attained higher average yield
and spawning stock biomass than all other control rules. The CCC rule and limiting the
constant-F or BB mles to a 15% change in target catch had the lowest yearly variability
in yield. The low yearly variability in yield provided by limiting target catch changes to
15%, however, came at the cost of frequently reducing biomass to low levels, so that in
many situations other control rules would be preferred.

The sensitivity of results to uncertainty about future lake Whitefish growth was
control rule specific and depended on whether stock growth was fast or slow. For fast
growth stocks, selecting control rules and policy parameters by incorrectly assuming that
future growth will be autocorrelated resulted in little cost from the optimum levels
relative to the alternative of incorrectly assuming future growth will be similar to recent
levels. For slow growth stocks, however, the robustness to choosing policy parameters
based on an erroneous assumption about future lake Whitefish growth depended on the

control rule and trade-off plot. The decision about how best to select control rules and

7

policy parameters will ultimately depend on how competing fishery objectives are
weighted relative to each other. Generally, however, control rules and policy parameters
for fast growth stocks Should likely be selected assuming future growth will be
autocorrelated, but a universal recommendation for slow growth stocks is less clear (i.e.,
depends on the control rule and fishery objectives).

Depending on how important different fishery objectives are, a control rule and
policy parameters other than the one currently in use (i.e., constant-F based on a total
annual mortality rate of 65%) may be worth considering. For example, a BB control rule
with appropriately selected policy parameters could likely produce nearly the same or
more yield, spawning stock biomass, and less risk with little cost in variability in yield
relative to the currently used policy. Similarly, the CCC control rule can likely provide
less variability in yield, but at the cost of yield. So, if maintaining low variability in yield
is more desirable than maximizing yield, a CCC control rule may want to be considered.
3. Overall Conclusions and Future Directions

The results of this dissertation have implications for the improved management of
lake Whitefish in the Great Lakes, but the results are also more generally applicable. In
Chapter 1, I found that model-based indices of abundance should likely replace non-
standardized indices in fitting stock assessment models. The factors important to the
standardization process also seem to be consistent among systems, and so should be
considered when standardizing CPE data for most fisheries. Likewise, updating stock
assessments for most fisheries to include standardized indices of abundance and
associated measures of uncertainty would likely produce more accurate estimates of

abundance and other population parameters, and so reduce assessment error, which in

8

Chapter 2 was shown to affect relative control performance. In addition to assessment
error, Chapter 2 highlighted several other characteristics and uncertainties of harvest
policy evaluations that have affected control rule performance, and so should be
considered when developing harvest policy analyses for any fishery. The results of
Chapter 2, however, also revealed that little research has historically considered these
characteristics. Chapter 3 added to the body of research that has considered factors
important to control rule performance. The CCC control rule, which was first published
in an analysis of Pacific halibut Hippoglossus stenolepis, had never been evaluated while
considering assessment error (Clark and Hare, 2004). Similarly, few published analyses
have considered control rules with limits on the interannual change in target catch. Lake
trout Salvelinus namaycush in 1836 Treaty-ceded waters are managed with such a
restraint, but given the generally poor performance of these control rules another option
may be warranted. Chapter 3 also evaluated the sensitivity of relative control rule
performance to one form of time-varying growth that had never been considered before,
and time-varying population parameters have been Shown to affect control rule
performance (Chapter 2). The results in regards to the rank order and sensitivity of the
control rules to this source of uncertainty are likely generally applicable to any fishery

experiencing similar conditions.

References

Battaile, BC. and T.J. Quinn 11. 2004. Catch per unit effort standardization of the
eastern Bering Sea walleye Pollock fleet. Fisheries Research 70 (2004): 161-177.

Bishop, 1., W.N. Venables, and Y-G. Wang. 2004. Analyzing commercial catch and
effort data from a Penaeid trawl fishery: A comparison of linear models, mixed

models, and generalized estimating equations approaches. Fisheries Research
70(2004): 179-193.

Campbell, RA. 2004. CPUE standardisation and the construction of indices of stock

abundance in a spatially varying fishery using general linear models. Fisheries
Research 70(2004): 209-227.

Clark, W.G., and SR. Hare. 2004. A conditional constant catch policy for managing the
Pacific halibut fishery. North American Journal of Fisheries Management 24:

106-113.

Cook, H.A., T.B. Johnson, B. Locke, and BI. Morrison. 2005. Status of lake Whitefish
in Lake Erie. In Proceedings of a workshop on the dynamics of lake Whitefish
and the amphipod Diporeia spp. in the Great Lakes. Edited by LC. Mohr and
T.F. Nalepa. Great Lakes Fishery Commission Technical Report 66. pp. 87-104.

Ebener, M.P., J.R. Bence, K. Newman, and P. Schneeberger. 2005. Application of
statistical catch-at-age models to assess lake Whitefish stocks in the 1836 treaty-
ceded waters of the upper Great Lakes. In Proceedings of a workshop on the
dynamics of lake Whitefish and the amphipod Diporeia spp. in the Great Lakes.
Edited by LC. Mohr and T.F. Nalepa. Great Lakes Fishery Commission
Technical Report 66. pp. 271-309.

Harley, S.J., R.A. Myers, and A. Dunn. 2001. Is catch-per-unit-effort proportional to
abundance? Canadian Journal of Fisheries and Aquatic Sciences 58: 1760-1772.

Healey, MC. 1975. Dynamics of exploited Whitefish populations and their management
with special reference to the Northwest Territories. Journal of the Fisheries
Research Board of Canada. 32: 427-448.

Helser, T.E., A.E. Punt, and RD. Methot. 2004. A generalized linear mixed model
analysis of a multi-vessel fishery resource survey. Fisheries Research 70(2004):
251-264.

Hoyle, J .A., T. Schaner, J .M. Casselman, and R. Derrnott. 1999. Changes in lake

Whitefish stocks in eastern Lake Ontario following Dreissena mussel invasion.
Great Lakes Research Review 4: 5-10.

10

Lumb, C.E., T.B. Johnson, H.A. Cook, and J .A. Hoyle. 2007. Comparison of lake
Whitefish growth, condition, and energy density between Lakes Erie and Ontario.
Journal of Great Lakes Research 33: 314-325.

Maunder, MN. and AB. Punt. 2004. Standardizing catch and effort data: a review of
recent approaches. Fisheries Research 70(2004): 141-159.

Maunder, MN. and P.J. Starr. 2003. Fitting fisheries models to standardized CPUE
abundance indices. Fisheries Research 63(2003): 43-50.

Maynou, F., M. Demestre, and P. Sanchez. 2003. Analysis of catch per unit effort by
multivariate analysis and generalised linear models for deep-water crustacean
fisheries off Barcelona. Fisheries Research 65(2003): 257-269.

Mohr, LG, and Nalepa, T.F. (Editors). 2005. Proceedings of a workshop on the
dynamics of lake Whitefish (Coregonus clupeaformis) and the amphipod Diporeia
spp. in the Great Lakes. Great Lakes Fishery Commission Technical Repport 66.

Pothoven, S.A., T.F. Nalepa, P.J. Schneeberger, and SB. Brandt. 2001. Changes in diet
and body condition of lake Whitefish in southern Lake Michigan associated with
changes in benthos. North American Journal of Fisheries Management: 21: 876-
883.

Quinn, T.J., II, and RB. Deriso. 1999. Quantitative Fish Dynamics. Oxford University
Press Inc. New York, New York.

Rose, GA. and D.W. Kulka. 1999. Hyperaggregation of fish and fisheries: how catch-
per-unit-effort increased as the northern cod declined. Canadian Journal of
Fisheries and Aquatic Sciences 56(supplement 1): 118-127.

Venables, W.N., and CM. Dichmont. 2004. GLMS, GAMS, and GLMMS: an overview
of theory for applications in fisheries research. Fisheries Research 70(2004): 319-
337.

Wang, H-Y, T.O. HOOk, M.P. Ebener, L.C. Mohr, and P.J. Schneeberger. 2008. Spatial
and temporal variation of maturation schedules of lake Whitefish in the Great
Lakes. Canadian Journal of Fisheries and Aquatic Sciences 65: 2157-2169.

Wilberg, M.J., and J .R. Bence. 2006. Performance of time-varying catchability
estimators in statistical catch-at-age analysis. Canadian Journal of Fisheries and
Aquatic Sciences 63: 2275-2285.

Wilberg, M.J., B.J. Irwin, M.L. Jones, and LR. Bence. 2008. Effects of source-Sink
dynamics on harvest policy performance for Yellow Perch in southern Lake
Michigan. Fisheries Research 94: 282-289.

11

CHAPTER 1

Deroba, J .J . and J .R. Bence. 2009. Developing model-based indices of lake Whitefish
abundance using commercial fishery catch and effort data in Lakes Huron,
Michigan, and Superior. North American Journal of Fisheries Management 29:
50-63.

The content of this chapter is intended to be identical to the cited publication and is based
on the accepted manuscript with changes that reflect corrections made during copy
editing. Any differences Should be minor and are unintended.

12

Abstract

Fishery catch per effort (CPE) is often used to assess relative fish abundance, and
in many Great Lakes and other freshwater applications this is based on either an average
or the ratio of sum of aggregate catch to sum of aggregate effort. In particular,
assessments used to estimate the abundance of lake Whitefish and recommend harvest
quotas in the 1836 Treaty-Ceded waters of Lakes Huron, Michigan, and Superior assume
that commercial CPE from gill-net and trap-net fisheries is proportional to abundance,
but CPE may change due to factors other than abundance, leading to violations of this
assumption. To account for sources of variation in CPE not attributable to abundance,
general linear mixed models (GLMMS) were developed for each management unit, and
least squares means (LSMS) for each year were used as the index of abundance. The
effect of the standardization by using the GLMM method was evaluated by examining
the temporal trends in the proportional difference between the LSMS and CPE (i.e.,
aggregate catch divided by aggregate effort for each year). Of the random effects
included in the final GLMM for the gill-net fishery, license holder accounted for the most
variation. The fixed effect of boat size category on CPE depended on lake, where on
average in Lake Superior there was little difference, but in Lakes Michigan and Huron
large boats had lower CPE than medium and small boats. CPE was on average higher
from October to December than in other months. The proportional difference between
the LSMS and CPE trended through time in some management units, suggesting that
adjusting fishery CPE for effects such as boat size, season, and license holder is
important. Factors influential to lake Whitefish commercial fishery CPE are similar to
factors that have been shown to be important in marine commercial fisheries.

13

Introduction

Lake Whitefish, C oregonus clupeaformis, has supported a historically important
fishery for Native American bands and a highly valued commercial fishery in the upper
Great Lakes (Lakes Huron, Michigan, and Superior). In the late 18003 and early 19003,
lake Whitefish were often the most highly valued commercial species and usually
comprised the greatest proportion of total yield from each of the upper Great Lakes
(Koelz 1926; Brown et a1. 1999). Lake Whitefish stocks collapsed in each of these lakes
in the 19303 and 403 due to overexploitation, sea lamprey, Petromyzon marinus,
predation, and pollution (Smiley 1882; Koelz 1926; Jensen 1976; Brown et al. 1999;
Ebener and Reid 2005). From the 19603 through the 19803, lake Whitefish stocks
rebounded in each of the lakes largely due to improved management of commercial
harvest, sea lamprey control, pollution remediation, and the introduction of salmonines
that reduced the abundance of the invasive alewife, Alosa pseudoharengus, and rainbow
smelt, Osmerus mordax (Ebener 1997; Mohr and Ebener 2005a). In the 19903, lake
Whitefish once again became the main commercial species, particularly in Lake Huron
where the species comprised over 80% of the total commercial yield (Mohr and Ebener
2005b)

In 1979, the rights of Native American bands to fish in the Michigan waters of the
upper Great Lakes, as reserved in a treaty signed in 183 6, were reaffirmed by US. federal
courts. Since the reaffirmation of treaty fishing rights, periodic stock assessments have
been conducted for stocks within Spatially defined management units, with the fishery
data and harvest from within each management unit treated as applying to a

reproductively isolated stock (Figure 1; Ebener et al. 2005). Stock assessments are

14

conducted and harvest recommendations based on the assessments are made annually for
each individual management unit. Within each management unit commercial fishery
catch and effort data are reported on a 10-minute by 10-minute statistical grid basis,
which allows for some spatial resolution within management units.

Since 2000, guidelines for the management of lake Whitefish have been set
according to a Consent Decree. The 2000 Consent Decree created a Technical Fisheries
Committee (TFC) and its Modeling Subcommittee (MSC) to conduct stock assessments
and Specify total allowable catches (TACs) and harvest regulating guidelines (HRGS, see
below). TACS are limits to catch, and are used in management units where some yield is
allocated to the state licensed fishery and some to the tribal fishery. HRGS are targets for
yield used to guide regulations for lake Whitefish in units where all yield is allocated to
the tribal fishery.

The MSC fits statistical catch-at-age (CAA) models to commercial fishery data to
estimate population numbers, mortality rates, fishery harvest, and other population
parameters of interest. The estimates of the population parameters are then used to
project each stock’s abundance into the future, and then a TAC or HRG is calculated by
applying a reference mortality rate to the estimate of the next year’s abundance.

The CAA models use fishery effort data and an assumed relationship between
fishing mortality and fishery effort. Age (a) and year (y) specific fishing mortality rates
(F) are estimated as the product of age specific selectivity (S) and year Specific “fishing

intensity” (f) for each of two fishery gears, gill-nets and trap-nets:
Fi,a,y = Si,afi,y; (1)

where i denotes gear type and,
15

fi, y = Er, yqi, yer, y ; (2)
where E is fishery effort specific to each gear type, q is catchability, and e is
multiplicative observation error. The details of the CAA models have been described in
Ebener et a1. (2005). Equation 2 is equivalent to assuming that the commercial fishery
catch per effort (CPE), estimated as the ratio of sum of aggregate catch to sum of
aggregate effort in each year, is on average proportional to average abundance over the
fishing year, and that deviations from this average relationship are independent variations
from year to year.

Violations of the assumption that CPE is proportional to average abundance can
occur due to changes in fishing power of gear, or if the Spatial and temporal distribution
of fishery effort is non-random (Quinn and Deriso 1999). Violations of this assumption
are called hyperdepletion when CPE declines faster than abundance at high stock sizes,
and hyperstability when CPE does not decline as drastically as abundance at high stock
sizes (Quinn and Deriso 1999). For example, an increase in the number of fishing
operations could cause some fishermen to operate in lower quality habitat. Thus, CPE
could decline even if fish abundance did not, resulting in hyperdepletion. Hyperstability
is the more common occurrence and leads to overestimation of biomass and
underestimation of fishing mortality, which has too ofien gone unrecognized and led to
fishery collapses (Rose and Kulka 1999; Harley et a1. 2001).

To account for some of the variation in CPE not attributable to changes in
abundance, and improve assessments and associated fishery management, CPE can be

“Standardized” by fitting statistical models to the catch and effort data, and then using

“year-effect” estimates as the index of abundance (Maunder and Punt 2004; Venables and
16

Dichmont 2004). Commonly, some form of general or generalized linear model is used
to standardize the CPE data (Maunder and Punt 2004). Year is usually included as one of
the explanatory variables because detecting trends in abundance over time is usually the
objective (Maunder and Punt 2004). Other explanatory variables often include a spatial
element or some measure of individual vessel fishing power (e.g., boat size) (Battaile and
Quinn 2004; Bishop et al. 2004).

Our objectives were (1) to standardize lake Whitefish CPE data in the upper Great
Lakes to attain an index of abundance that more accurately reflected changes in lake
whitefish biomass than CPE; (2) gain an improved understanding of factors that influence
commercial fishery CPE for lake Whitefish; and (3) compare the factors that are
important for this fishery with those found to influence CPE in other fisheries of the
world. Currently for lake trout, Salvelinus namaycush, in these waters, indices of
abundance are based on the least squares means (LSMS) for each year from a general
linear mixed model (GLMM; Deroba and Bence in press). Consequently, we explored
the use of a similar GLMM for lake Whitefish, and compared the temporal trends in the
LSMS for each year to that of the CPE. Our concern here is that the LSMS account for
sources of variation in CPE not considered when CPE is estimated as a ratio of sum of
aggregate catch to sum aggregate effort in each year, and might reveal substantially
different interannual trends in apparent relative abundance.
Methods
Study Area

Our study area was the waters relevant to the 1836 Treaty, which encompassed

the majority of Michigan waters of Lakes Superior, Huron, and Michigan (Figure l).

17

These waters were stratified into 18 management units with individual surface areas
ranging from 69,000 to 733,000 ha, and a total surface area of 5.8 million ha (Figure l;
Ebener et a1. 2005). Analyses were done separately for each management unit because
these are treated as reproductively isolated stocks and define the resolution of spatial
stratification used to manage lake Whitefish (see introduction; Ebener et a1. 2005).
Data and Analyses

Data were collected from commercial fishing operations as part of a requirement
for all licensed vessels to submit monthly reports that describe for each day of the month
the weight of fish landed, the amount of gear lifted, the 10-minute by 10-minute
statistical grid where the catch and effort occurred, and other auxiliary information
(Ebener et a1. 2005). Monofilament large-mesh gill-nets with 2 114-mm stretched mesh
and 6-14 m tall trap-nets accounted for nearly 100% of the lake Whitefish commercial
harvest, and analyses were only conducted on these two gear types. The range of years
included in this study differed by management unit and gear type, and some years are
missing because no catch or effort was reported (Table 1). Analyses were only
conducted on 12 of the 18 management units for the gill-net fishery, and 10 of the 18
management units for the trap-net fishery because few or no observations were recorded
within most years for some management units and gears.

CPE was estimated separately for gill-nets and trap-nets as the ratio of sum of
aggregate catch to sum of aggregate effort in each year, as is currently used in the CAA
models. Catch was measured as the round mass of Whitefish for both gears, while effort

was measured in 10003 of feet of net for gill-nets, and number of lifts for trap-nets.

18

GLMMS were fit separately for gill-nets and trap-nets, with log.= (CPE+1) as the
dependent variable. We applied a log, transformation because examination of the
distribution of the data showed that this was necessary to meet the assumption of
normality for general linear models (McCulloch and Searle 2001; Gelman and Hill 2007).
We added 1.0 to all CPE observations prior to transformation to address the (infrequent,
~0.001% for both gear types) occurrence of zero CPE observations. This added constant
represents a low CPE for gill nets and the lowest possible CPE for trap nets, and more
than 99% of CPE values exceeded 1.0 (the constant) for both gear types.

Our initial full model for gill-nets included fixed effects of year, month, and boat
size, and random effects of license holder, grid, and all possible two and three way
interactions. In preliminary analyses, interactions of a higher order than three ways were
not estimable for any management units, and so were excluded from firrther
consideration. Because not enough individual license holders fished with multiple boat
sizes, license holder and boat size were confounded when two and three way interactions
with license holder and two and three way interactions with boat size were included in
the same model. Furthermore, in preliminary analyses interactions with license holder
were only estimable for two management units, while interactions with boat size were
estimable in all management units. Consequently, all interactions with license holder

were also excluded from further consideration. Thus, the new “full” model included fixed

effects of year ((1),), month (13,"), boat size (71,), and random effects of license holder (6;),
grid (kg), and all two and three way interactions except those with license holder:

loge(CPE+l)=,u+ay +,Bm +yb+c1+kg +oym +pyb +qyg +rmb +smg

+tbg + umbg + dgmy + hgyb + fymb + 5iymbgl§
l9

where u is the overall mean, 0y", is the interaction of year and month, pyb is the
interaction of year and boat size, qyg is the interaction of year and grid, rmb is the
interaction of month and boat size, Smg is the interaction of month and grid, t bg is the
interaction Of boatsize and grid, umbg is the interaction of month and boat size and grid,
dgmy is the interaction of grid and month and year, hgyb is the interaction of grid and year

and boat size, jymb is the interaction of year and month and boat size, and 8iymbgl is

residual error for each observation, 1'. This model assumes that the random effects and
residual error are all independent and identically distributed as normal with a mean of
zero. Boat size was a categorical effect and sizes were defined as: small (3 20 ft),
medium (20-30 It), and large (2 30 ft).

The full model for trap—nets included fixed effects of year and month, and random
effects of license holder, grid, and all two and three way interactions:

loge(CPE+l)= p+ay +,6m +c1+kg +0ym +vyl+wm1+smg +ng +qyg
+Zyml +dgmy +aygl +emgl +5iymgl§

where vyl is the interaction of year and license holder, Wm] is the interaction of month
and license holder, xg’ is the interaction of grid and license holder, Zyml is the interaction
of year and month and license holder, ayg, is the interaction of year and grid and license

holder, 8mg] is the interaction of month and grid and license holder, and all other terms

are defined as for gill-nets. In four of the 10 management units analyzed for the trap-net
fishery, all of the observations came from one boat size category, and so this effect was

not evaluated.
20

Final models for both gear types were determined by evaluating which effects
could be removed using corrected Akaike’s information criterion (AICc) (Bumham and
Anderson 2002). Our model selection approach was to first consider which random
effects would be removed from the final model while keeping all fixed effects in the
model (N go and Brand 1997). Random effects were selected prior to fixed effects so that
the final models had the Simplest error structure possible (i.e., a random effect would be
eliminated rather than a fixed effect that explained similar sources of variation). Our
approach to selecting random effects was to drop each random effect one at a time, while
keeping all other effects in the model. Once a random effect was removed, AAlCc was
then calculated by subtracting AICc for the reduced model from AICc for the full model.
If AAICc was greater than 2.0 (Bumarn and Anderson 2002), the factor not present in the
reduced model was eliminated from the final model, otherwise the factor was retained.
We followed this approach because with 22 management unit and gear combinations and
12 potential random effects to consider for each, fitting and comparing all possible
models was not practical. A random effect was also dropped from the final model if the
variance estimate for that factor was zero. Restricted maximum likelihood (REML) was
used for model fitting when comparing models with different random effects, given its
superior performance in estimating random effects (McCulloch and Searle 2001).

Once the best set of random effects was selected, the best set of fixed effects was
selected by comparing AICc values for all possible combinations of fixed effects.
Models were fit using maximum likelihood (ML) instead of REML because comparisons
with AICc based on REML are not valid when comparing models with different fixed
effects (SAS 2003). During this process the previously determined best random effects

21

portion of the model was used. Year ((1,) was not evaluated during model selection

because the objective is to estimate a yearly index of abundance, and 30 year must be
retained in the final model. The AAICc values are not reported in the results because this
would require reporting a value for each factor that was included in the firll models for
each management unit and gear type (i.e., 298 values). Rather, we report the AAICc
values between a means model (i.e., a model with only a year effect) and the final model
(AAICc = AICc means model — AICc final model) to quantify the likely improvement
that the final models offer over the current indices of abundance that do not account for
factors other than year.

Generally, the same effects were included in the final model for each management
unit, but the models for some management units could be improved by the elimination of
an effect that improved model fit for the majority of the management units, or inclusion
of an effect that did not improve model fit for the majority of the management units. For
the Simplicity of reporting results in these analyses, we eliminated an effect in all
management units if it only improved model fit in a minority of management units.

LSMS for each year were calculated by summing the overall mean (u), the coefficient
estimate for each year ((1,), and the average of the coefficient estimates over all levels of
fixed effects other than year in the final models (SAS 2003). The LSMS for each year
from the final model, as determined by the majority, were nearly identical to the LSMS
from other models that improved model fit for a minority of management units.

Consequently, we believe that the conclusions of these analyses are robust to this

approach. However, if the estimated uncertainty (e.g., standard errors) associated with

22

LSMS (or alternatively year effects or other functions of model parameters) is important,
as in fitting stock assessment models to indices of abundance where the standard errors
are used to weight the indices of abundance relative to other data (e. g., Maunder 2001;
Maunder and Starr 2003), a different model than that reported as the final model here
may be warranted for some management units.

Differences in the back-transformed LSMS for each year and CPE+1 were
qualitatively examined by plotting the proportional difference (PD) between the two
measures across years for each management unit included in this analysis. PD was
calculated as:

D _ (CPE +1)
exp(LSM) '

The PD is a measure of how much larger or smaller CPE is than the LSMS. For example,
if PD=2 then the CPE is two times larger than the index of abundance based on the mixed
mode]. Since both the LSMS and CPE are relative indices, changes in PD over time are
of interest and not whether average PD differs from 1.0. Consequently, if PD varied
without trend we concluded that the two approaches generally suggested similar trends in
abundance through time, although differences may have existed for a given year.
Conversely, if PD trended through time we concluded that the index of abundance
provided by the two approaches suggested different temporal trends.

The relative effect of factors included in the final model on CPE was determined
by averaging coefficient estimates across management units and comparing the average
values. For random effects, the variance component estimates for each effect were used

in estimating the average; while for fixed effects, the coefficient estimates for each level

23

of a factor were used. For boat Size, the averages were estimated separately for each lake
because different boat sizes may perform differently in each lake.
Results
Gill-net Fishery

The final model for the gill-net fishery included fixed effects of year, month, and
boat Size, and random effects of license holder and the interaction of year and month:

loge(CPE+1) = ,u + ay + ,8," +7b +c1+oym +5iymbgl-

The final model improved model fit over a means model in all but one management unit,
with an average AAICc value of 362.5 and values ranging from -10 to 2514 (Table 2).
The final model may not have improved fit over a means model in WFM-06 because this
management unit had the smallest sample size (N=308; mean N=1452), which may not
provide enough data to adequately capture the variability in CPE caused by the various
factors. Of the random effects, the license holder effect accounted for the most variation
in CPE (Table 3). The effect of boat size depended on lake (Table 4). In Lake Superior,
CPE did not vary much among boat size classes. On Lake Huron, small and medium
boats had similar CPE, which was less than that for large boats. On Lake Michigan, CPE
ordered as medium > small > large boats. CPE was generally low during January
through September, highest in October and November, and intermediate between these
levels in December (Figure 2).

The index of abundance provided by the GLMMS suggested different temporal
patterns than CPE (i.e., PD trended through time) over some or all of the time series in
some management units for the gill-net fishery (Figure 3). In Lake Huron, the PD for

management units WFH-Ol and WFH-04 generally varied without trend, while in WFH-
24

02 PD declined during 1982-1983, but varied without trend for the remainder of the time
series. In Lake Michigan, PD in WFM-02 increased during 1987-1988 and then
decreased. In WFM-03, PD increased in variability over the time series and increased
during 1999-2001. PD in WFM-04 generally declined through time. In WFM-OS, PD
generally varied without trend, but declined during 1997-1999 and then increased. In
WFM-06, PD declined during 1993-1997. In Lake Superior, the PD in WFS-05, WFS-
06, WFS-07, and WFS-08 generally varied without trend, except during 1999-2001 in
WFS-05 when PD declined.
Trap-net Fishery

. The final model for the trap-net fishery included fixed effects of year and month,
and random effects of the interactions of month and year, year and license, and month
and year and license:

loge(CPE +1) = ,u + or), + ,6," + kmy + vy1+ pmy1+ aiml.
The final model improved model fit over a means model in all management units by an
average AAICc value of 170.1, with values ranging from 2.2 to 478.2 (Table 2). Of the
random effects, the interaction of year and license holder accounted for the most variation
in logc(CPE+l), even more than residual error (Table 3). CPE was generally low during
January through September, with the exception of May, highest in October and
November, and intermediate between these levels in December (Figure 2).
The index of abundance provided by the GLMMS showed different temporal

trends than CPE (i.e., PD trended through time) over all or some of the time series in
some management units for the trap-net fishery (Figure 4). In Lake Huron, the PD in

WFH-Ol and WFH-02 generally varied without trend, while the PD in WFH-04 varied
25

without trend until 1998 when PD increased to 2000 and then decreased. In Lake
Michigan, the PD in WFM-Ol, WFM-02, and WFM-03 generally varied without trend,
except during 2000-2001 in WFM-Ol when PD increased. In WFM-04 and WFM-OS,
PD varied cyclically with a period of approximately two years in WFM-04 and six years
in WFM-OS. In Lake Superior, the PD in WFS-07 generally varied without trend, while
the PD in WFS-08 increased during 1984-1986, but varied without trend during the few
other years of data.
Discussion

CPE is often assumed to be proportional to abundance, but CPE can change due
to factors other than abundance that cause violations of this assumption (Quinn and
Deriso 1,999; Battaile and Quinn 2004). Violations of the assumption of proportionality
can lead to inaccurate estimates of abundance from stock assessments, and in particular
hyperstability can increase the risk for fishery collapse (Rose and Kulka 1999; Harley et
a1. 2001). Indices of abundance based on commercial fishery catch and effort data are at
an especially high risk of violating the assumption of proportionality due to things such
as systematic changes in characteristics of the fishing fleet (e.g., technological
advancements, entrance and exit of individual vessels), non-random search effort, and the
spatial distribution of the fish stock (Rose and Kulka 1999; Harley et a1. 2001; Maynou et
a1. 2003; Battaile and Quinn 2004; Bishop et al. 2004; Campbell 2004). For these
reasons, fishery CPE data from many major marine fisheries are now often standardized
using various statistical models (e.g., general linear mixed models, generalized linear
models) that account for some of the variation in CPE not attributable to abundance, 30

that the “year-effect” becomes a more accurate index of abundance (Maunder and Punt

26

2004; Venables and Dichmont 2004). Factors commonly included in models used to
standardize CPE data include factors for time (usually year), location (e.g., grid in this
study), individual vessels, characteristics of vessels that affect catchability (e. g., vessel
size, horsepower, GPS), among other factors (Maunder and Punt 2004).

The temporal trends exhibited by standardized CPE data (e.g., LSMS) have
differed from that of non-standardized CPE data (e.g., ratio of aggregate catch to
aggregate effort in each year) in other studies (Maynou et a1. 2003; Battaile and Quinn
2004), as was true for some management units in our evaluation of Great Lakes Whitefish
fisheries. Thus, we believe that model-based indices of abundance should replace non-
standardized CPE in some lake Whitefish stock assessment models, especially those
management units where PD was shown to trend through time. Converting to the use of
model-based indices of abundance in the stock assessment models for these management
units would likely produce more accurate estimates (e.g., abundance estimates) than the
current approach of treating raw effort as an index of fishing mortality (equivalent to
using CPE as an abundance index). This outcome would also likely hold true for other
freshwater systems, where model based methods for standardizing CPE data have not
been used as frequently as in marine systems.

The reason for the changes in PD in this study can be partially explained by when
most fishing occurred and who fished in each year. For example, in 1988 in the WFM-02
gill-net fishery, fewer observations were made in the spring (i.e., when CPE is lower
relative to other times of year) and more observations were taken from license holders
with relatively high CPE than in other years, which may explain the spike in PD.
Similarly, in the WFM-04 trap-net fishery, peaks in PD occurred in years when more

27

observations came from license holders who did well in that year relative to other license
holders. Consequently, indices of abundance based on CPE in these and other areas
would most likely be driven by differences in the number of observations taken among
seasons or from difference license holders, and not due to changes in abundance as is
being assumed in stock assessments.

In addition to providing a more accurate index of abundance, the use of mixed
effects models also allows the uncertainty around the indices of abundance to be more
accurately quantified for each year, and this can be especially important if these estimates
of uncertainty are used to weight the importance of the yearly CPE indices in stock
assessment models (Helser et a1. 2004, Maunder and Starr 2003). Maunder and Starr
(2003) describe methods for how yearly indices of abundance can be weighted by their
coefficient of variation in fitting stock assessment models, and also found that stock
assessment estimates (e.g., abundance estimates) can be less accurate when each yearly
index of abundance is weighted equally, instead of using a year specific weight.
Furthermore, Helser et a1. (2004) found that ignoring the variability due to random
effects, including vessel and the interaction of vessel and year, similar to the effects of
license and the interaction of license and year in this study, may lead to an
underestimation of uncertainty in indices of abundance. Thus, if the CPE data used in
fitting lake Whitefish stock assessment models were replaced with model-based
standardized CPE indices and an associated estimate of uncertainty for each year (e.g.,
the standard errors around the LSMS), uncertainty in the indices of abundance would be
more accurately quantified and CAA stock assessment estimates would also likely be

more accurate. This benefit would accrue even in areas where CPE and model-based

28

indices Showed Similar temporal patterns (i.e., PD did not show any trends or systematic
temporal patterns).

We do not believe that calculating a fishery CPE index, by combining CPE each
year over strata defined based on statistical modeling, provides a viable alternative to the
use of indices directly derived from model-based methods. This conclusion applies
especially in the presence of the types of random effects we saw for Great Lakes lake
Whitefish data and that appear to be common to fishery CPE data from marine systems.
A large advantage of a model-based approach is that the complex correlated error
structure resulting from such random effects can be parsimoniously accounted for. The
studies cited above suggest that a stratification approach would either underestimate
uncertainty in the indices of abundance and lead to inaccurate stock assessment results by
ignoring variability attributable to random effects, or would require so many strata with
so few observations per stratum that the resulting indices would be poorly estimated. For
example, our model for the gill-net fishery would suggest strata need to account for
seasonality, boat size, and individual license, but available data only consist of monthly
summaries by license. Even if data were combined over similar months, few
observations would be available per stratum. Perhaps in some situations (e.g., if random
effects were less important), data from each year could be post-stratified into relatively
few strata. In such a situation, calculating indices based on combining raw results over
strata might be a viable approach, with the advantage of not requiring refitting of
statistical models each time a new year of data is collected.

An alternative approach to using model-based output as an index of abundance in

stock assessments is to integrate the standardization process into the estimation procedure

29

of the stock assessment models (Maunder 2001; Maunder and Langley 2004). Such an
approach still models CPE data in the same way as in our analysis here, but integrates the
CPE model as a sub-model of the overall assessment. Maunder (2001) found that
integrating the CPE standardization into the estimation procedure of the stock assessment
model provided a more accurate representation of the uncertainty in stock assessment
parameter estimates. The reason for this result, however, was unclear, and so more
research is needed in this area, especially given the programming and data management
challenges associated with integrating complex GLMM and related models for fishery
CPE into assessment models.

Standardization techniques used for fishery CPE data cannot ensure that all
sources of variation in CPE not attributable to changes in abundance have been
considered. For example, changes that are confounded with year and universally affect
the fishing fleet, or density dependent changes in catchability, cannot be accounted for
using model based standardization methods. Factors left untreated by standardization
methods should be addressed in the stock assessments where the CPE indices of
abundance are used, for example by allowing for time-varying catchability (Wilberg and
Bence 2006).

The factors in the final models for both the gill-net and trap-net fishery were
similar to models developed for other fisheries (Maynou et a1. 2003; Battaile and Quinn
2004; Bishop et a1. 2004; Helser et a1. 2004). This commonality suggests that similar
factors are likely to be important and necessary for consideration when standardizing
CPE data for most fisheries. Year is usually included as one of the explanatory variables

because detecting trends through time is often the objective for developing indices of

30

abundance, as in this study (Maunder and Punt 2004). Temporal factors on a finer scale
than year have also been included in statistical models used for CPE standardization in
order to account for systematic temporal patterns in fish abundance or catchability
(Battaile and Quinn 2004). Battaile and Quinn (2004) used a fixed effects analysis of
variance to standardize CPE data for the eastern Bering Sea walleye pollock, T heragra
chalcogramma, trawl fishery, and found a significant effect of time of day (i.e.,
categorical variable for daylight versus nighttime hours), with higher catch rates dming
the daylight hours. They suggested that catch rates were higher during daylight hours
because walleye pollock school during those times, but spread out to feed during
nighttime, which reduces catchability. In this study, month was included in the final
model for the gill-net and trap-net fisheries, with higher catch rates from October to
December. The higher catch rates in those months were likely caused by an increase in
the catchability of lake Whitefish facilitated by spawning aggregations, which usually
occurs during those times in most areas of the Great Lakes (Becker 1983). The results of
these studies suggest that temporal factors that account for systematic changes in fish
aggregating behaviors should be considered in models used to standardize CPE data
whenever possible

Various measures of vessel “power” have also been included in models used for
standardizing CPE data. Vessel “power” is any measure of the boat or crew that likely
affects catchability, and so affects the indices of abundance that result from CPE data
taken from those vessels. In the eastern Bering Sea walleye pollock trawl fishery, longer
vessels tended to have higher catch rates than shorter vessels as indicated by the

coefficient estimates for each vessel participating in the fishery (Battaile and Quinn

31

2004). For the trawl fishery directed at Norway lobster, Nephrops vorvegicus, and deep-
water red shrimp, Aristeus antennatus, in the northwestern Mediterranean Sea,
generalized linear models used for CPE standardization included measures of the gross
tonnage of vessels, engine horsepower, and total length (Maynou et a1. 2003). Generally,
longer more powerful vessels had higher catch rates. In the absence of direct measures of
vessel power, some surrogate could also be used. For example, Punt et a1. (1996)
included the number of crew on the vessel as a surrogate for vessel length in generalized
linear models used to standardize albacore, T hunnus alalunga, longline CPE data. For
the lake Whitefish fishery in this study, a categorical effect of vessel length was used for
the gill-net fishery as a measure of vessel power, but the affects on CPE were inconsistent
across lakes. This inconsistency makes broad conclusions about the relative success of
various vessel Sizes difficult, but the explanation may be in the characteristics of the lakes
themselves. The depth gradient of Lake Superior is relatively steep and permits access to
fishing grounds by all boat sizes, and so all boat sizes performed similarly. Conversely,
Lake Michigan offers more shallow fishing grounds that are more accessible to small and
medium Sized boats, and this may have resulted in higher catch rates than longer boats in
that lake. The reason for the relative performance of each boat size in Lake Huron,
however, is not clear.

A factor for individual vessel, such as license holder in this study, is also
commonly included in models for CPE standardization (Maynou et a1. 2003; Battaile and
Quinn 2004; Bishop et a1. 2004; Cooper et a1. 2004; Helser et a1. 2004). Similar to results
here, an individual vessel factor explained the most variability in CPE in the eastern

Bering Sea walleye pollock trawl fishery (Battaile and Quinn). Generalized linear

32

models that included vessel also explained the most variation in CPE for the deep-water
red shrimp trawl fishery in the Mediterranean (Maynou et a1. 2003). Cooper et a1. (2004)
and Helser et a1. (2004) also found that individual vessel and interactions with vessel
should be included in the final models used to standardize U.S. west coast groundfish
bottom trawl surveys. The results of Cooper et a1. (2004) and Helser et al. (2004) suggest
that even with survey data, standardizing CPE may be necessary, and the availability of
model-based indices should not replace the use of consistent survey sampling.

The consistent inclusion of an individual vessel effect indicates that individual
vessel may serve as a “catch all” for characteristics of boats not included in models
(Battaile and Quinn 2004). For example, Maynou et a1. (2003) suggested that the
inclusion of individual vessel likely accounts for the expertise of individual fishers or
unmeasured technical characteristics, such as investment in technology. The large
amount of variation explained by the random effect of license holder and interactions
with license holder in this study for both fishery gears also suggests that this factor is
accounting for the effects of some unmeasured characteristics, such as those suggested by
Maynou et al. (2003).

Making inference about the causal or biological mechanisms for some of the two-
and three-way interactions included in the final models in this study is not
straightforward. However, as Battaile and Quinn (2004) note, identifying causal
mechanisms is not required when standardizing CPE data, because the purpose is to
account for effects coincident with the variables included in the model. So, the specific

higher order interactions may not be indicative of anything biologically meaningful, only

33

that CPE varies coincident with combinations of those factors, either due to those factors
themselves or other variables that co-vary with them.

The random effect of grid was not included in the final models for either the gill-
net or trap-net fisheries, which is surprising considering that typically there is spatial
variation in fish density or fishing success. Campbell (2004) found that non-randomly
sampled locations led to biased indices of abundance, unless the total habitat area of the
stock was spatially stratified and each CPE observation was weighted by the relative
amount of sampling effort in the strata from where the observation was taken. This result
suggests that not accounting for spatial variation in sampling effort can lead to biased
indices of abundance. The effect of grid in this study may have not been included in final
models because the analyses were already run on spatially stratified stocks delineated by
management unit. However, the results of Campbell (2004) and the spatial variability
that likely exists in fish density and fishing success for most fisheries suggests that spatial
effects should always be considered when standardizing CPE data.

Acknowledgements

We are grateful to Michigan Department of Natural Resources (MDNR) and
Chippewa-Ottawa Resource Authority personnel who collected and provided data for this
project. We thank the 1836 treaty waters modeling subcommittee and personnel at the
Quantitative Fisheries Center at Michigan State University for commenting on
presentations based on this research. We would especially like to thank Mark Ebener and
Phil Schneeberger for their insights on characteristics of the lake Whitefish fishery and
these data. Discussions with Ty Wagner, Gretchen Anderson, and Melissa Mata on

mixed models and model selection aided this research. Funding for this project was

34

provided by the MDNR and US. Fish and Wildlife Service - Federal Aid for Sportfish
Restoration (Project F -80-R, Study 230713). This manuscript is publication 2009-06 of

the Quantitative Fisheries Center at Michigan State University.

35

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38

 

  

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Figure l.— 1836 Treaty-ceded waters and lake Whitefish management units in Lakes

Superior, Huron, and Michigan (Ebener et al. 2005).
39

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0.8 .

Gill-net Fishery

 

Average Coefficient

 

 

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Figure 2.—-Average coefficient estimates (i SE representing uncertainty resulting from
variability among management units) for the effect of month from a general linear mixed
effects model standardizing catch per effort (catch = aggregate round mass of lake
Whitefish) for the lake Whitefish gill-net fishery (top panel; effort = aggregate length of
net in 10003 of feet) and trap-net fisheries (bottom panel; effort = number of lifts) in the
1836 treaty-ceded waters of Lakes Superior, Huron, and Michigan. Coefficient estimates
were averaged across various years (generally 1981-2001) and lake Whitefish
management units included in this analysis.

40

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Table 1.—Years and lake Whitefish management units included in this analysis

for the gill-net and trap-net fisheries of the 1836 treaty-ceded waters of Lakes Superior,

Huron, and Michigan.

 

Gear Type

Trap-net

 

Years Included

 

 

Management Unit Years Included
WFH-01 1981-2001 1981-1982; 1986-2001
WFH-02 1982-2001 1983; 1986-1987; 1989-2001
WFH—04 1981 -2001 1981-1982; 1984-2001
WFM-O1 - 1981-1985; 1995-1998; 2000-2001
WF M-02 1986-2001 1986-2001
WF M—03 1986-2001 1986-2001
WF M-04 1981-2001 1989-2001
WF M-05 1981-2005 1981-2001
WF’ M-06 1985-1989; 1993-2001 -
WFS-OS 1986-2001 -
WF’S-OS 1985-2001 -
WFS-O? 1981-2001 1981; 1985-2001
WFS-OB 1981-2002 1981-1982; 1984-1986; 1996-2001

 

49

 

Table 2.————Differences between AICc values between final models and a means
model (i.e., model with only a year effect) for the lake Whitefish gill-net and trap-net
fisheries in the 1836 treaty-ceded waters in the management units of Lakes Superior,

Huron, and Michigan included in these analysis. Differences are reported as A AICc =

AICc from means model — AICc from final model.

 

 

 

 

 

 

Gear Type
Gill-net Trap net

Management
Unit A AICc A AlCc
WFH-01 536.1 281.3
WFH-02 173.9 324.8
WFH-04 508.1 121.9
WFM-01 - 95.1
WFM-02 93.5 28.4
WFM-03 677.7 478.2
WFM-04 556.4 212.4
WFM-05 320 2.2
WFM-06 -10.2 -
WFS-05 61.1 -
WFS-06 118.2 -
WFS-07 993.5 1 1 1.8
WFS-08 322.1 44.4

 

50

Table 3.—Average variance component estimates for residual error (01%),"ng ),

license holder (012 ), and month and year (0,30,) for the lake Whitefish gill-net fishery,

and random effect estimates of residual error (aim, ), year and license holder (0)221)’

month and year (0'31), ), and month and year and license holder (03M) for the lake

Whitefish trap-net fishery of the 1836 treaty-ceded waters of Lakes Superior, Huron, and
Michigan. Variance component estimates were averaged across lake Whitefish

management units included in these analyses.

 

 

 

 

 

Gear Type
Gill-net Trap-net
Variance Mean Variance Mean
Component Estimate Component Estimate
2 2
aiymbgl 0.47 0sz 0.17
2 2
‘71 0.22 0y! 0.29
2 2
“my 0.05 “my 0.09
2
- - “my! 0.09

 

51

 

Table 4.—Average estimates of the coefficients for different size classes of boat
for the gill-net fishery for lake Whitefish on the 1836 treaty-ceded waters of Lakes
Superior, Huron, and Michigan. Boats were classified as small (3 20 fl), medium (20-30

ft), and large (3 30 fi). Coefficients were averaged across lake Whitefish management

units included in these analyses for each lake.

 

 

Boat Lake Lake Lake

size Superior Huron Micflgan
Large 0.03 0.11 -0.28
Medium 0.05 -0.03 0.09
Small 0.00 0.00 0.00

 

52

 

CHAPTER 2

Deroba, J .J . and J .R. Bence. 2008. A review of harvest policies: Understanding relative
performance of control rules. Fisheries Research: 94: 210-223.

The content of this chapter is intended to be identical to the cited publication and is based
on the accepted manuscript with changes that reflect corrections made during copy
editing. Any differences should be minor and are unintended.

53

Abstract

Harvest policies use control rules and associated policy parameters to dictate how
fishing mortality or catch and yield levels are determined, and are necessary for rational
management. Common control rules include constant catch, constant fishing mortality
rate, constant escapement, or a few variations of these. The “best” among these control
rules for meeting common fishery objectives (e.g., maximizing yield) is a source of
controversy in the literature, and results are seemingly contradictory. To compare the
ability of control rules to meet widely used fishery objectives and identify potential
causes for these apparently contradictory results, we did a detailed review of relevant
literature. The relative performance of control rules at meeting common fishery
objectives is affected by whether uncertainty in estimated stock sizes is included in
analyses, and whether the maximum recruitment level (e.g., the asymptote of a Beverton-
Holt stock-recruit function) is varied in an autocorrelated fashion over time. Relative
performance of control rules also depends on fishery objectives and the amount of
compensation in the stock-recruit relationship. The influence of assessment error on the
relative performance of control rules depends upon whether policy parameters are fixed
using those that perform best without errors or not. Ideally, selection of a control rule
and policy parameters is done within the framework of a stochastic simulation that
considers key uncertainties. If this is not feasible, an alternative option is to “borrow”
control rules from a similar fishery and set policy parameters based on biological
reference points developed for a species with similar taxonomy and life history traits.

More research is needed to compare control rules when accounting for uncertainty in key

54

population parameters, when stock-recruitment or other population dynamic parameters
vary over time, and for fisheries with non-yield-based or competing objectives.
1. Introduction

Rational management of fish stocks requires determination of harvest or yield
levels that are consistent with management objectives. Historically, the “rules” for
setting harvest levels have been vague or non-existent (NRC, 1994). In many cases, this
resulted in forsaking long-term objectives for short-term gains. Consequently, examples
of fish stock declines and collapses are widespread (Myers and Worm, 2005). To prevent
future stock collapses, and allow rebuilding of stocks that are already depleted, more
explicit guidelines are required on how harvest levels should be set. Such guidelines are
referred to as harvest policies. When these guidelines specify the amount of catch, effort,
or fishing mortality by a specific, and usually simple, function of the current estimate of
the system state (e.g., the amount of spawning biomass) they are called control rules.

Fishery objectives partially determine the relative performance of different
control rules and are represented quantitatively in simulations and analyses through the
use of objective functions. Selection of objectives or objective functions can affect which
control rule is preferred, and thus it is critical to ensure resource user preferences and
broader societal goals for sustainability of the resource are incorporated into the chosen
objectives. The use of an objective that conflicts with the interests of the fishery could
cause mistrust from the fishing industry, or even fishery collapse. For example, in a
recreational fishery, where high catch rates and the size of harvested fish are likely to be

important, using a maximum yield objective function would be inappropriate. Although

55

this is true, most harvest policy work emphasizes yield-based objectives, and hence by
necessity, much of this review evaluates these.

Several methods are used to evaluate control rules for meeting given fishery
objectives. A variety of analytical methods can be used to show that a given control rule
performs better than all other candidates (i.e., is optimal) at achieving a given objective
(e.g., Gatto and Rinaldi, 1976). While these methods can provide quite general results,
they are feasible only for simple models of fishery systems that often are deterministic or
ignore key uncertainties. Stochastic dynamic programming is an efficient method for
selecting an optimal strategy at 'each time step, so that the result over the entire time-
horizon best meets a specified objective (e. g., Walters and Parma, 1996). While the
method can be analytical or numerical, most fishery applications are numerical. This
method is useful when one is interested in considering more flexible policies than a
simple control rule that remains constant over time. The computational cost of searching
over a wide range of strategies has also generally limited this approach to relatively
simple models. Much of the recent harvest policy literature considers models too
complex for the above methods, and often the focus is on tradeoffs among different
measures of performance, rather than finding the policy that is optimal for a single
objective. Consequently, much harvest policy work uses Monte Carlo simulations to
evaluate the performance of a specified control rule (function) and policy parameters for
the control rule (e. g., Eggers, 1993). Typically, multiplicative annual process error is
included in the stock-recruit relationship, which may or may not include autocorrelation.
Alternatively, or additionally, annual process error can be added to specific model

parameters. Other random error terms are often included to model assessment or

56

implementation error. When these simulations attempt to model uncertainty associated
with the stock assessment process and implementation of the control rule, this is called a
Management Strategy Evaluation (MSE; Polacheck et al., 1999). Typically, a range of
different policy parameters are considered. In some cases a wide enough range of policy
parameters is considered that this essentially constitutes a grid search, and optimal results
for a given control rule and objective can be identified. In rare cases, usually for very
simple stochastic models, an automated numerical search is done for parameters that
maximize an objective function. The results obtained by these “brute force” simulation
approaches are limited to the specific policy parameters (and other assumptions) chosen
for inclusion in simulations, and thus cannot prove that a particular control rule is optimal
for a given objective over a broad range of conditions. However, we believe induction
based on these studies, combined with consideration of results known from analytical
studies, can be very useful.

In many fisheries, managers must decide on a level of yield each fishing season,
ideally by using a harvest policy that is chosen because it meets fishery objectives (i.e.,
produces a large value for the objective function). Theoretically, a harvest policy could
be to set yield each year so that the objective function is maximized given the
information available at that time (Ricker, 1958; Larkin and Ricker, 1964; Tautz et al.,
1969). Such a policy would generally mean that yield is determined in a complex way by
current stock assessment results and other information (e. g., using stochastic dynamic
programming; Frederick and Peterman, 1995). In practice, determination of such optimal
policies can be a daunting or an infeasible computational task. Furthermore, such an

approach can lack appeal to managers and stakeholders because the intuitive basis of the

57

policy and why the current year’s allowable catch has changed from the previous year
may not be apparent. Perhaps as a consequence, nearly all harvest policies are based on
relatively simple control rules that can be viewed as relating fishing mortality to stock
abundance (usually biomass; Figure 1). However, which rules are best at meeting certain
fishery objectives is a source of controversy in the literature. Furthermore, the relative
performance of control rules depends upon the specific characteristics of the fishery and
underlying fish population dynamics that are incorporated into an evaluation.
Consequently, selecting an appropriate control rule can be an arduous task.

The objectives of this review are to (1) compare and contrast the performance of
various control rules for meeting common fishery objectives, and (2) identify potential
reasons for what seem to be contradictory results. First, we discuss a range of control
rules and objectives that are used in harvest policy studies. Second, we consider the
performance of different control rules when perfect knowledge is assumed about the
fishery, after which we examine the effect of imperfect information on stock size, which
is a feature of harvest policy analyses that has a particularly strong affect on control rule
performance. Other features of harvest policy analyses also affect policy performance,
such as the level of compensation in the stock-recruit relationship and whether certain
stock-recruit parameters are autocorrelated through time, and these are addressed within
the framework of the perfect and imperfect information sections. Third, we consider
approaches to choosing catch levels, fishing mortality rates, or thresholds necessary for
implementation of control rules. Finally, we offer conclusions and suggestions for

interpreting harvest policy analyses and identify future research needs.

58

2. Common control rules

We describe common control rules as background for our review of their relative
performance. Most rules can be categorized into three main types (Figure l) or a few
modifications of these (Figure 2), and explicitly or implicitly specify a relationship
between fishing mortality and stock abundance. We choose to specify control rules in
terms of fishing mortality because how this per capita mortality rate varies with
abundance summarizes the compensatory or depensatory effect of the rule. A constant
catch control rule removes the same number or biomass of fish each year, and is
depensatory in that it leads to high fishing mortality at low stock sizes (Figure 1; Quinn
and Deriso, 1999). A constant fishing mortality rate (also called a constant harvest rate)
uses the same fishing mortality regardless of stock abundance (Figure 1), and hence
harvest is proportional to biomass (Quinn and Deriso, 1999). When fishing mortality is
assumed to be directly proportional to fishing effort, constant fishing mortality rate rules
are also referred to as constant effort. A constant or fixed escapement control rule takes
all biomass over some specified target level. Control rules such as this are also referred
to as “bang-bang” policies in the resource economics literature, because when modeled in
continuous-time, harvest is intense above the threshold and zero otherwise (Figure l;
Nostbakken, 2006). This type of control rule is often used when fishing anadromous fish,
where a specified number of fish are allowed to pass a weir or other observation location
and the remainder of the run is removed. In open-ocean or lake fishing, such a control
rule is usually interpreted as allowing harvest of all fish over a threshold abundance or
biomass, so that fishing mortality is zero up to that threshold and then increases thereafter
(Figure 1).

59

+30

$33.6

Each of these basic control rules has a number of variants, many of which have
been suggested to retain what are viewed as positive features of a rule while addressing
some of its weaknesses. Here we review some of these important variants (Figure 2).
The conditional constant catch (CCC) control rule, a variant of constant catch, removes
the same number or biomass of fish each year unless removing that amount would exceed
some pre-determined maximum fishing mortality rate. If the constant catch amount
would cause fishing mortality to exceed this rate, then the rule reverts to a constant
fishing mortality rate at the pro-determined maximum (Figure 2B ; Clark and Hare,
2004). This control rule attempts to avoid the high fishing mortality rates that occur at
low stock sizes under a constant catch rule but retains the benefit of stable catches at high
stock sizes. Murawski and Idoine (1989) and Hjeme and Hansson (2001) suggest similar
control rules where the amount of harvest is reduced to a new low level (potentially zero)
when biomass falls below a threshold (Figure 2C).
Threshold control rules are suggested as modifications to constant fishing rate
rules and specify a biomass below which no fishing is permitted (the threshold), but a
coIIStar'rt fishing mortality rate is used otherwise (Figure 2A; Quinn and Deriso, 1999).
Variations of this basic form have also been suggested, such as decreasing fishing
mortality gradually below the threshold and increasing fishing mortality gradually above
the threshold, to produce compensatory and potentially stabilizing fishing mortality
(Figure 2E; Quinn et al., 1990; Eggers, l993; Sigler and Fujioka, 1993; Quinn and
Deriso, 1999; Ishimura et al., 2005). Control rules that scale fishing mortality or catch
do"VllWard when the population is below a threshold are known as biomass-based or

a -
dJ ustable rate rules, and fishing mortality or catch is usually adjusted in proportion to

60

 

population size (Figure 2E; Quinn and Deriso, 1999). Whether fishing mortality or catch
is adjusted with changes in biomass affects the relationship between fishing mortality and
biomass (Figures 2E and 2F) and thus has potentially different performance
characteristics. The “40-10” rule, which is used to manage U.S. west coast groundfish, is
an example of the latter type of biomass-based rule. Catch is reduced linearly as
spawning biomass declines below an upper threshold (40% of the unfished level) so that
no harvest is allowed when spawning biomass is below a lower threshold (10% of the
unfished level) (Hilbom et al., 2002; Punt, 2003; Punt, this issue). The result is that for a
40—10-like rule fishing mortality decreases nonlinearly (Figure 2F ). Engen et a1. (1997)
suggest a variation of a constant escapement rule called “proportional threshold
harvesting”, which has been used to manage U.S. west coast pelagic species since the
early 19803 (Pacific Fishery Management Council, 1998; Barange et al., in press). With
this control rule, only a fraction of the surplus above the threshold is harvested. The
resulting nonlinear relationship between fishing mortality rate and biomass can be viewed
as a biomass-based control rule, and appears similar to a 40-10-like rule (Figure 2D).

Proportional threshold harvesting is a special case of a 40-10-like rule with the upper
threshold set infinitely high (e. g., a “00-10” rule). So, for both control rules catch

increases linearly with biomass above a lower threshold, but for a 40-10-like rule the
slope of the relationship changes above an upper threshold.
3. Common fishery objectives

Fishery objectives are represented in harvest policy analyses using objective
functions, and these are used to compare the relative performance of control rules. A

frequently-used objective function is cumulative harvest over some fixed time horizon, or

61

the sum of annual values of a utility function over a time horizon, where the utility
function relates annual harvest to some economic, biological, or social construct (Quinn
and Deriso, 1999). Maximizing cumulative harvest is considered a risk neutral approach,
because performance is measured only by the total over the time horizon, with the
frequency of low and high annual values playing no role (Reed, 1979; Quinn and Deriso,
1999). More risk-averse objective functions penalize for extreme harvests in an effort to
avoid boom-or-bust fisheries (Walters and Pearse, 1996; Lande et al., 1997; Quinn and
Deriso, 1999). One risk-averse objective fimction is to maximize the long-term logarithm
of harvest, and this tends to avoid extreme harvests by placing an infinite penalty on zero
harvests (Ruppert et al., 1985). This objective function, however, is criticized as being
risk-averse only in terms of economic risk to the industry, and not biological risk to the
resource (Lande et al., 1997). Another risk-averse objective function is to maximize a
linear combination of average yield ()7) and the negative of the standard deviation (SD)
of yield over a given planning horizon (e. g., max[(1- 7t) I; - XSD]; Quinn et al. 1990;
Collie and Spencer 1993). This approach is relatively flexible in that the relative
influence of average yield and the standard deviation of yield can be controlled using the
weighting term, 7». An alternative, but less commonly used type of risk averse objective
accounts for how frequently or over what duration biomass or harvests have been at or
below a threshold (Enberg, 2004; Irwin et al., this issue)

Other objective functions have been formulated to maintain biomass or harvest at
predetermined target levels (Hightower and Grossman, 1987). This stability can be
accomplished by minimizing the sum of squared deviations between biomass or harvest

and the predetermined target levels. However, Hightower and Grossman (1987) criticize
62

objective functions that only consider maintaining harvest near a target because two
values of fishing mortality could result in the same equilibrium harvest. When rebuilding
a stock from a depleted state, the optimal fishing mortality is the higher of the two
equilibrium points, which also results in maintaining lower equilibrium abundance.
Another criticism of only considering harvest is that, for an age-structured population, the
same harvest is obtained for multiple age-structures. Consequently, when stock sizes
decline, maintaining harvest near the target requires increasing fishing mortality, which
can be destabilizing in terms of abundance and yield, creating a negative feedback
(Beddington and May, 1977; Lowe and Thompson, 1993). To remedy these problems,
Hightower and Grossman (1987) suggest using an objective function that simultaneously
minimizes the deviations of both harvest and biomass from target levels. Similarly, the
maximum harvest objective can also be combined with a constraint that requires the
biomass at the end of the planning horizon to be near a target level (Hightower and
Grossman, 1987). More generally, objective functions can be defined as even more
complex functions of multiple performance measures (e.g., Katsukawa, 2004).
Bioeconomic objective functions that aim to maximize profits have also been
developed (Clark, 1973). In a simple bioeconomic model, revenue R is assumed to be a
linear function of harvest and is found as the product of price (amount paid per unit fish)
P and harvest H:
R=PH.'
(Clark, 1973; Reed, 1979; Quinn and Deriso, 1999). Costs C are incorporated into the
model as the product of the cost per unit of fishing effort L and total effort E:
C =LE.

63

Net profit Q is the difference of the revenues and costs:

Q=R-C.
Costs can also be modeled as a function of stock size (Reed, 1979). Costs are most often
modeled as a decreasing function of abundance, which requires the assumption that catch
per effort (CPE) increases with abundance (Clark, 1973; Reed, 1979). Whether the
decrease in cost as abundance increases is linear will depend upon whether catchability
also varies with abundance (Reed, 1979). Bioeconomic objective functions can also
incorporate discount rates, where the value of capital invested in the current time
diminishes in the future due to inflation (Clark, 1973; Reed, 1979; Quinn and Deriso,
1999; Quinn and Collie, 2005). Objective functions incorporating discount rates are
referred to as maximizing the expected present value (Reed, 1979). “High” discount
rates have been blamed for the demise of some fish stocks, where the future value of
capital approaches zero, so that economically, the optimal course of action is to fish the
stock quickly to collapse (Clark, 1973). The use of negative discount rates is suggested
by some conservation groups as a way to conserve stocks because capital actually
increases in value in the future (Quinn and Deriso, 1999). Bioeconomic objective
functions that maximize profits also tend to favor larger stock sizes than maximum yield
objective functions (Clark, 1973; Deriso, 1987). Consequently, increasing effort beyond
the point that attains maximum profits in order to achieve maximum yield is not only
inefficient but can also incur other risks associated with smaller population sizes.
4. Relative performance with “perfect” information

4.1. Comparing control rules

64

Analyses of harvest policies often assume that decisions are made with “perfect”
information (i.e., no uncertainty or error), in terms of knowing the underlying dynamic
system model and its parameters, in knowing the current state of the system (e. g.,
biomass), and in being able to implement regulations to achieve a desired result.
Assuming perfect information allows for greater ease of computation, and likely reflects
the common practice of setting harvest quotas based on a point estimate of abundance
(Frederick and Peterman, 1995). Although many would agree that this is an unrealistic
assumption for most stocks (e. g., Engen et al., 1997), the results of studies based on
perfect information are still used as a guide, because they are viewed as likely to reflect
qualitative differences and outcomes that can be expected from the application of various
control rules under situations of “imperfect” information.

Assuming perfect information, constant escapement rules generally perform best
for maximizing cumulative yield, mean annual yield, or profits, usually followed in
performance by threshold or biomass based rules, constant fishing mortality rate rules,
and lastly constant catch rules, although this general conclusion may also depend on
assuming that maximum recruitment levels (i.e., the asymptote of a Beverton-Holt stock-
recruit firnction) are temporally independent (Table 1; Table 2). For semelparous stocks
(e. g., pacific salmon Oncorhynchus tshawytscha), Ricker (195 8) shows that constant
escapement control rules produce 24-5 7% higher long-term average harvest than constant
fishing mortality rate rules, depending on the shape of the stock-recruitment curve, when
both the escapement level and fishing mortality rate are set to attain the maximum
average yield. This general result is also supported by additional research on iteroparous

species and for a broad range of conditions (e.g., various stock-recruit relationships)

65

(Table 2). With surplus production models, a type III functional response, and
autocorrelated consumption rate, threshold rules can produce greater than 100% higher
average yield, higher sum of discounted yields, and higher sum of discounted rents than
constant fishing rate control rules, depending on the level of autocorrelation in
consumption rates (Collie and Spencer, 1993; Spencer, 1997). Constant fishing mortality
rate control rules, however, can outperform constant catch rules in terms of yield by 29%
or more (Jacobson and Taylor, 1985). Furthermore, even with catch set at maximum
sustainable yield (MSY) or the level that maximizes net revenue, several other studies
show that constant fishing mortality rate and biomass based control rules provide higher
long-term yield and profits (Table 2). Similarly, constant harvest rate rules can produce
the same or modestly higher average yield than the various CCC control rules (Hjeme
and Hansson, 2001; Clark and Hare, 2004).

In contrast to some of these studies, Walters and Parma (1996) show, using
stochastic optimal control methods, that constant escapement control rules are inferior to
constant fishing mortality rate control rules in terms of maximizing yield when the
asymptote parameter (maximum level of recruitment) of a Beverton-Holt stock-recruit
model is autocorrelated. This discrepancy likely occurs because optimal constant
escapement control rules are highly sensitive to the maximum level of recruitment (Lande
et al., 1997). When maximum recruitment is autocorrelated, controls on spawning
biomass exert imperfect control on expected recruitment. Walters and Parma (1996) also
report that with autocorrelated maximum recruitment, constant fishing mortality rate
control rules attain at least 85% of the theoretical maximum long-term yield (not

constrained by a constant control rule) for most populations. This result also holds true

66

when other stock recruitment parameters (i.e., slope near the origin) are simultaneously
autocorrelated with the asymptote parameter, but does not hold true when other stock-
recruitment parameters are autocorrelated by themselves. Few other studies evaluate the
effect of autocorrelated recruitment on the relative performance of harvest policies (Table
2), and none systematically evaluate the influence of additional alternatives for the form
of such autocorrelation.

Escapement and threshold control rules were developed to prevent over-
exploitation and maintain spawning biomass, and so such rules often maintain higher
biomass, lower variation in biomass, and result in less chance of over-exploitation than
other control rules (Table 1; Getz and Haight, 1989). Escapement and threshold control
rules maintain more consistent levels of biomass than other control rules, because other
rules allow some harvest regardless of the level of stock biomass, which can be
destabilizing in terms of abundance and yield (Beddington and May, 1977; Lowe and
Thompson, 1993). The destabilizing nature of continued fishing as abundance declines is
also made worse with depensation at low abundance (Collie and Spencer, 1993; Eggers,
1993; Walters and Parma, 1996), and this is one reason why some authors argue against
control rules like constant fishing mortality rates (Lande et al., 1997). Several studies
show that constant catch control rules consistently result in the maintenance of less
biomass and more instances of stock collapse than other rules that provide the same or
higher average harvest, likely because a constant catch control rule leads to high levels of
fishing mortality at low abundance (Figure 1; Table 2). Potter et al. (2003) conclude that
if maximizing revenues or yield are not high priorities, as in a recreational fishery, a

constant catch control rule may be useful to meet other fishery objectives (e. g., high

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recreational catch rates), but the catch level should be set low to prevent stock collapse.
Alternatively, the CCC control rule of Clark and Hare (2004) can maintain higher
average spawning stock biomass than a constant harvest rate control rule, but this
depends on the constant catch level and ceiling harvest rate. Thus, the CCC control rule
may be effective at preventing the high fishing mortality rates at low stock sizes that
occur with a strict constant catch control rule.

As a consequence of fishery closures, threshold and biomass based control rules
are also usually the optimal rule for quick rebuilding of depleted stocks (Table 1; Quinn
et al., 1990). Median rebuilding times to equilibrium biomass under a threshold control
rule are shorter than a constant fishing mortality rate control rule (Quinn et al., 1990).
Hightower and Grossman (1987) also show that the optimal rebuilding strategy is to
cease fishing until the threshold biomass level is reached, and use constant fishing
mortality above the threshold.

Relatively high yields and stable biomass almost always appear to come at the
cost of higher variability in yield (Ricker, 1958; Gatto and Rinaldi, 1976; Reed, 1979;
Lande et al., 1995; Lande et al., 1997). Constant escapement control rules usually result
in the highest variability in yield, followed by threshold and biomass based control rules,
constant fishing mortality rates, and then constant catch (Table 1; Table 2, but see
Enberg, 2004). The high variability of yield in constant escapement and threshold
control rules is caused by fishery closures in years when biomass is not above the
predetermined level (Lande et al., 1997; Lillegard et al., 2005). Constant fishing
mortality rate control rules do not require fishery closures, and so usually have less

variability in yield than constant escapement and threshold control rules, but also lead to

68

greater variability in population abundance. Constant fishing mortality rate control rules
also perform best at maximizing logarithm of yield, an objective function that places in
infinite penalty on zero harvest (Walters and Parma, 1996; Walters and Pearse, 1996;
Lande et al., 1997). Intuitively, a constant catch control rule will have zero variability in
catch, except in cases when abundance drops below the predetermined level of catch and
requires closing thefishery, or management cannot react quickly enough to close the
fishery after the catch limit has been attained (Koonce and Shuter, 1987; DiNardo and
Wetherall, 1999). However, the stability in yield of the constant catch control rule comes
at the cost of foregoing high yields at times when abundance is high, and the highest
variability in population abundance and hence risk of fishery collapse (Beddington and
May, 1977; Jacobson and Taylor, 1985; Quiggin, 1992; Potter et al., 2003). If consistent
yields and a stable market have a “much higher priority” than maximizing revenue, yield,
or minimizing risk of fishery collapse, then a constant catch control rule will be a
competitive option (Quiggin, 1992; Steinshamn, 1993; Potter et al., 2003).

The differences among control rules in catch/yield variability can be substantial.
In a simulation based on the northwestern Hawaiian Islands lobster fishery, mean yearly
percentage change in catch was less for a constant catch control rule (yearly variation in
catch for the constant catch rule was caused by fishery closures) than a constant fishing
mortality rate control rule (about 43% and 156%, respectively) across a range of catch
and fishing mortality rate levels (DiNardo and Wetherall, 1999). The various CCC
control rules maintain some of the benefits of a constant catch control rule; they can
produce less yearly variability in catch than a constant harvest rate strategy, with the

relative difference in variability depending on the values used for the CCC control rule

69

parameters (i.e., constant catch level and maximum harvest rate) (Hjeme and Hansson,
2001; Clark and Hare, 2004). Constant fishing mortality rate control rules can also
produce standard deviations in annual yield half that of threshold control rules (Collie
and Spencer, 1993), and Walters and Parma (1996) show that the advantage of constant
fishing mortality over constant escapement in terms of yield constancy is enhanced when
maximum recruitment is autocorrelated. The biomass-based “40-10” control rule also
maintains much lower standard deviation of average annual catch than an optimal
constant escapement control rule (Ishimura et al., 2005).
4. 2. Effect of the stock-recruit relationship

The relative performance of harvest policies, and the results of some studies
discussed above, can depend on the form of stock-recruit relationship used, and
particularly the extent of compensation in the relationship, particularly for threshold
control rules. Consequently, caution should be used when interpreting analyses that
compare various harvest policies because the results may depend on the amount of
compensation assumed to exist in the stock-recruit relationship. When recruitment is
highly compensatory (i.e., recruitment is weakly dependent on stock size), the potential
benefits of a threshold control rule (i.e., maximum yield or revenue) fail to materialize
because maintaining a given level of spawning stock no longer produces benefits in terms
of recruitment, but yield is generally still more variable than other control rules due to
fishery closures. Hightower and Lenarz (1989) assume recruitment decreases by 10%
when the spawning stock is reduced by 50% from the pristine level, making recruitment
highly compensatory, and show that a constant escapement control rule produces only

2% greater mean harvest than a constant effort control rule, but CV of harvest is 49%

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higher. For South African anchovy Engraulis capensis, Butterworth and Bergh (1993)
assume recruitment varies around a constant level independent of stock size and show
that a constant fishing mortality rate control rule produces the same yield as a constant
escapement control rule, but with less yearly variability in yield and less risk of the stock
falling below 20% of unfished biomass. Other studies that assume highly compensatory
stock-recruit relationships, where recruitment is independent of stock size over a broad
range, also report similar results for “40-10”, constant catch, and constant fishing
mortality rate control rules relative to threshold control rules (Steinshamn, 1998;
Ishimura et al., 2005). If these analyses had included a weaker compensatory response in
the stock-recruit relationship, the results likely would have been different, and the
benefits of threshold control rules (maximum yield or revenue) may have been preserved.
5. Relative performance with “imperfect” information

In reality, management must be conducted with “imperfect” information (i.e.,
uncertainty), and intuitively, this uncertainty should dictate more conservative or robust
harvest policies (Parma, 1993; Frederick and Peterman, 1995; Punt et al., 2002b; Quinn
and Collie, 2005). Most work on the effect of such uncertainty on harvest policy
performance is focused on the influence of errors in stock biomass estimates. Estimates
of biomass that are too high will ofien result in catch levels that are too high, placing the
stock at risk of overexploitation, or alternatively, increased catch may be sacrificed or the
fishery may be closed unnecessarily when population estimates are too low (Parma,
1993; Engen et al., 1997; DiNardo and Wetherall, 1999; Milner-Gulland et al., 2001).
Uncertainty in estimates of biomass can affect various performance measures used in

comparing control rules used in harvest policy analyses, including yield, variability in

71

yield, logarithm of yield, and probability of stock collapse. Generally, uncertainty in
estimates of biomass causes decreased yield (or logarithm of yield), increased variability
of yield, and increased probability of stock collapse for most control rules (Eggers, 1993;
Walters and Parma, 1996; Walters and Pearse, 1996; Lande et al., 1997; Engen et al.,
1997; Hilborn et al., 2002; Punt, 2003; Vasconcellos, 2003). Consequently, the
sensitivity of different control rules to the presence of “imperfect” information can affect
their relative performance (Table l).

5.1. Policy parameters unadjusted for uncertainty.

Most harvest policy analyses that compare control rules and account for
uncertainty in stock size estimates do so by first obtaining harvest policy parameters that
perform well without this uncertainty. They then compare the performance of control
rules for these pre-specified policy parameters. This method essentially mimics a
situation where managers are assumed to have chosen the policy parameters for a rule
based on an analysis that did not account for stock assessment errors. Here we review
studies of this type. In the next section we consider studies where policy parameters were
“adjusted” for uncertainty.

With unadj usted policy parameters, the superior relative performance of a
constant-escapement control rule for some performance variables is sensitive to errors in
estimates of biomass (Table 1). Engen et al. (1997) show that proportional threshold
harvesting results in larger expected cumulative yield than a constant escapement control
rule when uncertainty in biomass estimates are high, and nearly as large cumulative yield
and less variation in yield when uncertainty in biomass estimates are at “lower” levels, a

result also supported by more recent research (Milner-Gulland et al., 2001; Lillegard et

72

al., 2005). Proportional threshold harvesting also reduces the frequency of fishery
closures, and consequently yield variability (Engen et al., 1997; Lillegard et al., 2005). In
contrast, uncertainty in stock size estimates appears to favor constant escapement over
constant fishing mortality rate control rules, at least for the majority of studies where
recruitment is varied in a temporally uncorrelated fashion about a stationary stock
recruitment function; constant escapement control rules (MSY level of escapement)
generally produce higher average catch, average run size (i.e., number of spawners),
average logarithm of catch, and lower CV of catch than constant fishing mortality rate
control rules (i.e., MSY rate), and the disparity increases with increasing error (i.e., the
constant rate rule is more sensitive) (Eggers, 1993; Sladek Nowlis and Bollermann,
2002). These results contrast with the results for “perfect information,” where constant
fishing mortality rate control rules are optimal for maximizing logarithm of catch and
escapement rules typically have higher variability in catch due to fishery closures. The
higher variation in catch for constant fishing mortality rate control rules in the presence
of stock assessment errors may occur because higher than planned levels of fishing due to
errors are not be compensated for by subsequent reductions in fishing mortality. In the
short-term, this could produce lower variation than a constant escapement control rule,
but in the long-term an increased variation in stock size can lead to increased variation in
yield (Eggers, 1993).

A major caveat to the results presented in the previous paragraph is that a constant
fishing mortality rate control rule can be favored over a constant escapement control rule
in terms of yield, regardless of the level of uncertainty in biomass estimates for at least

one type of autocorrelated recruitment. Walters and Parma (1996) show that a constant

73

fishing mortality rate control rule performs better in terms of yield when the asymptote
parameter of a Beverton-Holt stock~recruit model is autocorrelated, even with uncertainty
in biomass estimates. This result also holds true when other stock recruitment parameters
(i.e., slope near the origin) are simultaneously autocorrelated with the asymptote
parameter, but does not hold true when other stock-recruitment parameters are
autocorrelated by themselves.

In contrast with the studies described above, Butterworth and Bergh (1993) and
Polacheck et al. (1999) show that the relative performance of constant catch, constant
fishing mortality rate, and constant escapement control rules generally remain similar to
situations of perfect information when uncertainty is added through the use of
management strategy evaluations. These studies suggest that under some circumstances
the relative performance of these control rules may be robust to the inclusion of
uncertainty.

5.2. Uncertainty adjusted policy parameters

An alternative to using policy parameters that work best for a control rule without
errors in stock size, is to select them so as to maximize the expected value of an objective
function averaged over these (or other) errors (e. g., over simulations). The relative
performance of various harvest policies can then be compared based on which policy
produces a larger expected value of the objective function. Such studies mimic a
situation where it is assumed that managers are taking into account uncertainty (e.g., in
stock assessment) when they decide on policy parameters.

When this approach has been compared with the case of perfect information,

more conservative fishing within a policy is again favored, and the relative performance

74

of different types of control rules is changed. For example, Frederick and Peterman
(1995) show that a constant fishing mortality rate control rule outperforms a constant
escapement control rule in terms of maximizing expected present value (measured in
dollars) and preventing harvest from falling below 10% of the deterministic equilibrium
level when uncertainty in the shape of the stock-recruit function (i.e., uncertainty in the
parameters of a Shepherd function) and error in biomass estimates were accounted for.
Frederick and Peterman (1995) also show that constant fishing mortality is favored in the
case of depensatory recruitment, which might be expected to be more favorable to
constant escapement control rules (Ricker, 1958; Larkin and Ricker, 1964; Tautz et al.,
1969; Collie and Spencer, 1993; Spencer, 1997). Katsukawa (2004) considers a wide
range of policy parameters for a biomass based control rule (Figure 2), which includes
constant fishing mortality rate and threshold control rules as limiting cases. The study
shows that substantial errors in stock assessments favors control rules more like constant
fishing mortality rate, whereas perfect information favors control rules that resemble
threshold rules. That is, such control rules tend to produce as much yield while
maintaining similar levels of biomass. Similarly, Sethi et al. (2005) uses stochastic .
optimal control methods to show that assessment error favors control rules that more
closely resemble a biomass-based policy than a constant escapement control rule, when
the objective is to maximize discounted yield. Similar results have previously been
reported by Clark and Kirkwood (1986). Vasconcellos (2003) also report higher and less
variable yields for constant fishing mortality rate rules than for constant escapement
rules, although to some extent this could be partly due to probabilistically incorporating
an autocorrelated asymptote to recruitment as in Walters and Parma (1996). Sethi et al.

75

(2005) show that implementation error alone does not influence the form of the control
rule, but it does appear to have an interactive effect with assessment error. These limited
studies that consider uncertainty adjusted results contrast in an important way with the
unadjusted results of the previous section; suggesting that accounting for uncertainty
when estimating policy parameters is warranted.
6. Selecting catch, fishing mortality, and threshold levels
6.1. Available options — simulations or biological reference points

Once a general family of control rule is chosen, managers must then decide on
policy parameters; the level of catch, fishing mortality, or threshold to apply. Ideally, this
decision is made through a management strategy evaluation that uses stochastic
simulation to incorporate uncertainty in stock assessments (e. g., parameter values and
biomass estimates), population dynamics (e. g., stock-recruit function), and
implementation (Annala, 1993; Francis, 1993; Frederick and Peterman, 1995, Polacheck
et al., 1999). This approach evaluates the robustness of control rules and policy
parameters to uncertainty, and prevents the need for selecting an arbitrary level or basing
the harvest policy on some biological reference point (BRP) that may be too conservative
or too aggressive depending on the stock. Furthermore, optimum levels of catch, fishing
mortality, or thresholds often become more conservative as uncertainty in assessments
increase, suggesting that estimates from deterministic simulations may be risk-prone
(Lowe and Thompson, 1993; Gibson and Myers, 2004; Lillegard et al., 2005).

Although constructing a stochastic simulation is ideal, this is not always feasible
due to data requirements and time and effort demands (Annala, 1993; Caddy and Mahon,

1995). Consequently, levels are often selected based on BRPs or historical experience

76

(Caddy and Mahon, 1995). The use of BRPs requires defining the various reference
points as targets or limits, but what qualifies as a target or limit can be confusing. Here
we propose similar definitions for targets and limits as those of Caddy and Mahon (1995)
and Caddy and McGarvey (1996). A target is a desirable state of the fishery (e. g., fishing
mortality) or resource (e.g., biomass) at which management action should aim, so that on
average the target is attained. A limit is a “dangerous” state of the fishery or resource
that should be avoided or exceeded with only a “low” level of probability or frequency.
In order to be effective, a limit must also be accompanied by some pre-defined
management actions that are to be taken based on specific evidence that the limit is likely
to have been exceeded, which would allow the fishery to rebound. Interpreting a limit as
requiring that there is some pre-determined “low” probability that the state of the fishery
or resource will exceed the limit can be problematic. Estimating such probabilities would
usually require a stochastic simulation model that considers key uncertainties, and often
reference points are being used because such a model is not available. Managers can still
make informed decisions, however, based on the historical performance of various BRPs,
and whether those BRPs seem better suited as a target or limit, given characteristics of
the fishery. Below we provide an overview of some of the reference point literature. For
a more detailed description and evaluation of each BRP consult the references in Table 3.
6.2. Constant catch levels

MSY has historically been used as a target for constant catch control rules, but the
pitfalls of MSY as a target are well known (Clark, 1973; Larkin, 1977; Sissenwine, 1978;
Hilborn and Walters, 1992; Caddy and Mahon, 1995 Quinn and Deriso, 1999; Quinn and
Collie, 2005). MSY now most often serves as a limit catch level or a starting point from

77

which constant catch levels are scaled downward to more conservative targets (Hilborn
and Walters, 1992; Annala, 1993; Overholtz, 1999; Mace, 2001). Maximum constant
yield (MCY) is one example of a catch level conceptually similar to MSY, but considers
random fluctuations in production, as opposed to assuming deterministic dynamics
following a Schaefer surplus production model (Sissenwine, 1978; Murawski and Idoine,
1989). A critical feature of MCY is that as variation (and possibly autocorrelation) in
production increases, given stock size, MCY decreases below MSY (Sissenwine, 1978;
Getz et al., 1987). Sissenwine (1978), however, warns against using estimates of MCY
as target levels because the fishing mortality rate associated with that level of catch can
be high, and cause declines in spawning stock biomass and subsequent recruitment. In
New Zealand during the 19903, developed fisheries for which a population model was
available to estimate MSY were managed with a constant catch level of 2/3 MSY
(Annala, 1993). This level was selected based on stochastic simulation results that found
that MCY can be as low as 60% of the deterministic MSY for some stocks (Annala,
1993). Constant catch levels in New Zealand have also been selected using other proxies
for MSY, with the exact method of estimation depending on data availability and
exploitation history of the fishery (Annala, 1993).

6.3. Constant fishing mortality rate F levels

Various BRP F values, for use in control rules that apply a constant F over all or

some range of biomass levels, have been suggested as either targets or limits. F m 3}, was

often used as a target, but has been criticized as being economically inefficient and
difficult to estimate reliably, and so should likely be treated as a limit or benchmark from

which more conservative fishing strategies are developed (Larkin, 1977; Koonce and
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Shuter, 1987; Sissenwine and Shepherd, 1987; Hilbom and Walters, 1992; Overholtz,
1999; Quinn and Deriso, 1999; Mace, 2001; Brodziak and Legault, 2005). Setting F
equal to M was also suggested as a means to attain MSY, but this rarely holds true
(Alverson and Pereyra, 1969; Francis, 1974; Deriso, 1982; Quinn and Deriso, 1999).
Furthermore, the relationship between yield and fishing mortality rate is generally flat

over a broad range of fishing mortality values, and so setting target fishing mortality rates

below F m 3y will often lose little in yield while maintaining a disproportionately higher

amount of biomass (Deriso, 1987; Hilbom and Walters, 1992; Ralston et al., 2000;

Dichmont et al., 2006b). Yield per recruit (YPR) analyses are used to formulate two

common BRPs, F max and F 0.1 (Deriso, 1987). Although sometimes used as targets, these

reference points cause stock declines over a broad range of conditions and should likely
be used as limits (Sissenwine and Shepherd, 1987; Clark, 1991; Jakobsen, 1992;

Goodyear, 1993; Leaman, 1993; Campana et al., 2002; Rahikainen and Stephenson,

2004; Quinn and Collie, 2005). F x% BRPs are based on spawning stock biomass or egg

production per recruit (S SBR) analyses. These BRPs have the advantage that stocks with

similar levels of compensation in the stock-recruit relationship can be cautiously

managed with the same F x% rate (Dorn, 2002). Combined with meta-analyses of stock-
recruit data (e.g., Myers et al., 1999; Dorn, 2002), appropriate F x% rates can be estimated

where stock specific estimates of productivity are lacking. However, levels of F x%

(usually in the range of 20%-40%) have historically been chosen based on yield
objectives and were treated as targets (Clark, 1991; Ralston et al., 2000; Brodziak, 2002;

79

Clark, 2002; Quinn and Collie, 2005). Because these levels of fishing were set without

incorporating recruitment and biomass as part of the objective, it is not surprising that the

selected F x% levels have proved inconsistent with an objective of maintaining stock

biomass above a specified threshold (Ralston et al., 2000). Several other BRPs have been

developed using SSBR analyses and a plot of stock-recruit data. F m (for recruitment

overfishing) is intended for use as a limit rate that explicitly avoids recruitment

overfishing (Sissenwine and Shepherd, 1987). F rep (for replacement), and similarly

Fmeds are suggested as targets to maintain current levels of biomass, but will only do so

in the absence of density dependence in the stock-recruit relationship (Sissenwine and

Shepherd, 1987; Mace and Sissenwine, 1993; Maguire and Mace, 1993; Quinn and

Deriso, 1999). Flow and F high are set relative to F rep and would likely lead to rebuilding
or stock declines, respectively (Jakobsen, l993). F st (for steady) is a BRP based on a

Leslie matrix model that is conceptually similar to F rep. (Quinn and Szarzi, 1993; Hayes,

2000).
6.4. Threshold levels

Threshold levels, for use in threshold and biomass-based control rules, have been
selected in a variety of ways. Perhaps the simplest method is to use a time series of
abundance data. Sigler and Fujioka (1993) define sablefish stocks to be overfished
whenever biomass falls below the historically lowest observed level. For overexploited
stocks, Overholtz et al. (1993) suggest using some percent level of biomass higher than

current biomass. When a stock specific threshold cannot be determined, thresholds
80

developed for other species with similar taxonomy and life history parameters can also be
applied (Mace and Sissenwine, 1993). Because these methods are somewhat arbitrary,
the management action that should be taken when biomass falls below these levels is
unclear.

Other less arbitrary biomass thresholds have also been developed. For
populations exhibiting compensation, Quinn and Deriso (1999) show how a parameter
can be added to a Graham-Schaefer surplus production model to estimate the point where
latent productivity becomes zero or negative, providing a threshold level of biomass,
which is often expressed as a percentage of unfished biomass. Zheng et al. (1993b)
develop a similar methodology generalized to a depensatory surplus production mode].
When a stock-recruit relationship is taken into account, a more elaborate population
model can be developed to estimate biomass at MSY for use as a target (or some other
MSY proxy) and some level below MSY for use as a threshold (Quinn and Deriso, 1999).
In the case of a depensatory stock-recruit relationship, the inflection point has been
suggested as a threshold level of biomass, and assuming that growth and mortality are
density-independent, the inflection point usually occurs below 20% of pristine biomass,
suggesting that 20% is generally a threshold below which fishing should stop
(Thompson, 1993). This conclusion is consistent with other studies that found that
spawning biomass should be maintained between 20% and 50% of unfished spawning
biomass as a way to ensure replacement and attain a large proportion of MSY (Quinn et
al., 1990; Clark, 1991; Fujioka et al., 1997; Booth, 2004). Conversely, Myers et al.
(1994) conclude that using 20% of unfished spawning biomass as a threshold may be

risky for stocks with “severe” depensation, and recommend using the biomass level that

81

produces 50% of the maximum recruitment as a robust threshold. Zheng et al. (1993b)
suggest two methods of estimating thresholds based on life-history parameters called
Fowler’s method and May’s method.

Many of the studies discussed above seek to determine a threshold independently
from a target value of fishing mortality. In some cases the fishing mortality rate is set at
levels that were determined as best for a constant fishing mortality rate control rule. An
alternative is to simultaneously search for the threshold level and level of fishing
mortality combination that maximize a given objective function in the framework of a
stochastic simulation. Zheng et al. (1993a) and Quinn et al. (1990) use this approach
with an objective function that considers both maximizing annual yield and minimizing
yearly variations in yield. In accord with simulation results, we expect that the optimal
fishing mortality rate at high biomasses would generally be higher for a biomass based
control rule than for a constant fishing rate control rule and thus there should be benefits
to searching for the best combination. However, results are probably too limited to allow
for rules of thumb on how much higher the fishing rate should be for a biomass-based
control rule in the absence of an explicit analysis.

7. Summary and conclusions

Harvest policies are a necessary feature of transparent fisheries management
because they ensure that the rules for how harvest will vary are evident to all
stakeholders. However, the application of an inappropriate harvest policy will result in a
failure to meet management objectives or potentially cause stock collapse. Rational
management requires that objectives be explicitly stated and that a harvest policy is

selected so as to best achieve those objectives. The results of this review provide some

82

guidance on what control rules might be worth considering for given objectives, and what
factors might influence their relative performance, and so should be included in analyses
of harvest policies.

Most research to date focuses on evaluating harvest policies under the assumption
of “perfect information” (i.e., no uncertainty or error; Table 2). These analyses often
identify optimal control rules for meeting certain fishery objectives under given
conditions, and highlight factors that might affect relative policy performance. Of
particular importance seems to be the shape of the stock-recruit relationship (i.e., level of
compensation), autocorrelation in recruitment, and whether depensatory mechanisms
exist (Ricker, 1958; Larkin and Ricker, 1964; Tautz et al., 1969; Hightower and Lenarz,
1989; Collie and Spencer, 1993; Walters and Parma, 1996; Lande etal., 1997; Spencer,
1997; Steinshamn, 1998; Ishimura et al., 2005). Some research also suggests that
variability in other population parameters, such as time-varying catchability, may also
have an effect on relative policy performance (Punt, 1997; Punt et al., 2002b; Dichmont
et al., 2006a; Dichmont et al., 2006c). We believe more needs to be learned about how
temporal variation in parameters, such as those governing the stock-recruitment
relationship, influences the performance of harvest policies.

Much less research focuses on comparing harvest policies while considering key
uncertainties (e. g., in the recruitment function, error in biomass, error in catch statistics).
One result of adding uncertainty is that policy parameters (e. g., a constant fishing
mortality rate) are generally shifted in a more conservative direction from those based on
treating point estimates of parameters governing population dynamics and fishery

behavior as known. Thus, research that assumes perfect information should be

83

interpreted cautiously, since uncertainty is a ubiquitous feature (Punt et al., 2002).
Furthermore, the relative performance of control rules depends on whether the policy
parameters have been adjusted for uncertainty. In general, we believe managers should
adjust parameters for uncertainty as is advocated in the Decision Analysis literature
(Peterman and Anderson 1999). This conclusion suggests that much more research on
the relative performance of control rules using uncertainty adjusted parameters is needed.

Greater uncertainty clearly reduces sustainable yields and other benefits of
fishing. The policy studies reviewed here that incorporate uncertainty in stock status or
underlying dynamics treat this as a constant fixture of the system. Additional studies are
needed that take an adaptive management view, and consider the interaction between
harvest policies and understanding of the fishery system (Walters, 1986).

Many resource economists conclude that constant escapement control rules
provide maximum profits, but they also generally do not consider the possibility of
autocorrelated recruitment, uncertainty, and they often assume that profits are linearly
related to harvest (Gatto and Rinaldi, 1976; Reed, 1979; Lande et al., 1995; Nostbakken,
2006). The linear relationship may not adequately consider the social and political
repercussions of a frequently closed fishery. We believe this is why constant escapement
control rules are not applied more often. For example, in the South African anchovy
fishery, a constant escapement control rule was abandoned for a constant fishing
mortality rate control rule within two years of being implemented because it became
obvious that fishery closures would be frequent (Cochrane et al., 1998).

Most research focuses on single management objectives (e. g., maximizing yield)

and the policies that are optimal for meeting single objectives. However, management

84

often involves competing objectives, and selecting a harvest policy that is optimal for one
objective involves a trade-off with some other objective (Quinn et al., 1990). For
example, constant escapement control rules that maximize long-term yield also often
maximize variability in yield (Walters and Parma, 1996). McGlade (1989) proposes an
intensive approach to deal with competing objectives called integrated fisheries
management, which explicitly models ecological, socioeconomic, legal, and institutional
aspects of a fishery into a single model. Management strategy evaluations can also
address uncertainties that occur throughout the management process, including the
ecological and socioeconomic aspects (Smith et al., 1999; Punt et al., 2002c; Dichmont et
al., 2006a,b,c). These approaches might produce optimal policies that differ from
traditional single objective approaches (McGlade, 1989). For example, consideration of
how closing a fishery affects the short-term economics and social atmosphere of fishing
communities would likely result in a different optimal policy than attempting to
maximize long-term profits alone. Generally, little is known about optimal policies for
meeting multiple competing objectives, and optimal policies in these situations might be
different than has been found for single objective approaches (Fieberg, 2004).

To deal with the trade-offs of competing objectives, some control rules attempt to
attain “the best of both worlds.” CCC control rules attempt to combine attractive aspects
of constant catch and constant fishing mortality rate control rules, so as to attain stable
catch with less risk than strict constant catch (Murawski and Idoine, 1989; Hjeme and
Hansson, 2001; Clark and Hare, 2004). Biomass based control rules are an alternative
that avoids frequent fishery closures and responds to declining biomass by reducing

fishing mortality, and so retains attractive features of constant fishing mortality (i.e., few

85

fishery closures) and constant escapement control rules (i.e., reduced harvest at low stock
size). To date, little research has focused on these control rules, particularly in the
presence of uncertainty. Furthermore, optimal methods for designing biomass based.
control rules (i.e., exactly how F should decline with biomass) have not been developed
and much work is needed on this and related topics.

Harvest policies are generally developed for single species fisheries, but increased
awareness of problems caused with by-catch, increased centralization of fishery control,
and increased knowledge of ecosystems may lead to attempts to apply harvest policies to
entire food-webs or ecosystems (Walters et al., 2005; Quinn and Collie, 2005; Matsuda
and Abrams, 2006). Walters et al. (2005) evaluates the ecosystem impacts of applying
constant catch control rules to multiple species simultaneously, with the catch level set at
MSY and estimated from single species assessments. They show that the ecosystem
changes caused by such a strategy results in MSY being unattainable for several species
and top predator populations most ofien declining. Similarly, Dichmont et al. (2006b)
uses a management strategy evaluation for Australia’s northern prawn Penaeus spp.

fishery and shows that when species are caught simultaneously, multiple species cannot

be sustainably harvested at individual F m 5y rates. Matsuda and Abrams (2006) develop

models to find the level of fishing effort that maximizes yield or profits from a food-web
using Simple linear rates of production and density dependence in growth for systems
With as many as six species and five trophic levels. ln many instances, maximizing yield
or Profits from the system involves eradicating top-predators in order to increase the
PTOdUCtion of lower trophic levels, particularly if the species in lower trophic levels are

more Valued. They conclude that further development of policies for entire food-webs
86

may require preventative measures to ensure top predators are not eradicated for the sake
of increased profits from lower trophic levels.

Fishing exerts selective pressures on fish stocks that can lead to the evolution of
life-history traits that affect productivity (e.g., growth, age at maturity), and this may also
affect relative policy performance (Heino, 1998; Conover and Munch, 2002; Swain et al.,
2007). Little is known, however, about how sensitive policy performance is to
evolutionary change, or whether such changes might also interact with other
characteristics known to effect policy performance (e. g., uncertainty in estimates of
biomass). This topic should remain an area of active research, and simulation studies that
account for evolutionary change induced through harvest would provide valuable insight
(e.g., Heino, 1998).

When an appropriate simulation study cannot be conducted to determine policy
parameters (e. g., target constant fishing mortality rate) that best achieve stated objectives,
BRPs likely provide the next best method for selecting fishing mortality rates and
thresholds. The effectiveness of any BRP will depend on the objectives of the fishery
and whether assumptions used in the development of a given BRP have been met.
Generally, the shape of the stock-recruit relationship, and whether density-dependence or
depensatory mechanisms are active will be of particular importance. Furthermore, if left
with no better alternative, BRPs can be cautiously applied to species with similar
taxonomy and life history characteristics (Mace and Sissenwine, 1993).
Acknowledgments

We are grateful to Mike Jones, Dan Hayes, Julie Nieland, two anonymous

referees, and the guest editor, Martin Dom, for providing comments on an earlier draft of

87

this manuscript. Conversations with Gretchen Anderson and Heather Dawson also
improved the organization and clarity of the text. Funding for this project was provided
by the Michigan Department of Natural Resources and US. Fish and Wildlife Service -
Federal Aid for Sportfish Restoration program (F 80-R7, Study 230713). This manuscript

is publication 2008-02 of the Quantitative Fisheries Center at Michigan State University.

88

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98

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99

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107

CHAPTER 3
EVALUATING HARVEST CONTROL RULES FOR LAKE WHITEFISH IN THE

GREAT LAKES: ACCOUNTING FOR VARIABLE LIFE-HISTORY TRAITS

Abstract

Lake Whitefish support a commercial fishery in the Great Lakes and experience
spatial and temporal variation in life history traits, such as size-at-age. Currently, the
fishery is managed by attempting to maintain a constant mortality rate. I used an age-
structured simulation model that incorporated stochasticity in life history traits,
uncertainty in future lake Whitefish growth, and other sources of uncertainty to compare
the current strategy with a range of alternative control rules, including conditional
constant catch (CCC), constant fishing rate (CF), biomass-based (BB), and CF and BB
rules with a 15% limit on the interannual change in the target catch. With appropriate
policy parameters, the CF and BB rules can simultaneously attain higher average yield
and spawning stock biomass than all other control rules. The CCC rule and limiting the
CF or BB rules to a 15% change in target catch had the lowest yearly variability in yield.
For control rules using policy parameters that produced the same yield, low biomass
levels were attained most frequently for the CF and BB rules with a 15% limit on target
catch and least often for the BB rule. The low yearly variability in yield provided by
limiting target catch changes to 15% comes at the cost of frequently reducing biomass to
low levels, so that in many situations other control rules would be preferred. The
sensitivity of results to uncertainty about future lake Whitefish growth was control rule

specific and depended on whether stock growth was fast or slow.

108

1. Introduction
1.1. Harvest Control Rules

Harvest control rules are guidelines that specify an amount of catch, fishing effort,
or fishing mortality as a specific, and usually simple, function of an estimate of the
current system state (e. g, spawning biomass; Deroba and Bence, 2008). Ideally, a harvest
control rule is selected based on a management strategy evaluation or simulation analysis
that compares control rules for their ability to meet competing fishery objectives (e. g.,
maximizing yield versus minimizing annual variation in yield), and considers key
uncertainties (e. g., shape of the stock-recruit curve) and sources of error in the
management process (e. g., assessment error; Smith et al., 1999; Punt et al., 2002; Kell et
al., 2006; Deroba and Bence 2008). Often times, however, control rules and the
parameters for a control rule are defined in an ad hoc manner, and so may not be optimal
for meeting given fishery objectives (Deroba and Bence, 2008). Furthermore, many
analyses have ignored sources of uncertainty and error that affect relative control rule
performance, and so few control rules have been thoroughly examined for their relative
ability to meet competing fishery objectives (Deroba and Bence, 2008). Few analyses
have also considered the effect of spatial or temporal variation in population parameters,
such as growth, maturity, or stock-recruitment relationships, and such factors can affect
control rule performance (Deroba and Bence, 2008).
1.2. Lake Whitefish Fishery History and Management

Lake Whitefish, Coregonus clupeaformis, have supported a historically important
subsistence fishery for Native American bands and a highly valued commercial fishery in
the upper Great Lakes (Lakes Huron, Michigan, and Superior). Lake Whitefish stocks

109

collapsed in each of these lakes in the 19305 and 19403 partially-due to overexploitation
(Smiley, 1882; Koelz, 1926; Jensen, 1976; Brown et al., 1999; Ebener and Reid, 2005),
but have since rebounded to once again become the main commercial species (Mohr and
Ebener, 2005). For example, lake Whitefish provide about 80% of the total commercial
yield from Lake Huron in each year (Mohr and Ebener, 2005).

In 1979, the rights of Native American bands to fish in the Michigan waters of the
upper Great Lakes, as reserved in a treaty signed in 1836, were reaffirmed by US. federal
courts. Since the reaffirmation of treaty fishing rights, periodic stock assessments have
been conducted for stocks within spatially defined management units, with the fishery
data and harvest from within each management unit treated as applying to a
reproductively isolated stock (Figure 1; Ebener et al., 2005).

Lake Whitefish stocks are also characterized by spatial and temporal variation in
various population parameters. For example, lake Whitefish growth in some areas of the
Great Lakes has declined in recent years, but similar declines have not occurred
everywhere despite similar ecosystem changes (e. g., Hoyle etal., 1999; Pothoven et al.,
2001; Cook et al., 2005; Mohr and Nalepa, 2005; Lumb et al., 2007). Growth rates,
maturity ogives, natural mortality, and stock-recruit relationships also likely differ
spatially among some of the management units due to factors such as different historical
exploitation patterns or long-term differences in environmental conditions experienced by
distinct stocks occurring across a latitudinal gradient (e. g., Wang et al., 2008).

Since 2000, guidelines for the management of lake Whitefish have been set
according to a Consent Decree. The 2000 Consent Decree created a Technical Fisheries

Committee and its Modeling Subcommittee (MSC) to conduct stock assessments and

110

recommend annual quotas for each individual management unit. Recommended yields
are treated as limits in units where yield is allocated between the state and tribal fishery,
and targets in units where all yield is allocated to the tribal fishery. The MSC fits
statistical catch-at-age (CAA) models to commercial fishery data to estimate pOpulation
numbers, mortality rates, fishery harvest, and other population parameters of interest.
The estimates of the population parameters are then used to project each stock’s
abundance into the future, and the target or limit quotas are determined so that the total
annual mortality rate equals 65% for ages experiencing the highest levels of fishing
mortality. The CAA models assume a constant natural mortality rate across ages and
time, and so this is equivalent to a constant fishing mortality rate (constant-F) control
rule.

The constant-F control rule and the parameters for the control rule (i.e., 65% total
annual mortality rate) are somewhat ad hoc and may not be optimal for meeting fishery
objectives. The value of 65% was based on the work of Healey (1975) who found that a
substantial proportion of lake Whitefish stocks with total annual mortality rates in excess
of 70% were depleted or precarious, whereas stocks with rates below 65% appeared to
have generally fared well. Jacobson and Taylor (1985) compared the relative
performance of constant-F and constant catch control rules in terms of annual yield and
variability in yield for lake Whitefish in northern Lake Michigan. Their analyses,
however, only evaluated two control rules, did not consider the spatial or temporal
variation in lake Whitefish population parameters (e. g., growth), and did not include
assessment error, which can affect the relative performance of control rules (Deroba and
Bence, 2008).

111

My objective was to evaluate alternative control rules in their ability to meet
fishery objectives (e. g., maximizing yield, minimizing annual variation in yield). To
address my objective, I developed a simulation model that compared several control rules
at meeting fishery objectives and considered key uncertainties (e. g., shape of the stock-
recruitment curve) and sources of error (e.g., assessment error).

2. Methods
2.]. Stocks in 1836 T realy waters

The simulation model developed and used in this study was based upon data and
assessments of lake Whitefish stocks from 1836 Treaty waters (Figure 1). The 1836
Treaty waters encompass much of the Michigan waters of Lakes Superior, Huron, and
Michigan (Figure 1). These waters are stratified into 18 management units with
individual surface areas ranging from 69,000 to 733,000 ha, and a total surface area of
5.8 million ha (Figure l; Ebener et al., 2005).

2. 2. Overview of simulations

I developed a stochastic simulation model to project the abundance of
hypothetical lake Whitefish stocks, based on characteristics of stocks in 1836 Treaty
waters. The model included age-3 through an age-12 “plus” group, which was an
aggregate group including age-12 and older. Selected performance metrics (section 2.9)
were used to compare the performance of various control rules (section 2.8). The
simulation model also included assessment and implementation error, and the sensitivity
of the results was evaluated to different values for each source of error (section 2.7). For

each value of the range of policy parameters searched for each control rule, 1000

112

simulations were run. Each simulation was a 250 year projection, but results were
presented based on a summary of the last 100 years.

Growth and maturity sub-models (sections 2.3 and 2.5) were estimated from
biological data based on samples from commercial trap-net catches. Separate sets of
growth parameters were estimated and simulations were run for two categories of stocks,
fast and slow grth (i.e., stocks with relatively longer or shorter mean lengths at age,
respectively). In some areas of 1836 Treaty waters, and more broadly in some areas of
the Great Lakes, lake Whitefish size-at-age has varied over time, particularly in recent
years (e.g., Hoyle et al., 1999; Pothoven et al., 2001; Mohr and Nalepa, 2005). One
possibility is that recent trends are part of longer-term fluctuations, so that similar long-
term variation will continue to occur as part of a correlated but stationary process.
Alternatively, there may have been a permanent change to the environment and recent
growth patterns are now a permanent property of these stocks. I developed two variants
of a growth model reflecting these alternatives (autocorrelated versus recent growth
patterns) and separate sets of simulations were done for each of these for both the fast'and
slow growth stocks.

Substantial uncertainty exists regarding the recruitment process for most species
(Myers et al., 1997; Myers et al., 1999). To acknowledge this, stock-recruitment
parameters used in each simulation were drawn randomly from a set of possible values,
which were based on fitting the recruitment sub-model (section 2.4) to stock and
recruitment time series developed for each management unit from the assessments for

that unit.

113

2. 3. Growth sub-models

As indicated in section 2.2, models were parameterized and simulations were run
for four growth scenarios: 1) autocorrelated, fast growth, 2) autocorrelated, slow growth,
3) similar to more recent years, fast growth, 4) similar to more recent years, slow growth.
Management units were categorized as fast or slow growing, and the models described in
sections 2.3.1 and 2.3.2 were parameterized separately based on data for stocks of each
category. Because growth is likely linked to maturity (e. g., Beauchamp et al., 2004), the
maturity sub-model was also fit separately for fast and slow growth categories (section
2.5). Management units were classified as fast or slow based on pairwise comparisons of
mean length at age between management units, and expert opinion (see Appendix A).
2. 3. 1. Growth autocorrelated
. My approach to allowing longer-term fluctuations in size-at-age was to model

length at age-3 in each year y by:

L3 y = Z3e¢y ea”; (1)

3

where Z3 was the mean length of an age-3 fish, ¢y and 8 Ly Were, respectively, the
autocorrelated and uncorrelated contributions to temporal process error:

, 2
~ N(0,0'L ); (2)

8L),

2
853/ =p¢¢y—1+7y;7y N N(O;0¢ ); (3)

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with the process errors. The parameters of this portion of the growth sub-model were

114

estimated based upon analysis of time-series of mean length-at-age data (see Appendix
A).
For ages greater than age-3, length in each age a and year y was simulated using

an incremental form of the von Bertalanffy model similar to that of Irwin et al. (2008):

L La_1,y_1 + ALa,y; (4)

a,y :

where

ALa,y "—' 1+6La_1’y_1+60y +8AL,a,y; (5)

and l and 9 were interecept and slope parameters, respectively. The growth

increment was influenced by a) y , a year-specific process error common to all ages, and

EAL, a, y a process error spec1fic to each year and age combination, where:

my ~ N(O;og',); 8AM“ ~ N(0;0§L )1. (6)
The parameters of this portion of the growth sub-model were again estimated from
observed mean length at age data by relating increments in mean length for a cohort to
current mean length (see Appendix A).

Weight at each age and year was modeled as a power function of length and mean

length at age-3 in years y+l and y+2, L3 y +1 y +2:

_ Z ‘60 .
Wa,y — TLa,yL3,y+1,y+2’ (7)

where T is the condition factor parameter, and 1 and (0 are curvature parameters (Quinn

and Deriso, 1999). I included average length at age-3 to allow weight at length to

respond to growth conditions. Length at age-3 represents a measure related to relatively

115

recent grth conditions (over the previous two to three years). Consequently mean
length at age-3 averaged over years y+1 and y+2 represents a measure of growth
conditions during a window roughly centered on year y. This modeling choice was
motivated in part by moderately large changes in the weight versus length relationship so
that weight at length tended to be positively correlated with length at age-3 in recent
years. The parameters of this portion of the growth sub-model were estimated using
multiple linear regression relating log transformed mean weight at age to log transformed
mean length at age and log transformed mean length at age-3 (see Appendix A).
2. 3. 2. Growth remained similar to recent levels

For the case of growth remaining similar to more recent levels, the growth sub-

models of section 2.3.1 were modified as follows. First, length at age-3 was simulated as

above (equation 1), except that p¢ was zero so that ¢y (equation 3) were uncorrelated.

Second, weight was determined solely as a power function of length (i.e., the power term

involving L3 y +1 y +2 was dropped from equation 7):

_ I
Way—1L6”.

The parameters for the growth sub-model for the recent growth scenarios were
also estimated similarly to the case of autocorrelated growth, but only data from the three
most recent years available from each management unit were used, with the exact range
of years depending on the management unit (see Appendix A).

2. 4. Stock-recruitment sub—models

Recruitment was defined as the number of age-3 lake Whitefish. Recruitment

followed Ricker stock-recruit dynamics for the 5th simulation:
116

R3, = asSSBye-flSSSBy egRy , (8)

y

where R was recruitment, SSB was spawning stock biomass, 0. was the number of recruits
per SSB at low SSB, B was the instantaneous decline in recruitment per SSB as SSB

increased, 8R), was autocorrelated temporal process error:

, 2
ERy = pngRy—l +§ys 9‘y ~ Nlo’o'Rsl (9)
and pRs and 0'12“ were the level of autocorrelation and variance. Stock-recruitment

parameters (a, ,3, p R , 0' 12?) were randomly selected with equal probability from a set of

possible values and retained for each simulation (hence they are subscripted by
simulation). These possible parameters of the stock-recruitment sub-model corresponded
to estimates for each assessed lake Whitefish stock in 1836 Treaty waters, obtained by
applying a general linear mixed model to assessment estimates of recruitment and stock
size using methods similar to those of Myers et al. (1999; see Appendix A).

Spawning stock biomass was measured in number of eggs:
_ a=12+ ' ,
SSB), — 261:3 Na,ymLa WaJFemx Eggs, (10)
where m La was proportion mature (see section 2.5), Fem was the proportion of females,

and Eggs was the number of eggs per kilogram of fish. Fem was estimated separately for
fast and slow growth simulations as the mean proportion of females used in fitting CAA

models in fast and slow growth management units, respectively, and Eggs equaled

117

19,937/kg for all simulations, which was also the value used in all CAA models (Ebener
et al., 2005).
2.5. Maturity sub-models

A separate maturity function was estimated for fast and slow growth simulations,

and probability of maturity m La was modeled as a logistic function of mean length-at-
age, weighted by the probability of being a length L given a mean length-at-age La and

variance 0' 2
La

 

= LL , ; 11
mLa 5(1 +e-K(La —7])]p I a 0.140 ( )

where K was the curvature parameter and n was the length at which the inflection point
occurs. The probability of maturity was weighted by plLlLa , 0'27: ) to account for the
a

variation around a mean length at age, and the subsequent variation around the

probability of maturity at a mean length at age. That is, fish of a given age class may be
more less likely to be mature depending on whether they were longer or shorter than the
mean length at age, and the weighting accounts for this variation. The parameters of the
logistic portion of the maturity sub-model were estimated using logistic regression using

data from only females (see Appendix A). The assumed length distributions,

plLlLa , 0'2 ), were based on a single estimated coefficient of variation (0.036) for
a
length at age, which together with mean length, La , was the basis for the 0'2 used
a

in equation 11 (see Appendix A).
118

2. 6. Population abundance sub-model

A vector of initial abundances at age (i.e., in year zero) was randomly selected
with equal probability from a set of vectors and retained for each simulation. This
method was necessary to scale the initial abundances at age to the set of stock-recruit
parameters chosen for each simulation. The suite of possible vectors corresponded to the
equilibrium abundances at age for each assessed lake Whitefish stock in 1836 Treaty
waters under a fishing mortality rate that would reduce spawning stock biomass per
recruit to 20% of the unfished level (see Appendix A). The vector of initial abundances
at age for each simulation was from the same stock as was used for selecting the vector of

stock-recruitment parameters. Abundance N in each age and year was then predicted:

—Z
Na,y=Na_1,y_le “’y; (12)

where Z was the total instantaneous mortality rate and equaled the sum of natural
mortality M and fishing mortality. Fishing mortality F was the product of fully-selected

fishing mortality and selectivity:

Fray = SL0 Fy; (13)
where SL0 was selectivity at mean length-at-age. Selectivity was modeled as a gamma

function of mean length-at-age (Quinn and Deriso, 1999), and approximated a trap-net
selectivity curve, which is a dominant gear used for lake Whitefish in these waters. In the
simulations, natural mortality was constant across ages and years, but differed between
simulations for fast and slow growth stocks, being set equal to the mean natural mortality
rate assumed in CAA assessment models for each stock in each growth category (Ebener

et al., 2005).
119

2. 7. Assessment and implementation error

The simulation model included assessment and implementation error, following
an approach similar to that of Punt et al. (2008). Assessment error was modeled as a
year-specific lognormal random deviation common to all ages with first-order
autocorrelation:

2/
A any- 0n/2
1mJ=N¢fl ( );(m

where N was assessed abundance, any was autocorrelated error:

2
any = anny_1+\l1—p35y; 5y ~ N(0;0'n ); (15)

and Pn was the level of autocorrelation.

Assessment error affected the target catch set by managers because target catches

A

C y were set by applying a fully selected desired fishing mortality rate 13' y to assessed

abundance rather than actual abundance:

 

éy=zr¥+ . ;(M)

where 1321,), was the product of fully selected desired fishing mortality and S La , and

2a,y was the sum of Pay and M.

The fully selected fishing mortality rates F}, that would result in the target catch
being removed when applied to actual abundance were found numerically using Newton-

120

Raphson iterations. A maximum of 3.0 was set on F y because C y were sometimes

unachievable.

Implementation error was included as a year specific lognormal random

deviation:
2 /
~ £Fy _(0-F/’2) 2
Few = SL0 Fye ; spy ~ N(0;0'F); (17)

where Fa, y was the actual fishing mortality rate exerted on the actual abundance

NW.

The sensitivity of results was tested using a range of parameter values for
assessment and implementation error (Table 1). The effect of different levels of

assessment and implementation error was compared to a baseline scenario, which was

defined as the middle value for each parameter (Table 1; 0'3 = 0.05, Pn = 0.7, 0% =

0.01). Rather than an experimental design that crossed all assessment and
implementation error parameters, each parameter was evaluated at a high and low level
while holding all other parameters at the baseline level (i.e., seven combinations). The
range of parameter values evaluated for assessment and implementation error are similar
to those of studies much like this one, including analyses of lake trout Salvelinus
namaycush in Lake Superior and yellow perch Percafalvescens in Lake Michigan (Irwin
et al., 2008; Nieland et al., 2008; Punt et al., 2008).
2.8. Control rules

The control rules evaluated were: conditional constant catch (CCC), biomass

based (BB), constant-F, and BB and constant-F with a 15% limit on the interannual
121

A

change in the target catch, C y (BB-lim, constant-Flim, respectively; Clark and Hare,

2004; Deroba and Bence, 2008). The CCC control rule used a constant target catch
unless removing that target catch exceeded some predetermined maximum fully-selected
fishing mortality rate, and so the CCC control rule was defined by two policy parameters;
a constant catch level and maximum fishing mortality rate (Clark and Hare, 2004). The
constant catch levels were set as a fraction of maximum sustainable yield (MSY; see
Appendix A). MSY was randomly selected from a suite of values and retained for each
simulation. The suite of possible values corresponded to values for each assessed lake
Whitefish stock in 1836 Treaty waters, and the value of MSY for each simulation was for
the same stock as was used for selecting the vector of stock-recruitment parameters. The

fully-selected fishing mortality rate that would result from removing the target constant

catch amount from the assessed abundance (N ), for comparison to the predetermined
maximum fishing mortality rate, was calculated numerically using Newton-Raphson

iterations. The BB control rule was similar to that of Katsukawa (2004) and was defined

by three policy parameters; a lower SSB threshold SSB LT below which 1}}, was set to a
low level, an upper SSB threshold SSB HT above which 13'), was set to a maximum rate

F sat , and F sat . As assessed spawning stock biomass SS’B y decreased from SSB HT

, E y decreased linearly with SSB y until E y equaled 0.05:

If SS‘By < SSBLT then Fy = 0.05

122

ssBy —SSBLT
SSBHT —SSBLT

 

If SSBLT < SSB}, S SSBHT then E), = max(Fsat , 0.05)

If SSBHT _<_ SS‘By then Fy = Fm. (18)

(Figure 2). All other control rules were also restrained to have a target fishing mortality

rate of at least 0.05 because I assumed some amount of fishing would always take place.

Preliminary analyses showed that results were not sensitive to this assumption. SSB LT
and SSB HT were set as a fraction of unfished SSB, SSBF=0 (see Appendix A). SSBF=0

was randomly selected from a suite of values and retained for each simulation, which was
necessary to scale the policy parameters that depended on a measure of SSB to the set of
stock-recruit parameters chosen for each simulation. The suite of possible values
corresponded to values for each assessed lake Whitefish stock in 1836 Treaty waters, and

the value of SSBF=0 for each simulation was for the same stock as was used for selecting

the vector of stock-recruitment parameters. SSB y was estimated in the same way as

SSB y (equation 10) except with N a, y replaced with Ill a, y (equation 14). The

constant-F control rule was a special case of the BB control rule with SSB LT and

SSB HT both set to zero, and was defined by one policy parameter; a level of fishing

mortality. The BB-lim and constant-Flim control rules worked in the same way as the
BB and constant-F rules except with the specified restriction on the target catch. For
each control rule, a range of values was evaluated for each policy parameter. The
constant catch parameter of the CCC rule was varied from 0.1MSY to 1.4MSY in

increments of 0.1, while the maximum fishing mortality rate parameter was varied from

123

0.2 to 3.0 in increments of 0.2. For the BB control rule, with and without the restraint on

interannual catch, SSB LT and SSB HT were varied from 0.OSSBF=0 to 1.05.3sz0 in

increments of 0.1, while F sat was varied from 0.05 to 3.0 in increments of 0.05. The
constant-F strategy, with and without the restraint on interannual catch, was evaluated
over the same range of values as F sat .
2. 9. Performance metrics

Plots of SSB versus yield Y, interannual variability in yield Yvar versus the

proportion of years that SSB fell below 20% of SSBF=0, Y versus Yvar, and Y versus the

proportion of years that SSB fell below 20% of SSBF=0 were used to examine the trade-
offs among potential competing fishery objectives and compare the performance of
control rules. In sections below, I refer to the proportion of years that SSB fell below
20% of SSBF=0 as “risk” because levels of SSB near this value have been used as a

biological reference point below which recruitment overfishing was likely to occur and so
should be avoided (Quinn et al., 1990; Clark, 1991; Thompson, 1993; F ujioka etal.,

1997; Booth, 2004). Mean Y and SSB over the last 100 years, the proportion of the last
100 years with SSB less than 20% of SSBF=0, and Y var over the last 100 years were

recorded for each simulation. The interannual variability in yield, defined as in Punt et

al. (2008) was calculated over the last 100 years for each simulation:

2 Y —Y_
Yvar: y>150‘y y 1l; (19)

Zy>150Yy

 

where

124

—z
Fa,yNa,y(1— e a’y]
W (20)

a,y '
Za’y

 

_ a=12+
Yy — Za=3

The trade-off plots described above were then constructed for each of three percentiles
calculated among simulations: the median, the percentile value less than 75% of the
values among simulations (i.e., 25th percentile for SSB and Y, 75th percentile for risk and
Yvar), and the percentile value less than 90% of the values among simulations (i.e., 10‘h

percentile for SSB and Y, 90th percentile for risk and Yvar).

 

The rank order performance of the control rules was evaluated for each growth i
scenario and trade-off plot by examining the combination of policy parameters that
resulted in the best performance for each control rule. This method equates to
determining the optimal control rule as if future growth (i.e., autocorrelated versus recent
growth patterns) was a known certainty.

To evaluate the sensitivity of control rule performance to uncertainties about
future growth, an optimal set of policy parameters (see below) was chosen for each
control rule, trade-off plot, and growth scenario. The optimal set of policy parameters for
each future growth scenario was then applied to the alternative fiiture growth scenario
(i.e., autocorrelated versus recent growth patterns), but for the same type of stock growth
(i.e., fast or slow growing). The difference in performance between the optimal set of
policy parameters and the set of policy parameters being applied under the wrong future
growth scenario was used as the measure of sensitivity. This method equates to
evaluating how well a control rule would perform if policy parameters were chosen

assuming one type of future growth was true, when in fact the alternative growth future

125

was true. The optimal set of policy parameters for each trade-off plot was defined as the

set that: maximized yield and maintained SSB above 50% of SSBF=0, minimized

variability in yield and produced risk less than 0.40, maximized yield and produced
variability in yield less than 0.4, and maximized yield and produced risk less than 0.40.
This method of selecting optimal policy parameters was only used to illustrate the
sensitivity of control rule performance to uncertain future growth, and because this does
not necessarily reflect desired tradeoffs, should not be used for management without
careful consideration of fishery objectives.
3. Results
3.1. Overview of results

Varying the level of implementation error had little effect on the relative or
absolute performance of the control rules, and consequently, all the results below are for
the baseline level. Varying the parameters related to assessment error affected the
relative performance of some control rules, but only for trade-off plots that included
variability in yield (Section 3.4). For the other performance metrics, the relative and
absolute performance of the control rules varied little among the different levels of
assessment error parameters (see Appendix B), and this was consistent among growth
scenarios. Thus, the choice of optimal parameters would also generally be robust to the
level of assessment error. As a consequence, results for the sensitivity of the control
rules to varying assessment error parameters (Section 3.4) include example graphs based
on simulations of fast growth similar to more recent levels, and the results in all other
sections are for baseline levels of assessment error. Results for the different percentiles

showed similar trade-offs among performance metrics and relative differences among

126

control rules; so only results for the median are considered further. The rank order
performance of the control rules for each trade-off plot was also the same for all levels of
each source of uncertainty (see Appendix B), and these rank orders are presented in
Section 3.2 with example graphs based on simulations of fast growth similar to more
recent levels.

3. 2. Rank-order performance of control rules

For the plot of SSB versus Y, the BB control rule performed best, providing more
Y at a given level of SSB and higher SSB at a given level of Y than other control rules
(Figure 3). The BB control rule was followed in performance by constant-F, CCC, and
the BB-lim and constant-Flim control rules (Figure 3).

For the plot of Yvar versus risk, the CCC, BB-lim, and constant-Flim control rules
provided less Yvar at a given level of risk than other control rules (Figure 3). These same
control rules, however, were also more risky at a given level of Yvar than other control
rules (Figure 3).

For the plot of Y versus Yvar, the CCC, BB-lim, and constant-Flim control rules
provided less or similar Yvar at a given level of Y than other control rules (Figure 4). The
BB control rule, however, attained more Y at a given level of Yvar, and was followed in
performance by the constant-F, CCC, and the BB-lim and constant-Flim control rules
(Figure 4).

For the plot of Y versus risk, the BB control rule performed best, providing more
Y at a given level of risk and less risk at a given level of Y (Figure 4). The BB control
rule was followed in performance by constant-F, CCC, and the BB-lim and constant-Flim

control rules (Figure 4).

127

3.3. Sensitivity to future growth uncertainty
3.3.1. Fast growth stocks

For SSB versus Y, yield was generally insensitive to future growth, and the BB
and constant-F control rules were less sensitive than other control rules. All of the
percent changes in yield from the optimum were less than 6%, as were the changes in
SSB for the BB and constant-F control rules (Table 2). For the CCC, BB-lim, and

constant-Flim control rules, the percent changes in SSB were at least 10%, and SSB
decreased from the optimum and below 50% of SSBF=0 (i.e., the level used to define

optimal) when policy parameters were chosen as though grth would be similar to
recent levels and autocorrelated growth was the true future, but increased from the
optimum for the opposite situation (Table 2). So, control rules and policy parameters
chosen by incorrectly assuming future growth will be autocorrelated cost little in yield
and produced more SSB than the optimum, relative to incorrectly assuming future growth
will be similar to recent levels, which produced less SSB than the optimum.

For Yvar versus risk, results were insensitive to the future growth scenario. For
all control rules, the percent change from the optimal levels was 0.00 (Table 2).

For Y versus Y var, results were generally insensitive to the future growth scenario.
All of the percent changes in yield were less than 5%, and the changes in variability in
yield were all less than 8% (Table 2). Variability in yield increased from the optimum
and, for the BB rule, above 0.40, when policy parameters were chosen as though growth
would be similar to recent levels and autocorrelated growth was the true future, but
decreased from the optimum for the opposite situation (Table 2). So, control rules and

policy parameters chosen by incorreCtly assuming fiiture growth will be autocorrelated

128

 

cost little in yield and produced less variability in yield than the optimum, relative to
incorrectly assuming future growth will be similar to recent levels, which produced more
variability in yield than the optimum.

For Y versus risk, yield was generally insensitive to the future growth scenario,
but risk was more sensitive. All of the percent changes in yield were less than 5%, but
the changes in risk were more variable (Table 2). Risk increased from the optimum and,
for the BB-lim and constant-Flim rules, to 0.40, when policy parameters were chosen as
though growth would be similar to recent levels and autocorrelated growth was the true
future, but decreased from the optimum for the opposite situation (Table 2). So, control
rules and policy parameters chosen by incorrectly assuming future growth will be
autocorrelated cost little in yield and produced less risk than the optimum, relative to
incorrectly assuming future growth will be similar to recent levels, which produced more
risk than the optimum.

3.3.2. Slow growth stocks

For SSB versus Y, the CCC, BB, and constant-F control rules were less sensitive
to the future growth scenario than the BB-lim and constant-Flim rules. All of the percent
changes in SSB and yield were less than 5% for the CCC, BB, and constant-F control
rules (Table 2). For the BB-lim and constant-Flim rules, however, yield decreased and
SSB increased from the optimum when policy parameters were chosen as though growth
would be similar to recent levels and autocorrelated growth was the true future (Table 2).
Results for these control rules were less consistent when policy parameters were chosen
as though growth would be autocorrelated, but growth similar to recent levels was the
true future. For the BB-lim rule, both yield and SSB decreased from the optimum, and

129

 

SSB was less than 50% of SSBF=0 (Table 2). For the constant-Flim rule, yield increased

but SSB decreased below 50% of SSBF=0 (Table 2). So, the costs and benefits of choosing

policy parameters based on assuming an incorrect future for lake Whitefish growth
depended on the control rule. _

For Y var versus risk, results were insensitive to the future growth scenario, except
for the CCC control rule. For the CCC control rule, variability in yield and risk increased _ L

from the optimum when policy parameters were chosen as though growth would be 5

 

similar to recent levels and autocorrelated growth was the true fiiture (Table 2). When H
policy parameters were chosen as though growth would be autocorrelated and growth
similar to recent levels was the true future, the percent changes were less than 3%, and
variability in yield increased while risk decreased from the optimum levels (Table 2). So
for the CCC control rule, policy parameters chosen by incorrectly assuming future
growth will be autocorrelated cost little in variability in yield and produced slightly less
risk than the optimum, relative to incorrectly assuming future growth will be similar to
recent levels, which produced more variability in yield and risk than the optimum.

For Y versus Y var, sensitivity to the future growth scenario depended on the
control rule, but the BB control rule was the most sensitive. For the BB and constant-F
control rules, yield and variability in yield increased from the optimum (above 0.40 for
variability in yield) when policy parameters were chosen as though growth would be
similar to recent levels and autocorrelated growth was the true future, but decreased from
the optimum for the opposite situation (Table 2). For the other control rules, yield and
variability in yield decreased from the optimum when policy parameters were chosen as

though growth would be similar to recent levels and autocorrelated growth was the true
130

future (Table 2). When policy parameters were chosen as though growth would be
autocorrelated and growth similar to recent levels was the true future, yield decreased and
variability in yield increased from the optimum (Table 2). So, the costs and benefits of
choosing policy parameters based on assuming an incorrect future for lake Whitefish
growth will depend on the control rule.

For yield versus risk, results were generally more sensitive to the future growth
scenario than other trade-off plots. For all control rules, yield and risk decreased from
the optimum when policy parameters were chosen as though growth would be similar to
recent levels and autocorrelated growth was the true future, but in the opposite situation,
yield decreased or was the same and risk increased from the optimum, and above 0.40 for
the BB-lim rule (Table 2). So, control rules and policy parameters chosen by incorrectly
assuming future growth will be similar to recent levels produced costs in yield at the
benefit of less risk than the optimum, relative to incorrectly assuming future growth will
be autocorrelated, which produced costs in yield and risk from the optimum.

3. 4. Sensitivity to assessment error parameters

Varying assessment error parameters affected the performance of the control rules

for trade-off plots that included Yvar. For the plot of Yvar versus risk, control rules that

performed well at each performance metric increased in superiority over other control

rules as pn was decreased (Figure 5) or 0'3 was increased (Figure 6). Specifically, the

CCC, BB-lim, and constant-Flim control rules increased in superiority in terms of Yvar at
a given level of risk, and the BB and constant-F rules increased in superiority in terms of
attaining less risk at a given level of Yvar. For the plot of Y versus Yvar, the CCC, BB-

lim, and constant-Flim control rules increased in superiority in terms of Yvar at a given
131

level of Y as Pn was decreased (Figure 7) or 0'3 was increased (Figure 8), but an

increase in the superiority of the BB and constant-F control rules in terms of Y at a given
level of Yvar did not materialize.
4. Discussion

In this study, the BB control rule provided more yield and less risk than other
control rules with all else being equal, and was followed in rank-order by constant-F,
CCC, and the BB-lim and constant-Flim control rules, which is consistent with similar
research (Irwin et al., 2008; Punt et al., 2008). Irwin et al. (2008) used a similar BB
control rule for a recreational yellow perch Percaflavescens fishery in southern Lake
Michigan and found that the BB control rules produced higher yields and less risk than a
constant-F control rule at given levels of SSB. Punt et al. (2008) used a BB control rule
that reduced catch (instead of F) linearly with SSB for groundfish off the US. west coast
and found that the BB control rules produced higher yield and less risk than a constant-F
control rule at low levels of productivity, but performance was nearly equal for high
productivity.

The CCC, BB-lim, and constant-Flim control rules provided less interannual
variation in yield than other control rules, but at the cost of yield and risk. Clark and
Hare (2004) found that the CCC control rule could produce similar yields and SSB than a
constant-F control rule, but with less variability in yield for Pacific halibut Hippoglossus
stenolepis. Their simulations, however, did not include parameter uncertainty in the
stock-recruit relationship or assessment error. The results of this study suggest that
including these sources of uncertainty affects the relative performance of the CCC control

rule, as has been shown for other control rules (Deroba and Bence, 2008). For roundfish
132

stocks managed by the International Council for the Exploration of the Sea, limits on the
interannual change in target catch that prevented quotas from being decreased often
resulted in less yield and greater frequency of low SSB than a constant-F control rule
(Kell et al., 2006), which is consistent with the findings of this study where the BB-lim
and constant-Flim control rules performed worst in terms of yield and risk of low
spawning stock with all else being equal (e. g., constrained to provide some specified
level of spawning stock or yield). The relative performance of limiting the interannual
change in target catch, however, can depend on how tight the restraint is on the
interannual change, productivity, variability in recruitment or growth, and current status
of the stock (Punt et al., 2002; Kell et al., 2006).

The rank order performance of the control rules, while treating future growth as
known, was robust to the type of autocorrelated growth evaluated in this study, and the
growth scenarios in general, but time varying population dynamics have been shown to
affect relative performance (Walters and Parma, 1996; Deroba and Bence, 2008).
Walters and Parma (1996) showed that a constant fishing mortality rate control rule
performed better in terms of yield when the asymptote parameter of a Beverton—Holt
stock—recruit model was autocorrelated, and this was counter to when this parameter of
the stock-recruit model was constant. Whether catchability is treated as time-varying in
stock assessments also has an effect on control rule performance (e. g., Dichmont et al.,
2006). Few studies have evaluated the effect of time-varying parameters, but more
research is warranted in this area (Deroba and Bence, 2008).

The robustness of control rule performance to uncertainty about future lake
Whitefish growth, and the most robust future lake Whitefish growth to assume for

133

selecting policy parameters, depended on whether stock growth was fast or slow. For fast
growth stocks, selecting control rules and policy parameters by incorrectly assuming that
future growth will be autocorrelated resulted in little cost from the optimum levels
relative to the alternative of incorrectly assuming future growth will be similar to recent
levels. For slow growth stocks, however, the robustness of which future lake Whitefish
growth to assume for selecting policy parameters depended on the control rule and trade-
off plot. The decision to select control rules and policy parameters based on some
assumption about future lake Whitefish growth will ultimately depend on how competing
fishery objectives are weighted relative to each other. Generally, however, control rules
and policy parameters for fast growth stocks should likely be selected assuming future
grth will be autocorrelated, but a universal recommendation for slow growth stocks is
less clear (i.e., depends on the control rule and fishery objectives).

The results were generally robust to the level of assessment error. As reported
here, Punt et al. (2008) found that assessment error affected results for Yvar, but other
performance metrics similar to those included in this study were robust to this source of
uncertainty. Irwin et al. (2008) did not include a measure of yield variability, but also
found that other performance metrics similar to those included in this study were
insensitive to varying assessment error. Conversely, Katsukawa (2004) reported that the
superiority of BB control rules over constant-F control rules in terms of yield, diminished
with increasing assessment error variance. This contradiction may have occurred because
Katsukawa (2004) did not include other sources of uncertainty (e. g., shape of the stock-
recruitrnent curve) that may outweigh the effect of assessment error on the relative

performance of control rules. Alternatively, Katsukawa (2004) summarized tradeoffs in

134

 

terms of yield versus the minimum biomass over a time-horizon, and stocks managed in
the face of greater assessment uncertainty might suffer more extremes in stock size.

In this study, limiting the interannual change in target catch by 15% was inferior
or at best similar to other control rules for all performance metrics, and in some cases was
more sensitive to uncertainty in future lake Whitefish growth. So, using alternative
control rules would likely cost little relative to limiting the interannual change in target
catch by 15%, and would produce benefits in most situations. This result may not be
general, however, as benefits associated with limiting the interannual variability in target
catch depend on fishery objectives, the degree to which the interannual change is
restrained, stock status, and other population parameters such as growth variability (Kell
etaL,2006)

Depending on the relative weight of fishery objectives, a control rule and policy
parameters other than the one currently in use (i.e., constant-F based on a total annual
mortality rate of 65%) may want to be considered for lake Whitefish populations in Lakes
Huron, Michigan, and Superior. For example, a BB control rule with appropriately
selected policy parameters could likely produce nearly the same or more yield, spawning
stock biomass, and less risk with little cost in variability in yield relative to the currently
used policy. Similarly, the CCC control rule can likely provide less variability in yield,
but at the cost of yield. So, if maintaining low variability in yield is more desirable than
maximizing yield, a CCC control rule may want to be considered.

Not all dynamics or uncertainties about lake Whitefish were included in this study,
and unanticipated changes in the future may require periodic reviews of this evaluation
(Butterworth, 2008). For example, this study did not include density dependent growth,

135

 

which

1115 i

this

4
L1‘

4‘
0

cause
a like
coal
it on
But:

Mu

("014115

Iltl?

which has been shown to occur for lake Whitefish (Henderson et al., 1983; Kratzer et al.,
2005). Density dependence was not included because the recent declines in lake
Whitefish growth that have occurred in some areas generally happened over a time period
when abundance has declined or remained relatively stable, and so could not have been
caused by density dependence (e. g., Lumb et al., 2007). Density dependence is, however,
a likely compensatory response in lake Whitefish and so should be considered if
conditions arose to make such dependence important. To address such changes that may
be outside the realm of uncertainties included in a management strategy evaluation,
Butterworth (2008) recommended scheduling periodic reviews to consider whether
evaluations should be updated. If radical unanticipated changes occur, Butterworth
(2008) recommended making an ad hoc adjustment to the pre-agreed control rule until
the management strategy evaluation can be updated and tested for robustness to the
recent changes. Alternatively, stakeholders could agree on a pre-determined default
management plan that would be applied temporarily until the management strategy
evaluation is reviewed (Butterworth, 2008). Such scheduled maintenance of this
evaluation would also be prudent given the uncertainties and variability in lake Whitefish

population dynamics.

136

 

Bear:

3901’:

Bro“

Bun:

C00

Der

References

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Booth, A.J. 2004. Determination of cichlid specific biological reference points.
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Ebener

'1.

ltleh

Heels

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H031

lm‘ir

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139

Smiley, CW. 1882. Changes in the fisheries of the Great Lakes during the decade,
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Smith, A.D.M., K.J. Sainsbury, and RA. Stevens. 1999. Implementing effective
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Wang, H-Y, T.O. Hook, M.P. Ebener, L.C. Mohr, and P.J. Schneeberger. 2008. Spatial

and temporal variation of maturation schedules of lake Whitefish in the Great
Lakes. Canadian Journal of Fisheries and Aquatic Sciences 65: 2157-2169.

140

 

lrcan ll urndan
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o
as

 

 
 

W FS-ll-l

  

w rs-os w rsoo . C a n a d a

%
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Michigan WFS-08 ‘l.
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WFH-03 3
. J
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Figure l.— 1836 Treaty-ceded waters and lake Whitefish management units in Lakes

Superior, Huron, and Michigan (Ebener et al. 2005).

141

 

Fsat

 

Fishing Mortality

 

0.05

 

 

SSBLT ssiaHT
Spawning biomass relative to the unfished level

Figure 2.—Example of the biomass based control rule used in this analysis (solid line).

Dashed lines are provided as a reference for defining the policy parameters.

142

EmEo 91780.0: mnmésmsm 0.00.. 0.0.080 88.5 800.8. 0.85 an» 003...... ...... 82...... 0.83.500. $500.:Q ... 0.85 588
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39.8 0.

Yield (kg)

Yield (kg)

Yield (kg)

mooooo 1
mooooo 1
500000 1
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o
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mmw 3.50:0.

Proportion of years with Proportion of years with

Proportion of years with

888 < 20% unfished $38 838 < 20% unfished 888 888 < 20% unfished SSB

..o 1
oh 1
oh 1
oh 1
PM 1

 

 

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5.200.510 So...

144

 

050.0 0.1 >0 ... .1. 9.8 0. 0.800. ..0. 300.00 .00... 0.25 0.00.00 5.0.0.500. 0100...... ... 0.0... :00. 00.00.... 0.... 300.00 «.0...

0300 0.00.00 0300....0: 0.. 000.0 2.... 0002.....m 0.00.. 0.0.0000 .000 ...00 3.x. 0.. ...0 00.15.00 .00. am... 00.08....

145

0
r

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Variability in yield Variability in yield Variability in yield
0 o _. _. N O O -* -* N .0 .O 7‘ .-‘ N
'o '01 'o '01 'o 'o '01 b '01 'o o 01 o 01 o

l J l J

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Proportion of years with Proportion of years with Proportion of years with
SSB < 20% unfished SSB SSB < 20% unfished SSB SSB < 20% unfished SSB

9.99.0.0?
omxsmooo

 

 

 

 

J l l 1 J A o o
N N
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146

 

.u.m0.0 m.l.<.00.0.. 5.0.0.500. 00.00:...N ... 0.0.0 .0000 800.00 0.000....00 0., 000.0 2.... 0002.....m 0.00.. 0.0.0000 .000 0.0.. 8.x. 0..
...0 0.....0..00 .0<0. ..0. 0000....0 000000.00... 000 ....0.0...0...0..0.. 00.0.. <0..0..00. ...0 9:0... 0.. 00.000.40.000: ... 000000.00... 00.0. 00.

0000. .0 ob 0. 0.0. 000 .,00. E02... 0......0. .0 .000... .0<0.0 .000 .0... .0. 00.0..0v. 000.8. 00.00 0.0 0.00.0000 00... 050.0 m.

147

91915 05111qule

maul ua mumemA

'9 omfiyd

Proportion of years with Proportion 0' years With Proportion of years with
383 < 20% unfished sse 833 < 20% unfished SSB sse < 20% unfished ssa

 

 

 

 

9.0.0.090 -°-°-°-°-°—“ 9.09.090
ONAmmOOON‘bmmo 010001000
p;1111J'J1¥1119L11141
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\ ~.
9‘ .o
0‘ 01
3
.1 -1 ll
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N N~ .N-
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Proportion of years with Proportion of years with Proportion of years with
883 < 20% unfished SSB SSB < 20% unfished SSB SSB < 20% unfished 333

o o o o o _. o o o o o _.

. . . . . . . . . . . . o o o o ..
o N :s o: oo o o N .0 o: oo o '0 i0 '0 ‘o: g 'o
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148

 

050.0 0..I>0 .: 050.0 0. 0.800. 2.... .00 0.30:. 0. 00.000.410.33: 000000.003 0.8. 00. 0000. .0 ...0 0000.50 .0<0. 8.... 0:0 .0.

000000.003 0.3. <0...0:00 0000. .0 ob. 0. one.

149

916M U! mem

Q'l

new U! 01101211211

S'l

 

'9 amfii :1

Proportion of years with Proportion of years with Proportion of years with
883 < 20% unfished SSB SSB < 20% unfished SSB SSB < 20% unfished SSB

.0 .0 .0 .0 .0 r"

o N «5 O) on o
9 1 1 1 1 1 1
0

90

UL

 

0'2

Proportion of years with
SSB < 20% unfished SSB

9.0.0990
010001030

| i k 1 4L J

00

i

 

0'2

 

 

O O O O O .
'0 '0 '0 '0 0 'o
P 4 i L4
0
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0
Proportion of years with

888 < 20% unfished SSB

OOOOO-t

 

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9111111
0
.04
UI
dd
0
A
01
01
o

 

150

9.9.0.09.“
003001000

1 l l L 1

3L7"...

90
— .0

0|.
u
”-2

[0'0

Q'l

 

0'2

Proportion of years with
SSB < 20% unfished SSB

PPPPP.‘
01010010110

1 J L 1 1 J

1......

J

.9
o

 

.0

OI

.0 3N

'0“ II
p
N

_. o

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O

 

050.0 0.110 .0 050.0 0. 0.800. 2.... 800.00 0.0.0 <0.000 800.0: 80.00000. <0...00....0 .0 0.0.0.

151

050.0 0.

In yield

Variabili

In yield

ield Variabili '

Iny

Variabili

Na.1

..0 1

00 1

00.1

1.05.11» 1. . 1

.00” 0.0

O ““

 

 

0..

N...
00 1
90 1

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~00000 000000

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. . .. .ut\v . ..

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000000

 

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00 1

90 1

00w1

 

 

. .

000000

~00000

0

000000

 

 

0..

N00000 000000
50.0 :6.

.

000000

N001
00..

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0 00's

 

N001

..0 1

00.1

00.1

J1 .

~00000 000000

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o. o 00 0.x. 0003‘

0

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0..
0

N001

00 1

00.1

.90-

 

0..

0 .

000000

N00000

000000

 

 

888 388
<00 :6.

000000

152

30:8 m.|1>m 3 Emcaa 0. 98000 $09 05 9:9: om $883330: 5 ammommBoa 039 35— 8 90 ammo—mam _m<o_ 00.3. mg

”58259: 949. $1350 38.— 8 0.2 ca 0.00. Ba 0,2 32:»: Ema 53% 8808. 0:88:55: $1005? 0: «WE.

153

30:8 0.

 

 

 

 

 

 

 

 

 

 

  

 

NI I
q: .. 2: ET 5o
.0 Nb Nb ,
m. 0
V. 1. 1
.mm0.0 4.0 A
.h 2 A S 4
0
.m oo o:
W O -.., O ““
000 111I11 1llifi ill a 11 1 000 H d d
0 N00000 000000 000000 0 ~00000 000000 000000
M NO 1
v.
.m em 5 1
W S 1 8 1
.m
r
.a 0501 all. 090 1 . «mini
v 00 o 0. .0X‘ 0 000 .0 o 0.0.0.0.‘0
0.0 10 1\‘I1 0. -0 _ 0.0 7 J J
Au 0 N00000 000000 000000 0 ~00000 000000 000000
Mm N001
V.
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m 8 1
a
.m on 1 . n V/
V .
9o 11- ,11T1 1 1

 

 

0 ~00000 000000
<53 :5, <5: :60

000000

154

 

Table 11—The different assessment and implementation error parameter values

 

 

evaluated.
Parameter Value
Assessment error variance, 0'5 001, 0,05, 0,20

Assessment error autocorrelation, p ’1 0.0, 0.7 0.9

Implementation error variance, 0'}: 00’ 0.01, 0.0625

 

 

 

155

 

0.00—0 N.1l0100 000830000 00 00300— 0280 02.08088 800 80.5 000000 0000350 90 0002.800 0:08 0005 88 238000.. 0823
3080008880 8800 80000 0.00 000: 00. 0.2: 000003 0: 0008300000 30300 000 0.00 800 000 £02 03250 0805 0: 0000 .0803:
00000 $088. .38 00:0 00 <0_:0m 00000 000: 0320. 0000000 00010000000 08 08 0000230000 0m 08 00:00N 0085088 000000
00000000 08 $4000 00:88 :08 238080 082.00. 000 08 00 08 0080 8000008 0000a 00 .000 00000300000 30300 000500 0% 000
2000-03. 0.0" m2. 000: ~02. 050 $0000 00 008090000 08 08 00802 000000 #05 08 00030— 000 0m 00:00N 0080888 000000
0000350 08 02.89 388 00—8 2008000 03050. 0N0§0=0 0800 0008000 <0E0m 08 802.80 00 0 @0000: 00 08 0000000 _0<0_.

 

 

 

 

 

 

 

 

 

 

156

8000.0: 0.2 0000 052
>080. 0:88 035: 0003010
0.5088885 .8003 >Sooo:0_080 30003
00302830. 02883 008:
<85 <0. 000 3003 0-3 0.03 :3 000000 T3 0.00 013 30000 3 0.00 3 004000 3 can 3
<<0<<mr me 0.: 3 0.00 3 0.00 3 0.00 3 0.00 $3 0.00 $003 0.; 0+: 0.00 :03
<85 <0. <8. 000003 0-3 0.00 0+3 000000 T3 0.3 T: 30000 0-3 0.00 0-3 000000 0-3 0.0» 0+3
<85 <0. amx 000003 0-3 0.00 $003 000000 0-3 0.00 0-3 000000 0-3 0.00 0.00? 400000 0-3 0.00 0303
0.03000 00000
<85 <0. 000 30040013 0.0» 100 03080 0+3 0.00 I: 00003 0+: 0.00 T00 0033 TB 0.3 $00
<<0_.<m. max 000 3 0.00 3 000 3 0.00 3 0.00 3 0.00 3 0.00 3 0.00 3
<85 <0. <8. 000000 0+: 0.0; $3 0033 T3 0.00 0-3 0033 $03 0.02.03 000000 :00 0.00 :3
<85 <0. max 000000 3 0.35.0? 000000 Ev 0.00 0.3 .3003 0; 9.5 :3 000000 0-: 0.00 G03
00:08::n
<85 <0. 000 00403 3 0.00 3 000000 3 0.3 3 3.0003 3 0.00 3 0033 3 0.00 3
<<0q<m. max 0.00 3 0.00 3 0.00 3 0.00 3 0.00 3 0.00 3 0.00 3 0.00 3
<85 <0. <<0< unmomm T00 0.00 $3 0~010¢3 0.0m T3 30000 $3 0.0.» 0+3 30000 0-3 0.00 0-3

<85 <0. max unmomm 0-00 0.30703 0N0; 00 A00 0.00 0.03 30000 T: 0.40 A03 000000 :3 0.3 $003
0.03000 0000.5 <33 0 3.x. :3:
<85 <0. 000 N330 $00 0.00 0-3 3300 0.00 0.0.3 0100 400303 0.: 0.00 0+3 33000 T3 0.00 0-3
<<0<<m. max 0.00 3 0.00 3 0.00 3 0.00 3 0.8 3 0.00 3 0.00 3 0.00 3
<85 <0. <<0~ Nooowo A1: 0.0; $00 300nm 0-: 0.0m T: 03030 0-3 0.00 T3 0330 0-3 0.00 0+3
<85 <0. wax N00821: 0.00 0+»: 3030 0-: 0.3 0.3 ..3030 0-3 0.00 :3 $0000 T3 0.0.0 0.53
00:08:70" i=3 0 3.0 :3:

<85 <0. 000 00030 0+3 0.00 :00 0.00000 T3 0.00 013 40030 0.: 0.00 013 2.200 $00 0.00 0-3
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APPENDIX A
Appendix A describes the details of how parameters for each sub-model of the
simulation were estimated.
A. I. Classifying management units as fast or slow
Two complimentary methods were used to categorize management units as fast or

slow growing. Mean length at age of fish was estimated among months for each year and

management unit combination (La, y,u ). Multiple linear regressions were then fit by age

with Ky,“ as the dependent variable and year (5y) and management unit ((1! u ) as

categorical explanatory variables:

I: ’u =w+§y+wu+a

y y.u;

where m was the overall intercept and 8 y u was residual error. Pairwise comparisons
3

of the least squares means for each management unit were conducted. Generally, WFSO7
and WFMOS had significantly larger mean lengths at age than other management units
(P< 0.05) and so were categorized as fast growth, while all other management units were
classified as slow (Table A1). To buttress these categorizations, a lake Whitefish
biologist familiar with the data was asked to rank the management units as fast or slow,
and his categorizations confirmed these analyses (Mark Ebener, personal
communication). Not unexpectedly, the growth models parameterized (see the main text
and below) using the data from the management units in the slow growth category led to

lower expected mean lengths at age than for the fast growth category (Table A2).

157

 

A. 2. Growth sub-models
Data on growth and maturity were available from nine management units for a
varying range of years (Table A1). The parameters for the growth sub-model with

autocorrelated length at age-3 were estimated using a general linear mixed mode] using

data from ages 4-8 with log(Za,y,u) as the dependent variable, a fixed effect of age

(Va ), and a random effect for the interaction of year class and management unit (I), u )

that had an AR( 1) error structure:

 

I.

loglL )=6+va +br’u +8

0, y,u a, y,u ;
where a was the overall intercept, r denotes year class, u denotes management unit, and

5a,y,u was the residual error ~ N (0; 0% ), and:
br,u = p¢br—l,u + 7r;
where 7 r ~ N (0; 0' g ) and other symbols were defined as in the main text. Mean

length at age-3 Z3 was estimated as the exponent of three times a (i.e., log length at age-

O). During preliminary analyses, simulated L3, y were sometimes unrealistically high or

low. So, L3, y was capped at 10% smaller and 10% larger than the smallest and largest

observed age-3 fish in the data, respectively (Table A3). For fast growth simulations, the
caps were never hit. lFor slow growth simulations the upper cap was hit in about 3% of
years and the lower cap in about 9% of years.

The parameters of the growth sub-model for ages greater than three were

estimated using a general linear mixed model with the increment in mean length for a
158

cohort (Ma, y ) as the dependent variable, a fixed effect of La—l,y—1 , and a random

effect for the interaction of year and management unit (C y u )

A140,), = A+6La—l,y—l +Cy,u +5AL,a,y;

where Gym ~ N(0; 03,) , 8AL,a,y was residual error ~ N(0;0’§L ), and other

symbols were defined as in the main text.

The parameters of the weight portion of the growth sub-model with autocorrelated

 

length at age-3 were estimated using a multiple linear regression with log transformed

mean weight at age (log(Wa’ y ”as the dependent variable and log(La, y ) and

108(Z3,y+1,y+2 ) as fixed effects:
log(Wa,y )2 log(r) + Z log(La,y )+ (0108(53,y+1,y+2 )+ 8W,a,y;

where 8W, a, y was residual error ~ N (may; ) and other symbols were defined as in

the main text.
A. 3. Stock-recruitment sub-model

The parameters of the stock-recruitment sub-model were estimated using a
general linear mixed model, similar to that described in Myers et al. (1999). The model
was parameterized using estimates of stock and recruitment from medium and high
quality CAA models, ranked by the 1836 Treaty waters modeling sub-committee as of
2007, in each management unit. Each CAA model was changed from penalizing
recruitment estimates that deviated from the expectations of a Ricker stock-recruitment

curve as described in Ebener et al. (2005), to estimating a series of deviations around a

159

population scaling factor parameter with the deviations being required to sum to zero.
That is, the CAA models were changed so that recruitment estimates were not penalized

for deviating from some pre-specified stock-recruit relationship. The recruitment

estimates in each year for each management unit (Kym) were then standardized as in

Myers et al. (1999):

~

Ry u = Ry,uSSBRF:O,u(1— e‘Mu );

3

where SSBR 17:0,” was the spawning stock biomass per recruit at the unfished level for

each management unit, and Mu was the natural mortality rate in each management unit

estimated using Pauly’s equation (Ebener et al., 2005). Parameters of the stock-
recruitment model were then estimated for a variation of the log transformed Ricker

model (Myers et al., 1999):

I? ~
lOgLES—B] = a + gu + fluSSBy,u + 8R,y,u;
y,u

where a was the overall intercept, gu was the random effect of management unit,

8 R, y,u was temporally autocorrelated residual error, and :

. 2 ,
8R,y,u = pRugR,y-1,u + gy; gy ~ N(0’0Ru )
where remaining symbols were defined as in the main text. To estimate each a u , the

units were converted back from the standardized units of recruitment:

67+
8 gu

SSBRF=O,u(1 —e‘Mu )'
160 ‘

 

au

 

SSBRF=0,u was calculated for each management unit using parameters used in

each unit’s CAA model. Weight at age and the proportion of females mature at age were
estimated for each unit as the average over years. M and the proportion of females in the
population were set to the same constant value as was used in the CAA model for each
unit, and the number of eggs per kilogram of fish was set to 19,93 7/kg, which was the
value used in all CAA models (Ebener et al., 2005).
A4. Maturity sub-model

The parameters of the maturity sub-model were estimated using logistic
regression on data from females:

1g[1_£g_’(’;_)j=m

where p(m) was the probability of maturity and :9 was the intercept. Length at the

inflection point (77) was estimated as the quotient of .9 and - K‘ (:9 /- K ).

The p(LlLa , 0i ) was calculated by assuming that the variability around La
a

. 2
. The variance terms, 0' L , were
a a

followed a normal distribution with variance 0' 1%
calculated by multiplying La by the mean coefficient of variation (CV; 0.036) of the

mean lengths at age estimated among months for each year and management unit
combination. A single CV was used because the CVs for the mean lengths at age for

each year and management unit combination showed no trend with mean length.

161

 

A .5. Maximum sustainable yield and unfished SSB

Maximum sustainable yield, used to define the parameters of the CCC control
rule, was calculated for each management unit by finding the fully selected fishing
mortality rate that maximized the product of yield per recruit and the equilibrium
recruitment for each management unit. Yield per recruit was calculated separately for
fast and slow growth stocks using the expected mean lengths, weights, selectivity, and
proportion mature for each age predicted by the growth and maturity sub-models
described here and in the main text, and the values of natural mortality and proportion of
females in the population used in the simulations for each type of stock growth (i.e., fast
and slow; see main text). Equilibrium recruitment was calculated for each management
unit using the relationship between the spawning stock biomass per recruit curve,
calculated using the life history parameters predicted by growth and maturity sub-models
for each type of stock growth (i.e., fast and slow), and the stock-recruit relationship for

each management unit (Quinn and Deriso; 1999, pg. 475). This relationship was also

used to find the equilibrium SSBF=0 used to define the SSB LT and SSB HT policy

parameters.

162

Table Al—Growth category and the range of years for which a random sample of
commercial trap-net data were available from lake Whitefish management units in the
1836 Treaty-ceded waters of Michigan used in parameterizing grth and maturity sub-

 

 

models.

Management Unit Years of Growth and Maturity Data Growth Category
WF H01 1984-2007 slow
WFH02 1987; 1991 -2007 slow
WFH04 1980; 1986; 1 988-2006 slow
WFH05 1986; 1988-1990; 2000-2007 slow
WFM01 1992; 1995-1996; 2000-2007 slow
WFM02 1987; 1 990-2003 slow
WFM05 1981-1984; 1986-1991; 1993-1995; 1997; 2002 fast
WFSO7 1 980; 1 982-1 984; 1 986-1 988; 1991-2007 fast
WFSO8 1966; 1982; 1984-1986; 1996-2007 slow

 

163

 

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164

Table A3—Upper and lower caps placed on simulated length (mm) at age-3 lake
Whitefish for fast and slow growth category simulations.

 

Growth Category
Cap Fast Slow
Upper 539 601
Lower 228 21 0

 

 

 

 

165

 

APPENDIX B

This appendix presents additional trade-off plots beyond those presented in the
main text. Displaying all the results for four performance metrics, five control rule
variants, three levels of productivity, seven levels for the parameters of assessment and
implementation error, and four growth scenarios would require 1,512 panels. Displaying
all these results in this appendix was not feasible.

The subset of trade-off plots shown here support statements in the main text.
Figures B 1 -B4 illustrate that varying the parameters related to assessment error had little
effect on the relative or absolute performance of control rules for trade-off plots not
involving variability in yield. Figures BS-B8 illustrate that the rank order performance of

the control rules is robust to the growth scenarios.

166

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Exploited Fish Populations, University of Alaska Sea Grant College Program
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Uriarte, and A. Yatsu. In press. Current trends in the assessment and
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Roy, Y. Oozeki and J. Albeit, editors. Climate Change and Small Pelagic Fish.
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Battaile, BC. and T.J. Quinn 11. 2004. Catch per unit effort standardization of the
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Beauchamp, K.C., N.C. Collins, and BA. Henderson. 2004. Covariation of growth and
maturation of lake Whitefish. Journal of Great Lakes Research 30(3): 451-460.

Becker, G.C. 1983. Fishes of Wisconsin. The University of Wisconsin Press. Madison,
Wisconsin.

Beddington, J. R., and J. G. Cooke. 1983. The potential yield of fish stocks. FAO
Fisheries Technical Paper 242.

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