MODELS TO AID IN THE SELECTION OF PROCEDURES USED TO MANAGE LAKE
ERIE WALLEYE (SANDER VITREUS)
By
Aaron M. Berger

A DISSERTATION
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
DOCTOR OF PHILOSOPHY
Fisheries and Wildlife
Ecology, Evolutionary Biology, and Behavior
2011

ABSTRACT
MODELS TO AID IN THE SELECTION OF PROCEDURES USED TO MANAGE LAKE
ERIE WALLEYE (SANDER VITREUS)
By
Aaron M. Berger
Management procedures define the set of actions that will be used to guide effective
fisheries management. Common procedures include collecting data, conducting a population
assessment, and defining a set of harvest control rules to formulate a harvest policy. The
objectives of my dissertation research were structured to address some of the key questions
associated with each of these procedures in the management of Lake Erie walleye (Sander
vitreus); thereby providing science-based support to some of the more critical decisions
concerning rational walleye management. Walleye are intensely managed in Lake Erie because
of the economic, social, and cultural value of the fishery to the North American Great Lakes
region and because it is an ecologically important species (apex predator) in Lake Erie. I begin
by introducing the walleye fishery, providing the essential context from within which it is
currently managed (chapter 1), before explicitly evaluating each research objective. The first
research objective (chapter 2) was to investigate if accommodation for spatial structure at scales
relevant to walleye movement patterns, at the expense of model complexity, improved the annual
population assessment procedure. There was strong statistical evidence that incorporating
spatially referenced vulnerability and catchability parameters improved model fit, and the change
altered estimates of stock size and fishing mortality. The second research objective (chapter 3)
was to improve a data collection procedure – research survey indices of walleye abundance – by
statistically accounting for factors inherent in survey data that confound the ability to detect true

trends in population abundance. Models recognized several factors (e.g., net set type, secchi
depth, sampling week, and the presence of hypoxia) affecting the direction and magnitude of
predicted abundance trends, though a different combination of factors were identified for
Canadian and United States surveys. The third objective (chapter 4) was to directly aid decisionmakers by quantitatively comparing the performance of alterative walleye harvest policies under
three different data collection and population assessment schemes while explicitly incorporating
uncertainty in the management process (i.e., to conduct a management strategy evaluation).
Because uncertainty leads to risk, quantitatively accounting for uncertainty gives managers a
measure of how risky a particular management decision may be and provides a risk assessment
framework in which to compare tradeoffs among alternative management procedures. Results
indicate that harvest policy performance and the ensuing tradeoffs between conflicting objectives
were conditional on the choice of a data collection and assessment scheme. For the explicit
policies evaluated, annual age-structured procedures outperformed other procedural schemes
(i.e., triennial age-structured and annual survey index) and provided the overall best balance
between harvest and risk-related tradeoffs. However, the extra effort associated with
implementing annual SCA management procedures only provided a modest improvement in
policy performance over triennial SCA management procedures.

ACKNOWLEDGEMENTS
Many individuals contributed to my academic success and social well-being during my
time at Michigan State University. The chair of my graduate committee, Dr. Mike Jones, was an
exceptional asset – from well-directed guidance to ease of engagement (and much more in
between) – a student couldn’t ask for a better mentor. My experience and research were greatly
improved through engagements with and critiques by the other members on my graduate
committee: Drs. Jim Bence, Yingming Zhao, and Meredith Gore. I would like to acknowledge
the QFC and the talented individuals therein for the uncountable number of discussions,
immeasurable amount assistance, and general camaraderie that was shared. My wife Carrie and
our two boys, Henry and Charlie, provided unyielding support, often times when it could not be
reciprocated. A special thank-you goes to my mother (Susan Berger) and my mother-in-law
(Kathy Becker) for extensively traveling between Wisconsin and East Lansing many, many
times to help out with the boys so that I could focus on my research.
The research contained in this dissertation would not have been possible without the
support (both data and commentary) of the Great Lakes Fishery Commission and, in particular,
member agencies (Ontario Ministry of Natural Resources, Michigan Department of Natural
Resources, Ohio Department of Natural Resources, Pennsylvania Fish and Boat Commission,
and New York State Department of Environmental Conservation) and individual walleye task
group members affiliated with the Lake Erie Committee. Support for this research was provided
by the Ontario Funding for Canada-Ontario Agreement (7-02) Respecting to the Great Lakes
Basin Ecosystem to Dr. Yingming Zhao, Lake Erie Management Unit of the Ontario Ministry of
Natural Resources, the Saginaw Bay Walleye Club, and Michigan State University.
iv

The material presented in Chapters 2-4 was prepared in manuscript form with a specific
scientific journal in mind. Therefore, I would like to acknowledge the intended coauthors of
these manuscripts: Dr. Michael L. Jones, Dr. James R. Bence, and Dr. Yingming Zhao. Despite
being in manuscript form, there will inevitable be differences between what is presented here and
what is eventually published.

v

TABLE OF CONTENTS

LIST OF TABLES ..................................................................................................................... VIII
LIST OF FIGURES ...................................................................................................................... XI
CHAPTER 1 
INTRODUCTION .......................................................................................................................... 1 
REFERENCES ...................................................................................................................... 9 
CHAPTER 2
ACCOUNTING FOR SPATIAL POPULATION STRUCTURE AT SCALES RELEVANT TO
LIFE HISTORY IMPROVES STOCK ASSESSMENT: THE CASE FOR LAKE ERIE
WALLEYE SANDER VITREUS................................................................................................... 13 
Abstract ............................................................................................................................... 14 
Methods ............................................................................................................................... 20 
Lake Erie and the Walleye Population ...................................................................... 20 
Data Sources .............................................................................................................. 21 
Base Assessment Model ............................................................................................. 23 
Alternative Models and Model Selection ................................................................... 26 
Sensitivity Analysis .................................................................................................... 29 
Results ................................................................................................................................. 29 
Best Assessment Model .............................................................................................. 29 
Influence of the Spatial Structure Assumption on Assessment Results ...................... 30 
Model Sensitivity........................................................................................................ 32 
Discussion ........................................................................................................................... 32 
Acknowledgments ............................................................................................................... 37 
APPENDICES ..................................................................................................................... 39 
APPENDIX 2A: Main Tables and Figures ................................................................ 40 
APPENDIX 2B: Description of Symbols and Equations .......................................... 50 
APPENDIX 2C: Comparisons of Observed and Predicted Values ........................... 55 
APPENDIX 2D: Sensitivity Analysis ....................................................................... 60 
REFERENCES .................................................................................................................... 62 
CHAPTER 3 
IMPROVING FISHERY-INDEPENDENT INDICES OF ABUNDANCE FOR A
MIGRATORY WALLEYE POPULATION ................................................................................ 69 
Abstract ............................................................................................................................... 70 
Introduction ......................................................................................................................... 71 
Methods ............................................................................................................................... 74 
Study Area.................................................................................................................. 74 
Survey Design ............................................................................................................ 75 
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Confounding Variables .............................................................................................. 76 
Models to Standardize Catch Rates ........................................................................... 77 
Model Selection Procedure........................................................................................ 80 
Extraction of Standardized Indices ............................................................................ 81 
Results ................................................................................................................................. 82 
Discussion ........................................................................................................................... 86 
APPENDICES ..................................................................................................................... 93 
APPENDIX 3A: Main Tables and Figures ................................................................ 94 
REFERENCES .................................................................................................................. 105 
CHAPTER 4 
THE EFFECT OF ALTERNATIVE WALLEYE (SANDER VITREUS) MANAGEMENT
PROCEDURES ON HARVEST POLICY CHOICE AND PERFORMANCE ......................... 113 
Abstract ............................................................................................................................. 114 
Introduction ....................................................................................................................... 116 
Methods ............................................................................................................................. 119 
Study Population...................................................................................................... 119 
Approach Overview ................................................................................................. 119 
Operating Model ...................................................................................................... 121 
Management Procedures ......................................................................................... 124 
Performance Measures ............................................................................................ 127 
Sensitivity Analysis .................................................................................................. 128 
Results ............................................................................................................................... 128 
Selection of harvest policy ....................................................................................... 128 
Harvest policy performance .................................................................................... 129 
Discussion ......................................................................................................................... 132 
Acknowledgments ............................................................................................................. 137 
APPENDICES ................................................................................................................... 139 
APPENDIX 4A: Main Tables and Figures .............................................................. 140 
APPENDIX 4B: Additional Policy Performance Comparisons .............................. 161 
REFERENCES .................................................................................................................. 168 

vii

LIST OF TABLES

Table 2.1.—Commercial fishery, recreational fishery, and survey data series relating to both the
western and central basins of Lake Erie that were used to inform analyses. Error structure and
weights refer to that assumed in statistical catch-at-age assessment models. Catch, CPE, and
effort weights are proportional to the inverse of the assumed variance associated with each data
series and normalized to a single estimated variance associated with a standard data series
(Ontario survey). Age composition (proportion) weights correspond to the annual effective
sample size of aged fish (west basin/central basin). ..................................................................... 41
Table 2.2.—Relative comparison of walleye SCA assessment models describing alternative
hypotheses about the applicability of spatially referencing basins combined with a particular
estimation method to describe assumptions for vulnerability and catchability (see text for further
details). Vulnerability parameters were either estimated freely (unconstrained) or constrained to
follow a gamma function. Catchability (q in Table 2.5) was either assumed constant or allowed
to vary according to discrete blocks of time. Models are ranked according to differences in DIC
(∆DIC) from the model with the least DIC value. K is the estimated effective number of
parameters. .................................................................................................................................... 42
Table 2.3.—Spatially-referenced and time-varying values of catchability (q) for each model
component as estimated by the overall best walleye spatial (BSM) and aggregate (BAM) models.
Note that posterior standard deviations (SD) are presented on a different scale than highest
posterior density estimates. ........................................................................................................... 43
Table 2.4.—Descriptions of symbols in Table 2.5 and 2.6 describing the base assessment model.
....................................................................................................................................................... 51
Table 2.5.—Equations for population and observation submodels used in the base walleye
assessment model. ......................................................................................................................... 53
Table 2.6.—The objective function was the posterior negative log density calculated by summing
weighted individual normal and log-normal likelihood and prior components for all source
combinations. Highest posterior density estimates minimized this function. .............................. 54
Table 2.7.—Sensitivity to the selection of the overall best spatial (BSM) and aggregate (BAM)
models resulting from data source weighting and natural mortality (M) assumptions. For all
cases, the best spatial and aggregate model was structurally the same as the best models shown in
Table 2.2. Upward and downward adjustments (%) to the nominal assumption were made for
each identified model component. Data source weights were implemented in the objective
function to control how strongly each data set influenced model fit. These included commercial
and recreational effort and total catch, survey total catch-per-effort (CPE), and the effective
sample sizes (Neff) for commercial, recreational, and survey age composition data. Estimated
viii

total abundances (N) are shown for the last year (2008). Differences in DIC (ΔDIC) show the
relative improvement in model fit (lower DIC values) when basin-level spatially referenced
parameters were applied. .............................................................................................................. 61
Table 3.1.—Number of sites used in the analysis that were sampled during annual Canadian
(CAN) and United States (US) fishery-independent gill net surveys in the west and central basins
of Lake Erie. Canadian sites were selected following a stratified (depth) random design each
year, and United States sites followed a stratified (depth) fixed design (not all sites sampled
every year and new sites added opportunistically). ...................................................................... 95
Table 3.2.—Reference levels for categorical variables and mean values for continuous variables
used to standardized Canadian (CAN) and United States (U.S.) fishery-independent surveys. .. 96
Table 3.3.—Source of variation from estimated random effects (βi’s) and residual variation (εi’s)
associated with the best models used to standardize Canadian and United States fisheryindependent surveys. ..................................................................................................................... 97
Table 3.4.—Comparison of the relative importance of fixed effect factors (αi’s) included in the
best model used to standardize Canadian and United States fishery-independent surveys.
Estimates (±1 SE) of fixed effects from the overall best model are shown for each survey and
assumed error structure. Each factor was evaluated by removing it from the overall best model
(random effects held constant) and assessing the resultant change in AICc (ΔAICc) such that
larger values signify increased importance in model fit. The base model is shown as a reference
point, describing differences in catch rates due solely to year and basin effects (i.e., trends of
interest) prior to accounting for other factors. The factors week and sub-basin were included in
the best model through random effect interaction terms (see Table 3) and thus were not further
evaluated here. The combination of αy + αb + αyb represents effects describing the annual trend
of interest for each basin. .............................................................................................................. 98
Table 4.1.—Description of symbols used in operating and assessment models. Values used to
drive simulations were either explicitly established or taken as a sample from the joint posterior
distribution (MCMC) associated with the most recent statistical catch-at-age stock assessment.
..................................................................................................................................................... 141
Table 4.2.—Model equations used in catch-at-age operating (OM) and assessment (AM) models.
..................................................................................................................................................... 143
Table 4.3.—Candidate data collection, population assessment, and harvest policy management
procedures. Each management strategy scenario examined included the choice of a single type
of harvest control rule (feedback, FB; constant F, Fx; and conditional constant catch, CC)
informed by one of three data collection and assessment schemes. Abbreviations include: F =
instantaneous fishing mortality; N = total estimated population abundance; TAC = total
allowable catch; CPE = catch-per-effort; and M = millions. ...................................................... 146
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Table 4.4.—The statistical catch-at-age assessment procedure estimated population parameters
by minimizing the posterior negative log likelihood calculated by summing weighted individual
normal and log-normal likelihood and prior components for all source combinations. Highest
posterior density estimates minimized this function. .................................................................. 147
Table 4.5.—Performance statistics used to evaluate tradeoffs among candidate management
strategies. Statistics were calculated by averaging over the 50-year time projection for each
simulation and management scenario combination. ................................................................... 148
Table 4.6.—Ranked performance of harvest policies for each performance measure evaluated.
The first policy set is used to compare annual SCA (SCAA) to annual SI (SIA) procedures. The
second policy set is used to compare annual SCA to triennial SCA (SCAT) procedures. Lower
numbers refer to higher rankings and better performance. ......................................................... 149 

x

LIST OF FIGURES

Figure 2.1.—The west basin (WB), central basin (CB), and east basin/Pennsylvania ridge
(EB/PR) geomorphologic regions of Lake Erie have distinct bathymetric and water quality
attributes. The main walleye population occurs in the west and central basins. ......................... 44
Figure 2.2.—Mean age composition (%) of recruited walleye smoothed over 20 minute
longitudinal bins (defined by bin midpoint). Age composition changed markedly with longitude
as relatively older (larger) walleye tend to move further east (central basin) while younger
(smaller) walleye tend to remain near spring spawning grounds (western basin). Data are from
gillnet surveys (September – October) for years when both Ontario and Ohio/Michigan surveys
were conducted concurrently (1990 – 2008). ............................................................................... 45
Figure 2.3.—Highest posterior density estimates of age-2 and older walleye abundance (millions
of fish; panel A) and fully selected instantaneous fishing mortality (panel B) from the overall
best model with basin-level parameters (BSM; solid line) and the best model without basin-level
parameters (BAM; dashed line). The median (bar) percent difference (calculated across years,
1978-2008; circles) between estimates from BSM and BAM decrease with age for walleye
abundance (panel C) and increase with age for fishing mortality (panel D). ............................... 46
Figure 2.4.—Posterior distributions for estimates of annual total walleye abundance (age-2 and
older) from the best spatial (BSM; solid line) and aggregate (BAM; dashed line) models. The
peak of each curve represents the highest posterior density estimate while the spread represents
estimated precision........................................................................................................................ 47
Figure 2.5.—Comparison of vulnerability estimates (loge; ± 1 posterior SD) between the overall
best model (BSM) which includes basin-level spatially referenced vulnerability parameters from
the west (solid) and central (dash) basins and the best aggregate model (BAM) which does not
spatially reference basins (dotted; see Table 2.2 for description). Estimates were relative to age4, the reference level, which was set to one (zero on the loge scale) and thus had no uncertainty
associated with it. In both models, recreational fishery age-2 vulnerability was allowed to
change in 2004 (not shown but declined in all cases) because of a regulatory amendment
increasing the minimum harvestable length. ................................................................................ 48
Figure 2.6.—Time series of observed (filled circle) and predicted (BSM: solid line; BAM:
dashed line) fishery harvest (thousands of fish) for commercial (Ontario waters) and recreational
(Ohio and Michigan waters) fisheries in the west and central basins, Lake Erie. ........................ 56
Figure 2.7.—Time series of observed (filled circle) and predicted (BSM: solid line; BAM:
dashed line) fishery mean age for commercial (Ontario waters) and recreational (Ohio and
Michigan waters) fisheries in the west and central basins, Lake Erie. ......................................... 57
xi

Figure 2.8.—Time series of observed (filled circle) and predicted (BSM: solid line; BAM:
dashed line) CPE (catch-per-effort) from annual Ontario gill net surveys and combined
Ohio/Michigan gill net surveys in the west and central basins, Lake Erie. .................................. 58
Figure 2.9.—Time series of observed (filled circle) and predicted (BSM: solid line; BAM:
dashed line) survey mean age from annual Ontario gill net surveys and combined Ohio/Michigan
gill net surveys in the west and central basins, Lake Erie. ........................................................... 59
Figure 3.1.—Canadian (Ontario) and United States (Michigan and Ohio) fishery-independent gill
net surveys were used to index the west (W) and central (C) basin Lake Erie walleye population.
Dots indicate the locations of sampling sites for the most recent year (2008), which was a
standard sampling year in Canadian waters and an intensive sampling year in US waters. Large
sample sizes to the north enabled the analysis of sub-basin effects on catch rates (W1, W2, C1C4). Overall site selection followed a stratified (depth) random sampling design (CAN) and a
stratified (depth) fixed sampling design (US). .............................................................................. 99
Figure 3.2.—Histogram of observed walleye (age-2 and older) catch rates in numbers of
individuals from Canadian (1990-2008; panel A) and United States (1983-2008; panel B)
fishery-independent surveys. The proportion of sites with zero catch was high (0.36) in the
Canadian survey and low (<0.02) in the United States survey. .................................................. 100
Figure 3.3.—Fits of alternative error distributions to observed mean and variance in walleye CPE
for Canadian and United States fishery-independent surveys. Each observation corresponds to a
year for years with 5 or more sites sampled (only excludes U.S. 1983)..................................... 101
Figure 3.4.—Standard diagnostic plots that evaluate the adequacy of the overall best log-linear
model used to standardize positive catch rates for the Canadian fishery-independent survey.
Plots assess model fit (A) and adequacy (B) qualitatively and evaluate assumptions of constant
variance (i.e., no trend in C) and normality (i.e., straight line in D)........................................... 102
Figure 3.5.—Standard diagnostic plots that evaluate the adequacy of the overall best log-linear
model used to standardize positive catch rates for the United States fishery-independent survey.
Plots assess model fit (A) and adequacy (B) qualitatively and evaluate assumptions of constant
variance (i.e., no trend in C) and normality (i.e., straight line in D)........................................... 103
Figure 3.6.—Trends in walleye relative abundance for Canadian (CAN) and United States (US)
fishery-independent surveys in the west and central basins. The lower panel for each region
compares trends in walleye relative abundance as inferred from a standardized index (mean
(solid line), 95% confidence interval (dotted lines)) and a nominal index (normalized to the first
year standardized index value; circles). The upper panel for each region shows the proportional
difference (PD; solid line) between the raw nominal and standardized indices of walleye
abundance and the mean PD across the time series (dotted line). .............................................. 104

xii

Figure 4.1.—The west basin (WB), central basin (CB), and east basin (EB) geomorphologic
regions of Lake Erie have distinct bathymetric and water quality attributes. The main walleye
population occurs in the west and central basins. ....................................................................... 150
Figure 4.2.—Alternative relationships for walleye stock size and age-2 recruitment dynamics.
The best fitting three parameter (alpha, beta, error) Ricker stock-recruitment function (solid line)
from the most recent SCA assessment model (points) was one possible realization of the true
dynamics. Others (e.g., dashed lines) were developed (one for each simulation using MCMC;
see text for details) to illustrate uncertainty associated with defining an underlying stockrecruitment relationship. ............................................................................................................. 151
Figure 4.3.—Selected harvest policies that were used to translate assessment information
(estimated population abundance (SCA), panel A; standardized survey CPE (SI), panel B) into
an allowable fishing mortality rate (F), which was then used to derive total allowable catch
(TAC). In application, TAC was obtained directly from survey CPE (T.3.32; shown against F
here to facilitate visual comparisons). Specific control rules (see Table 4.3) were used to describe
alternative feedback (FB - solid line, panel A and B), constant fishing mortality (Fx - dotted line,
panel A), and conditional constant catch (CC - dashed line, panel A) types of harvest policies.
..................................................................................................................................................... 152
Figure 4.4.—Plots show the distribution of mean commercial harvest (# of age-2 and older) over
a 50-year time horizon for each set of management procedures. Alternative types of harvest
control rules that were evaluated included constant fishing mortality (Fx, where x is the mortality
rate; top panel), feedback (FB, see figure 4.3 for graphical representation; middle panel), and
conditional constant catch (CC; bottom panel) based policies that were informed by either an
annual or 3-year statistical catch-at-age (SCA) or an annual survey index of abundance (SI) set
of management procedures (see Table 4.3 for details). Subscripts associated with FB policies
refer to restricting annual deviations in fishing mortality to no more than 20% of the previous
year (FB20%); fishing mortality set by moving average according to the three most recent years
(FB3MA); a constant catch employed during interim (non-assessment) years (FBCC); and the
fishing mortality rate held constant during interim years (FBCF). Box plots indicate the median
th

th

(line within the box), the 25 and 75 percentiles (lower and upper box boundaries,
th

th

respectively), the 10 and 90 percentiles (lower and upper error bars, respectively), and
th

th

observations below the 10 and above the 90 percentiles (open circles). ............................... 153
Figure 4.5.—Stability in commercial harvest for alternative sets of management procedures.
Plots show the distribution of the variation (coefficient of variation; CV) in commercial harvest
over a 50-year time horizon. Panels, box plots, and abbreviations follow the same convention
laid out in Figure 4.4. .................................................................................................................. 155
Figure 4.6.—Risk that population size declines to an undesirable level for alternative sets of
management procedures. Plots show the distribution of the mean percentage of years that
xiii

walleye abundance falls below 15 million (age-2 and older) over a 50-year time horizon. Panels,
box plots, and abbreviations follow the same convention laid out in Figure 4.4. ...................... 156
Figure 4.7.—Risk that the population is below a standard reference point for alternative sets of
management procedures. Plots show the distribution of the mean percentage of years that
walleye spawning stock size is less than 20% of the unfished spawning stock size over a 50-year
time horizon. Panels, box plots, and abbreviations follow the same convention laid out in Figure
4.4................................................................................................................................................ 157
Figure 4.8. Tradeoff between levels of commercial harvest and the risk associated with falling
below a population reference point for alternative data collection and assessment procedures
using constant fishing mortality rate (Fx; top panel) and feedback (bottom panel) policies.
Tradeoffs associated with conditional constant catch policies have been superimposed (single
symbols, bottom panel). Points represent the median value from the distribution of simulated
results. ......................................................................................................................................... 158
Figure 4.9. Tradeoff between levels of stability in commercial harvest (coefficient of variation;
CV) and the risk associated with the population falling to an undesirable level for alternative data
collection and assessment procedures using constant fishing mortality rate (Fx; top panel) and
feedback (bottom panel) policies. Tradeoffs associated with conditional constant catch policies
have been superimposed (single symbols, bottom panel). Points represent the median value from
the distribution of simulated results. ........................................................................................... 159
Figure 4.10. Tradeoff between levels of commercial harvest and recreational catch-per-effort
(CPE) for alternative data collection and assessment procedures using constant fishing mortality
rate (Fx; top panel) and feedback (bottom panel) policies. Tradeoffs associated with conditional
constant catch policies have been superimposed (single symbols, bottom panel). Points represent
the median value from the distribution of simulated results. ...................................................... 160
Figure 4.11.—Sensitivity of select performance measures to the spatial allocation of commercial
fishing mortality (following “recent” or “historical” trends; see text details). Shown are results
based on feedback (FB) harvest control policies for each of three data collection and assessment
schemes (annual SCA, annual SI, and 3-year SCA). The ordinate represents multiple scales.
Box plots and abbreviations follow the same convention laid out in Figure 4.4. ....................... 162
Figure 4.12.—Plots show the distribution of mean walleye abundance (# of age-2 and older) over
a 50-year time horizon for alternative sets of management procedures. Panels, box plots, and
abbreviations follow the same convention laid out in Figure 4.4. .............................................. 163
Figure 4.13.—Stability in population size for alternative sets of management procedures. Plots
show the distribution of the variation (coefficient of variation; CV) in walleye abundance over a
50-year time horizon. Panels, box plots, and abbreviations follow the same convention laid out
in Figure 4.4. ............................................................................................................................... 164
xiv

Figure 4.14.—Plots show the distribution of mean recreational catch-per-effort (CPE) over a 50year time horizon for alternative sets of management procedures. Panels, box plots, and
abbreviations follow the same convention laid out in Figure 4.4. .............................................. 165
Figure 4.15.—Plots show the distribution of mean age (# years) in the population over a 50-year
time horizon for alternative sets of management procedures. Panels, box plots, and abbreviations
follow the same convention laid out in Figure 4.4...................................................................... 166
Figure 4.16.—Plots show the distribution of mean commercial yield over a 50-year time horizon
for alternative sets of management procedures. Panels, box plots, and abbreviations follow the
same convention laid out in Figure 4.4. ...................................................................................... 167 

xv

CHAPTER 1
INTRODUCTION

Lake Erie is the smallest by volume of the five Laurentian Great Lakes, but it produces
the highest fishery yields (Munawar and Munawar 1982). The nutrient-rich, eutrophic to
mesotrophic going from west to east, waters of the lake provide the basis for a lucrative coolwater fishery. The Lake Erie percid fishery (represented historically by walleye, yellow perch,
sauger, and the now extinct blue pike) has been both a socially and economically important
resource throughout the twentieth century, representing about a quarter of the total commercial
harvest and recreational effort in all of the Great Lakes combined (Koonce et al. 1999; Brown et
al. 1999; Bence and Smith 1999). In recent years, the fishery has been dominated by catches of
walleye and yellow perch with a conservative regional economic impact estimate of over $1
billion (U.S.) per year (ASA 2006; Roseman et al. in press). Oversight and management are
critical to ensure that this multi-use fishery remains sustainable. Maintaining a healthy walleye
population has been recognized as a necessary condition to achieve broader fish community
goals (Ryan et al. 2003), because walleye, the dominant terminal predator in much of the lake,
act to stabilize the food web with top down predatory control (Knight and Vondracek 1992;
Makarewicz and Bertram 1993).
The walleye fishery is managed by the Lake Erie Committee (LEC) under the auspices of
the Joint Strategic Plan for Management of Great Lakes Fisheries (GLFC 1981). The LEC
consists of a representative from each member authority (four U.S. states and one Canadian
province) and is charged with setting annual harvest levels within the walleye quota management
1

zone (the west and central basins).  Management of walleye harvest is currently guided by an
exploitation policy with a set of governing control rules, such that the allowable rate of fishing is
lower when abundances are low and higher when abundances are high (Wright et al. 2005;
Locke et al. 2005; Jones and Bence 2009). The annual fishing rate is then translated into a total
allowable catch (TAC) quota and allocated among authorities and fisheries (recreational and
commercial) by the LEC. The commercial walleye fishery is exclusive to Canadian waters and
has limited fishing capacity with a finite number of licenses available; the recreational fishery is
largely in U.S. waters (97% and 95% of total recreational harvest and effort, respectively; WTG
2009). Implementation of the exploitation policy requires knowledge of walleye population
abundance. This is currently estimated on an annual basis using a statistical catch-at-age (SCA)
stock assessment model that is informed by both fishery-dependent and fishery-independent
sources of data (WTG 2009).
The research undertaken in this dissertation was designed to address questions associated
with establishing suitable management procedures for the Lake Erie walleye fishery.
“Management procedures” refer to the set of procedures commonly applied in pursuit of rational
fisheries management including the collection of representative data, an assessment of
population status, and the application of a harvest policy (Butterworth et al. 1997; Butterworth
2007). Improving the population assessment (chapter 2) and the interpretation of survey data
(chapter 3) may help to reduce uncertainty associated with walleye population status and thus
improve the efficacy of the harvest policy. Quantitatively evaluating trade-offs between
alternative walleye management strategies (chapter 4) given uncertainty in the management
process should provide valuable insight into the development of robust fishing policies and,
2

through the explicit involvement of stakeholders, credence in the resultant policy. The scope and
relevance of this work extends beyond management of Lake Erie walleye because improving the
way in which ecological knowledge, statistical methods, and decision science interact and
ultimately result in science-based management decisions is of general importance to the
conservation and management of freshwater and marine fisheries, and is an active area of
research in fisheries science (Lane and Stephenson 1998; Peterman 2004).
A central component in the management process is the yearly assessment of population
status. Because a vast majority of walleye in Lake Erie occur in the west and central basins, the
population in this area is assessed independently of the smaller eastern basin population and is
managed by allocating a total allowable catch (TAC) quota to each authority. The general
structure of the current assessment model has been used as the standard evaluation tool to
describe the walleye population since 2001 (Walleye Task Group 2002). As information on
walleye population dynamics improves, alternative model structures (i.e., assumptions about the
factors influencing walleye dynamics) should be explored periodically. For example, recent
evidence suggests spatial differences in the age composition of walleye going from west
(younger individuals near major spawning grounds) to east (older individuals utilizing more
favorable habitat, further from spawning areas; Wang et al. 2007), which could imply a need for
spatially incongruent assumptions about how vulnerable walleye of a given age (or size) are to
fishing or survey sampling. Uncertainty surrounding catchability – the theoretical proportion of
fish caught with one unit of effort – is a common source of process error in stock assessment
models. Because not accounting for major changes or trends in catchability has been show to
bias estimates (Wilberg and Bence 2006; Chen et al. 2008), it is important to also periodically
3

test assumptions regarding catchability in stock assessment models. Improving the stock
assessment model is one way to increase knowledge about the population and improve
management performance.
Chapter 2 investigates whether incorporating spatial structure at scales relevant to
walleye movement patterns improves the annual population assessment procedure. Several
alternative model formulations were developed and evaluated across assumptions relating to
walleye vulnerability, catchability, and spatial structure. Results indicate a clear preference for
incorporating spatial structure into the stock assessment by applying regional vulnerability and
catchability parameters. Estimates of stock size and fishing mortality changed using the
improved best spatial model over the best non-spatial or aggregate model. Accounting for key
life history differences among individuals in the population (such as movement rates) can have a
consequential impact on assessment results, and thus management advice that follows.
Improving the quality of data used in population assessments is another way to enhance
management performance. Standardization of data that originate from either the fishery itself or
from independent surveys can lead to marked improvements in data quality (Hilborn and Walters
1992; Maunder and Punt 2004). Standardization is the process of fitting statistical models to
catch and effort data to account for confounding factors before extracting the effect of interest
(e.g., annual abundance index; Quinn and Deriso 1999; Maunder and Punt 2004; Ye et al. 2005).
For example, fishery-independent catch-per-effort (CPE) data are collected from annual research
surveys and implemented as auxiliary time series indices of relative abundance to help improve
SCA assessment model accuracy and precision (Deriso et al. 1989; Quinn and Deriso 1999;

4

Chen et al. 2003). However, there are many factors other than abundance that can influence
survey catch rates and potentially render the nominal (or unadjusted) survey index misleading.
Chapter 3 investigates whether statistically accounting for factors inherent in survey data
(i.e., catch rate standardization) has an influence on resulting abundance trends. General and
generalized linear mixed models were used to standardize Canadian and United States fisheryindependent surveys at the basin-level. Spatial, temporal, and environmental factors were
recognized as affecting the direction and magnitude of predicted abundance trends, resulting in
considerable annual variation in the difference between indices. Yet, overall abundance trends
across the time series were generally similar between the standardized and nominal (nonstandardized) indices. Alternatively, trends in abundance differed markedly between basins due
to discrepancies in availability (population structure) and selectivity (gear efficiency) to fishing
gear. Standardized indices for walleye population assessments are recommended because these
account for factors other than abundance clearly demonstrated to influence catch rates.
Uncertainty is pervasive in fisheries management; thus it is prudent to account for this
uncertainty when providing management advice. Consequently, it is beneficial to consider
uncertainty associated with the entire management process (e.g., management strategy
evaluation; MSE) when attempting to decide what management strategy will best meet
objectives. Because population assessment and harvest strategy procedures are often linked in a
closed system loop (i.e. the population assessment procedure influences the harvest strategy and
in turn the harvest strategy influences the population assessment), it is especially critical that
these procedures be evaluated concurrently (National Research Council 1998). By explicitly
incorporating uncertainty into the management process, a more realistic range of plausible
5

outcomes from a given management strategy can be evaluated through simulation and then
compared among alternative strategies so that information regarding the expected performance
of each strategy is available to managing authorities. This method allows managers to
quantitatively compare and contrast alternative harvest policy scenarios for a given data
collection and population assessment method.
Similar to decision analysis (Peterman and Anderson 1999), management strategy
evaluation utilizes the general themes of adaptive management and risk assessment (Walters
1986; Butterworth and Geromont 1997; Smith et al. 1999; Sainsbury et al. 2000). The five
general steps in a management strategy evaluation (de la Mare 1996; Cox and Kronlund 2008)
are to:
1. define clear management objectives
2. develop performance measures for each objective
3. identify candidate management procedures (data collection, stock assessment,
harvest strategy)
4. conduct a prospective evaluation of procedures against objectives
5. communicate results to decision-makers

This approach provides an objective basis for acquiring information on which to base
management decisions, which can be particularly beneficial when there are multiple, conflicting
objectives.
The current Lake Erie walleye harvest strategy applies a feedback (or state-dependent)
policy that sets the fishing mortality rate according to the projected abundance in the upcoming
6

year (Locke et al. 2005). This policy specifies a constant rate of fishing at low and high
abundances and proportional rates (according to population abundance) at intermediate
abundances. The Lake Erie Committee broadly defines the state of the fishery into four
categories: crisis (<15 million fish), rehabilitation (15-20 million fish), maintenance (20-40
million fish), and high quality (>40 million fish). This particular policy has been in use since the
completion of the 2005 Lake Erie walleye management plan. Harvest policy performance should
be revisited periodically to ensure that the current management strategy is operating as expected,
and that there are no alternative management procedures that would be preferred.
Chapter 4 investigates whether the choice of management procedures (i.e., a data
collection and population assessment scheme) influences the selection and performance of
alterative walleye harvest policies. Candidate management procedures included (1) using annual
fishery and survey data to inform a statistical catch-at-age (SCA) assessment model; (2) the same
as in one except where survey data are collected triennially; and (3) using annual survey data as
an indicator of population status. Results from simulations indicate that harvest policy
performance and the ensuing tradeoffs between conflicting objectives were conditional on the
choice of a data collection and assessment scheme. In general, annual age-structured procedures
outperformed the two other procedural schemes examined and provided the overall best balance
between harvest and risk-related tradeoffs. However, the extra effort associated with
implementing annual SCA management procedures only provided a modest improvement in
policy performance over triennial SCA management procedures. For the analysis presented in
chapter 4, I focused on steps 3 and 4 of a management strategy evaluation. Management
objectives (step 1) and performance measures (2) were assumed through discussions with
7

members of the LEC and the communication of results to decision-makers (step 5) left to other
forums. Results from chapter 4 are currently being used by LEPMAG (Lake Erie Percid
Management Advisory Group) in the application of a full management strategy evaluation.

8

REFERENCES

9

REFERENCES
ASA (American Sportfishing Association). 2006. Economic impact of Great Lakes
fishing by state in 2006. http://www.asafishing.org/statistics/saleco_trends/
2006ei_glakes_state.html (Accessed July 15, 2010).
Bence, J.R., Smith, K.D. 1999. An overview of recreational fisheries of the Great Lakes, in:
Taylor, W.W., Ferreri, C.P. (Eds.), Great Lakes fisheries policy and management: a binational
perspective. Michigan State University Press, East Lansing, pp. 259-306.
Brown, R.W., Ebner, M., Gorenflo, T. 1999. Great Lakes commercial fisheries: historical
overview and prognosis for the future, in: Taylor, W.W., Ferreri, C.P. (Eds.), Great Lakes
fisheries policy and management: a binational perspective. Michigan State University Press,
East Lansing, pp. 307-354.
Butterworth, D. S., and Geromont, H. F. 1997. Evaluation of a range of possible simple interim
management procedures for the Namibian hake fishery. Report to the Ministry of Fisheries
and Marine Resources, Namibia. 28 pp.
Butterworth, D.S., Cochrane, K.L., and De Oliveria, J.A.A. 1997. Management procedures: a
better way to manage fisheries? The South African experience, in: Pikitch, E.K., Huppert,
D.D., Sissenwine, M.P. (Eds.), Global trends: fisheries management. American Fisheries
Society Symposium, 20. Bethesda, Maryland, pp. 83-90.
Butterworth, D.S. 2007. Why a management procedure approach? Some positives and negatives.
ICES J. of Mar. Sci. 64, 613-617.
Chen, Y., Chen, L., Stergiou, K.I. 2003. Impacts of data quantity on fisheries stock assessment.
Aquat. Sci. 65, 1-7.
Chen, Y., Jiao, Y., Sun, C., Chen, X. 2008. Calibrating virtual population analysis for fisheries
stock assessment. Aquat. Living Res. 21, 89-97.
Cox, S.P. Kronlund, A.R. 2008. Practical stakeholder-driven harvest policies for groundfish
fisheries in British Columbia, Canada. Fish. Res. 94, 224-237.
de la Mare, W.K. 1996. Some recent developments in the management of marine living
resources, in: Floyd, R.B., Sheppard, A.W., De Barro, P.J. (Eds.), Frontiers of Population
Ecology. CSIRO Publishing, Melbourne, pp. 599–616.
Deriso, R.B., Neal, P.R., Quinn II, T.J. 1989. Further aspects of catch-age analysis with auxiliary
information. Can. Spec. Pub. Fish. Aquat. Sci. 108, 127-135.
10

GLFC (Great Lakes Fishery Commission, Editor). 1981. A joint strategic plan for
management of Great Lakes fisheries. Available from http://www.glfc.org/pubs/jsp81.pdf
[accessed 12 June 2010].
Hilborn, R., Walters, C.J. 1992. Quantitative Fisheries Stock Assessment. Kluwer Academic
Publishers, Norwell, MA.
Knight, R.L., Vondracek, B. 1992. Changes in prey fish populations in western Lake Erie, 196988, as related to walleye, stizostedion-vitreum, predation. Can. J. Fish. Aquat. Sci. 50, 12891298.
Koonce, J.F., Locci, A.B., Knight, R.L. 1999. Contribution of fishery management in walleye
and yellow perch populations of Lake Erie, in: Taylor, W.W., Ferreri, C.P. (Eds.), Great
Lakes fisheries policy and management: a binational perspective. Michigan State University
Press, East Lansing, pp. 397-416.
Jones, M.L., Bence, J.R. 2009. Uncertainty and fishery management in the North American
Great Lakes: lessons from applications of decision analysis. Am.Fish. Soc. Symp. 70, 10591081.
Lane, D.E., Stephenson, R.L. 1998. A framework for risk analysis in fisheries decision-making.
ICES J. Mar. Sci. 55, 1-13.
Locke, B.L., Belore, M., Cook, A., Einhouse, D., Kenyon, R., Knight, R., Newman, K.,
Ryan, P., Wright, E. 2005. Lake Erie walleye management plan. Available from
http://www.glfc.org/lakecom/lec/WTG_docs/other_reports_and_docs/wmp20051207.pdf
[accessed 15 May 2008].
Makarewicz, J. C. Bertram, P. 1993. Evidence for the restoration of the Lake Erie ecosystem.
BioScience 41, 216-223.
Maunder, M.N., Punt, A.E. 2004. Standardizing catch and effort data: a review of recent
approaches. Fish. Res. 70, 141-159.
Munawar, M., Munawar, I.G. 1982. Phycological studies in Lakes Ontario, Erie, Huron and
Superior. Can. J. Bot. 60, 1837-1858.
NRC (National Research Council). 1998. Improving fish stock assessments. National
Academy Press. Washington D.C.
Peterman, R.M., Anderson, J.L. 1999. Decision analysis: a method for taking uncertainties into
account in risk-based decision making. Human and Ecol. Risk. Assess. 5, 231-244.
Peterman, R.M. 2004. Possible solutions to some challenges facing fisheries scientists and
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managers. ICES J. Mar. Sci. 61, 1331-1343.
Quinn and Deriso. 1999. Quantitative Fish Dynamics. Oxford University Press, New York, NY.
Roseman, E.F., Drouin, R., Garden, M.E., Knight, R.L., Tyson, J., Zhao, Y. In press. Managing
inherent complexity for sustainable walleye fisheries in Lake Erie, in: Taylor, W.W., Lynch,
A.J., Leonard, N.J. (Eds.), Great Lakes fisheries policy and management: a binational
perspective, second edition. Michigan State University Press, East Lansing.
Ryan, P.A., Knight, R., MacGregor, R., Towns, G., Hoopes, R., Culligan, W. 2003.
Fish-community goals and objectives for Lake Erie. Great Lakes Fisheries Commission Spec.
Publ. 03-02, Ann Arbor, Michigan. 56 p.
Sainsbury, K.J., Punt, A.E., Smith, A.D.M. 2000. Design of operational management strategies
for achieving fishery ecosystem objectives. ICES J. Mar. Sci. 57, 731-741.
Smith, A.D.M., Sainsbury, K.J., Stevens, R.A. 1999. Implementing effective fisheriesmanagement systems – management strategy evaluation and the Australian partnership
approach. ICES J. Mar. Sci. 56, 967-979.
Walters, C.J. 1986. Adaptive management of renewable resources. The Blackburn Press, New
Jersey.
Wang, H, Rutherford, E.S., Cook, H.A., Einhouse, Haas, R.C., Johnson, T.B., Kenyon, R.,
Locke, B., Turner, M.W. 2007. Movement of walleyes in Lakes Erie and St. Clair inferred
from tag return and fisheries data. Trans. Am. Fish. Soc. 136, 539-551.
Wilberg, M.J., Bence, J.R. 2006. Performance of time-varying catchability estimators in
statistical catch-at-age analysis. Can. J. Fish. Aquat. Sci. 63, 2275-2285.
WTG (Walleye Task Group). 2002. Report for 2001 of the Lake Erie walleye task group.
Great Lakes Fishery Commission. Ann Arbor, MI.
WTG (Walleye Task Group). 2009. Report for 2008 of the Lake Erie walleye task group.
Great Lakes Fishery Commission. Ann Arbor, MI.
Wright, E., Belore, M., Cook, A., Culligan, B., Einhouse, D., Johnson, T., Kayle, K.,
Kenyon, R., Knight, R., Newman, K. 2005. Decision analysis application for Lake
Erie walleye management: final report to the Lake Erie Committee. Great Lakes Fishery
Commission. Ann Arbor, Michigan.
Ye, Y., Pitcher, R., Dennis, D., Skewes, T. 2005. Constructing abundance indices from scientific
surveys of different designs for the Torres Strait ornate rock lobster (Panulirus ornatus)
fishery, Australia. Fish. Res. 73, 187-200.
12

CHAPTER 2

Accounting for spatial population structure at scales relevant to life history improves stock
assessment: the case for Lake Erie walleye Sander vitreus

13

Abstract
Stock assessments commonly allow parameters to vary across fishery or jurisdictional
boundaries, often by treating each region as a unit stock. However, animals generally disperse in
response to spatial habitat features to satisfy particular life history requirements, and these
features are often not congruent with fishery or jurisdictional boundaries. Thus, populations are
often spatially structured at scales distinct from those acknowledged in assessments.
Furthermore, when the spatial-structure arises from dispersal of a common pool of recruits,
redefining unit stock boundaries may not adequately capture these dynamics. Here we test the
utility of spatially referencing parameters (vulnerability and catchability) in a statistical catch-atage stock assessment model as a simple approach to account for life history variation of walleye
(Sander vitreus) when information on explicit movement rates is unavailable. We apply several
alternative assessment models to Lake Erie walleye – a population identified as displaying agespecific differences in the extent of dispersal from spawning grounds – to investigate the
importance of accounting for spatial heterogeneity at ecologically important scales in stock
assessments. Comparisons of the most parsimonious assessment models (based on a deviance
information criterion) with and without spatially referenced parameters (by basin) highlighted
the importance of estimating regional vulnerability and catchability. There was strong statistical
evidence that incorporating spatially referenced parameters at a scale relevant to walleye
dispersal patterns improved model fit, and the change altered estimates of stock size and fishing
mortality. For example, estimates of total age-2 and older walleye abundance in the most recent
year decreased by 16% (34% for ages 7 and older) and fully selected fishing mortality increased
by 70% after incorporating walleye spatial population structure. These results emphasize the
14

importance of considering spatial aspects in stock assessments at scales relevant to the life
history of the species or group of species under consideration.

15

Introduction
Fishery stock assessments are often conducted using statistical models to infer critical
demographic information (e.g., spawning stock biomass, age composition) from catch and
survey observations (NRC 1998). A stock assessment model links how we think fishery,
biological, and environmental processes that affect a population operate in time and space (i.e.,
system dynamics) with observations from one or more data sources to better understand current
status and historical changes in the population. Empirical data provide the basis for informing
assessment models, so these data should represent the temporal and spatial scales within which
population dynamics are hypothesized to operate (Levin 1992). Stock assessment models are
regularly fitted to time series data; however, many assessments implicitly assume that the stock
is spatially homogenous, effectively ignoring spatial structure (Goethel et al. 2011). Regarding
the population as a single ‘dynamic pool’ is a common assumption in modern stock assessments
despite clear recognition of the importance of spatial fisheries management (Walters and Martell
2004; Ciannelli et al. 2008; Cadrin and Secor 2009; Goethel et al. 2011).
Population assessments that have accounted for spatial structure typically have done so at
scales defined by fishery or jurisdictional boundaries (e.g., Hampton and Fournier 2001;
Montenegro et al. 2009; Stewart et al. 2011). However, animals often disperse in response to
spatial habitat features to satisfy particular life history requirements (e.g., foraging,
reproduction), which results in non-homogenous patterns of abundance across the landscape at
scales usually distinct from conventional management boundaries. When responses differ
among groups of individuals within a population (contingent theory; Clark 1968; Secor 1999), as
is often the case, the population will tend to exhibit some degree of spatial organization. For
16

example, differential dispersal ability (i.e., diffusive instability; Levin 1976) of individuals can
lead to non-uniform spatial organization. Accounting for spatial structure in stock assessments at
scales relevant to life history may lead to more precise population estimates and derived
management parameters. For example, it is possible that estimates will be sensitive to patterns
of spatial variation in age-specific fishing mortality that result from dispersal or migratory
behavior (Yakubu and Fogarty 2006), and thus models which account for these patterns could
provide better estimates of stock status and exploitation history.
There are two general classes of techniques to incorporate spatial differences into
assessment models which differ in whether explicit movement information is utilized. First,
explicit movement information can be incorporated into models that follow individuals
(Lagrangian approach) or fluxes in the population at points in space (Eulerian approach) to
quantify changes to geographically apportioned subpopulations through time (Turchin 1998;
Quinn and Deriso 1999; Goethel et al. 2011). These approaches demand substantial model
complexity and require movement information that is costly and often unavailable. Second,
spatially referenced parameters can be applied within an assessment model to account for the net
effects of movement on observations of population structure at local sites (Quinn and Deriso
1999; Walters and Martell 2004). The benefits of this simpler, implicit spatial approach include
making the stock assessment process more transparent (simplifying the modeling process),
practical (eliminating the necessity for cost prohibitive movement information), and applicable to
many fisheries. For example, vulnerability (defined here as the product of gear selectivity and
species availability to the fishery or survey) could be allowed to vary among regions to reflect

17

spatial differences in population structure that result from age-specific differences in the extent,
duration, or timing of fish movements.
Parameters in stock assessments are often allowed to vary spatially among fisheries,
jurisdictions, or other divisions convenient for management (Goethel et al. 2011) to account for
differences in catch (e.g., Montenegro et al. 2009), fishing mortality (e.g., Ralston and O’Farrell
2008), or population structure (e.g., Punt et al. 2000; Stewart et al. 2011). However, there has
been comparatively less effort to match model scale to ecologically-driven boundaries, owning
to gaps in knowledge and data limitations (Cope and Punt 2011). Defining the appropriate
spatial resolution remains a challenge, yet more attention should be devoted to incorporating
scales relevant to the life history of the species or group of species under consideration and
identifying the affect it has on key management parameters. For example, Saunders et al. (2009)
found that blacklip abalone (haliotis rubra) management units off the southern coast of Australia
that were redefined according to life history metrics rarely overlapped existing management
units. Cope and Punt (2009) applied a set of clustering algorithms to standardized catch rate data
to delineate management units at spatial scales relevant to Pacific cod (Gadus macrocephalus)
life history.
Walleye (Sander vitreus) is a highly vagile species in both riverine and lacustrine
environments with dispersal distances exceeding 160 km (Todd and Hass 1993; Wang et al.
2007). In Lake Erie, longitudinal dispersal of walleye from their primary spawning locations in
the western basin appear to be related to size or age (Kershner et al. 1998; Jones et al. 2003;
Wang et al. 2007), which could result in differential age composition, and hence age-specific
vulnerability patterns, across the lake. Lake Erie walleye may disperse away from spawning
18

grounds (Wang et al. 2007) to maximize growth (Kershner et al. 1999) by responding to
longitudinal changes in forage availability and temperature (Kershner et al. 1999), water clarity
(Ludsin et al. 2001), and dissolved oxygen gradients. Population status is of particular
management concern because of the socio-economic importance of walleye to the region and
because of its ecological role as the dominant terminal predator in the lake. The fishery consists
of two main sectors: a commercial fishery exclusive to Canadian waters with limited fishing
capacity (finite number of licenses available) and a recreational fishery largely in U.S. waters
(97% and 95% of total recreational harvest and effort, respectively; WTG 2009).
Implementation of rational management often demands precise estimates of population
abundance. Lake Erie walleye population parameters are estimated on an annual basis using a
statistical catch-at-age (SCA) stock assessment model that is informed by both fishery and
fishery-independent sources of data (WTG 2009). The current SCA assessment model assumes
that the walleye population acts as one homogenous unit, applying spatially referenced
selectivity and catchability parameters at fishery/jurisdictional boundaries to allow for
differences between north (commercial/Canadian) and south (recreational/U.S.) regions. The
goal of this research was to assess whether spatially referencing vulnerability and catchability
parameters in a statistical catch-at-age stock assessment model at scales relevant to walleye life
history improves assessment model fit and the precision of estimates used in management.
Herein, we 1) assess evidence for spatial structuring of the walleye population in Lake Erie by
comparing models that assume homogeneity (aggregate models) to those that allow for basinlevel population structure (implicit spatial models), and 2) contrast resulting inferences to
investigate the importance of incorporating stock structure at scales relevant to species
19

movement patterns in assessments, even when information on explicit movement rates is
unavailable.  

Methods
Lake Erie and the Walleye Population
th

3

Lake Erie is the 11 largest freshwater lake by volume (483 km ) in the world. The lake
is divided into three distinct basins (Figure 2.1), which contribute to considerable longitudinal
variation in limnological attributes across the lake. The western basin is the shallowest (mean
depth = 7.4 m) and most biologically productive of the three basins; the central basin (18.5 m) is
intermediate in productivity; and the eastern basin (24.4 m) is the least productive (Ryan et al.
2003). Other general patterns in the physical environment along a west-east gradient are also
prominent such as water temperature (decreasing) and water clarity (increasing). These features
combine to provide a gradient of habitats suitable for warm-water (west basin), cool-water (west
and central basin), and cold-water species (east basin).
Walleye, a cool-water species, predominantly occur in the west and central basins of
Lake Erie. Since 1978, this area has consistently produced more than 95% of the total annual
walleye harvest in Lake Erie (WTG 2009). Moreover, a vast majority of walleye spawn in areas
associated with the western basin (the Maumee and Sandusky Rivers and a mid-lake reef
complex; Regier et al. 1969; Busch et al. 1975; Figure 2.1). Despite common observations of
spawning site fidelity in walleye (Crowe 1962; Spangler et al. 1977), gene flow does occur at
moderate rates in these basins, indicating a single intermixing stock (Strange and Stepien 2007).
The fishery is managed via the Great Lakes Fishery Commission (GLFC) under the auspices of
20

the Joint Strategic Plan for Management of Great Lakes Fisheries (GLFC 1981) with
representatives from each member authority (four U.S. states and one Canadian province).
Managing authorities (guided by the GLFC) recognize the west and central basin walleye
population as the primary population of interest and the area within which quotas are allocated
and implemented (hereafter referred to as the walleye population; Locke et al. 2005; Figure 2.1).
Accordingly, we adopt these boundaries to define the walleye population under consideration for
all analyses presented in this paper (i.e., eastern basin population was excluded).
Prior to conducting stock assessments, age composition data (proportion of the total catch
by age) collected during 1990-2008 from northern (Canadian) and southern (U.S.) fishery
independent surveys was used to assess the scale at which population structure was most
distinguishable. Observed age compositions changed markedly with longitude as relatively older
(larger) walleye tend to move further east (central basin) while younger (smaller) walleye tend to
remain near spring spawning grounds (western basin), indicating that the population is not
strictly spatially homogenous (Figure 2.2). However, the proportion of individual age classes in
each basin was relatively stable over time. Previous analyses indicated that the most
parsimonious explanation of spatial differences in age composition was longitudinal at the basinscale (A. Berger unpublished data). Based on this, the ecological relevance of in situ habitat
gradients between basins and previously described life history behavior for Lake Erie walleye
(Kershner et al. 1999; Wang et al. 2007), exploration of SCA models with spatially referenced
parameters were conducted at the basin-scale.

Data Sources
21

Time series of fishery-dependent and fishery-independent data were acquired for the
period 1978–2008 when available from GLFC member agencies (Table 2.1). Commercial catch
totals (biomass) and fishing effort (km of gillnet set) were reported monthly by 10-minute spatial
grid. Numbers caught by age for the commercial fishery were determined from the catch
biomass for each market classification and statistical district (strata) based on aged and weighed
catch subsamples. Recreational catch-at-length and fishing effort (angler hours) estimates were
available by month and 10-minute grid based on creel surveys and from charter boat reports.
Catch-at-length was subsequently converted into catch-at-age using annual age-length keys.
Fishery-independent surveys were conducted annually from August – November and utilized as
auxiliary indices of abundance (catch-per-effort (CPE)). In Canadian waters, a stratified (depth)
random gill-net survey (number of sites ranged from 75-94 annually) was conducted jointly by
the Ontario Ministry of Natural Resources (OMNR) and the Ontario Commercial Fishers’
Association. In U.S. waters, a stratified (depth) fixed-site gill-net survey (number of sites ranged
from 4-53 annually) was conducted jointly by the Ohio Department of Natural Resources
(ODNR) and the Michigan Department of Natural Resources (MDNR). Walleye captured during
surveys were weighed and measured for length. All walleye captured in the Canadian survey
were aged. On the U.S. side, subsamples were aged and age compositions of survey CPE were
calculated using age-length keys. Walleye catch-at-age and CPE-at-age data were binned into
six age classes beginning with age-2 (when walleye become vulnerable to fishing) and extending
to an age-7 and older combined group (age-7 is the point where scale-otolith aging agreement
begins to substantially decline). Hard structures (otoliths and anal fin spines) replaced soft
structures (scales) in 2004-2005 as the basis for aging walleye.
22

Base Assessment Model
We implemented a Bayesian SCA assessment model using Automatic Differentiation
Model Builder (ADMB; Fournier et al. 2011) software. SCA models are age-structured with
assumed errors in the observations of catch-at-age that are used to fit cohorts of fish forward
through time (Megrey 1989). We followed the general approach outlined in Fournier and
Archibald (1982) and Deriso et al. (1985) for parameterizing catch-at-age models with auxiliary
information, including separating fishing mortality into year and age components. In addition to
catch-at-age data, auxiliary data sources are necessary to ensure model parameters are
identifiable (Doubleday 1976; Pope 1977, Deriso et al. 1985). Fishing effort data and
information on relative abundances from fishery-independent surveys (CPE) provided the
necessary information to separate estimates of fishing mortality and abundance. Highest
posterior density parameter estimates were obtained by minimizing the posterior negative log
density (details below). We employed Monte Carlo Markov Chain (MCMC) simulations with a
Metropolis-Hastings algorithm to acquire posterior density distributions for parameters and
quantities of interest (e.g., total abundance, abundance-at-age, and exploitation rates). We used
th

15 000 MCMC samples to estimate posterior distributions – resulting from saving every 100

sample of a 2.5 million sample chain and then ignoring the first 10 000 samples (chain burn-in to
reduce the influence of starting values) (Gelman et al. 2004). Using the CODA package in
program R (Plummer et al. 2006), we assured that chains converged to stationarity (Gelman and
Rubin’s diagnostic test; Gelman and Rubin 1992) and that there was adequate information
available to predict posterior distributions for each parameter (the sample size after being
adjusted for autocorrelation was well below 15 000 for all parameters).
23

The general structure of our base assessment model consisted of population and
observation submodels (Table 2.5), and was an extension of the model currently used to aid
regulation of walleye harvest since 2001. Walleye population dynamics were based on annual
+

time intervals beginning in 1978 and six age classes (2, 3, 4, 5, 6, and 7 ) for a single aggregated
population. Based on previous tagging studies (as noted in Locke et al. 2005), we assumed the
-1

natural mortality rate to be constant and known without error (M = 0.32 yr ). Biomass was
calculated as the product of estimated abundance-at-age and observed mean weight-at-age,
where mean weights were obtained from OMNR and ODNR surveys (Eq. 2.5.8).
To facilitate comparisons with spatially implicit models that allowed for basin-level
vulnerability and catchability parameters, we disaggregated fishery catch-at-age and survey
CPE-at-age into annual values by basin so that our base model used the same fishery and survey
data set as the spatial models. We chose to pursue spatially implicit models that recognize basins
to account for spatial heterogeneity at an ecologically important scale.
Age-specific vulnerability (i.e. product of gear selectivity and species availability to
capture), relative to a fully vulnerable age, was estimated as a free parameter (no assumed
functional form). For each fishery and survey, vulnerability was assumed to be time and spaceinvariant, with the exception of Ohio and Michigan recreational fisheries, which allowed for a
temporal change in age-2 vulnerability in 2005 to reflect a regulatory increase in the minimum
harvestable length. Catchability was assumed constant (time and space invariant) for each
fishery/survey, implying a direct proportionality between expected fishing mortality on a given
age of fish and observed fishing effort, with actual fishing mortality varying from direct

24

proportionality based on multiplicative year, basin, and fishery specific errors (Eq. 2.5.4 and
2.5.5).
We fit the model to observed harvest, effort, survey, and age composition data for each
basin (Table 2.6). The basin-specific recreational and commercial harvest at-age and survey
CPE data were recast in the form of annual totals and proportions at age. This was done so that
basin-specific totals for a fishery or survey could be modeled as lognormal with proportions at
age treated as arising from sampling a multinomial distribution, as suggested by Fournier and
Archibald (1982). The objective function was the posterior negative log density, with some
constants dropped, which included additive components associated with the log-likelihood for
each data source and for a prior for effort deviations (errors in the effort—fishing mortality
relationship; Fournier et al. 1998). The prior for effort deviations assumed a normal distribution
(Eq. 2.6.3), whereas non-informative uniform priors (Gelman et al. 2004) on the log-scale were
placed on the remaining parameters (number of recruits each year, abundance-at-age in the first
year, vulnerability, catchability, and the error variance associated with a single data source, the
OMNR survey). The uniform priors were implemented by constraining the allowable range for
these parameters, and were not explicitly included in the objective function (Maunder and Starr
2001).
The use of auxiliary information such as fishing effort (combined with an assumed
relationship to fishing mortality) or survey abundance indices can greatly enhance the quality of
stock assessments (Fournier and Archibald 1982; Deriso et al. 1985). However, the relative
quality of different data sets often vary and appropriate weighting terms need to be assigned to
control how strongly each data set influences the fit of the assessment model. Weights were
25

assumed to be inversely proportional to the variance associated with each data source (Quinn and
Deriso 1999). In effect, relative weights were used to scale the error variance of each data
source to that estimated for the OMNR survey. Relative weights for assumed lognormal
distributed catch, effort, and CPE time series were established for all data sources (Table 2.1) by
using a survey to solicit expert opinions from Lake Erie managers and assessment biologist about
the relative quality (magnitude of observation and process error variance) of each data set (WTG
2010). Proportions assumed to arise due to multinomially-distributed aged samples were
weighted according to the effective sample size (i.e. an adjusted number of walleye aged each
year), which was found by iteratively adjusting effective sample sizes of the objective function
components to match the residual variance (McAllister and Ianelli 1997). Effective sample sizes
were set for each data source, directly applied to years when aging was performed with hard
structures (otolith or spine), and down weighted 10% when aging was performed with scales to
account for the higher mean error rate among age groups when assigning ages with scales (scale
error was evaluated by comparing scale estimates of age with otolith estimates of age).

Alternative Models and Model Selection
We evaluated 11 alternative assessment models to assess key structural assumptions
associated with the parameterization of vulnerability and catchability (Table 2.2). The main goal
here was to evaluate how basin-level vulnerability parameters may help to account for
differential dispersal movements of walleye by age, but in doing so we felt it necessary to
investigate additional alternative hypotheses about both vulnerability and catchability as the two
are inextricably related (both are scaling factors on age-specific fishing mortality). Alternative
26

models differed from the base assessment in the following ways: i) vulnerability was assumed to
follow a gamma function of age, ii) vulnerability was allowed to vary spatially (by basin), iii)
catchability was allowed to vary temporally (by blocks of time), and iv) catchability was allowed
to vary spatially (by basin). The gamma function was used to specify a smooth, reduced
parameter, vulnerability curve because it is sufficiently flexible to fit dome-shaped curves such
as those often associated with gill-net catches or monotonically increasing curves such as those
often associated with trophy sport fishery catches. Using the gamma vulnerability function,
fishery and survey vulnerability-at-age was defined as

,

where a is age, k is timeblock, j is the age that maximizes vulnerability, and α (shape) and β
(scale) are parameters. Specification of the temporal blocks between which catchability was
allowed to change arose from discussions with GLFC member agency biologists who were
directly involved in data collection and had practical knowledge of major ecosystem (e.g.,
introduction of Dreissenid spp.) or fishing (e.g., harvest regulation) changes during the study
period. The number of blocks varied by data source (4 time blocks: Ohio recreational fishery; 3
time blocks: commercial fishery, Michigan recreational fishery, ODNR/MDNR survey; 2 time
blocks: OMNR survey).
We reduced the total number of candidate models a priori by restricting hypothesized
changes in vulnerability or catchability to be similar across all data sources (except for the use of
catchability time blocks where changes were data source specific) and by constraining
27

catchability to be spatially homogenous except in cases where vulnerability was allowed to vary
by basin. Such restrictions ensured that results would be interpretable within the context of our
proposed hypotheses and helped to keep the number of models to a manageable level.
Regardless of the inclusion or omission of basin-specific parameters, we used the assessment
models to estimate quantities (e.g., abundance and mortality) for the population as a whole
because that is the level at which the harvest control rule is implemented. As noted above, to
facilitate model comparisons, observed data were disaggregated by basin for all model versions,
whether catchability or vulnerability were basin-specific or not.
Deviance information criterion (DIC; Spiegelhalter et al. 2002) was used to evaluate the
relative performance of each model. DIC is an information theoretic index sharing some
similarities with AIC, which is often used when models are fit by maximum likelihood
(Spiegelhalter et al. 2002). Like AIC, the index trades off model fit (deviance) with model
complexity (effective number of parameters). Deviance is defined as twice the negative loglikelihood (Gelman et al. 2004). The effective number of parameters is the difference between
the mean deviance and the deviance associated with the best fit parameters. For this purpose we
used highest posterior density estimates. We calculated DIC as the mean deviance from the 15
000 saved MCMC runs plus the effective number of parameters based on the same MCMC
sample. When the goal is to select among alternative models to provide management advice, DIC
seems to perform well at choosing the best structural model for predicting unobserved quantities
(Wilberg and Bence 2008). Following Spiegelhalter et al. (2002), we considered models with a
difference in DIC (∆DIC) of less than 7 units from the best model (lowest DIC) to be plausible
and thus used to make inferences.
28

Sensitivity Analysis
Sensitivity to the selection of the overall best spatial and aggregate models resulting from
alternative data source weighting and natural mortality assumptions were explored. We
evaluated the data weighting assumptions by increasing and decreasing weights by 200% and
50%, respectively, from the nominal assumption. Natural mortality (M) was adjusted by 25%
-1

above or below the nominal value of 0.32yr . Catchability and vulnerability assumptions were
tested explicitly within our analytical framework (DIC model selection), and as such, we did not
further evaluate them. Differences in DIC (ΔDIC) between the best spatial and aggregate models
were then calculated for each perturbation and compared to the nominal ΔDIC value.

Results
Best Assessment Model
The most complex model we considered, which had age-specific selectivities and allowed
for spatial differences in vulnerability and spatial differences as well as time-blocks for
catchability, far outperformed all alternative models (best spatial model, BSM; Table 2.2). No
other model was plausible and the DIC model weight for this model was 1.0. It is instructive to
make pairwise comparisons between models that are identical except for including one of the
effects. In such comparisons simplification invariably led to a poorer fit (larger DIC). The
largest degradation occurred by changing vulnerability from being freely-estimated age-specific
parameters to following a gamma distribution, followed by not allowing for spatial vulnerability,
not allowing for spatial catchability, and then not allowing for time blocks in catchability.
29

Influence of the Spatial Structure Assumption on Assessment Results
Comparisons were made between BSM and the best non-spatial or aggregate model
(BAM; Table 2.2) to evaluate the importance of accounting for spatial population heterogeneity.
The two models were different solely by the inclusion (BSM) and exclusion (BAM) of basinlevel estimates of vulnerability and catchability. Hence, BAM allowed for differences in
vulnerability and catchability at a jurisdictional or fishery defined scale (latitudinal), whereas
BSM extended that to include an ecologically relevant scale (basin; longitudinal) defined by
dispersal patterns. BSM produced much more reasonable fits to all data sources than BAM
given a substantial amount of contrast in the observed data (Appendix C; Figure 2.6-2.9). Mean
deviations between observed values and predicted values were substantially larger for BAM
(compared to BSM) with values ranging from 18-61% (11-19%) for fishery catch and 23-144%
(22-59%) for survey CPE data sources. Deviations between observed and predicted proportions
at age ranged from 4-10% (4-7%) of the predicted value for both fishery and survey data sources.
Estimates of key management parameters were dependent upon the assumptions
regarding spatial structure. Despite having similar overall trends, absolute estimates of total and
age-specific population quantities were substantially different between best models (Figure 2.3).
Compared to BAM, results using BSM suggest an 11% lower mean population size (16% lower
in the last year), a 61% increase in mean instantaneous [fully selected] fishing mortality (70%
increase in the last year), and a 26% decrease in the proportion of older individuals (age-7 and
older) in the population (21% decrease in the last year). The most recent estimates of age-2
walleye recruitment decreased by 6% and estimates of spawning stock biomass (kilograms of
30

age-5 and older walleye) decreased by 19%. The magnitude of the difference between BSM and
BAM estimates increased with age for abundance (negative direction) and fishing mortality
(positive direction; Figure 2.3c-d). Although there was overlap in the posterior distributions for
total walleye abundance between best models, uncertainty associated with these estimates was
substantially reduced using BSM in most years (Figure 2.4). For example, CVs (coefficient of
variation: standard deviation of posterior distribution divided by the highest posterior density
estimate) increased considerably for estimates of abundance (40%) and recruitment (28%) in the
last year when using BAM.
The overall BSM suggested that fishery and survey vulnerability estimates differed by
basin, reflecting longitudinal differences in walleye availability and gear efficiency (Figure 2.5).
In general, vulnerability for younger (smaller) walleye was higher in the western basin, whereas
vulnerability for older (larger) walleye was higher in the central basin. This basin-level contrast
in vulnerability patterns was evident in both the northern (Canadian) and southern (U.S.)
surveys, suggesting that longitudinal differences in vulnerability may be mostly due to
differences in population structure rather than gear efficiency, because gear and survey
techniques differ between Canada and the U.S. BAM estimates were mainly intermediate of
those from BSM, but more closely followed west basin patterns.
The overall BSM suggested that fishery and survey catchability estimates differed by
basin and time blocks (Table 2.3), reflecting temporal and longitudinal differences in how
fishing mortality relates to fishing effort and how catch rates relate to total abundance.
Catchability estimates were larger in the west basin for all data source and time block
combinations, with the exception of larger central basin estimates associated with the Ohio
31

recreational fishery post-1985. The time blocks that were selected to represent major temporal
shifts in catchability seemed appropriate (differences generally greater than 1 standard deviation)
for most data sources. Estimates from BAM were consistent with the smaller of the two basinspecific estimates from BSM. In almost all cases (10 of 12), uncertainty (CVs) associated with
catchability estimates increased when using BAM.

Model Sensitivity
The underlying model structure of the BSM and BAM remained consistent across all
sensitivity trials and was the same as that described in Table 2.2. Model selection results and the
subsequent directional effect on abundance in the last year (2008) were insensitive to data source
weighting schemes and assumptions of natural mortality (Appendix D; Table 2.7). For most
trials, the difference in DIC was similar to the nominal value (ΔDIC = 619). The exception to
this was the assumption related to the effective sample size for age composition data (Neff).
Adjusting the relative importance of age composition data considerably altered ΔDIC values, but
not to the extent required to alter inferences (ΔDIC < 7).

Discussion
The Lake Erie walleye population has been identified as displaying consistent spatial
structuring (Wang et al. 2007; A. Berger unpublished data), likely due to the location of
spawning sites and age-specific dispersal distances from spawning grounds, which suggests that
a homogenous population model may not be the most appropriate. Because explicit movement
information between walleye sub-populations was unavailable, we incorporated spatially
32

referenced vulnerability parameters into a single, spatially implicit population assessment model
to account for the net spatial effects of such differential dispersal behavior. Differences in
vulnerability can ultimately result from disparity in the proportions of walleye at age that are
available for capture (population structure) and from spatial differences in how effective fishing
gear is at retaining walleye (gear efficiency). Data were unable to differentiate which
mechanism was responsible for improved fit when parameters were spatially referenced.
However, we suggest that population structure was the main factor contributing to basin-level
differences in vulnerability. Northern (Canadian) and southern (U.S.) fishery independent
surveys used the same sampling gear within their respective jurisdiction irrespective of sampling
location, yet vulnerability patterns remained different between basins in both cases. Further,
consistent patterns in observed age/size composition that appeared across the lake seemed to be
associated with physical habitat characteristics (Kershner et al. 1999; Wang et al. 2007), linking
what we know about walleye ecology to observed differences in spatial population structure. For
example, larger (older) walleye have been noted to disperse further from warming summer water
temperatures in the western basin to the east than smaller (younger) individuals in search of food
resources in cooler water temperatures to optimize growth (Kershner et al. 1999).
Inferences about the Lake Erie walleye population were affected by spatially referencing
the population dynamics model to account for life history patterns at an ecologically relevant
scale. In particular, assessment results that are used to inform walleye management were
influenced by the choice of best model which included (BSM) or excluded (BAM) basin-level
vulnerability and catchability parameters. Vulnerability estimates from the BAM (homogeneity
assumption) were more similar to those attributed to the west basin in the overall BSM (Figure
33

2.5), which was a result of the aggregate model attempting to optimize fit by following walleye
trends in the more heavily populated (and generally more intensely fished) western basin.
Estimates of catchability from the overall best model also differed by basin suggesting that the
relationship between fishing effort and fishing mortality (and similarly survey CPE and
population abundance) varied by the area where fishing (and the surveys) occurred. Spatial
differences in catchability seem plausible and were somewhat expected given the considerable
contrast in fishable habitat between the west (shallow, low visibility) and central (deep, high
visibility) basins.
There was strong statistical evidence that incorporating spatially referenced parameters at
a scale relevant to walleye dispersal patterns improved model fit, and the change altered
estimates of stock size and fishing mortality. This finding was insensitive to the assumed natural
mortality rate and to alternative data weighting schemes, providing a robust indication of the
importance of accounting for life history variation in stock assessment models. Although the
differences we illustrate are not drastic compared to changes in assessment estimates that are
sometimes seen when assessment models are changed, they are large enough to be of practical
management concern. Divergent population estimates that resulted from the choice of best
model (based on assumptions of spatial population structure) were mainly a consequence of the
interplay between basin-level differences in walleye availability and catchability due to walleye
dispersal patterns. Similar to results for Pacific albacore (Fournier et al. 1998), ignoring walleye
spatial structure significantly reduced the predictive power (precision) of the population dynamic
model.

34

Fisheries management is often guided by harvest policies that utilize state-dependent
control rules to translate current population estimates, such as abundance or biomass, into the
following year’s fishing rate (e.g., total allowable catch). Increasingly often, the selection of a
harvest policy is aided by conducting simulation experiments where performance metrics used to
evaluate alternative policies depend on the chosen assessment model. For example, Cox and
Kronlund (2008) demonstrated important differences (and similarities) in policy performance
between data-based and model-based assessments. Williams (2002) showed that ignoring the
size-structure of discarding rates in the assessment model altered the selected harvest policy,
resulting in harvests above the maximum sustainable yield. More research is needed to evaluate
how robust exploitation policies are to alternative assessment models and assumptions of spatial
population structure (e.g., Punt and Hobday 2009). For example, does accounting for structure
using spatially referenced parameters affect policy performance in a meaningful way over
models that do not spatially reference parameters? Herein, we show that alternative assumptions
regarding population structure can considerably affect quantities necessary for rational
management (e.g., estimates of population size, fishing mortality, and population age structure),
which could ultimately influence harvest policy decisions.
Appropriately accounting for spatial structure in assessments appears to be important.
Previous simulation studies have shown that allowing for spatial structure, when present, can
both reduce bias and improve precision of estimates. For example, Punt (2003) found that less
biased and more precise estimates resulted from separate stock assessments carried out at small
spatial scales as opposed to pooling data across spatial regions. Sub-dividing the stock
assessment into smaller spatial levels can also be convenient for satisfying assumptions (Quinn
35

and Deriso 1999). In contrast, Butterworth and Geromont (2000) showed that biased estimates
of fundamental management parameters can also result when a single homogenous population is
unnecessarily sub-divided. In many cases, the decision to spatially disaggregate observed
information will be dependent upon the level of spatial heterogeneity present in the population
and sample sizes. Hobday and Punt (2009) used an information-theoretic approach to decide on
appropriate assessment spatial scale. Spatially referencing some parameters is one possible
approach when entirely separate stock assessments at a finer scale does not seem appropriate and
explicit modeling of dispersal is not possible. We illustrated this approach for Lake Erie walleye
and justified estimating additional parameters on information-theoretic grounds. Survey data
suggest that walleye age compositions change continually along a longitudinal gradient (Figure
2.2). Future work could investigate whether finer-scale spatial referencing of parameters is
justified for Lake Erie walleye, perhaps by modeling parameters as a function of longitude.
Integrating tagging data into stock assessment models can help facilitate the estimation of
key parameters such as natural mortality or movement rates (Punt et al. 2000; McGarvey et al.
2010) and can reduce uncertainty in spatial assessments (Punt et al. 2000). Yet explicitly
modeling spatial dynamics requires more extensive information (e.g., spatial population
structure, movement, and site-specific demographics) and may propagate uncertainty (Conroy et
al. 1995). In the case of Lake Erie walleye, information about age-specific movement rates (e.g.,
timing and duration) between the west and central basins of Lake Erie would be especially
critical for developing a spatially explicit model, although there could be advantages to
incorporating movements at a finer spatial scale. Future work should investigate the advantages

36

and tradeoffs of incorporating tagging data into a spatially explicit assessment model as data
become available, in contrast with the approach of spatially referencing parameters.
In application, spatially referencing vulnerability parameters to account for regional
differences in distribution (e.g., “fleets” model; Cope and Punt 2011) is appropriate when age- or
size-classes are not uniformly distributed over space and the proportion of each age- or size-class
in each spatial stratum does not change over time (this was generally the case for Lake Erie
walleye). Density-dependent distributions, for example, would be problematic for this approach.
The approach presented here can be a practical way to incorporate spatial population structure
into stock assessments, particularly when the spatial-structure arises from dispersal of a common
pool of recruits such that simply redefining unit stock boundaries inadequately captures
important dynamics.
The assessment models evaluated herein were based on the current walleye assessment
model used as an input to the management process on Lake Erie. Important differences were
from choices we made in how to model vulnerability and data distributions, and were
necessitated by the need to use disaggregated data and basin specific error terms for the
relationships between fishing mortality and effort, in order to make statistical comparisons
between aggregate and spatial models. Consequently, results presented here should be viewed as
providing evidence on the importance of incorporating spatial population dynamics in
assessment models, rather than suggesting specific alternative stock size estimates for
management of Lake Erie walleye.

Acknowledgments
37

The authors would like to acknowledge the Lake Erie Committee, the walleye task group,
and member agencies (Ontario Ministry of Natural Resources, Michigan Department of Natural
Resources, Ohio Department of Natural Resources, Pennsylvania Fish and Boat Commission,
and New York State Department of Environmental Conservation) for engaging in helpful
discussions and for providing access to data. This paper was improved with helpful comments
provided by M. Gore. Support for this research was provided by the Ontario Funding for
Canada-Ontario Agreement (7-02) Respecting to the Great Lakes Basin Ecosystem to Y.Z., Lake
Erie Management Unit of the Ontario Ministry of Natural Resources, the Saginaw Bay Walleye
Club, and Michigan State University.

38

APPENDICES

39

APPENDIX 2A

Main Tables and Figures

40

Table 2.1.—Commercial fishery, recreational fishery, and survey data series relating to both the
western and central basins of Lake Erie that were used to inform analyses. Error structure and
weights refer to that assumed in statistical catch-at-age assessment models. Catch, CPE, and
effort weights are proportional to the inverse of the assumed variance associated with each data
series and normalized to a single estimated variance associated with a standard data series
(Ontario survey). Age composition (proportion) weights correspond to the annual effective
sample size of aged fish (west basin/central basin).
Series

Type

Source

Years

Total Catch
Total Catch

Commercial
Recreational

Ontario
Ohio

1978 - 2008
1978 - 2008

lognormal
lognormal

0.91
0.85

Total Catch

Recreational

Michigan

1978 - 2008

lognormal

0.76

Effort
Effort

Commercial
Recreational

Ontario
Ohio

1978 - 2008
1978 - 2008

lognormal
lognormal

0.89
0.86

Effort

Recreational

Michigan

1978 - 2008

lognormal

0.80

Total CPE
Total CPE

Survey
Survey

Ontario
Ohio/Michigan

1990 - 2008
1983 - 2008

lognormal
lognormal

1.00
0.86

Age Composition
Age Composition

Commercial
Recreational

Ontario
Ohio

1990 - 2008
1978 - 2008

multinomial
multinomial

106/56
156/146

Age Composition
Age Composition
Age Composition

Recreational
Survey
Survey

Michigan
Ontario
Ohio/Michigan

1986 - 2008
1990 - 2008
1983 - 2008

multinomial
multinomial
multinomial

124/110/76
100/395

a

a

a

Error Structure Weight

Ontario = Ontario Ministry of Natural Resources; Ohio = Ohio Department of Natural Resources;
a
Michigan = Michigan Department of Natural Resources. Data available for the west basin only.

41

Table 2.2.—Relative comparison of walleye SCA assessment models describing alternative
hypotheses about the applicability of spatially referencing basins combined with a particular
estimation method to describe assumptions for vulnerability and catchability (see text for further
details). Vulnerability parameters were either estimated freely (unconstrained) or constrained to
follow a gamma function. Catchability (q in Table 2.5) was either assumed constant or allowed
to vary according to discrete blocks of time. Models are ranked according to differences in DIC
(∆DIC) from the model with the least DIC value. K is the estimated effective number of
parameters.
SCA Assessment Models
Vulnerability

Catchability

Estimation

Spatial

Estimation

∆DIC

K

yes
yes
yes
yes

free
free
free
free

yes
yes
no
no

time blocks
constant
time blocks
constant

0.0
62.0
119.5
165.0

180.4
177.8
161.8
169.3

no
no
yes
yes
yes
yes
no
no

free
free
gamma
gamma
gamma
gamma
gamma
gamma

no
no
yes
yes
no
no
no
no

time blocks
constant
time blocks
constant
time blocks
constant
time blocks
constant

619.4
645.1
2712.2
2749.3
2869.1
2874.5
3272.4
3289.8

133.9
136.0
154.8
144.1
129.1
124.2
121.7
119.1

Spatial
a

b

a

Best spatial model (BSM; with basin-level referenced parameters) and
best aggregate model (BAM; no basin-level referencing).

42

b

Table 2.3.—Spatially-referenced and time-varying values of catchability (q) for each model
component as estimated by the overall best walleye spatial (BSM) and aggregate (BAM) models.
Note that posterior standard deviations (SD) are presented on a different scale than highest
posterior density estimates.
Spatial (west)
Data Source
Fishery
Commercial

Time Block

-5

Spatial (central)
-6

-5

Aggregate
-6

-5

-6

q (10 ) SD q (10 ) q (10 ) SD q (10 ) q (10 ) SD q (10 )

1978 - 1986
1987 - 2000
2001 - 2008

0.88
0.67
0.72

1.74
0.96
1.37

0.50
0.39
0.39

0.97
0.57
0.78

0.56
0.38
0.38

1.10
0.58
0.89

Recreational (OH)

1978 - 1985
1986 - 1993
1994 - 2003
2004 - 2008

8.02
1.58
2.83
2.13

13.33
2.76
4.46
4.98

5.76
2.74
4.14
3.57

11.69
5.24
6.67
8.40

5.95
1.68
2.48
2.09

11.02
3.36
4.38
5.75

Recreational (MI)

1978 - 1985
1986 - 2003
2004 - 2008

2.81
1.50
0.98

6.05
1.96
2.45

-

-

3.00
1.32
0.87

8.61
2.25
3.55

1990 - 1998
1999 - 2008

0.06
0.05

0.07
0.07

0.02
0.01

0.02
<0.01

0.03
0.02

0.05
0.03

1983 - 1986
1987 - 2003
2004 - 2008

0.29
0.41
0.14

0.57
0.48
0.29

0.20
0.26
0.11

0.40
0.30
0.23

0.21
0.29
0.11

0.41
0.38
0.31

Survey
Ontario
Ohio/Michigan

43

.1.—The west basin (WB central basin (CB), a east basin
B),
and
n/Pennsylva ridge
ania
Figure 2.
(EB/PR) geomorphol
logic regions of Lake Er have disti
rie
inct bathyme
etric and wa quality
ater
attributes The main walleye pop
s.
pulation occu in the we and centr basins.
urs
est
ral

44

.2.—Mean age composit
a
tion (%) of recruited wal
r
lleye smooth over 20 minute
hed
Figure 2.
longitudi bins (defined by bin midpoint). Age compo
inal
n
osition chang markedly with longitude
ged
y
as relativ older (la
vely
arger) walley tend to mo further e (central basin) while younger
ye
ove
east
e
(smaller) walleye ten to remain near spring spawning gr
)
nd
rounds (wes
stern basin). Data are fro
om
gillnet su
urveys (Septe
ember – Oct
tober) for ye when bo Ontario a Ohio/Mi
ears
oth
and
ichigan surveys
were con
nducted conc
currently (19 – 2008).
990

45

Figure 2.
.3.—Highest posterior de
t
ensity estimates of age-2 and older w
2
walleye abun
ndance (mill
lions
of fish; panel A) and fully selecte instantane
p
ed
eous fishing mortality (p
g
panel B) from the overal
m
ll
best mod with basin
del
n-level param
meters (BSM solid line) and the bes model wit
M;
)
st
thout basin-l
level
paramete (BAM; dashed line). The median (bar) perce differenc (calculated across yea
ers
n
ent
ce
d
ars,
1978-200 circles) between estim
08;
b
mates from BSM and BA decreas with age f walleye
B
AM
se
for
abundanc (panel C) and increase with age for fishing m
ce
fo
mortality (pan D).
nel

46

.4.—Posterio distributio for estim
or
ons
mates of annu total walleye abunda
ual
ance (age-2 a
and
Figure 2.
older) fro the best spatial (BSM solid line) and aggreg (BAM; d
om
s
M;
)
gate
dashed line) models. Th
he
peak of each curve re
e
epresents the highest pos
e
sterior densit estimate w
ty
while the spr
read represe
ents
estimated precision.
d

47

.5.—Compar
rison of vuln
nerability est
timates (loge; ± 1 poster SD) betw
rior
ween the ove
erall
Figure 2.
best mod (BSM) which include basin-leve spatially re
del
w
es
el
eferenced vu
ulnerability p
parameters f
from
the west (solid) and central (dash basins and the best agg
c
h)
d
gregate mod (BAM) w
del
which does n
not
spatially reference ba
asins (dotted see Table 2.2 for descr
d;
2
ription). Est
timates were relative to agee
48

4, the reference level, which was set to one (zero on the loge scale) and thus had no uncertainty
associated with it. In both models, recreational fishery age-2 vulnerability was allowed to
change in 2004 (not shown but declined in all cases) because of a regulatory amendment
increasing the minimum harvestable length.

49

APPENDIX 2B
Description of Symbols and Equations

50

Table 2.4.—Descriptions of symbols in Table 2.5 and 2.6 describing the base assessment model.

Symbol

Description

M
λf
λs
λε

Subscript Indicators (range/level)
age (2-7+)
year (1978-2008)
fishery (commercial = 1; recreational (OH) = 2; recreational (MI) = 3)
survey (Ontario = 1; Ohio/Michigan = 2)
region (west basin = 1; central basin = 2)
recreational vulnerability time block (1978-2003; 2004-2008)
Assumed Values
-1
instantaneous rate of natural mortality (0.32 yr )
weight for fishery catches (relative to standard data source; Table 1)
weight for survey index catch rates (relative to standard data source; Table 1)
weight for fishery effort deviations (relative to standard data source; Table 1)

C y,r,f
I y,r,s
P y,a,r,f
P y,a,r,s
n
E y,r,f
w y,a

Observed Data
total numbers of walleye caught by fishery and region
survey abundance index
proportions of catch at age by fishery and region
proportions at age from survey abundance index
sample size (number of years data)
fishery effort
mean weight

Ry
Ga
qf
qs
v a,f,k
v a,s
σ std
ε y,r,f

Estimated Parameters
Recruitment for each year
Initial abundances at age (>2) in the first year
catchability coefficient for each fishery
catchability coefficient for each survey
vulnerability at age for each fishery and time block
vulnerability at age for each survey
coefficient of variation of standard data source (Ontario survey)
effort deviations

F y,a,r,f
Z y,a
N y,a
Ny
By

Calculated Parameters
instantaneous fishing mortality rate
instantaneous total mortality rate
abundance at age in year y
total abundance in year y
total biomass in year y

a
y
f
s
r
k

51

Table 2.4.—(cont’d).
, , ,
, ,
, , ,
, ,
, , ,
, , ,

eff

N
σf
σs
σε

model predicted catch at age
model predicted total catch
model predicted survey abundance index at age (catch per unit effort)
model predicted survey abundance index
model predicted proportions of catch at age
model predicted proportions at age from survey abundance index
effective sample size
coefficient of variation for fishery catches (σ std / λf)
coefficient of variation for survey index catch rates (σ std / λs )
standard deviation for effort deviations (σ std / λε)

52

Table 2.5.—Equations for population and observation submodels used in the base walleye
assessment model.
Equation

Reference

Population Submodel
Recruitment and initial numbers at age

	

,

(2.5.1)
(2.5.2)

,

Mortality rates

∑ ∑

, , ,

, , ,

,

, , 	

, , ,

, ,

,

(2.5.3)
, ,

(2.5.4)

, ,

, ,

(2.5.5)

Population dynamics
,

|

,

,

,

,

,

∑

,

(2.5.6)
,

,

(2.5.7)
(2.5.8)

,

Observation Submodel
, , ,

, , ,

, , ,
,

	

,

(2.5.9)

,

, , ,

(2.5.10)

, ,

, , ,
, , ,

1

,

,

.

,

(2.5.11)

, , ,

(2.5.12)

, ,

53

Table 2.6.—The objective function was the posterior negative log density calculated by summing
weighted individual normal and log-normal likelihood and prior components for all source
combinations. Highest posterior density estimates minimized this function.
Components

Source

,

,

∑

,

, ,

∑

∑

	

r1,2; f1,2,3	

, ,
, ,

∑

,

∑

, , ,

ln	

∑

,

∑

, , ,

ln	

(2.6.1)

r1,2; s1,2,3

, ,

, ,

Reference

(2.6.2)

	

r1,2; f1,2,3	

	

(2.6.3)

, , ,

r1,2; f1,2,3	

	

(2.6.4)

r1,2; s1,2,3	

	

(2.6.5)

, , ,

		

	

54

APPENDIX 2C

Comparisons of Observed and Predicted Values

55

.6.—Time se
eries of obse
erved (filled circle) and p
predicted (BSM: solid lin BAM:
ne;
Figure 2.
dashed li
ine) fishery harvest (thou
h
usands of fis for comm
sh)
mercial (Onta waters) and recreati
ario
ional
(Ohio and Michigan waters) fisheries in the west and cen
w
ntral basins, Lake Erie.

56

Figure 2.
.7.—Time se
eries of obse
erved (filled circle) and p
predicted (BSM: solid lin BAM:
ne;
dashed li
ine) fishery mean age for commercia (Ontario w
m
r
al
waters) and r
recreational (Ohio and
Michigan waters) fish
n
heries in the west and ce
e
entral basins Lake Erie.
s,

57

.8.—Time se
eries of obse
erved (filled circle) and p
predicted (B
BSM: solid li BAM:
ine;
Figure 2.
dashed li
ine) CPE (ca
atch-per-effo from ann Ontario gill net surv
ort)
nual
veys and com
mbined
Ohio/Mic
chigan gill net surveys in the west an central ba
n
n
nd
asins, Lake E
Erie.

58

Figure 2.
.9.—Time se
eries of obse
erved (filled circle) and p
predicted (B
BSM: solid li BAM:
ine;
dashed li
ine) survey mean age fro annual Ontario gill net surveys an combined Ohio/Michigan
m
om
O
nd
d
h
gill net su
urveys in the west and central basins Lake Erie.
e
s,
.

59

APPENDIX 2D

Sensitivity Analysis

60

Table 2.7.—Sensitivity to the selection of the overall best spatial (BSM) and aggregate (BAM)
models resulting from data source weighting and natural mortality (M) assumptions. For all
cases, the best spatial and aggregate model was structurally the same as the best models shown in
Table 2.2. Upward and downward adjustments (%) to the nominal assumption were made for
each identified model component. Data source weights were implemented in the objective
function to control how strongly each data set influenced model fit. These included commercial
and recreational effort and total catch, survey total catch-per-effort (CPE), and the effective
sample sizes (Neff) for commercial, recreational, and survey age composition data. Estimated
total abundances (N) are shown for the last year (2008). Differences in DIC (ΔDIC) show the
relative improvement in model fit (lower DIC values) when basin-level spatially referenced
parameters were applied.
BSM
Model Component

Adjustment DIC

N

BAM
DIC

N

ΔDIC

Data Source Weights
effort

200
50

70320 43.05
70341 46.94

70930 51.17
70979 52.95

610
638

catch

200
50

70301 46.74
70355 43.43

70948 51.87
70967 51.83

647
612

Index survey CPE

200
50

70390 44.23
70310 46.46

70997 52.80
70933 51.10

607
623

Age comp. (Neff)

200

133202 45.52

134291 47.32

1089

50

35675 46.52

36057 52.99

383

125
75

70355 57.69
70349 38.42

70963 64.70
70945 41.97

608
596

Mortality
M

61

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62

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68

CHAPTER 3
Improving Fishery-Independent Indices of Abundance for a Migratory Walleye Population

69

Abstract
The primary goal of many fishery surveys is to provide an unbiased representation of
population trends. Even when surveys are designed to be representative of the population being
assessed, there are often biotic and abiotic factors other than abundance that can vary over time
and influence catch rates and thus inferences about abundance trends. This is particularly true
for highly mobile species such as walleye (Sander vitreus) because of interannual variation in the
timing, extent, and duration of movements. We developed general and generalized linear mixed
models to standardize Canadian and United States fishery-independent surveys used to provide
an index of basin-level walleye population trends in Lake Erie (1983-2008). In Canadian waters,
the probability of a non-zero catch was associated with the type of gill net set (“canned” had a
positive effect over “bottom”; +), the presence of hypoxia (-), and secchi depth (-). Positive
catch rates were associated with the set type (+), water depth (+), and the presence of hypoxia
(-). In United States waters, survey catch rates were associated with secchi depth (-) and surface
water temperature (+). For each case, the best model included random effects (interactions
between year, week, basin, and sub-basin) which accounted for a modest amount of the total
variation. General abundance trends were similar between the standardized and nominal indices,
but we observed substantial annual variation in the direction and magnitude of the difference
between indices. Overall trends in abundance differed markedly between basins due to
discrepancies in availability (population structure) and selectivity (gear efficiency) to fishing
gear. We recommend the use of standardized indices for walleye population assessments
because these account for factors influencing catch rates other than changes in abundance.

70

Introduction
The Lake Erie percid fishery is a socially and economically valuable resource,
representing nearly a quarter of the total commercial harvest (metric tons) and recreational effort
(angler-hours) in all the Laurentian Great Lakes combined (Bence and Smith 1999; Brown et al.
1999; Koonce et al. 1999). Prior to the 1960s, the fishery included major contributions from
sauger (Sander Canadensis), walleye (Sander vitreus), yellow perch (Perca flavescens), and blue
pike (Sander vitreus gl.); more recently the fishery has become solely dependent upon catches of
walleye and yellow perch (Ryan et al. 2003). Maintaining a healthy walleye population has been
recognized as a necessary condition to achieve broader fish community goals (Ryan et al. 2003),
because walleye, the dominant terminal predator in much of the lake, act to stabilize the food
web with top down predatory control (Knight and Vondracek 1992; Makarewicz and Bertram
1993). As the sport and commercial fisheries are highly valued, ensuring long-term
sustainability of the walleye population remains a paramount management objective (Locke et al.
2005). Over the past decade, annual landings of Lake Erie walleye have exceeded 2 800 mt on
average, 61% from commercial harvest and 39% from recreational harvest (WTG 2009).
Stock assessments are conducted to provide decision makers with pertinent regulatory
information such as population trends, demographic rates, and occurrences of overfishing in
order to implement effective harvest management. A statistical catch-at-age (SCA) stock
assessment model, informed by both fishery-dependent and fishery-independent data, is used to
estimate Lake Erie walleye population parameters of interest to decision makers (WTG 2009).
Fishery-independent catch-per-effort (CPE) data are collected from annual research surveys and
implemented as auxiliary time series indices of relative abundance to help improve SCA
71

assessment model accuracy and precision (Deriso et al. 1989; Quinn and Deriso 1999; Chen et
al. 2003). A basic assumption in many stock assessments is that CPE is directly proportional to
average abundance with the coefficient of proportionality called catchability – the proportion of
the population caught with one unit of survey effort (Hilborn and Walters 1992). There are
many reasons why this direct proportionality might not be the case (e.g., hyperstability, cf
Hilborn and Walters 1992), but the assumption remains very common in fishery assessments. In
addition, there are many factors other than abundance that can influence survey catch rates and
potentially render the nominal survey index misleading. For example, spatial and temporal
variation in environmental conditions, such as water temperature and clarity, are likely to
influence the encounter rates of fish with survey gear. Although methods exist to allow for
spatial and temporal variations in catchability within stock assessment models (e.g., state space
methods; Schnute 1994; Wilberg et al. 2010), large changes at unknown times or locations still
pose substantial difficulties. Consequently, correcting for known factors affecting abundance
indices remains a priority (NRC 1998; Wilberg et al. 2010).
One way to account for confounding factors (and thus decrease the extent to which
catchability varies) is to develop a standardized index by fitting statistical models to catch and
effort data and then extracting the temporal effect of interest (Quinn and Deriso 1999; Maunder
and Punt 2004; Ye et al. 2005). This process usually involves selecting data points and
explanatory variables to be used in the analysis and an appropriate statistical model (e.g., general
or generalized linear models) and error distribution (e.g., Poisson, lognormal, or gamma). On
Lake Erie, two fishery-independent gill net surveys are used to collect walleye CPE data to index
the population: a Canadian survey administered jointly by the Ontario Ministry of Natural
72

Resources and the Ontario Commercial Fisheries’ Association to the north, and a United States
survey administered jointly by the Ohio Department of Natural Resources and the Michigan
Department of Natural Resources to the south (Figure 3.1). The two surveys are treated as
independent indicators of relative abundance because they are assumed to have differing abilities
to capture fish of a given size or age (i.e., selectivity patterns).
The Lake Erie walleye population does not appear to be distributed randomly. Instead
there is consistent longitudinal spatial patterning of individuals by size (or age) such that a
greater proportion of larger, older individuals tend to migrate further from spring spawning
grounds in the west basin than smaller, younger individuals, apparently to optimize growth by
taking advantage of seasonal water quality and foraging conditions favorable to these older fish
(Kershner et al. 1999; Wang et al. 2007; Berger et al. in press). Surveys occur in autumn during
a time when migratory walleye are actively returning to the west basin (Wang et al. 2007; pers.
comm., C. Vandergoot, Ohio Department of Natural Resources, 1 June 2011), and interannual
variation in the timing and extent of migration could present inconsistencies in survey data,
altering survey catchability and obscuring abundance trends. Given that the portion of the target
population that is available can vary spatially and seasonally, these factors are important to
consider when interpreting what survey CPE indicates about abundance.
A wide range of factors have been included in statistical models developed to standardize
catch rates: location (Punt et al. 2000; Tian et al. 2009), time (Rodriguez-Marin et al. 2003;
Deroba and Bence 2009), vessel (Battaile and Quinn 2004; Helser et al. 2004; Tyson et al. 2006),
catch rates of other species (Punt et al. 2001), and environmental factors (Buijse et al. 1992;
Smith and Page 1996; Hart et al. 2011). For example, Smith and Page (1996) identified water
73

temperature and salinity as factors influencing trawl survey catch rates of Atlantic cod. The use
of environmental variables has been recognized as an important contribution when standardizing
data or accounting for varying catchability (NRC 1998). In this paper, we examine how sitelevel environmental variation in low dissolved oxygen (hypoxia), surface water temperature,
water clarity and depth, and set type of survey gear influence walleye catch rates.
The stock assessment model used to assess the status of Lake Erie walleye considers
observed population trends from fishery-independent surveys as highly informative (i.e., surveys
have comparatively more influence on how the model is fit than fishery-dependent data; Berger
et al. in press; WTG 2010), and thus have considerable influence on resulting population
estimates used for management. Therefore, it is critical to have a fishery-independent index that
as best as possible accounts for factors that might confound real abundance trends. We sought to
1) develop a standardized index of relative abundance from annual survey data for Lake Erie
walleye; 2) identify a set of factors that significantly contribute to the standardized index; and 3)
compare trends between standardized and nominal (non-standardized) CPE data.

Methods
Study Area
Lake Erie is the smallest of the Laurentian Great Lakes in terms of volume yet is the most
productive (Beeton et. al. 1999). The lake consists of three main basins. The west basin (mean
depth = 7.4 m) and central basin (18.5 m) support warm and cool-water fisheries, while the east
basin (24.4 m) is dominated by cool and cold-water species. Walleye are most abundant in the
west and central basins of Lake Erie; although smaller populations do reside in the eastern basin;
74

it is this west/central basin population for which stock assessment and harvest policy
management procedures have been used to set annual harvest levels. The analyses presented in
this paper focuses on this population.

Survey Design
Catch rates (or CPE) were computed from annual gill net survey data as the total catch
(numbers of age-2 and older walleye) divided by the total effort (days standard net fished) at
each site. Nets were set and retrieved generally during daylight hours, allowing them to fish over
a single night. Survey sites were rarely sampled more than once in the same year (<2% of sites).
In such cases, catch rates were averaged across repeated samples after removing foul sets. A
subset of selected sites were omitted (15% CAN; 7% US) from our analyses because of missing
effort, location, or environmental covariate data. A different standard gill net configuration was
used in Canadian and U.S. waters, although configurations remained consistent through time
within each jurisdiction. The number of survey sites sampled differed by year, basin, and
jurisdiction (Table 3.1). The annual index of abundance was calculated as the average catch rate
across sites for each year and jurisdiction (non-standardized version; hereafter referred to as the
nominal index).
The Canadian gill net survey was initiated in 1989 as a fish community index (OMNR
2009) and expanded to include sites in both the west and central basins in 1990. Sampling
locations were selected at random each year among bottom depth strata (west basin: 0-10 and
>10 m; central basin: 0-15, 15-20, and >20 m) with the number of locations in each stratum
being proportional to area (Figure 3.1). At each location, gill nets were set on the bottom and
75

suspended in the water column (“canned”) at a depth determined by bottom depth and random
selection (west basin: 1.8m; central basin: 5m, 11m, 17m). Individual sites were thus uniquely
identified by latitude, longitude, and depth. In general, west basin sites were sampled in
September and central basin sites in October to mid-November. The standard Canadian survey
gill net set consisted of 25 monofilament mesh panels (each 15.25 x 1.8 m) graded at 1.25, 1.5,
1.75, 2.0, 2.25, 2.5, 2.75, 3.0, 3.5, 4.0, 4.5, 5.0, 5.5, and 6.0 inch increments (32 to 152 mm) for a
total net length of 0.38 km. Two panels of each mesh size were fished, except for the smallest
sized (<2.0 in) meshes where a single panel was fished.
The U.S. gill net survey was initiated in 1978 to primarily index walleye and white bass
and expanded to include sites in both the west and central basins in 1983 (ODW 2009; Thomas
and Hass 2009). Sampling occurred at fixed locations throughout the west basin and largely
along the western half of the central basin during the month of October. In the central basin,
sites were selected along transects perpendicular to shore and stratified by depth (<5, 5-10, 1015, 15-20, and >20 m). Standard U.S. survey gill nets were fished suspended in the water
column (1.8 m below the surface) at each location. Each net set consisted of 13 randomly
ordered nylon multifilament mesh panels (each 30.5 x 1.8 m) graded from 2.0 to 5.0 inches (51127 mm) in 0.25 inch (6 mm) increments for a total net length of 0.40 km.

Confounding Variables
Temporal, spatial, and environmental variables were identified as prospective covariate
factors based on prior knowledge of walleye movement and habitat selection behavior, and the
availability of relevant data. Separate analyses were conducted for Canadian and U.S. surveys
76

because of the difficulty in separating spatial effects from differences in how the surveys were
implemented. Factors associated with Canadian survey sites that were examined included year
(1990-2008), week (ordered 1 to 8 by Julian days; week 1 and 8 represented 14 days to capture
sites sampled unusually early and late), basin (West, Central), sub-basin (W1,W2,C1,C2,C3,C4;
Figure 3.1), surface water temperature (°C), secchi depth (m), water depth (m), the presence of
-1

hypoxia (<4mg·L O2), and the type of set for gill nets (“bottom”, “canned”). In U.S. waters,
factors examined included year (1983-2008), week (ordered 1 to 6 by Julian days), basin, surface
water temperature, secchi depth, water depth, and hypoxia. Surface water temperature, secchi
depth and water depth were treated as continuous variables; all others were treated as categorical
2

variables. Correlations among the environmental covariates were low (max r = 0.15), so
analytical problems due to collinearity (Maunder and Punt 2004) were not considered serious.
Preliminary analyses based on sample sizes and model selection results (see Model Selection
Procedure) indicated the use of week over bi-week as an intra-annual temporal factor and the
inclusion (Canadian) and exclusion (U.S.) of sub-basin as a spatial factor nested within basin to
further account for the effect of sampling location on catch rates.

Models to Standardize Catch Rates
One difficulty with the Canadian survey CPE data was the high proportion of sites with
zero catch (0.364; Figure 3.2). A large number of sites with zero catches can invalidate model
assumptions, restrict analytical capabilities (e.g., log transformations), reduce estimator
efficiency, and influence ensuing inferences if not properly handled (Pennington 1983; Maunder
and Punt 2004). We therefore applied a delta approach (“Delta models”) within a generalized
77

linear mixed model (GLMM) framework (Aitchison and Brown 1957; Lo et. al. 1992; Vignaux
1994), which has been shown to lead to more consistency between model assumptions and
observed catch rates (Ortiz and Arocha 2004). The delta approach is a two-stage process
whereby the proportion of survey sites with a non-zero CPE is modeled first (a Bernoulli process
often evaluated using the binomial error distribution) followed by a model evaluating CPE given
that it is not zero (often using the lognormal, gamma, or censored versions of the Poisson or
negative binomial error distribution). The relative abundance index is then calculated as the
probability of a non-zero catch multiplied by the expected CPE given that it is non-zero (Punt et.
al. 2000). Here, we assumed the proportions of non-zero catches followed a binomial error
distribution and positive CPE values followed a lognormal error distribution. The lognormal was
chosen because of a good fit to the relationship between the variance and mean of observed
walleye CPE (Figure 3.3). Other error distributions (gamma and censored Poisson and negative
binomial) did not result in a better fit to these data. The logit link function (loge (x) – (loge(1 x))) was used to map the nonlinear binomial response data (zero or non-zero catch) to the linear
predictors.
General linear mixed models were fitted to standardize U.S. survey CPE data because
assumptions of normality were reasonably met using a loge transformation (log(x+1)), the
proportion of sites with no catches was small (0.016), and because the lognormal error model fit
observed data reasonable well (Figure 3.3). Subsequent analyses revealed that results were
insensitive to the choice of dealing with zero catches (simply discarding sites with zero catches
or adding a small constant (CPE+1) before log-transforming).

78

Prospective factors were identified as either fixed or random effects based on properties
of the data (e.g., explicit use of all possible levels of an effect would warrant a fixed effect), the
theoretical scope of inference desired, and the anticipated presence of random variations in
distribution among levels of a particular factor or from statistical interactions. Fixed effects
included year (y), week (w), basin (b), sub-basin (l), surface water temperature (t), secchi depth
(s), water depth (d), presence of hypoxia (h), type of gill net set (n), and the interaction between
year and basin (part of the effect of interest; described further below). Random effects included
all other 2, 3, and 4-way interactions with year, basin, sub-basin, and week. The distribution
associated with each random effect was assumed to be normal (on the logit scale for binomial
data and on the log scale for positive data) with a mean of zero and a variance estimated by the
model.
For the Canadian survey, the fully parameterized mixed model for the binomial case
where observations were whether CPE was positive or not was

g(E(Xywbtsdh)) = u + αy + αw + αb + αl + αt + αs + αd + αh + αn + αyb + βyw + βyl + βwb +
βwl + βbl + βywb + βywl + βybl + βwbl + βywbl;

and the mixed model for the lognormal case on CPE given that CPE was positive was

loge(CPEywbtsdh) = u + αy + αw + αb + αl + αt + αs + αd + αh + αn + αyb + βyw + βyl +
βwb + βwl + βbl + βywb + βywl + βybl + βwbl + βywbl + εywbltsdhn.
79

For the United States survey, the fully parameterized mixed model with lognormal error was

loge (CPEywbtsdh+1) = u + αy + αw + αb + αt + αs + αd + αh + αyb + βyw + βwb + βywb
+εywbtsdh.

The function g(E(Xi)) is the inverse of the logit link function and specifies the expected
proportion of positive CPE values from individual binomial observations; u is the overall mean
evaluated at the reference level for categorical effects and the mean value for continuous effects
(Table 3.2); αi is the parameter coefficient for fixed effect i; βi is the parameter coefficient for
random effect i; and εi is the residual error term. All analyses were conducted using the lme4
package (Bates et al. 2011) implemented in the R statistical computing environment (R Core
Development Team 2011).

Model Selection Procedure
Reduced models (i.e., fewer parameters) were evaluated for improved goodness of fit by
using Akaike’s information criterion corrected for small sample sizes (AICc) to select the best
model (Akaike 1973; Burnham and Anderson 2002). Following Deroba and Bence (2009), a
modified backward selection approach was used to compare alternative mixed models for each
survey dataset because of the large number of possible models (all subsets ≥ 56 models). The
80

best set of random effects was identified first while holding all fixed effects constant by dropping
those random effects from the final model that appreciably deteriorate model fit (a change in
AICc (ΔAICc) of more than 2), beginning with the higher order interactions. All subsets of fixed
effects were then evaluated using the best set of random effects. Lognormal error models were
fit using restricted maximum likelihood (REML; McCulloch and Searle 2001) when selecting
among random effect components and by maximum likelihood when selecting among fixed
effect components. After a final model was chosen the model was fit using REML. The
binomial model was fit by maximum likelihood using a Laplace approximation to integrate out
random effects in all cases.
The relative importance of specific factors affecting walleye survey indices was assessed
by calculating the difference in AICc from the best model and a model reduced by the factor of
interest (ΔAICc = AICc reduced model - AICc best model). In this way, factors associated with
larger ΔAICc values particularly influenced model fit, and thus were identified as a significant
source of undesired variation in the abundance index. The fixed effects of year, basin and the
interaction of year and basin were not assessed in this manner because these factors were kept in
the final model to describe the annual abundance trend of interest regardless of assessed
importance (as measured by ΔAICc).

Extraction of Standardized Indices
A basin-level annual index of abundance was extracted from the final model for each
survey. To do so, all other factors included in the final model were set to their respective
81

reference levels (categorical variables) or mean values (continuous variables) (Table 3.2). For
the delta-lognormal approach to handling zero catches, the Canadian standardized index was
calculated by multiplying the probability of a nonzero catch (estimated from best binomial error
model) by the expected catch rate given that the catch was nonzero (estimated from lognormal
error model) for each basin and year combination (Punt et. al. 2000). The United States
standardized index was simply the extracted basin by year expected catch rates. Binomial
estimates were back transformed to proportions using the inverse logit function. Log
transformed estimates were back transformed to mean values by applying the standard bias
adjustment:

CPE

,

exp

	

1,

where τ is the estimated effect for each basin and year combination (i.e., αy + αb + αyb), and s is
the standard error of τ. Approximate confidence intervals were calculated by back transforming
loge intervals for log-normal models (Candy 2004) and by applying a normal approximation of
the loge catch rate for delta-lognormal models (Shono 2008). Confidence intervals represent
error bounds related to a change in the year effect from the reference level (first year in this
case).

Results

82

A single best model was specified according to AICc for each data set (Canada zero/nonzero; Canada positive CPE; US CPE). In each case, the overall best model included both
random- and fixed-effect factors. Despite the fact that several alternative, yet plausible models
were identified (ΔAICc < 2), we present results from the single best model because other
plausible models differed solely by the addition of a single parameter that, in all cases, had an
estimated 95% confidence bound overlapping zero and resulted in similar abundance trends
(more than 0.99 correlation with the single best model).
There were differences in the selection of random effects (i.e., interaction terms between
spatial and temporal factors used to account for variance in CPE) for each data set (Table 3.3).
Positive random variations in non-zero Canadian survey CPE were apparent among years,
weeks, basins and sub-basins, although the predominant source of variation (12% of the total)
was attributed to spatial differences at the smallest resolution evaluated (i.e., the basin and subbasin interaction term (βb,l), Table 3.3). A moderate amount of the total variance (13%)
associated with the probability of a non-zero catch in Canadian waters was attributed to the
interaction among year, week, and sub-basin factors. In U.S. waters, a small amount of the total
variance in loge(CPE+1) was attributed to weekly differences in sampling time for each year and
basin. In all three cases, the amount of the total variation explained was small relative to the
residual variation.
The overall best fixed effects model for each data set included both categorical and
continuous environmental variables (Table 3.4). For the Canadian survey, the probability of a
non-zero catch was associated with, in order of importance, set type (“canned” had a positive
83

effect over “bottom”; +), the presence of hypoxia (-), and secchi depth (-). When catches were
non-zero, the catch rate was associated with the set type (“canned”; +), water depth (+), and the
presence of hypoxia (-). The salient factor influencing Canadian survey catch rates was the type
of net set, the factor describing the general location in the water column where standard gill nets
were set (either “canned” at depth or on the bottom), as drastic declines in model fit occurred
when it was removed (Table 3.4). For the United States survey, catch rates loge(CPE+1) were
associated with secchi depth (-) and surface water temperature (+). However, secchi depth had a
greater influence on model fit (Table 3.4). Factors that marginally influenced model fit but were
not incorporated into the final model included surface water temperature (CAN models) and the
presence of hypoxia (US model).
Standard general and generalized linear model diagnostics were used to evaluate the
goodness of fit for models used to standardize fishery-independent surveys. For both Canadian
(Figure 3.4) and United States (Figure 3.5) surveys, positive catch rates fit reasonably well to the
log-linear model. Plots of observed versus expected values (panel A) indicated that these models
did an adequate job reducing variance in the data, however some lack of fit was apparent at the
lowest CPE values. Residuals seemed to behave adequately in accordance with model
assumptions; no trend with the expected value (model specified correctly, panel B),
homoscedastic (constant variance across expected values, panel C), and appeared to be normally
distributed on the loge scale (panel D). Additionally, there was no evidence of overdispersion or
extra binomial variation (variance inflation factor ( ̂ ) ~ 1) related to the full, fixed effects only
model describing the proportion of non-zero catches in Canadian waters. The variance inflation
factor ( ̂ = 0.98) was estimated by taking the ratio of the residual deviance to the residual degrees
84

of freedom. Quantile-quantile plots provided graphical evidence that the assumption of
normality for random effects was reasonably met (not shown here).
After accounting for potential confounding factors, the coefficients describing annual
differences by basin (αy, αb, and αy,b) from the overall best models were used to develop
standardized indices of walleye abundance, and compared to nominal indices (lower panel of
each quadrant, Figure 3.6). In general, years with the highest- and lowest-ranked indices were
similar between model-based (standardized) and data-based (nominal) approaches. However,
rankings differed considerably among basins and surveys in many cases. In Canadian waters, for
nd

example, the 2

highest central basin standardized abundance index in the time series occurred
th

in 2006, whereas the west basin 2006 index was the 10 highest. Similarly in U.S. waters, the
rd

th

1996 central basin index was ranked 3 highest, yet it ranked much lower (14 ) in the west
basin. Since 1990, when Canadian and U.S. surveys operated concurrently, the single highest
standardized Canadian abundance index was distinctly in 2005 in both basins, due largely to a
very strong 2003 year class showing up in the 2005 survey. The 2003 year class did not show up
th

th

as strongly in U.S. western and central basin surveys (2005 ranked 7 and 4 , respectively).
General abundance trends were mostly similar between standardized and nominal indices
(nominal value within standardized 95% confidence interval; Figure 3.6) for each survey and
basin combination. Because indices are relative, a constant difference in scale between
standardized and nominal indices was not of importance. However, there was noticeable annual
variation in the direction and magnitude of the difference, suggesting that standardized surveys
indicate a different index of walleye abundance compared to the nominal survey. This can best
85

be seen by plotting the proportional difference (PD; upper panels, Figure 3.6) between the two
indices and looking for departures from a constant PD. Hence, PD values are unit less and
indicate how many times greater the nominal index is compared to the standardized index.
Although annual variability in PD was present in all cases, there was some evidence that this
variation was trending with a decreasing PD in the Canadian central basin index and an
increasing PD in the United States western basin index. A trend in PD suggests that factors not
accounted for in the nominal abundance index have a directional temporal effect on the
standardized index, ultimately suggesting deviating abundance trends between the nominal and
standardized indices or a differential trend in catchability that is not accounted for by factors
used in the analysis.

Discussion
Fishery-independent surveys have been used to assess relative changes in Lake Erie
walleye population abundance over time. Our model of standardized catch rates suggested a
different temporal pattern of abundance compared to nominal catch rates for each survey and
basin combination. In some cases, the standardized index suggested changes in year-to-year
abundance in the opposite direction as the nominal index, and the difference between standard
and nominal indices may be trending across the time series. The former implies a completely
opposite indication of population status in a given year (i.e., from increasing to decreasing or
vice versa). The latter is of particular concern because it implies that the nominal index could be
incorrectly characterizing relative abundance at an increasing or decreasing rate through time,
thereby misleading managers and potentially affecting management decisions. Although in
86

many cases the nominal index was within the standardized estimated 95% confidence interval,
we recommend the use of the standardized index because it accounts for inconsistencies in
survey data not attributed to changes in abundance.
Discrepancies in abundance trends between surveys could be a result of spatial
differences in availability (population structure) and selectivity (gear efficiency) to fishing gear
or due to differences in survey design and sample sizes (Table 3.1). There are clear differences
in walleye population structure longitudinally in Lake Erie as a result of spawning activity and
other seasonal environmental conditions (Kershner et al. 1999; Wang et al. 2007; Berger et. al. in
press), however latitudinal differences, as defined by the international border, are less clear. A
broader range of individuals at size were vulnerable to survey gear in northern waters because
Canadian standard nets spanned a broader range of mesh sizes than United States nets. Thus,
recruitment variability could be one explanation of differences in the relative size of indices
between surveys as the Canadian survey would be more effective at capturing newly recruited
(smaller) walleye, particularly during high recruit years (e.g., the 2005 recruit class) when
juveniles would be expected to grow at a collectively slower rate (i.e., density dependent growth;
Venturelli et al. 2010). Further, stratified fixed-site survey designs (United States survey) cannot
be expected to provide the same information as stratified random designs (Canadian survey)
when the sampling unit displays inconsistent spatial patterning (Hilborn and Walters 1992; NRC
1998), at least not without some form of adjustment (e.g., spatial interpolation or “kriging”).
This phenomenon is further exacerbated when sample sizes differ by several orders of magnitude
between survey designs (Table 3.1). Thus, Canadian and United States fishery-independent
surveys should remain separate indicators of population size. Experimentally fishing nets side87

by-side to normalize catchability and combine surveys may be an insufficient adjustment in and
of itself because of differences in survey design and the influence of localized environmental
factors on catch rates.
Fishery-independent surveys are often used as an auxiliary source of information to
supplement fishery dependent data when fitting stock assessment models (Deriso et al. 1989,
NRC 1998). When survey indices of abundance considerably influence stock assessment model
fit (i.e., highly weighted component in the model objective function; Quinn and Deriso 1999), as
is the case for Lake Erie walleye, management parameters that result from the assessment will be
sensitive to the quality of survey data. Further, because walleye abundance trends inferred from
Canadian and United States standardized surveys (1990-2008) differed in terms of the relative
change in magnitude and direction (28% of years) of indices, defining weights for each survey
index (more weight given to higher quality data) are of critical importance and assessment results
should always be evaluated for sensitivity to assigned weights. Empirical variances associated
with standardized CPE indices could be used to set weights between surveys, although variances
calculated from non-random, systematic or fixed location sites may not represent the population
on whole (Hilborn and Walters 1992). Maunder and Starr (2003) suggest the use of within year
CVs (coefficient of variation) instead of averaging over years to capture interannual differences
in precision between individual index values, especially in the presence of strong outliers, when
fitting fisheries assessment models to CPE abundance indices. For Lake Erie walleye,
interannual variability in index value CVs was modest for the Canadian (range = 0.46-0.65) and
United States (0.34-0.69) survey.

88

Lake Erie walleye move in response to seasonal conditions to optimize growth (Kershner
et al. 1999), resulting in a general longitudinal migratory pattern where the extent of movement
is positively related to walleye size or age (Kershner et al. 1999; Wang et al. 2007; Bowlby and
Hoyle 2011; Berger et al. in press). To adjust for annual differences in the timing and extent of
2

walleye movements as it relates to survey timing and location, random effect terms (σ i; Table
3.3) were implemented to account for random fluctuations in and correlations between catch
rates among interacting spatial and temporal factors. For example, 13.2% of the variation in the
proportion of non-zero catches resulted from differences among each combination of year, week,
and sub-basin. For each best model, random effect terms were identified as important sources of
variability in catch, and the inclusion of these could result in abundance indices with reduced and
more appropriately characterized uncertainty (Helser et al. 2004) and improved stock assessment
results (Chen et al. 2003).
Recognizing variability in catchability and availability as a result of environmental
factors and accounting for this variation when interpreting survey data has received more
attention recently (Maunder et al. 2006; Tian et al. 2009), particularly in light of directional
environmental change (Hart et al. 2011). Site-level measurements of surface water temperature,
lake depth, water clarity, and the presence of hypoxic conditions taken during autumn sampling
events influenced Lake Erie walleye survey catch rates. Surface water temperature and water
depth are perhaps the most commonly assessed environmental factors when standardizing fishery
or survey indices of abundance because these data are either directly measured or easily
interpolated from location information. For example, Schmalz and Staples (2011) found that
walleye gill net catchability in a large Minnesota lake was influenced by both water temperature
89

and depth. In Canadian waters, gill nets set on the bottom of the lake captured far fewer walleye
than gill nets set in the water column (“canned”). In United States waters, surface water
temperature was a marginally important factor describing catch rates, though the largest
discrepancy between nominal and standard indices was associated with unusually cold water
temperatures during the sampling period (PD, west basin 2008; Figure 3.6). Secchi depth had a
negative effect on positive catch rates (US) and the proportion of non-zero catches (CAN). For
example, the largest differences (PDs; Figure 3.6) between nominal and standardized catch rates
th

in the central basin were associated with high (>75 percentile) mean secchi depths. In addition
to being sub-optimum habitat for walleye (i.e., decreased availability; Lester et al. 2002), areas
of increased water clarity can also decrease gear efficiency by increasing net avoidance behavior
(Buijse et al. 1992; Olin et al. 2004). In general, survey nets were set infrequently (e.g., ~3% of
-1

CAN central basin sites) in hypoxic conditions (dissolved oxygen ≤ 4 mg·L ), although positive
catch rates and the proportion of non-zero catches in Canadian waters decreased substantially
(48% and 28%, respectively) at sites with low levels of dissolved oxygen. Other prospective
environmental factors that might be expected to influence walleye catch rates but where
comprehensive data was limiting for the current analysis include wind direction and speed
(Roseman et al. 2005; Zhao et al. 2009; Hart et al. 2011), current direction and speed (Roseman
et al. 2005; Zhao et al. 2009), and wave or seiche height (Trebitz 2006; Rydell et al. 2010).
It is commonly accepted that the use of CPE as an index of abundance – one of the most
fundamental relationships in fisheries stock assessment – can be problematic and misleading
when applied to fishery dependent data (NRC 1998; Harley et al. 2001; Maunder et al. 2006)
because CPE may not be directly proportional to abundance across the time series. This
90

phenomenon can have major ecological, social, and economic implications as was the case with
the collapse of the northwestern Atlantic cod fishery (Rose and Kulka 1999; Gien 2000; Frank et.
al. 2005). In contrast, problems associated with using fishery-independent data as an abundance
index have not received as much attention because the objective of these surveys is usually to
representatively sample the target population. Yet, non-linearity in the proportionality between
abundance and CPE can still arise in survey data (e.g., Swain et al. 1994; Hansen et al. 2004),
despite accounting for as many confounding factors as possible given available data. Thus, the
assumption of constant catchability may remain invalid and applying several methods to adjust
for space or time-varying catchability when using survey abundance indices may be prudent
(Wilberg and Bence 2006; Wilberg et al. 2010). In fact, the result that Canadian and U.S.
surveys had different abundance trends suggests that catchability was drifting over time or that
the surveys sampled different populations; either way, how these indices are used in the stock
assessment should be evaluated further.
Inconsistencies in survey data that arise from behavioral processes can be very
challenging to overcome. For highly mobile species, for example, survey indices of abundance
may remain inaccurate because of seasonal or local changes in distribution within and among
management units used in population assessments (Schwarz and Seber, 1999; Gerber et al.,
2003). Although the knowledge base is growing (e.g., Wang et al. 2007; Zhao et al. in press), a
comprehensive treatment of walleye movement and migratory patterns in Lake Erie and the
ensuing impact it has on rational management remains a critical goal. Such information could
provide insight into specific factors that affect the timing, extent, and duration of walleye
migratory patterns and how these influence abundance indices used in stock assessment.
91

Surveys used to index the Lake Erie walleye population could be improved by gathering more
information related to walleye movements (e.g., prey distribution), coordinating the collection of
environmental data among jurisdictions, increasing the power to detect temporal trends (Wagner
et al. 2009), and incorporating movement metrics inferred from tagging data directly into the
stock assessment to improve interpretation of survey index data. The current work disaggregates
survey data by basin (owing to population structure; Wang et al. 2007; Berger et al. in press) and
jurisdiction (owing to differences in gear mesh sizes and survey design). Future work should
explore the sensitivity of population trends at alternative disaggregation levels because the
spatial scale at which catch rate and environmental data are aggregated can greatly influence the
standardization of index data (Tian et al. 2009).

Acknowledgements
We thank Jim Bence and Meredith Gore of the Department of Fisheries and Wildlife at
Michigan State University for helpful comments and contributions that improved this
manuscript. Survey gill net data were collected by fisheries biologists affiliated with the Ontario
Ministry of Natural Resources (Wheatley office), Ohio Department of Natural Resources
(Sandusky and Fairport offices), and Michigan Department of Natural Resources (Lake St. Clair
office). Support for this research was provided by the Ontario Funding for Canada-Ontario
Agreement (7-02) Respecting to the Great Lakes Basin Ecosystem to Y.Z., Lake Erie
Management Unit of the Ontario Ministry of Natural Resources and Michigan State University.

92

APPENDICES

93

APPENDIX 3A

Main Tables and Figures

94

Table 3.1.—Number of sites used in the analysis that were sampled during annual Canadian
(CAN) and United States (US) fishery-independent gill net surveys in the west and central basins
of Lake Erie. Canadian sites were selected following a stratified (depth) random design each
year, and United States sites followed a stratified (depth) fixed design (not all sites sampled
every year and new sites added opportunistically).

Year
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008

CAN
West Central

37
29
38
38
36
22
40
27
25
44
42
40
44
44
44
44
42
28
44

92
120
125
110
64
54
60
124
100
76
142
122
144
142
139
166
120
141
138

U.S.
West Central
2
2
2
2
7
6
6
9
7
10
4
4
4
10
10
8
8
10
7
9
9
11
14
10
14
12

2
5
1
5
10
12
8
8
7
7
4
5
6
6
6
6
7
8
3
4
6
22
26
35
16
25

95

Table 3.2.—Reference levels for categorical variables and mean values for continuous variables
used to standardized Canadian (CAN) and United States (U.S.) fishery-independent surveys.

Variable

CAN

U.S.

year
week
basin
sub-basin
hypoxia
set type

1990
1
west
W1
no
bottom
16.8
2.5
16.6

1983
1
west
no
14.3
1.4
12.3

surface water temp. (°C)
secchi depth (m)
water depth (m)

96

Table 3.3.—Source of variation from estimated random effects (βi’s) and residual variation (εi’s)
associated with the best models used to standardize Canadian and United States fisheryindependent surveys.

Canadian Survey

United States Survey

Log-normal

Best Model

βy,w,l

0.045

Log-normal

βy,b,l

Best Model

2
σi

Source

Source

2

σi
0.054

0.012

βy,w

0.031

βw,b,l

0.020

εywbtsdh

0.916

βy,w

0.039

βy,l

0.003

βw,b

0.029

βw,l

0.000

βb,l

0.118

εywbltsdhn

0.742

βy,w,l

0.132

βy,w

0.000

βy,l

0.000

βw,l

Binomial

βw,b

0.000

Notes: y is year; w is week; b is basin; and l is sub-basin (others refer to text).

97

Table 3.4.—Comparison of the relative importance of fixed effect factors (αi’s) included in the
best model used to standardize Canadian and United States fishery-independent surveys.
Estimates (±1 SE) of fixed effects from the overall best model are shown for each survey and
assumed error structure. Each factor was evaluated by removing it from the overall best model
(random effects held constant) and assessing the resultant change in AICc (ΔAICc) such that
larger values signify increased importance in model fit. The base model is shown as a reference
point, describing differences in catch rates due solely to year and basin effects (i.e., trends of
interest) prior to accounting for other factors. The factors week and sub-basin were included in
the best model through random effect interaction terms (see Table 3) and thus were not further
evaluated here. The combination of αy + αb + αyb represents effects describing the annual trend
of interest for each basin.

Model

Factor

Canadian Survey
Log-normal
best: αy +α b +α yb +α w +α l +α d +α h +α n

ΔAICc Estimate

SE

Binomial
best: αy +α b +α yb +α w +α l +α d +α h +α n

base: αy +α b +α yb
United States Survey
Log-normal
best: αy +α b +α yb +α w +α t +α s
base: αy +α b +α yb

0.025
-0.565
0.522

0.007
0.181
0.042

αs
αh
αn

0.00
1.20
4.88
143.54
238.38

-0.087
-0.945
1.144

0.048
0.356
0.097

αt
αs

base: αy +α b +α yb

αd
αh
αn

0.00
12.48
8.05
144.10
259.30

0.00
0.44
37.25
34.75

0.030
-0.438

0.017
0.074

Notes: y is year; w is week; b is basin; l is sub-basin, t is surface water temperature, s is
secchi depth, d is water depth, h is the presence of hypoxia, and n set type.

98

.1.—Canadia (Ontario) and United States (Mic higan and O
an
Ohio) fishery
y-independen gill
nt
Figure 3.
net surve were used to index th west (W) and central (C) basin La Erie wal
eys
he
ake
lleye populat
tion.
Dots indi
icate the loca
ations of sam
mpling sites for the most recent year (2008), whi was a
t
r
ich
standard sampling ye in Canad waters and an intens
ear
dian
a
sive samplin year in US waters. La
ng
S
arge
sample si
in
izes to the north enabled the analysis of sub-basi effects on catch rates (W1, W2, C
d
n
C1C4). Ove
erall site sele
ection follow a stratifi (depth) r
wed
fied
random samp
pling design (CAN) and a
n
d
stratified (depth) fixe sampling design (US)
d
ed
).

99

.2.—Histogr of obser
ram
rved walleye (age-2 and older) catch rates in num
e
h
mbers of
Figure 3.
individua from Can
als
nadian (1990
0-2008; pane A) and Un
el
nited States (
(1983-2008; panel B)
fishery-in
ndependent surveys. Th proportion of sites wit zero catch was high (0
he
n
th
h
0.36) in the
Canadian survey and low (<0.02) in the Unit States su
n
d
)
ted
urvey.

100

Figure 3.
.3.—Fits of alternative error distribu
a
e
utions to obse
erved mean and variance in walleye CPE
e
for Canad and Un
dian
nited States fishery-indep
f
pendent surv
veys. Each o
observation c
corresponds to a
year for years with 5 or more site sampled (only exclude U.S. 1983
y
es
es
3).

101

.4.—Standar diagnostic plots that evaluate the a
rd
c
e
adequacy of the overall best log-line
f
ear
Figure 3.
model us to standa
sed
ardize positiv catch rate for the Can
ve
es
nadian fishe
ery-independ survey.
dent
Plots asse model fit (A) and ad
ess
dequacy (B) qualitatively and evaluat assumptio of consta
q
y
ate
ons
ant
variance (i.e., no tren in C) and normality (i straight line in D).
nd
i.e.,

102

.5.—Standar diagnostic plots that evaluate the a
rd
c
e
adequacy of the overall best log-line
f
ear
Figure 3.
model us to standa
sed
ardize positiv catch rate for the Un
ve
es
nited States f
fishery-indep
pendent surv
vey.
Plots asse model fit (A) and ad
ess
dequacy (B) qualitatively and evaluat assumptio of consta
q
y
ate
ons
ant
variance (i.e., no tren in C) and normality (i straight line in D).
nd
i.e.,

103

.6.—Trends in walleye relative abun
r
ndance for C
Canadian (CA and Uni States (U
AN)
ited
US)
Figure 3.
fishery-in
ndependent surveys in th west and central basin The low panel for each region
he
ns.
wer
compares trends in walleye relati abundanc as inferre from a sta
s
w
ive
ce
ed
andardized in
ndex (mean
(solid lin 95% con
ne),
nfidence interval (dotted lines)) and a nominal in
ndex (normal
lized to the f
first
year stan
ndardized ind value; ci
dex
ircles). The upper panel for each reg
l
gion shows t proportio
the
onal
differenc (PD; solid line) betwe the raw nominal and standardized indices of walleye
ce
d
een
n
d
abundanc and the mean PD acro the time series (dotte line).
ce
m
oss
ed

104

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105

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CHAPTER 4
The effect of alternative walleye (Sander vitreus) management procedures on harvest policy
choice and performance

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Abstract
Rational management of fisheries requires consideration of multiple, and often
conflicting, societal objectives. Management procedures (data collection, population assessment,
and harvest policy) are the actions taken to ensure that fishery performance best meets objectives
specified by stakeholders. Computer simulations have proven to be effective tools for
facilitating the expected performance of alternative management procedures given system and
management uncertainties, thus providing valuable insights to decision-makers. Simulation
analyses were used here to evaluate how the choice of data collection and population assessment
procedures influenced the selection and performance of alternative harvest policies. Candidate
management procedures included using relatively complex (annual age-structured), complex but
less frequent (triennial age-structured), and simple (survey index) data collection and population
assessment approaches to inform three general types of harvest control rules (constant fishing
mortality, feedback, and conditional constant catch). A suite of common policy performance
metrics were computed for each case and compared among candidate procedures. Results
indicate that harvest policy performance and the ensuing tradeoffs between conflicting objectives
were affected by the choice of a data collection and assessment scheme. In general, annual SCA
procedures outperformed the other procedural schemes evaluated here, providing the best overall
balance between the harvest and risk-related tradeoffs that were explicitly considered in
simulations. However, annual SCA procedures only afforded a modest improvement in policy
performance over triennial SCA procedures in exchange for the extra effort associated with
implementing annual management procedures. Ultimately, the choice of data and assessment

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procedures are of non-trivial significance when it comes to the quality and quantity of
information, costs, and effort associated with managing fisheries.

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Introduction
Contemporary fisheries management often entails, in some cases under statutory
obligation (MSA 2007; FMA 2011), the development and subsequent application of well-defined
management plans to guide long-term “optimal” resource use and prevent overfishing. The
decision-laden process of developing comprehensive management plans along with the general
call for science-based decision-making has resulted in an increased use of model-based
approaches (e.g., closed-loop simulations) as decision support tools. Management strategy
evaluation (MSE) is one such tool that has been applied to many marine fisheries worldwide
(e.g., Butterworth and Geromont 1997; Smith et al. 1999; Punt 2011) to compare and contrast the
relative performance of alternative management procedures (data collection, stock assessment,
and harvest control rules) against a set of operational objectives while accounting for
uncertainties associated with each procedure in the management cycle (Walters and Hilborn
1976; De la Mare 1996; Sainsbury et al. 2000). The goal of such analyses is often to aid in the
selection of an appropriate harvest policy, given a particular assessment method and data
collection scheme. However, the choice of assessment and data procedures can also have
important consequences for the performance of procedures used to manage fisheries.
Incorporating alternative assessment methods and data collection schemes into an MSE-type of
framework can provide information about the expected consequences for and tradeoffs among
alternative management strategies with different economic realities (i.e., the need to reduce
management costs) that by necessity play a role in management choice.
Three important questions that fishery managers must address when developing
management plans are: (1) what data should be collected to monitor the population of interest;
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(2) how should the information be used to evaluate population status; and (3) what rules should
be used to determine suitable harvests? In most cases, the answers to these questions are
governed by biological characteristics of the population, public demand for the resource,
budgetary constraints, and uncertainty. Management agencies must operate within the confines
of an annual budget such that decisions on how to allocate finite resources to manage a particular
fishery are made in the context of multiple agency and fishery objectives. However, choices
pertaining to how 1 (monitoring data) and 2 (population assessment) affect the choice and
performance of 3 (harvest policy) are rarely evaluated. These choices have become more critical
as the demand for science-based fisheries management has increased at a faster pace than the
availability of resources (e.g., funds, data, or qualified personnel) required to perform the
necessary science (MSA 2007; U.S. Dept. of Commerce and U.S. Dept. of Education 2008).
The frequency and complexity of data gathering and assessment schemes are two
management choices that are likely to have distinct investment tradeoffs, both in terms of
biological and economic expectations. It is reasonable to expect that management performance
from a complex, data-intensive scheme (e.g., statistical age-structured assessment) would differ
according to the frequency with which it was applied, or in relation to a simpler, less costly
scheme (e.g., fishery-independent index). However, if there were insignificant biological
differences in terms of harvest policy choice and long-term system performance between
schemes, rational management would suggest the use of the most cost-effective set of procedures
so that limited monitoring and assessment resources could be re-allocated elsewhere (Hansen and
Jones 2008). In some cases, management performance has been shown to improve (Hilborn

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1979; Ludwig and Walters 1985) or have little long-term conservation implications (Cox and
Kronlund 2008) when using simplified assessment procedures.
Population assessment procedures generally occur at regular time intervals, with
assessment frequency being dictated, ideally, by species life history and management goals. For
example, some Pacific salmon stocks are managed using in-season monitoring and assessment
schemes to regularly update population status throughout the fishing season in pursuit of
constant escapement harvest policies (e.g., Robb and Peterman 1997; Su and Adkison 2002). At
the other extreme, multi-year catch limits have been proposed for many whale species using
procedures at 5-year intervals (IWC 2007). Clearly, there is a balance between the frequency of
updating (or feedback) management actions and species longevity when considering optimizing
harvest, stock rebuilding time after over-depletion, costs of management, or other fishery
objectives. Alternatively, simply delaying pre-defined management action (e.g., due to political
opposition) has been shown to severely degrade policy performance and exacerbate undesirable
circumstances (Shertzer and Prager 2006).
Alternative data collection and assessment schemes will undoubtedly influence
operational management in one way or another. Using closed loop simulations to compare the
tradeoffs associated with different schemes can be particularly useful for decision-makers
because it highlights the potential opportunity costs associated with foregone decisions within a
risk assessment framework. Here, we apply this approach to the Lake Erie walleye (Sander
vitreus) fishery to guide management for this socially, culturally, and economically valuable
fishery. Specifically, we investigate whether 1) the ordinal performance and 2) the absolute

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performance of candidate harvest policies change under three alternative data collection and
assessment schemes across a suite of common performance measures.

Methods
Study Population
Lake Erie is the smallest of the Laurentian Great Lakes in terms of volume yet is the most
productive (Beeton et al. 1999). The west basin (mean depth = 7.4 m) and central basin (18.5 m)
support lucrative warm and cool-water fisheries, while the east basin (24.4 m) is dominated by
cool and cold-water species. Walleye are most abundant in the west and central basins of Lake
Erie (Figure 4.1) with 98% and 97% of the historical walleye harvest and effort, respectively,
occurring in this area (WTG 2009). As a result, data collection, stock assessment and harvest
policy management procedures are used to set harvest levels (total allowable catch, TAC) in this
area. Eastern basin stocks remain small, and thus are not currently incorporated into lake-wide
TACs. Walleye are exploited by a commercial gillnet fishery exclusive to Canadian waters and a
recreational hook-and-line fishery mainly in United States waters. All analyses presented here
focus on the management of the west and central basin walleye population.

Approach Overview
Closed-loop simulations of the entire management process were used to compare how
different management procedures performed across a range of plausible conditions. The general
steps included (sensu Punt 2006):

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(1) Develop a model to describe the true population dynamics for the purpose of
simulations, often termed operating model (OM).
(2) Parameterize the OM using information from the most recent population assessment
and best available knowledge.
(3) Project the OM forward through time while imposing one set of candidate
management procedures.
a. At each time step
i.

Generate observed data from OM conditioned by population structure.

ii.

Conduct stock assessment (SA) procedure using new observations.

iii.

Use results from SA procedure to inform harvest policy procedure and set
catch levels (i.e., TACs).

iv.

Apply SA informed TAC to the OM.

v.

Use the OM to project forward one time step accounting for actual
harvest.

b. Repeat over time horizon.
(4) Repeat steps 2-3 many times and compile performance measures.
(5) Repeat steps 2-4 for each set of candidate management procedures.
(6) Repeat steps 2-5 to evaluate sensitivity to key model assumptions.

The full routine resulted in 250 individual 50-year projections from which performance
metrics were then computed for 18 sets of candidate management procedures and then repeated
twice to evaluate sensitivity.
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Operating Model
Walleye population dynamics were simulated using a stochastic age- and spatiallystructured operating model (OM) that followed the general structure of the walleye statistical
catch-at-age stock assessment model (SCA) developed in chapter 1, but was informed by
updated survey information (standardized survey data; chapter 2). Model notation (Table 4.1)
and equations (Table 4.2) describe the dynamics of both the OM and SCA. The OM tracked a
+

single population of age-2 through an age-7 group of walleye (‘plus’ symbol indicates all fish
age-7 and older) through time and was implemented using AD model builder software (Fournier
2011). To facilitate comparisons among candidate management strategies, the same set of
random numbers were used to generate OM stochasticity for each set of management procedures
tested.
Several types of uncertainty were incorporated into the analysis. Structural uncertainty
(or model process error) was acknowledged by applying a different set of initial conditions and
population parameters used to initialize and control the OM for each simulation (Jones and
Bence 2009). Each set was one Markov chain Monte Carlo (MCMC) sample of the stationary
joint posterior distribution from the most recent (2008) catch-at-age stock assessment model as
approximated by using MCMC with the Metropolis-Hastings algorithm (Gelman et al. 2004).
Initial conditions included abundance at age in the most recent two years; two years previous
was needed to calculate spawning stock size (Eq. 4.2.10 (Table 4.2 equation 10)). Parameters
(and control variables; Table 4.2) governing the ‘true’ population dynamics included a Ricker α,
β, and lognormal error terms; intercept, slope, and normal error terms for the relationship
between recreational effort and abundance; catchability; vulnerability; standard deviations for
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effort, catch, and CPE observations; and the spatial distribution of commercial fishing mortality
(further specifics provided below). This approach allowed for two levels of recruitment (and
recreational effort) uncertainty: 1) lognormal error inherent to a single MCMC sampled Ricker
stock-recruitment function (mean squared error on loge scale), and 2) structural error associated
with selecting a particular set of Ricker parameters (i.e., parameters were estimated from each
MCMC sample of stock and recruitment to generate a time series of recruits for a given
simulation; Figure 4.2). Uncertainty associated with imperfect observations (observation error)
was incorporated by distorting simulated data prior to executing assessment procedures. As
such, lognormal errors were applied to fishing effort (Eqs. 4.2.19-4.2.20), catch (Eq. 4.2.22), and
survey CPE (Eq. 4.2.23) observations. Error in observed proportions-at-age (Eqs. 4.2.24-4.2.25)
was incorporated by using a multivariate-logistic function with constant age and gear standard
deviations (Table 4.1; Schnute and Richards, 1995; Cox and Kronlund 2008). Assessment
uncertainty was applied by updating the OM with fishing mortality rates informed by a particular
harvest policy using assessment-based estimates of abundance (Irwin et al. 2008). In effect,
assessment-based fishing mortality rates were converted into TACs, which were then used in
conjunction with the simulated ‘true’ abundance to calculate fishing mortality rates applied to the
OM (Eqs. 4.2.27-4.2.28). Lognormal policy implementation error (Table 4.1) was applied to the
policy-specified commercial fishing mortality rate to account for uncertainty associated with
imperfect adherence to policy measures (Eq. 4.2.30).
Population dynamics were composed of recruitment and mortality processes incremented
on an annual basis. Recruitment to the fishery was assumed to occur at the beginning of the year
for age-2 fish with recruitment size being a Ricker function (lognormal error (Eq. 4.2.3)) of
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spawning stock size two years prior. An upper bound of 200 million walleye was imposed on
projected recruitment to prevent unrealistically large recruitment events that resulted from
extreme positive errors associated with the tail end of the lognormal distribution. Spawning
stock size was a measure of the total number of eggs produced by females during the year by
applying age-specific estimates of walleye maturity (Wang et al. 2009) and fecundity (Muth and
Ickes 1993) to the total number of females in each age category (Eq. 4.2.10).
Total mortality consisted of removals due to fishing and deaths due to natural causes.
-1

The instantaneous natural mortality rate was assumed known and constant at 0.32yr .
Instantaneous fishing mortality depended upon year, age, and region for each fishery. The
operational harvest policy was used to set a target TAC, of which a percentage (43.1%; WTG
2009) was allocated to the commercial fishery and then distributed between regions (i.e. west
and central basins; Eq. 4.2.29) according to the “recent” or “historical” spatial distribution of
fishing as estimated by the most recent stock assessment (see sensitivity analysis). The “recent”
period (2001-2008) corresponded to a time of initially rebuilding walleye stocks as set forth in
the Lake Erie coordinated percid management strategy (Locke et al. 2005). The “historical”
period (1990-2008) included all years since the beginning of conducting region inclusive fisheryindependent surveys. Summing mean weight of the catch across ages and regions resulted in
total commercial yield (Eq. 4.2.26). The recreational fishery was assumed to be self-regulating
by allowing the amount of recreational effort expended to be a linear function of population
abundance (Eq. 4.2.20; Jones and Bence 2009). As a result, recreational fishing mortality was
not explicitly set by the operational harvest policy (Eq. 4.2.21). Individual cohorts declined
through time according to total mortality (Eqs. 4.2.7-4.2.8), thus assuming no population-level
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emigration. The sum of all age-classes included in the OM represented total walleye abundance.
Biomass was the product of abundance-at-age and mean weight-at-age, summed across ages (Eq.
4.2.9).
Catchability and vulnerability scaling parameters were used to solve for remaining OM
unknowns: age- and region-specific recreational fishing mortality (Eq. 4.2.21) and survey CPE
(Eq. 4.2.13); and region-specific commercial fishing effort (Eq. 4.2.19). Catchability was
defined as the proportion of the population caught with one unit of fishing or survey effort
(Hilborn and Walters 1992). Vulnerability was the product of gear selectivity and species
availability to capture, which was used to capture differences in regional availability owing to
spatial population structure.

Management Procedures
A set of management procedures – a data collection and stock assessment scheme along
with the choice of harvest policy – constituted a management strategy (Table 4.3). Three
different data collection and stock assessment schemes were used to assess the performance of
three general types of harvest control rules: constant fishing mortality rules, feedback or state
dependent fishing mortality rules, and conditional constant catch rules (Figure 4.3). Control
rules specify guidelines used to adjust management based on the current assessed state of the
population (Deroba and Bence 2008). In all, the combination of alternative candidate
management procedures constituted the evaluation of 18 different management strategy
scenarios (see Table 4.3 for descriptions).

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Walleye population assessments were conducted using either a model-based approach
(SCA) or a data-based approach (survey index of abundance (SI)) within the simulation
framework. The SCA assessment procedure was informed by annual fishery data and survey
data that was “collected” (i.e., observed from the OM with error) either annually or every third
year. Details on the structure and parameterization of the SCA model are outlined in Table 4.2
and can be found in chapter 1, but in general follows that outlined in Fournier and Archibald
(1982) and Deriso et al. (1985) with region- and year-specific estimates of catchability and
region- and age-specific estimates of vulnerability. Population estimates were obtained by fitting
the model to observed harvest, effort, survey, and age composition data for each region (Table
4.4). For the SI approach, CPE indices of relative abundance were “collected” from fisheryindependent surveys using information on simulated population size and vulnerability and
catchability parameter values that were used to initialize the OM (Eq. 4.2.13). Survey
catchability was based on the relationship between standardized, according to spatial, temporal,
and environmental external factors (see chapter 2 for details), CPE and population abundance.
Observed CPE values for each survey and region combination were then averaged to form a
single annual population index.
A suite of harvest policies were implemented for each of three general types of control rules to
supply contrast in the evaluation of alternative data collection and assessment schemes (see
Table 4.3 for descriptions). Policies that impose a constant fishing mortality rate (F0.1, F0.3,
F0.5, and F0.7 examined here) rule were implemented by using annual and 3-year SCA estimates
of absolute abundance, with TACs being set according to equations 4.2.27-4.2.29. For the 3-year
case, TAC was held constant during interim years. Alternatively, feedback policies (FB) impose
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dynamic control rules, usually set as a function of some state of the fishery or population
(Hilborn and Walters 1992; Deroba and Bence 2008). The feedback policy used here allowed
fishing mortality to increase at intermediate population sizes for SCA procedures (Wright et al.
2005; Jones and Bence 2009) and intermediate CPE indices for SI procedures (Figure 4.3). The
functional relationship developed for the SI feedback policy was constructed to match as close as
possible the total allowable catch that would have resulted when using the SCA feedback policy
(Eqs. 4.2.31-4.2.32). In effect, estimates of survey catchability from the most recent stock
assessment model were used to make the connection between standardized survey CPE values
used in the SI feedback policy and total abundance used in the SCA feedback policy. Other
candidate policies that were evaluated imposed a three year moving average rule (FB3MA) and a
20% maximum annual deviation rule (FB20%) to the general feedback policy, restricting year to
year changes in fishing mortality in an attempt to improve harvest stability. In cases where
feedback policies were used with 3-year procedures, harvest during the interim period was
governed by a constant TAC rule (FBCC) or a constant fishing mortality rule (FBCF). The third
general set of control rules evaluated, conditional constant catch (CC; Figure 4.3), maintained
commercial catches at 5 million walleye unless the population fell below 15 million (SCA-based
procedures) or a CPE of 3.29 (SI-based procedures) at which point a constant F0.1 policy (or the
equivalent for SI-based procedures) was initiated until recovery. A constant commercial fishing
TAC of 5 million walleye was used because industry personnel have identified this as the level
of harvest needed to maintain existing infrastructure.

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Performance Measures
Select summary statistics from each simulation, calculated across the time horizon, were
compiled to produce a distribution of expected performance for each candidate set of
management procedures. Performance measures were selected to be representative of those
commonly considered when conducting MSEs (Punt 1993; Butterworth and Punt 1999;
Rademeyer et al. 2007), such as expectations relating to sustainability, risk, and industry stability
(Table 4.5). Mean walleye abundance and age, recreational fishery CPE, and commercial fishery
harvest and yield were metrics used to evaluate long-term expected conditions. Risks associated
with a given policy were quantified as the percentage of years the population fell below 15
million walleye (classified as a population in “crisis”; Locke et al. 2005) and as the percentage of
years the spawning stock size fell below 20% of the unfished spawning stock size. Variation
associated with annual commercial harvest and total abundance was used to quantify measures of
stability.
For each performance measure, policies were sequentially ranked to qualitatively
compare the ordinal performance (i.e., relative selection) of policies common to annual and 3year SCA procedures (F0.1, F0.3, F0.5, F0.7, and FB; FBCF for the 3-year FB policy) and between
polices common to annual SCA and SI procedures (FB, FB20%, FB3MA, and CC). Lower
rankings referred to better performance (e.g., a high measure of harvest stability would be ranked
low). Absolute performance metrics were also compared to evaluate quantitative differences in
policy expectations and tradeoffs among the three data collection and assessment schemes.
Comparisons focus on total commercial harvest, variation in commercial harvest (industry
stability), and risk-based performance measures because other performance metrics evaluated
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had a strong positive (commercial yield) or negative (recreational CPE and average age)
correlation with commercial harvest performance or because of a lack in contrast among policies
(population abundance). Thus, comparisons using these performance metrics are not discussed
in detail, but are presented graphically in the appendix (Figures 4.12-4.16).

Sensitivity Analysis
Sensitivity to the allocation of regional commercial fishing mortality (“recent” or
“historical”) was evaluated because of the influence spatial population structure had on predicted
walleye population dynamics (chapter 1). The full suite of candidate management procedures
was evaluated and performance metrics computed for each case. Inferences relating to study
objectives were then examined for each set of results.

Results
The selection (rank order) and performance of harvest policies under three different data
collection and assessment schemes was insensitive to the values used to allocate commercial
fishing mortality (“recent” or “historical”) between regions (Figure 4.11). This was not too
surprising given that the difference between allocation arrangements was small (~4%, on
average). The remaining results are presented using the “recent” allocation construct as it is
more applicable to current fishery dynamics.

Selection of harvest policy

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The rank order of harvest policies was influenced by the choice of a data collection and
stock assessment procedure for some performance measures (Table 4.6). However, rank order
was mostly unaffected for measures pertaining to population and industry stability and
management risk (Table 4.6). Of those that were affected, discrepancies in rank order between
annual SCA and SI procedures were considerable and prevalent (7 of 9 cases), whereas only
minor discrepancies were detected between annual and 3-year SCA procedures (3 of 9 cases).
Rank order was insensitive to the choice of annual and 3-year SCA procedures with regards to
commercial harvest, population abundance and stability, recreational CPE, and risk-related
performance measures. Only risk-related performance measures were insensitive to rank order
between annual SCA and SI procedures.

Harvest policy performance
Absolute measures of policy performance were dependent upon the choice of
management strategy. In general, there were performance costs associated with those policies
examined utilizing annual SI and less frequent (3-year) SCA management procedures. In
comparison to annual SCA procedures, annual SI procedures generally resulted in decreased
performance. For example, the SI-informed FB policy resulted in a 24% decline in expected
commercial harvest (Figure 4.4) and a 32% increase in commercial harvest CV (decrease in
stability; Figure 4.5) compared to the SCA-informed FB policy. A similar pattern was apparent
(decrease in harvest and decrease in harvest stability) between the SI procedure and SCA
procedure when using the CC harvest policy. FB control rules that enforced interannual
restrictions (FB20%, FB3MA) improved harvest stability substantially compared to the
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unrestricted FB policy for SI procedures, resulting in a reversal of the comparative performance
between annual SI and SCA procedures. Although apparent for harvest stability, this reversal
was not evident for other performance measures. Management risk (Figures 4.6-4.7) also
increased when using SI-procedures for all but one policy evaluated (FB, slight decrease). The
CC policy provided the highest amount of risk associated with attaining an undesirable
population state.
The application of 3-year SCA procedures resulted in minor to modest effects on policy
performance when compared to annual SCA procedures. Total commercial harvest increased
with higher constant Fx policies for both annual and 3-year SCA procedures, but the distribution
of results remained similar between procedures across Fx policies (Figure 4.4). The relative
performance of the 3-year SCA procedure was comparatively worse at higher constant F
policies, resulting in a lower median harvest for the F0.7 policy compared to the annual SCA
procedure. Despite the minor SCA procedure – Fx policy interaction for total commercial
harvest, stability in commercial harvest remained fairly constant across constant Fx policies for
each procedure, though the 3-year SCA procedure was less stable than the annual SCA
procedure (increase in CV of ~13%) and the distribution of results were more variable (Figure
4.5). Regardless of SCA assessment timing, FB policies performed most similarly to the
constant F0.3 policy. Still, the 3-year FBCC (or FBCF) policy did slightly better (worse for
FBCF) in terms of commercial harvest and slightly worse (better) in terms of stability in harvest
than all three of the annual-based FB policies (FB, FB20%, and FB3MA) which performed
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similarly. For both SCA procedures, policies with higher expected levels of commercial harvest
were associated with a higher risk of achieving an undesirable population state (Figures 4.6-4.7).
There was slightly higher management risks associated with the 3-year procedure compared to
the annual procedure despite the fact that, for some policies, the 3-year procedure had lower
expected harvests. The exception to this was the 3-year feedback policy with constant fishing
mortality during interim years (FBCF) which maintained low management risk, comparable to
annual SCA FB policies.
Tradeoffs between diverse, and often competing, measures of policy performance were
conditional on the choice of a data collection and assessment scheme. Key tradeoffs between
measures of median commercial harvest and risks associated with an undesirable population state
(Figures 4.8-4.9) or to median recreational catch rates (Figure 4.10) were comparatively more
favorable for annual SCA procedures than for 3-year SCA procedures when using constant Fx
policies. For example, annual SCA procedures resulted in less risk for the same amount of
harvest (or more harvest at the same risk level; Figure 4.8) as that for 3-year SCA procedures
while also increasing stability (Figure 4.9). For FB policies, tradeoffs were generally more
favorable for annual and 3-year SCA procedures over SI procedures. Both SCA procedures
allowed for similar amounts of increased harvest over that expected using the SI procedure while
maintaining a comparable risk level (Figure 4.8). Thus, there was no clear loss in terms of
harvest and risk tradeoffs between annual and 3-year SCA procedures. Similar performance
tradeoffs were identified between SCA-based FB policies and constant F0.3 policies. Tradeoffs

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associated with CC policies provided the largest contrast between competing performance
measures and were substantially different than those for FB or constant Fx policies.

Discussion
Fisheries management is fraught with tough decisions, most of which are made with
little, and highly uncertain, information in an attempt to balance conflicting fishery objectives
(e.g., desire for the highest possible commercial harvest and increasing the number of
recreational angler trips). One imperative decision is the selection of a harvest policy to guide
rational management (Quinn and Deriso 1999; Deroba and Bence 2008), which was shown here
to be conditional on the specific data collection and population assessment scheme used to define
policy parameters. The use of alternative schemes had considerable influence on the expected
performance of candidate policies, implying that policies that best meet stakeholder objectives
will depend upon the selection of data collection and population assessment procedures.
In general, annual SCA procedures outperformed the other procedural schemes and
provided the overall best balance between harvest and risk-related tradeoffs. However, there was
only a small loss in performance when less rigorous/costly procedures were used. If, for
example, less frequent population assessments were implemented, the resulting savings in
management cost could be used to increase survey sample sizes (chapter 2), improve walleye
habitat, further model development and testing, or commit to other research needs (Locke et al.
2005). This is not a pathological example or obscure set of circumstances as there were
comparatively small differences in terms of harvest – risk tradeoffs (Figures 4.8-4.10) between
annual and 3-year SCA procedures, suggesting that alternative uses of assessment resources
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warrants examination. Indeed, there are other implicit tradeoffs associated with practical
fisheries management, such as opportunity costs that were not a formal part of this analysis. The
results presented here do provide quantitative measures (or mathematical expectations) of real
decision tradeoffs between conflicting biological and fishery related management objectives,
allowing decision-makers to avoid the common pitfalls associated with qualitative (or individual
decision-maker) expectations driving the perceived best management strategy (Plous 1993;
Hammond et al. 1999; Butterworth et al. 2010). Ultimately, selecting a harvest policy can be a
difficult task; especially when population abundance is driven primarily by recruitment, as is the
case for Lake Erie walleye, because moderate contrasts in fishing mortality are just not that
influential on long-term population dynamics.
In addition to biological and fishery performance, managing authorities must also
consider information costs (i.e., expense associated with acquiring policy parameters) and
stakeholder understanding when developing a management strategy (Hansen and Jones 2008).
Complex procedures (e.g., age-structured estimates of absolute abundance; SCA) tend to be
more data intensive, costly to implement, and less transparent than comparatively simpler
procedures (e.g., survey index of relative abundance; SI). In some cases, very little has been
gained in terms of long-term policy performance when using complex, model-based procedures
over simple, data-based procedures (Hilborn et al. 2002; Cox and Kronlund 2008). This can
result from having survey data that tracks population trends well or from the use of misleading
fishery data, supplying biased information to model-based assessments (Apostoloki and Hillary
2009). For Lake Erie walleye, policy performance was by and large reduced when informed by
survey index (SI) rather than SCA-based management procedures. One possible reason is that
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the two surveys, each with different survey designs, used to index walleye population status have
exhibited different short-term trends in abundance (chapter 2), increasing uncertainty associated
with population status; this has been shown to affect harvest policy performance (Katsukawa
2004). If age-structured data are available, it may better to do an age-structured assessment
(Butterworth and Punt 1999), especially when the population has been dominated by large year
classes (Cooke 1999), as has been the case for Lake Erie walleye more recently. Moreover, it is
much more difficult in practice to define survey-based control rules for TAC-managed fisheries
compared to rules based on procedures that estimate absolute measures of population abundance
and fishing mortality (Hilborn et al. 2002; Cox and Kronlund 2008).
The use of data-based procedures to set harvest policy parameters has received more
attention recently (Cox and Kronlund 2008; Apostoloki and Hillary 2009; Pomarede et al. 2010).
In contrast, much less attention has been devoted to evaluating how the frequency of population
assessments influences harvest policy choice. Certainly, species life history will play a role in
deciding the periodicity (e.g., season, year, or every so many years) of candidate assessment
cycles in order to capture major shifts in population dynamics, particularly for populations driven
strongly by recruitment dynamics. Fully recruited Lake Erie walleye (age-2 and older) have
-1

moderate annual survival rates (mean = 0.61 yr ) and longevity (~20 years), suggesting that 3year cycles may be adequate for this species. Although for most performance measures the 3year SCA procedures evaluated here performed moderately worse than comparable annual SCA
procedures, there was one case (FBCF; 3-year feedback policy with constant fishing mortality
during interim years) where assessment timing made little difference. For the analysis of this
policy, interim year TACs were set according to the interim constant fishing mortality rate (as
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specified by the policy) and “true” population abundance. Yet, in practical applications some
other information about relative or absolute population size (e.g., a fishery-dependent index or
estimates from a tagging program) will be needed to inform this type of policy during interim
years. The FBCF policy was evaluated here not because of practicality, but rather as basis from
which to infer general characteristics between annual and 3-year SCA procedures. Further
evaluations of this type of control rule, including uncertainty associated with setting interim year
TACs, are needed.
There are many types and configurations of control rules that are used to define harvest
policies and guide rational fisheries management (Deroba and Bence 2009). Harvest policies
evaluated in this analysis were chosen to facilitate comparisons between alternative data
collection and assessment procedures while representing some of the more common types of
control rules in use today (e.g., constant fishing mortality, feedback or state dependent, and
conditional constant catch). Because of innate differences in the definition of and application of
policy parameters among alternative data collection and assessment procedures, comparing the
relative performance of these procedures can be difficult. As such, interim year fishing mortality
rates for 3-year procedures were held constant (as previously discussed) and every effort was
made to match, using empirical relationships, feedback policies based on relative abundance
(survey index CPE; SI procedures) with those based on absolute abundance (SCA procedures).
For applications where supporting empirical data to define candidate CPE-TAC policy
relationships is lacking (i.e. estimates of absolute abundance and fishing mortality), survey index
information is typically used to inform future exploitation in relative terms only and thus is
typically used in an adaptive management framework (Apostolaki and Hillary 2009). Although,
135

Cox and Kronlund (2008) applied a survey index management procedure to directly set annual
TACs by estimating a harvest policy scaling parameter and an autocorrelation parameter using
multiple linear regression on historical catch limits and survey indices.
There is growing evidence to suggest that Lake Erie walleye may emigrate from the
quota management area (west and central basin proper) to the east basin (Wang et al. 2007; Zhao
et al. 2011) and up the Detroit river corridor (Wang et al. 2007). Both operating and assessment
population dynamic models developed here assumed no emigration (or immigration) was
occurring. The number and extent of regional tagging studies is increasing on Lake Erie,
shedding light on both inter- and intra-lake walleye movement. Some of the critical questions
that remain relate to spawning site fidelity (do emigrants return and contribute to the local
spawning stock?) and to movements in relation to the quota management zone (is there age-, sexor season-specific differences in the extent and duration of this movement?). In any case, current
assumptions about population closure should not affect comparative results, though they could
systematically influence absolute measures of performance.
Results presented here provide a basis from which to test further candidate management
procedures. For example, an SI-based procedure that applied a smoothing function to survey
indices over short time durations (Cox and Kronlund 2008) may perform better than the simple
SI procedure evaluated in the current analysis. Or, perhaps a set of procedures that utilize
complex SCA assessments to statistically capture triennial changes in catchability or selectivity
with simple and easily interpretable SI procedures during interim years would perform favorably.
The latter approach would certainly not yield much in terms of economic savings, but it may
have substantial benefit in terms of increasing process transparency. Further analyses could also
136

investigate alternative assumptions about the recreational fishery. The current belief, albeit
somewhat controversial, is that the recreational fishery is linearly self-regulating (recreational
effort follows a linear function of population abundance). Given the contention, other competing
beliefs (e.g., a logistic relationship or other asymptotic function) should also be evaluated to see
how results are affected. It would also be advantageous to extend the current OM to explicitly
include the costs associated with different management procedures. The resulting
“bioeconomic” model could be used to directly evaluate the end costs and benefits of using
simpler or less frequent assessments. Lastly, results from this work describing the relative
performance of alternative management procedures should be interpreted within the context of
those particular policies evaluated here, and not broadly inferred to all situations and
circumstances. For example, only one set of policy parameters was evaluated for feedback
control rules, so to make general conclusions about feedback versus constant F policies (in
general or for Lake Erie walleye) would be inappropriate.

Acknowledgments
The authors would like to acknowledge the Lake Erie Committee, the walleye task group,
and member agencies (Ontario Ministry of Natural Resources, Michigan Department of Natural
Resources, Ohio Department of Natural Resources, Pennsylvania Fish and Boat Commission,
and New York State Department of Environmental Conservation) for engaging in helpful
discussions and for providing access to data. Also, a great deal of gratitude must be conveyed to
various Lake Erie walleye stakeholder groups for attending distant workshops and providing
valuable insights that were integral to this work. Thanks to Weihai Liu for programming
137

guidance and bug deterrence and to the Michigan State high performance computing center for
providing access to ‘pleasantly parallel’ computing. This paper was improved with helpful
comments provided by J. Bence and M. Gore. Support for this research was provided by the
Ontario Funding for Canada-Ontario Agreement (7-02) Respecting to the Great Lakes Basin
Ecosystem to Y.Z., Lake Erie Management Unit of the Ontario Ministry of Natural Resources,
the Saginaw Bay Walleye Club, and Michigan State University.

138

APPENDICES

139

APPENDIX 4A

Main Tables and Figures

140

Table 4.1.—Description of symbols used in operating and assessment models. Values used to
drive simulations were either explicitly established or taken as a sample from the joint posterior
distribution (MCMC) associated with the most recent statistical catch-at-age stock assessment.
Symbol Description

Value

Index variables (levels)

		a
		y
		f

+

Age (2-7 )
Year
Fishery (commercial = 1; recreational (OH) = 2;
recreational (MI) = 3)
Survey (Ontario = 1; Ohio/Michigan = 2)
		s
Region (west basin = 1; central basin = 2)
		r
		OM Actual (simulated) value from operating model
Assessed (estimated) value from population assessment
		AM
State and control variables

		N
		F
		Z
		M
		C
		I
		P
		E
		TAC
		B
		Y
		A
		λ

		S
		m
			f
		w
		n

Abundance
Fishing mortality
Total mortality
Natural mortality
Fishery catch
Survey CPE
Proportions at age
Fishing effort
Total allowable catch
Biomass (kgs)
Yield (kgs)
Allocation of F (by region) and TAC (by fishery)
Data source weight (relative to standard data source)
Recruitment (simulated)
Intermediate year recruitment projectioin
Initial abundance for the most recent two years
Fishing effort (simulated)
Recreational fishing mortaltiy (simulated)
Spawning stock size (# eggs)
Maturity
Fecundity (1000s of eggs/female)
mass (kgs)
Sample size (# years data)

141

0.32

MCMC (region); 0.431 (f =1)
MCMC
MCMC
MCMC (f >1)

0.32, 0.88, 0.99, 1, 1, 1
7, 57, 106, 155, 204, 328
0.75, 1.08, 1.42, 1.7, 1.91, 2.51

Table 4.1.—(cont’d).

		σ f
		σ s
		σ ε

Predicted catch
Predicted survey CPE
Predicted proportions at age
Effective sample size
CV for fishery catch (σstd / λf)
CV for survey CPE (σstd / λs )
Standard deviation for effort deviations (σ std / λε)

Structural Parameters
Recruitment
		R
Initial abundance in the first year
		G
Catchability
		q
Vulnerability
		v
		σ std CV for standard data source (Ontario survey)

MCMC
MCMC

Distributional Parameters

		 α
		 β
		 τ
σ
		 η
σ
			ε
		 ν
σ
		 γ
		 δ
   κ
σ
		 ϕ
σ
		 ψ
σ
		 ω
σ
		 ξ
σ

Ricker alpha
Ricker beta
Recruitment process error
Standard deviation for recruitment error
Intermediate year recruitment projection error
Standard deviation for recruitment projection error
Effort deviations
Effort observation error
Standard deviation for effort observation error
Intercept for recreational E to N relationship
Slope for recreational E to N relationship
Process error for recreational E to N relationship
Standard deviation for recreational E to N error
Fishery catch observation error
Standard deviation for fishery catch observation error
Survey CPE observation error
Standard deviation for survey CPE observation error
Proportions at age observation error
Standard deviation for proportions at age observation error
Policy implementation error
Standard deviation for implementation error

142

MCMC
MCMC
MCMC
0.38

MCMC
MCMC
MCMC
MCMC
MCMC
MCMC
0.2, 0.2, 0.2, 0.2, 0.2, 0.2
0.05

Table 4.2.—Model equations used in catch-at-age operating (OM) and assessment (AM) models.
Reference

Equation

Source

Population model
(4.2.1)

	

,

(4.2.2)

AM
AM

,

;	

(4.2.3)

(4.2.5)

,

;	 	~	
∑ ∑

(4.2.6)

, , ,

,

(4.2.7)

,

(4.2.8)

,

(4.2.4)

∑

(4.2.10)
(4.2.11)

, , ,

(4.2.13)

, , ,

(4.2.14)

, , ,

OM, AM
, ,

;	

,

,

AM

,

OM, AM

OM

, , ,

OM

,

1

,

	

,

,

.

, ,
, ,

0,

OM, AM

, ,

, , ,

~	

OM, AM

,

,

, ,

,

,

, , ,

(4.2.12)

AM

, , 	
,

,

OM

, , ,

,

∑

(4.2.9)

0,

0,

, ,

|

	~	

,

;

, , ,

,

OM
OM

, , ,

OM

, ,

Observation model
(4.2.15)
(4.2.16)

, , ,

(4.2.17)

, , ,

(4.2.18)

, , ,

, , ,

, , ,

1

,

	

,

,

, , ,

AM

, ,

,

AM

, ,

.

,

, , ,

,

AM
AM

, ,

143

Table 4.2.—(cont’d).
(4.2.19)
(4.2.20)

,

, ,
, ,

,

(4.2.22)

, ,

,

∑
∑

, ,

, ,

, ,

, ,

, , ,

∑

∑ ∑

(4.2.26)

, ,

	~	

0,

0,

OM
OM

~

, ,

~

0,

OM

0,

OM
OM

, ,
, , ,

∑

, , ,

∑

;	

OM

, , ,
∑

, , ,

∑

~

, ,

∑

, , ,

, , ,

;	

;	

, ,

, , ,

0,

	

, ,

, , ,

, , ,

(4.2.25)

~
, ,

											

, , ,

(4.2.24)

, ,

	

(4.2.21)

(4.2.23)

;	

, ,

OM

, , ,

OM

,

Policy implementation
(4.2.27)

1

	

OM

(4.2.28)

1

	

OM

(4.2.29)
(4.2.30)

1

,

	

;	

,

~

OM

0,

OM

Feedback (state dependent)

(4.2.31)

AM, OM

0.1
0.02
0.0075
0.35

0.2
0.05

144

	 	 15
	15 	 	
	20 	 	
	 	 40

20
40

Table 4.2.—(cont’d).
(4.2.32)

AM, OM

0.373
0.576
0.422
1.068
	

	

	

0.67
0.342	
14.732	
	
	 	

145

	
	 3.29
	3.29 	
	 6.58
	6.58 	
	 23.35
	
	 23.35

Table 4.3.—Candidate data collection, population assessment, and harvest policy management procedures. Each management
strategy scenario examined included the choice of a single type of harvest control rule (feedback, FB; constant F, Fx; and conditional
constant catch, CC) informed by one of three data collection and assessment schemes. Abbreviations include: F = instantaneous
fishing mortality; N = total estimated population abundance; TAC = total allowable catch; CPE = catch-per-effort; and M = millions.
Management Procedure
Data Collection

Population Assessment Harvest Policy

Annual
Fishery and survey Catch-at-age (SCA)

Scenario Description

FB
(FB20%)

1
2

(FB3MA )

3

(F0.1, F0.3, F0.5, F0.7)
(CC)

Triennial (suvey); Annual (fishery)
Fishery and survey Catch-at-age (SCA)

9
10
11

(CC)

Survey index (SI)

FB
(FB20%)
(FB3MA )

Survey

4-7
8

12

(FBCC)

13

(FBCF)
(F0.1, F0.3, F0.5, F0.7)

F set according to N (see Fig. 3, eq. 4.2.31)
same as above except F not allowed to deviate more than 20%
from year to year
same as two above except F set by averaging the most recent
three years
F constant at 0.1, 0.3, 0.5, and 0.7 levels
F set so TAC=5M unless N<15M at which point F0.1 is applied
F set according to survey CPE (see Fig. 3, eq. 4.2.32)
same as above except F not allowed to deviate more than 20%
from year to year
same as two above except F set by averaging the most recent
three years
F set so TAC=5M unless CPE<3.29 at which point the
equivalent of F0.1 is applied

F set according to N (Fig. 3, eq. 4.2.31); TAC adjusted every
third year and constant during the interim
14 F set according to N (Fig. 3, eq. 4.2.31); TAC adjusted every
third year with constant F during the interim
15-18 F constant at 0.1, 0.3, 0.5, and 0.7 levels; TAC adjusted every
third year and constant during the interim

146

Table 4.4.—The statistical catch-at-age assessment procedure estimated population parameters
by minimizing the posterior negative log likelihood calculated by summing weighted individual
normal and log-normal likelihood and prior components for all source combinations. Highest
posterior density estimates minimized this function.
Reference

Components

Source
, ,

(4.4.1)

,

∑

(4.4.2)

,

∑

(4.4.3)

,

∑

(4.4.4)

∑

,

∑

, , ,

ln	

(4.4.5)

∑

,

∑

, , ,

ln	

, ,

	

r1,2; f1,2,3	

, ,

r1,2; s1,2,3

, ,

, ,

	

r1,2; f1,2,3	

	

, , ,

r1,2; f1,2,3	

	

r1,2; s1,2,3	

	

	

147

, , ,

		

	

	

Table 4.5.—Performance statistics used to evaluate tradeoffs among candidate management
strategies. Statistics were calculated by averaging over the 50-year time projection for each
simulation and management scenario combination.
Perfomance statistics
N (#)
N stability
Harvest (#)
Harvest stability
Yield (kgs)
CPE (#/angler hr)
Age composition (%)
% years N < 15M
% years SSS < 20% SSSunfish

Description
Mean population abundance
CV of population abundance
Mean commercial harvest
CV of commercial harvest
Mean commercial tield
Mean receational catch-per-effort
Mean age
Percentage of years abundance falls below 15 mi
Percentage of years spawning stock size falls belo
20% of the unfished spawning stock size

Notes: CV = coefficient of variation

148

Table 4.6.—Ranked performance of harvest policies for each performance measure evaluated. The first policy set is used to compare
annual SCA (SCAA) to annual SI (SIA) procedures. The second policy set is used to compare annual SCA to triennial SCA (SCAT)
procedures. Lower numbers refer to higher rankings and better performance.
Performance
Measures

Com.
Harvest

Policy set 1 SCAA SIA

Com. Harvest
(CV)
SCAA SIA

% Years % Years SSB
N < 15M < 20% SSBunfish Abundance
SCAA SIA

SCAA SIA

Abundance
(CV)

SCAA SIA SCAA SIA

Recreational
Age
CPE
Composition
SCAA SIA

SCAA SIA

Com.
Yield
SCAA SIA

FB
FB20

2
3

3
4

3
4

4
2

1
2

1
2

1
2

1
2

3
4

2
1

3
2

3
1

3
1

3
2

4
3

2
1

2
3

3
4

FB3MA

4

2

2

3

3

3

3

3

2

3

4

4

4

4

2

4

4

2

CC

1

1

1

1

4

4

4

4

1

4

1

2

2

1

1

3

1

1

Policy set 2 SCAA SCAT SCAA SCAT SCAA SCAT SCAA SCAT SCAA SCAT SCAA SCAT SCAA SCAT SCAA SCAT SCAA SCAT
FB

3

3

5

5

2

2

2

2

3

3

2

2

2

2

3

2

3

4

F0.1

5

5

1

1

1

1

1

1

1

1

1

1

1

1

1

1

5

5

F0.3

4

4

2

2

3

3

3

3

2

2

3

3

3

3

2

3

4

3

F0.5

2

2

3

4

4

4

4

4

5

5

4

4

4

4

4

4

2

2

F0.7

1

1

4

3

5

5

5

5

4

4

5

5

5

5

5

5

1

1

149

Figure 4.
.1.—The west basin (WB central basin (CB), a east basin (EB) geom
B),
and
n
morphologic
regions of Lake Erie have distinc bathymetric and water quality attr
o
ct
r
ributes. The main walley
ye
populatio occurs in the west and central bas
on
d
sins.

150

Figure 4.
.2.—Alterna
ative relation
nships for wa
alleye stock size and age recruitme dynamics.
e-2
ent
The best fitting three parameter (alpha, beta, error) Ricke stock-recr
e
(
er
ruitment fun
nction (solid line)
from the most recent SCA assess
t
sment model (points) wa one possib realizatio of the true
l
as
ble
on
e
s.
d
one
using MCMC
C;
dynamics Others (e.g., dashed lines) were developed (o for each simulation u
see text for details) to illustrate uncertainty associated wi defining an underlyin stockf
o
u
a
ith
ng
recruitme relationship.
ent

151

Figure 4.
.3.—Selected harvest po
d
olicies that were used to t
w
translate ass
sessment info
formation
(estimate population abundance (SCA), pan A; standa
ed
n
e
nel
ardized surve CPE (SI), panel B) in
ey
nto
an allowa fishing mortality rat (F), which was then u
able
te
h
used to deriv total allow
ve
wable catch
(TAC). In applicatio TAC was obtained di
I
on,
s
irectly from survey CPE (T.3.32; sho against F
E
own
t
here to fa
acilitate visu comparisons). Specif control ru (see Tab 4.3) were used to des
ual
fic
ules
ble
e
scribe
alternativ feedback (FB - solid line, panel A and B), con
ve
l
nstant fishin mortality ( x - dotted line,
ng
(F
panel A), and conditi
ional constan catch (CC - dashed lin panel A) types of har
nt
C
ne,
rvest policie
es.
152

Figure 4.
.4.—Plots sh the distr
how
ribution of mean comme
m
ercial harves (# of age-2 and older) over
st
2
a 50-year time horizo for each set of manag
r
on
s
gement proce
edures. Alte
ernative type of harvest
es
t
control ru that wer evaluated included co
ules
re
onstant fishin mortality (Fx, where x is the mort
ng
tality
rate; top panel), feedb
back (FB, se figure 4.3 for graphica representa
ee
al
ation; middle panel), and
e
d
condition constant catch (CC; bottom panel) based poli
nal
b
icies that we informed by either an
ere
d
n
annual or 3-year stati
r
istical catch-at-age (SCA or an annu survey in
A)
ual
ndex of abun
ndance (SI) set
of manag
gement proce
edures (see Table 4.3 for details). S ubscripts associated wit FB policie
T
r
th
es
153

refer to restricting annual deviations in fishing mortality to no more than 20% of the previous
year (FB20%); fishing mortality set by moving average according to the three most recent years
(FB3MA); a constant catch employed during interim (non-assessment) years (FBCC); and the
fishing mortality rate held constant during interim years (FBCF). Box plots indicate the median
th

th

(line within the box), the 25 and 75 percentiles (lower and upper box boundaries,
th

th

respectively), the 10 and 90 percentiles (lower and upper error bars, respectively), and
th

th

observations below the 10 and above the 90 percentiles (open circles).

154

Figure 4.
.5.—Stability in commer
y
rcial harvest for alternati sets of m
t
ive
management procedures.
Plots sho the distrib
ow
bution of the variation (c
e
coefficient o variation; CV) in comm
of
mercial harv
vest
over a 50
0-year time horizon. Pan
h
nels, box plo and abbr
ots,
reviations follow the sam conventio
me
on
laid out in Figure 4.4
i
4.

155

Figure 4.
.6.—Risk tha population size declin to an und
at
n
nes
desirable lev for alterna
vel
ative sets of
f
managem procedu
ment
ures. Plots show the dist
s
tribution of t mean percentage of y
the
years that
walleye abundance falls below 15 million (ag
a
fa
ge-2 and old over a 50
der)
0-year time horizon. Pa
anels,
box plots and abbrev
s,
viations follo the same convention laid out in F
ow
e
n
Figure 4.4.

156

Figure 4.
.7.—Risk tha the popula
at
ation is below a standard reference p
d
point for alte
ernative sets of
managem procedu
ment
ures. Plots show the dist
s
tribution of t mean percentage of y
the
years that
walleye spawning sto size is le than 20% of the unfis
s
ock
ess
%
shed spawni stock siz over a 50-year
ing
ze
time hori
izon. Panels box plots, and abbreviations follow the same c
s,
w
convention laid out in Fi
igure
4.4.

157

Figure 4. Tradeoff between lev of comm
.8.
f
vels
mercial harv and the r associate with falli
vest
risk
ed
ing
below a population re
p
eference poi for altern
int
native data co
ollection and assessment procedures
d
t
s
using con
nstant fishing mortality rate (Fx; top panel) and f
r
feedback (bo
ottom panel) policies.
)
Tradeoff associated with conditi
fs
ional constan catch poli
nt
icies have be superimp
een
posed (singl
le
symbols, bottom pan
nel). Points represent the median val from the distribution of simulate
r
e
lue
n
ed
results.
158

Figure 4. Tradeoff between lev of stabil in comm
.9.
f
vels
lity
mercial harve (coefficie of variati
est
ent
ion;
CV) and the risk asso
ociated with the populati falling to an undesirable level fo alternative data
ion
o
or
e
collection and assessment proced
n
dures using constant fish
c
hing mortalit rate (Fx; to panel) an
ty
op
nd
feedback (bottom pan policies Tradeoffs associated w conditio constan catch polic
k
nel)
s.
with
onal
nt
cies
have been superimpo
osed (single symbols, bo
ottom panel). Points repr
.
resent the m
median value from
mulated resu
ults.
the distribution of sim
159

Figure 4.
.10. Tradeof between le
ff
evels of com
mmercial har
rvest and rec
creational cat
tch-per-effor
rt
(CPE) fo alternative data collect
or
e
tion and asse
essment proc
cedures usin constant f
ng
fishing morta
ality
rate (Fx; top panel) and feedback (bottom pan policies Tradeoffs associated w conditio
a
k
nel)
s.
with
onal
constant catch policie have been superimposed (single s
es
n
symbols, bot
ttom panel). Points repr
resent
the media value from the distrib
an
m
bution of sim
mulated resul
lts.
160

APPENDIX 4B

Additional Policy Performance Comparisons

161

Figure 4.
.11.—Sensit
tivity of selec performan measure to the spat allocation of commercial
ct
nce
es
tial
n
fishing mortality (fol
m
llowing “recent” or “hist
torical” trend see text d
ds;
details). Sho are resu
own
ults
based on feedback (F harvest control polic for each of three dat collection and assessm
FB)
c
cies
h
ta
ment
schemes (annual SCA annual SI and 3-year SCA). The ordinate rep
A,
I,
r
e
presents multiple scales.
.
Box plots and abbrev
viations follo the same convention laid out in F
ow
Figure 4.4.

162

Figure 4.
.12.—Plots show the dis
s
stribution of mean walley abundanc (# of age-2 and older) over
ye
ce
)
a 50-year time horizo for alterna
r
on
ative sets of managemen procedure Panels, b plots, and
f
nt
es.
box
d
abbreviat
tions follow the same co
onvention lai out in Fig
id
gure 4.4.

163

.13.—Stabili in popula
ity
ation size for alternative sets of mana
r
agement pro
ocedures. Pl
lots
Figure 4.
show the distribution of the varia
e
n
ation (coeffic
cient of varia
ation; CV) in walleye ab
n
bundance ov a
ver
50-year time horizon Panels, bo plots, and abbreviatio follow th same conv
t
n.
ox
d
ons
he
vention laid out
in Figure 4.4.
e

164

Figure 4.
.14.—Plots show the dis
s
stribution of mean recrea
ational catch
h-per-effort (
(CPE) over a 50year time horizon for alternative sets of mana
e
r
agement pro
ocedures. Pa
anels, box pl
lots, and
abbreviat
tions follow the same co
onvention lai out in Fig
id
gure 4.4.

165

Figure 4.
.15.—Plots show the dis
s
stribution of mean age (# years) in th population over a 50-y
#
he
n
year
time hori
izon for alter
rnative sets of managem procedu
o
ment
ures. Panels, box plots, a abbrevia
,
and
ations
follow th same conv
he
vention laid out in Figure 4.4.

166

Figure 4.
.16.—Plots show the dis
s
stribution of mean comm
mercial yield over a 50-year time hor
rizon
for altern
native sets of managemen procedure Panels, b plots, an abbreviati
f
nt
es.
box
nd
ions follow t
the
same con
nvention laid out in Figu 4.4.
d
ure

167

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168

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