SIMULATION ANALYSES OF INTEGRATED TAGGING AND CATCH-AT-AGE ANALYSIS
MODELS AND APPLICATION TO LAKE ERIE WALLEYE
By
Matthew T. Vincent

A DISSERTATION
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
Fisheries and Wildlife – Doctor of Philosophy
2017

ABSTRACT
SIMULATION ANALYSES OF INTEGRATED TAGGING AND CATCH-AT-AGE ANALYSIS
MODELS AND APPLICATION TO LAKE ERIE WALLEYE
By
Matthew T. Vincent
Integrated tagging and catch-at-age analysis (ITCAAN) models incorporate tag-recovery data within
statistical catch-at-age models for spatially-explicit assessment of fish stocks. I investigated two
tag-recovery frameworks for ITCAAN models that assumed natal homing spawning behavior:
release-conditioned and recovery-conditioned. In Chapter 1, I investigated the performance of a
release-conditioned ITCAAN model under varying levels of parameter complexity, movement rates,
data quality, and misspecification of natural mortality or reporting rates. The release-conditioned
ITCAAN model simultaneously estimated movement rates, natural mortality, and tag reporting
rates, though accuracy and precision of model estimates decreased with greater model complexity
and fewer tags released. In Chapter 2, I investigated a recovery-conditioned ITCAAN model under
a range of model complexities, different movement rates, misspecification of natural mortality or
reporting rates, and spatially varying reporting rates. The recovery-conditioned ITCAAN model
accurately estimated relative reporting rates at low intermixing rates. Biased estimates of individual
population abundance resulted when intermixing was high and the reporting rate was assumed to
be spatially constant, but the true reporting rates were not. I recommend recovery-conditioned
ITCAAN model only be used for assessment of intermixed fish stocks when there is high certainty
of spatially constant reporting rates. Both release- and recovery-conditioned ITCAAN models
had difficulty estimating individual population abundances and reporting rates under high rates of
movement and large differences in population sizes. For both ITCAAN frameworks, estimation of
both natural mortality and reporting rates reduced the accuracy and precision of model estimates, but
estimates were less biased than misspecifying one of these parameters by 50%. In all investigated
simulations, parameter estimates from the release-conditioned ITCAAN model were more accurate
and precise compared to the recovery-conditioned ITCAAN model. In Chapter 3, I examined

the ability of a release-conditioned ITCAAN model to estimate time-varying natural mortality
and reporting rate parameters and sensitivity to tag-shedding, high-reward tag-recovery data, and
seasonal movement dynamics. Natural mortality and reporting rate estimates were most precise
and accurate when estimated in 5-year time blocks. Estimation of natural mortality and reporting
rates as temporally constant when reporting rates decreased linearly over time caused severe bias
in abundance estimates, especially as the frequency of high-reward tag release events decreased.
I recommend that high-reward tags be released annually to increase the precision and accuracy
of ITCAAN model estimates. The release-conditioned ITCAAN model was sensitive to whether
the operating model simulated tag-shedding and seasonal movement dynamics. In Chapter 4, a
release-conditioned ITCAAN model was applied to Lakes Erie and Huron walleye (Sander vitreus)
data and estimates were compared to current assessment models. Reasonable fits to all data sources
were obtained for an ITCAAN model that estimated a single reporting rate for all recreational
fisheries and assumed the effective sample size of the tag-recovery data was equal to the number
of tags released divided by 10. Estimates of population abundance from the ITCAAN model
were similar to the model currently used to manage Lake Huron walleye. Conversely, estimates of
abundance and natural mortality for the western/central basin of Lake Erie were lower compared
to the assessment model currently used to manage the stock. Estimates of natural mortality and
abundance for the eastern basin of Lake Erie from the ITCAAN model were larger than estimates for
the current assessment model. Based on results from Chapters 1 and 3 the estimates of abundance
for the eastern basin of Lake Erie may be overestimated. Given the level of movement within and
between Lakes Erie and Huron, ITCAAN models may be a beneficial assessment methodology for
management. I recommend future tagging studies of walleye on Lakes Erie and Huron be designed
such that high-reward tags and standard-reward tags be released annually so that ITCAAN models
can provide accurate abundances, natural mortality, and reporting rates estimates. Additionally, I
recommend creel surveys be conducted on the Huron-Erie corridor by the Michigan Department of
Natural Resources and Ontario Ministry of Natural Resources and Forestry to measure the currently
unaccounted for walleye harvest, which is likely a significant source of mortality.

ACKNOWLEDGEMENTS

This dissertation would not have been possible without the help from a multitude of people
to whom I would like to express my sincere gratitude. Primarily, I would like to thank Dr.
Travis Brenden for his counseling and willingness to discuss the myriad questions that occurred
during this process. Additionally, the quick turn-around and thorough revisions of the writing
contained herein are immensely appreciated. I would also like to acknowledge my graduate
committee members: Drs. Jim Bence, Andy Finley and Dan Hayes for their contributions and
recommendations to this research. Interactions and discussions with graduate students, post-docs,
and staff of the Quantitative Fisheries Center provided additional insight and inspiration. The
graduate students of the Fisheries and Wildlife Department at MSU were instrumental in providing
distractions, entertainment, and relaxation through social gatherings and willingness to play on
various intramural sports teams. Last, but by no means least, I would like to thank my family and
friends for encouragement and support as I pursued my academic interests.
Partial funding for this research was provided by grant 2012.1250 from the Great Lakes Fishery
Trust and 2013_BRE_44025 from the Great Lakes Fishery Commission. Additional funding
support was provided by Supporting Partners of the Michigan State University Quantitative Fisheries
Center. The data used in Chapter 4 were provided by the Walleye Task Group and Michigan DNR.
Specifically, I would like to thank Dave Fielder for providing his model of Lake Huron walleye
and the associated data; I am obliged to Jason Robinson, Andy Cook, Megan Belore, Matt Faust,
and Michael Hosack for providing data. This work would not have been possible without the High
Performance Computing Center provided by the Institute for Cyber-Enabled Research at Michigan
State University. Specifically, I would like to thank Pat Bills for answering many of my questions
and providing additional insight of high performance computing and Dirk Colbry for introducing
the concepts of how to use the system and leverage the computing power to my advantage through
parallel computing. This dissertation was formated using the LATEXpackage developed by Alan
Munn and additional code he provided, for which I am very appreciative.
iv

PREFACE

The chapters in this dissertation were drafted as standalone papers that will be submitted for
publication in peer-reviewed journals. Chapter 1 was submitted and accepted for publication in
the Canadian Journal of Fisheries and Aquatic Sciences. When submitted, all other chapters will
include one or more co-authors. Consequently, all chapters are written with first person, plural
narratives, even though I am listed as the sole author of the dissertation. All references are formatted
in a style consistent with the Canadian Journal of Fisheries and Aquatic Sciences.

v

TABLE OF CONTENTS

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

ix

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

xi

INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Lakes Erie and Huron Walleye . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
CHAPTER 1

SIMULATION TESTING THE ROBUSTNESS OF A MULTI-REGION
TAG-INTEGRATED ASSESSMENT MODEL THAT EXHIBITS NATAL HOMING AND ESTIMATES NATURAL MORTALITY AND REPORTING RATE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Lakes Erie and Huron walleye . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Operating Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
ITCAAN Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Simulation Scenarios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Group 1: Varying Movement and Reporting Rate and Natural Mortality
Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Group 2: Sensitivity to Misspecified Reporting Rate and Natural Mortality
Group 3: Data Quality . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Group 4: Spatial Complexity in Reporting Rates and Natural Mortalities . .
Group 5: Equal Productivity . . . . . . . . . . . . . . . . . . . . . . . . .
Performance Metrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Operating Model Trends in Abundance . . . . . . . . . . . . . . . . . . . . . . . .
ITCAAN Model Convergence . . . . . . . . . . . . . . . . . . . . . . . . . . . .
ITCAAN Model Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Recruitment Relative Error . . . . . . . . . . . . . . . . . . . . . . . . . .
Movement Rate Actual Error . . . . . . . . . . . . . . . . . . . . . . . . .
Natural Mortality and Reporting Rate Relative Error . . . . . . . . . . . .
Total Abundance Relative Error . . . . . . . . . . . . . . . . . . . . . . .
Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
APPENDICES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
APPENDIX 1.A TABLES AND FIGURES . . . . . . . . . . . . . . . . . . . . . . .
APPENDIX 1.B
PARAMETER LIST AND MODEL EQUATIONS . . . . . . . . . .
BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

vi

18
18
18
21
22
23
26
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29
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30
31
31
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34
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36
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46
47
61
67

CHAPTER 2

PARAMETER ESTIMATION PERFORMANCE IN A RECOVERY-CONDITIONED
INTEGRATED TAGGING CATCH-AT-AGE ANALYSIS MODEL . . . . . 73
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
Lakes Erie and Huron Walleye . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
ITCAAN Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
Simulation Scenarios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
Group 1: Estimation of Movement, Relative Reporting Rates, and Natural
Mortality Under Varying Intermixing Rates . . . . . . . . . . . . 81
Group 2: Regionally Varying Reporting Rates . . . . . . . . . . . . . . . . 82
Group 3: Sensitivity to Misspecified Natural Mortality and Equal Productivity 83
Performance Metrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
ITCAAN Model Convergence . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
Model Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
Total Abundance Relative Error . . . . . . . . . . . . . . . . . . . . . . . 85
Population Abundances Relative Error . . . . . . . . . . . . . . . . . . . . 86
Natural Mortality and Relative Reporting Rates Relative Error . . . . . . . 87
Movement Rate Relative Error . . . . . . . . . . . . . . . . . . . . . . . . 88
Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
APPENDIX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

CHAPTER 3

TESTING COMMON ASSUMPTIONS USED IN SIMULATIONS OF
MULTI-REGION INTEGRATED TAGGING AND CATCH-AT-AGE ANALYSIS MODEL PERFORMANCE . . . . . . . . . . . . . . . . . . . . . .
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Lakes Erie and Huron Walleye . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Operating Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
ITCAAN Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Simulation Scenarios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Tag Shedding and Release of High-Reward Tags . . . . . . . . . . . . . . .
Time-Varying Natural Mortality . . . . . . . . . . . . . . . . . . . . . . .
Time-Varying Reporting Rates . . . . . . . . . . . . . . . . . . . . . . . .
Time-Varying Natural Mortality and Reporting Rates . . . . . . . . . . . .
Decreasing Reporting Rates . . . . . . . . . . . . . . . . . . . . . . . . .
High-Reward Releases Every 5 or 10 Years . . . . . . . . . . . . . . . . .
Seasonal Movement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Performance Metrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
ITCAAN Model Convergence . . . . . . . . . . . . . . . . . . . . . . . . . . . .
vii

109
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119
120
120
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123
123
124
124
124

ITCAAN Model Performance .
Total Abundance . . .
Population Abundance
Movement Rate . . . .
Natural Mortality . . .
Reporting Rate . . . .
Discussion . . . . . . . . . . . . . .
Acknowledgments . . . . . . . . . .
APPENDIX . . . . . . . . . . . . . . .
BIBLIOGRAPHY . . . . . . . . . . . .

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125
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136
137
149

A MULTI-REGION INTEGRATED TAGGING CATCH-AT-AGE ANALYSIS OF LAKE ERIE AND HURON WALLEYE . . . . . . . . . . .
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
ITCAAN Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Model Assumptions and Limitations . . . . . . . . . . . . . . . . . . . . . . .
Comparison to Existing Models . . . . . . . . . . . . . . . . . . . . . . . . . .
Management Recommendations . . . . . . . . . . . . . . . . . . . . . . . . .
Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
APPENDICES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
APPENDIX 4.A TABLES AND FIGURES . . . . . . . . . . . . . . . . . . . . .
APPENDIX 4.B
DATA SOURCES . . . . . . . . . . . . . . . . . . . . . . . . .
APPENDIX 4.C
PARAMETER LIST AND MODEL EQUATIONS . . . . . . . .
BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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155
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196
201
206

CHAPTER 4

CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214

viii

LIST OF TABLES

Table 1.A.1:

Abbreviations used in figures and text, model characteristics, and convergence rates of the ITCAAN model for investigated scenarios. . . . . . . . . . 47

Table 1.A.2:

Distributions and variance or effective sample size (ESS) assumed to simulate different data sources and stock-recruitment productivity assumptions
for scenarios investigated. . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

Table 1.B.1:

Symbols and descriptions of variables used in Operating and ITCAAN
models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

Table 1.B.2:

Equations used to model and estimate population dynamics in Operating
and ITCAAN models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

Table 2.A.1:

Regional reporting rates, average fishing mortality, unfished spawning
stock biomass, and recruitment steepness specified in the operating model
for investigated scenarios, where SSB is spawning stock biomass. . . . . . . 96

Table 2.A.2:

Abbreviations, model characteristics, and convergence rates of simulation
scenarios to investigate the influence of parameterization and movement
(Group 1), spatially varying reporting rate (Group 2), and misspecification of natural mortality or reporting rate (Group 3), where movement is
estimated unless noted. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

Table 3.A.1:

Abbreviations used in figures and text, operating and ITCAAN model characteristics, number of iterations need to reach 1000 converged estimates,
and convergence rates of the ITCAAN model for investigated scenarios. . . . 138

Table 4.A.1:

Number of standard (S) and reward (R) tags released from 1993 to 2015
and tag retention parameters for Ontario Ministry of Natural Resources
(OMNRF) in the Lake Huron region and in western basin of Lake Erie,
Michigan Department of Natural Resources (MDNR) in the Lake Huron
region and in the western basin of Lake Erie, Ohio in the western basin
of Lake Erie, New York State Department of Environmental Conservation
(NYSDEC) and Pennsylvania Fish and Boat Commission combined in the
eastern basin of Lake Erie and the instantaneous retention (Îą) and chronic
shedding (β) parameters for each agency. . . . . . . . . . . . . . . . . . . . 183

ix

Table 4.A.2:

Region of activity, variance ratios for observed values and processes error
of catchability coefficients for fisheries and surveys modeled. An X in the
selectivity, catchability, reporting rate or annual F column indicates these
parameters were estimated for this fishery/survey. Reporting rates with
the same superscript were assumed to have the same values. . . . . . . . . . 185

Table 4.A.3:

Data availability for fisheries and surveys modeled in a three region ITCAAN model for Lakes Erie and Huron Walleye, where § indicates tag
recoveries were combined and modeled as a single fishery. . . . . . . . . . . 186

Table 4.C.1:

Symbols and descriptions of variables used in Operating and ITCAAN model.201

Table 4.C.2:

Equations used to model and estimate population dynamics in ITCAAN
models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203

Table 4.C.3:

Likelihood Equations and penalties used in the ITCAAN model. . . . . . . . 205

x

LIST OF FIGURES

Figure 1.A.1:

Movement dynamics simulated by the four-region operating model assuming natal homing. The left half of the figure represents fish during
spawning at the beginning of every year, which are assumed to return to
their natal population to spawn. The right half of the figure shows the
distribution of fish during the remainder of the year that mix to all harvest
regions and stay for the rest of the year. . . . . . . . . . . . . . . . . . . . . 50

Figure 1.A.2:

Ricker stock-recruit relationships used to create the recruitment dynamics
of the four populations in the simulation. Note the large difference in axes
scale between the two panels. . . . . . . . . . . . . . . . . . . . . . . . . . 51

Figure 1.A.3:

Total abundance trends of each population for two different scenarios in
a spatially-explicit operating model for 1000 simulation iterations. The
left column of figures is for populations with 1% movement and the right
column is for populations with 20% movement to non-natal regions. The
lines show three examples of simulated time series of abundance for each
population. Whiskers on the boxplots extend to 1.5 times the interquartile
range or the most extreme observed data point, whichever is less extreme.
Relative errors outside the whisker range were not plotted. . . . . . . . . . 52

Figure 1.A.4:

Relative error (%) of annual recruitment estimates for each population
of an ITCAAN model under different movement rates and parameter estimation assumptions (scenario Group 1) for 1000 simulation iterations.
Table 1.A.1 lists the model abbreviations and corresponding model components. Whiskers on the boxplots extend to 1.5 times the interquartile
range or the most extreme observed data point, whichever is less extreme.
Relative errors outside the whisker range were not plotted. Note the
difference in y-axis scale among populations. . . . . . . . . . . . . . . . . 53

Figure 1.A.5:

Relative error (%) of recruitment estimates for each population of an
ITCAAN model under scenarios investigating misspecfied natural mortality and reporting rates, data quality, spatial complexities, and equal
productivities (scenario Groups 2–5) for 1000 simulation iterations. Table 1.A.1 lists the model abbreviations and corresponding model components. Whiskers on the boxplots extend to 1.5 times the interquartile
range or the most extreme observed data point, whichever is less extreme.
Relative errors outside the whisker range were not plotted. Note the
difference in y-axis scale among populations. . . . . . . . . . . . . . . . . 54

xi

Figure 1.A.6:

Actual error of movement rates from all populations to individual harvest
regions of an ITCAAN model under different movement rates and parameter estimation assumptions (scenario Group 1) for 1000 simulation
iterations. Table 1.A.1 lists the model abbreviations and differences in
operating and ITCAAN models. Whiskers on the boxplots extend to 1.5
times the interquartile range or the most extreme observed data point,
whichever is less extreme. Actual errors outside the whisker range were
not plotted. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

Figure 1.A.7:

Actual error of movement rate estimates from all populations to individual harvest regions of an ITCAAN model under scenarios investigating
misspecified natural mortality and reporting rates, data quality, spatial
complexities, and equal productivities (scenario Groups 2–5) for 1000
simulation iterations. Table 1.A.1 lists the model abbreviations and corresponding model components. Whiskers on the boxplots extend to 1.5
times the interquartile range or the most extreme observed data point,
whichever is less extreme. Actual errors outside the whisker range were
not plotted. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

Figure 1.A.8:

Relative error (%) of natural mortality and regional reporting rate estimates of an ITCAAN model under different movement rates and parameter
estimation assumptions (scenario Group 1) for 1000 simulation iterations.
Table 1.A.1 lists the model abbreviations and corresponding model components. Whiskers on the boxplots extend to 1.5 times the interquartile
range or the most extreme observed data point, whichever is less extreme.
Relative errors outside this range were not plotted. . . . . . . . . . . . . . . 57

Figure 1.A.9:

Relative error (%) of natural mortality (first plot in each pair) and reporting rate (second in pair) estimates for each region of an ITCAAN model
under scenarios investigating misspecfied natural mortality and reporting
rates, data quality, spatial complexities, and equal productivities (scenario Groups 2–5) with BEst20 plotted as a reference for 1000 simulation
iterations. Table 1.A.1 lists the model abbreviations and corresponding
model components. Whiskers on the boxplots extend to 1.5 times the
interquartile range or the most extreme observed data point, whichever is
less extreme. Relative errors outside this range were not plotted. Circles
indicate a parameter specified in the ITCAAN model, and boxplots only
presented in region 1 were estimated as spatially constant. . . . . . . . . . . 58

Figure 1.A.10: Relative error (%) of total abundances for all years aggregated from an
ITCAAN model for all simulation scenarios described in Table 1.A.1
for 1000 simulation iterations. Whiskers on the boxplots extend to 1.5
times the interquartile range or the most extreme observed data point,
whichever is less extreme. Relative errors outside the whisker range were
not plotted. Note the difference in scale between the top and bottom panel. . 59
xii

Figure 1.A.11: Relative error (%) of population-specific abundances and total abundances (summed across populations) for 1000 simulation iterations of an
ITCAAN model for a 1% movement with natural mortality and reporting
rate fixed at true values in the left column and in the right column 20%
movement with natural mortality and reporting rate estimated. The lines
show three examples of time series of relative error in abundance estimates for a single simulation in each population. Whiskers on the boxplots
extend to 1.5 times the interquartile range or the most extreme observed
data point, whichever is less extreme. Estimates outside the whisker range
were not plotted. Note the difference in y-axis scale among populations. . . 60
Figure 2.A.1:

Relative error (%) of abundance summed across populations for a four region ITCAAN model under different intermixing rates and parameter estimation assumptions (Group 1), spatially varying reporting rates (Group
2), and misspecification of natural mortality and equal productivities
(Group 3) for 1000 simulation iterations. The grey colored boxplot corresponds to the y-axis on the right side of the bottom plot. Table 2.A.2 lists
the model abbreviations and corresponding model components. Whiskers on the boxplots extend to 1.5 times the inter-quartile range or the
most extreme relative error, whichever is less extreme. Relative errors
outside the whisker range were not plotted. . . . . . . . . . . . . . . . . . 98

Figure 2.A.2:

Relative error (%) of population abundance for a four region ITCAAN
model under different intermixing rates and parameter estimation assumptions. The grey colored boxplots corresponds to the y-axis on the
right side of the figure. Table 2.A.2 lists the model abbreviations and
corresponding model components. Whiskers on the boxplots extend to
1.5 times the interquatile range or the most extreme relative error, which
ever is less extreme. Relative errors outside the whisker range were not
plotted. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

Figure 2.A.3:

Relative error (%) of population abundance for a four region ITCAAN
model under spatially varying reporting rates (Group2) and misspecification of natural mortality and equal productivities (Group 3) for 1000
simulation iterations. The grey colored boxplots corresponds to the yaxis on the right side of the figure, note that only population 3 of scenario
RV1Canc and population 4 of scenario RV2Canc corresponds to the axis
on the right. Table 2.A.2 lists the model abbreviations and corresponding
model components. Whiskers on the boxplots extend to 1.5 times the
interquatile range or the most extreme relative error, which ever is less
extreme. Relative errors outside the whisker range were not plotted. . . . . 100

xiii

Figure 2.A.4:

Relative Error (%) of relative reporting rates and natural mortality for a
four region ITCAAN model under different intermixing rates and parameter estimation assumptions (Group 1), spatially varying reporting rates
(Group2) and misspecification of natural mortality and equal productivities (Group 3) for 1000 simulation iterations. Table 2.A.2 lists the model
abbreviations and corresponding model components. Dots indicate parameters that are fixed within the ITCAAN model at incorrect values.
Whiskers on the boxplots extend to 1.5 times the interquatile range or the
most extreme relative error, which ever is less extreme. Relative errors
outside the whisker range were not plotted. . . . . . . . . . . . . . . . . . . 101

Figure 2.A.5:

Relative Error (%) of movement rates of all populations to a harvest
region for a four region ITCAAN model under different intermixing
rates and parameter estimation assumptions (Group 1), spatially varying
reporting rates (Group2) and misspecification of natural mortality and
equal productivities (Group 3) for 1000 simulation iterations. Table 2.A.2
lists the model abbreviations and corresponding model components. Dots
indicate parameters that are fixed within the ITCAAN model at the true
value. Whiskers on the boxplots extend to 1.5 times the interquatile range
or the most extreme relative error, which ever is less extreme. Relative
errors outside the whisker range were not plotted. . . . . . . . . . . . . . . 102

Figure 3.A.1:

Examples of annual natural mortalities and reporting rates for the commercial fishery in region 1 simulated by a truncated first-order autoregressive process. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140

Figure 3.A.2:

Matrices used to simulate seasonal movement and the average annual
movement rates for the Season scenario, where the rows are the natal
population the fish come from and the columns are the region to which
the fish move. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

Figure 3.A.3:

Relative error (%) of abundance summed across populations for a four
region ITCAAN model under differing assumptions of tag loss, frequency
of high-reward tag releases, whether movement was simulated annually
or seasonally, the true dynamics of natural mortality and reporting rates,
and parameterization in the ITCAAN model. Table 3.A.1 lists the model
abbreviations and corresponding model components. Whiskers on the
boxplots extend to 1.5 times the inter-quartile range or the most extreme
relative error, whichever is less extreme. Relative errors outside the
whisker range were not plotted. . . . . . . . . . . . . . . . . . . . . . . . 142

xiv

Figure 3.A.4:

Relative error (%) of population abundance for a four region ITCAAN
model under differing assumptions of tag loss, frequency of high-reward
tag releases, whether movement was simulated annually or seasonally, the
true dynamics of natural mortality and reporting rates, and parameterization in the ITCAAN model. Table 3.A.1 lists the model abbreviations and
corresponding model components. Whiskers on the boxplots extend to
1.5 times the interquartile range or the most extreme relative error, which
ever is less extreme. Relative errors outside the whisker range were not
plotted. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

Figure 3.A.5:

Same as Figure 3.A.4 but for the movement rate for all populations into
the region. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144

Figure 3.A.6:

Same as Figure 3.A.4 but for natural mortality (top plot) and reporting
rate parameters (bottom 4 plots), where the boxplot on the left of each
pair for the bottom 4 plots is the relative error for the commercial fishery
and the boxplot on the right is for the recreational fishery. . . . . . . . . . . 145

Figure 3.A.7:

Relative Error (%) of annual natural mortality for varying frequencies of
high-reward tag releases and when natural mortality was estimated annually, in 5-year time blocks, or as temporally constant. Scenario abbreviations and model components are presented in Table 3.A.1. Whiskers
on the boxplots extend to 1.5 times the interquartile range or the most
extreme relative error, which ever is less extreme. Relative errors outside
the whisker range were not plotted. . . . . . . . . . . . . . . . . . . . . . . 146

Figure 3.A.8:

Relative Error (%) of annual reporting rates of the commercial fishery in
region 1 for scenarios where reporting rates were simulated as linearly
decreasing and high-reward tags were released annually or every 5 or
10 years, crossed with reporting rates estimated annually, in 5-year time
blocks, or as temporally constant. Scenario abbreviations and model
components are presented in Table 3.A.1. Whiskers on the boxplots
extend to 1.5 times the interquartile range or the most extreme relative
error, which ever is less extreme. Relative errors outside the whisker
range were not plotted. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147

Figure 3.A.9:

Same as Figure 3.A.8, but for the recreational fishery in region 1. . . . . . . 148

Figure 4.A.1:

Boundary lines of the three regions modeled by the ITCAAN Model and
location of tag releases indicated by triangles (A). Tag recovery locations
for tags that were released in HUR (B), the WLE (C), and the ELE region
(D) between 1993 and 2015 indicated by circles. . . . . . . . . . . . . . . 187

xv

Figure 4.A.2:

Estimates and 95% confidence interval of reporting rate for the recreational fisheries across all regions, natural mortality for the Huron, WLE,
and ELE regions and movement rates from WLE population to HUR,
where the x-axis is the value the weighting factor for the tag-recovery data. . 188

Figure 4.A.3:

Estimated total walleye abundance in the three regions of the ITCAAN
model for the time period 1993 through 2015 for five weighting factors
of the tag-recovery data, where the tag weighting factor is the value that
the multinomial likelihood was divided by. . . . . . . . . . . . . . . . . . . 189

Figure 4.A.4:

Observed (open circles) and predicted (solid line) catch per effort of
walleye of the six fishery-independent surveys used in a three region
ITCAAN model for Lake Huron and Lake Erie. . . . . . . . . . . . . . . . 190

Figure 4.A.5:

Observed (open circles) and predicted (solid line) number of walleye
harvested by fishery from a three region ITCAAN model for Lake Huron
and Lake Erie. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191

Figure 4.A.6:

Selectivity at age for fisheries and surveys operating in the three regions
of a tag integrated catch-at-age model for walleye in Lake Huron and
Lake Erie. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192

Figure 4.A.7:

Total instantaneous regional mortality at age experienced in the three
regions estimated by a tag integrated catch-at-age model for Lake Erie
and Huron walleye. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193

Figure 4.A.8:

Estimated population abundance from assessment models currently used
to manage the walleye fisheries in Lakes Huron and Erie (solid line)
with 95% confidence interval (green hashed region) and from a three
region tag integrated catch-at-age model that estimates intermixing of the
populations (dashed line) with the 95% confidence interval (shaded region). 194

Figure 4.A.9:

Recruitment of age-2 walleye to the Lake Huron, western and eastern
basin Lake Erie populations as estimated by a three region tag-integrated
catch-at-age assessment model and the 95% confidence interval shown
by the shaded region. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195

xvi

INTRODUCTION

Marine and freshwater organisms are harvested to feed an ever-growing human populous. However,
ecosystem capacity to sustain harvest is inherently limited because species have a finite capacity
to replace harvested biomass through growth and reproduction. Therefore, fisheries management
is often focused on maximizing yield from a population, while simultaneously maintaining a
spawning stock abundant enough to successfully reproduce and replace the current stock (i.e.,
sustainable fishing) (Hilborn and Walters 1992). Management policies designed to keep biomass
within sustainable levels are often based on the results of stock assessment methods, which estimate
current and historical abundances, mortality components, and recruitment levels (Butterworth and
Punt 1999; Punt et al. 2001).
Assessment models have become increasingly complex, but many still make the assumption
that harvest and survey data are from one reproductive unit and immigration and emigration rates
for the region are negligible (Beverton and Holt 1957; Hilborn and Walters 1992; Goethel et al.
2011). However, there is increasing recognition that this assumption is commonly violated in
both freshwater and marine systems (Haist et al. 1999; Punt et al. 2000; Humston et al. 2004;
McGarvey et al. 2010; Goethel et al. 2015a; Vandergoot and Brenden 2014). The inclusion of
spatial dynamics in stock assessment models are at the forefront of current assessment modeling
research (Goethel et al. 2011). Throughout this dissertation, a stock will be defined as an exploited
fishery unit defined by the region of harvest, typically a management area (Cadrin et al. 2004).
Populations will be defined as interbreeding groups of individuals that are self-sustaining and share
similar life history characteristics. In the context of modeling, the boundaries of a population
can be delineated based on environmental characteristics of the region or through management
boundaries set by jurisdictional authority. Consequently, boundaries used to designate regions for
stock assessment may not have any biological significance to the populations they are intended
to assess. Incorrect estimation of abundance and productivity by assessment models can easily
lead to the overexploitation of populations. When intermixing is high, less productive stocks are
1

susceptible to overharvest if management actions and assessment methods do not account for spatial
dynamics of the species (Ying et al. 2011; Guan et al. 2013; Hulson et al. 2013; Molton et al. 2013;
Li et al. 2014). The collapse of some economically important fish stocks has been partly attributed
to inadequately accounting for the spatial dynamics that arise from movement, such as Atlantic cod
(Gadus morhua; Fu and Fanning 2004; Hutchinson 2008) and many Pacific salmon populations
(Oncorhynchus spp.; Morishima and Henry 1999). Therefore, accounting for the movement of fish
when assessing intermixed populations is difficult, but imperative for the sustainable management
of all harvested populations.
Incorporation of spatially-explicit stock dynamics in assessment models has long been a subject
of interest (Skellam 1951; Beverton and Holt 1957; Jones 1976). However, information regarding
movement of individuals between management regions and intermixing of spawning fish populations is often lacking, and inhibits the development of spatially-explicit assessment models (Goethel
et al. 2011). Data on the movement rates of fish is obtained primarily from tagging studies using
either conventional or electronic tags (Jones 1959; Ishii 1979; Hilborn 1990). Therefore, most
models that include spatial dynamics of stocks have incorporated tagging data into the model’s
framework. Integrated tagging and catch-at-age analysis (ITCAAN) assessment models incorporate recovery information from tagging studies as data components within statistical catch-at-age
(i.e., integrated) assessment models. These models have been used to estimate the abundance and
mortality rates of multiple species (Maunder 2001; Fielder and Bence 2014; Goethel et al. 2015a).
However, parameter estimability in ITCAAN models has not been rigorously tested, and previous
simulation analyses of ITCAAN models have all assumed reproductive mixing of multiple subpopulations when testing model performance (Maunder 2001; Hulson et al. 2011, 2013; Goethel
et al. 2015b). Reproductive mixing of multiple subpopulations occurs when individuals from a
spawning populations move to a new region and then spawn in the new region, where they may stay
indefinitely (i.e., individuals become part of the spawning population in the region; Goethel et al.
2011). Alternatively, populations can mix among regions during periods of harvest but return to
their natal regions to reproduce each year. This type of movement has been referred to as population

2

overlap (Porch et al. 2001) and overlapping populations with natal homing (Goethel et al. 2011).
Spatially-explicit models that incorporate natal homing movement characteristics do not always
perform the same as models with reproductive mixing of multiple subpopulations (Cope and Punt
2011; Ying et al. 2011; Guan et al. 2013; Li et al. 2014). Testing parameter estimability of ITCAAN models accounting for natal homing and other movement dynamics is needed as differences
in model structure may affect model performance.
The inclusion of tagging data in ITCAAN models ostensibly allows the estimation of parameters beyond those generally estimated in traditional assessment models; however, the extent
of parameterization that can accurately be estimated by incorporating tagging data is uncertain.
Mixing rates, natural mortality, and reporting rates are parameters that potentially can be estimated
in ITCAAN models. Estimation of mixing or movement rates of populations is an essential process for spatially-explicit assessment models, and incorporating tagging data will likely inform the
estimation of these rates. Catch-at-age models typically use an a priori estimate of natural mortality (Doubleday 1976; Deriso et al. 1985), though attempts have been made to estimate natural
mortalities using information inherent in the age composition and simulations suggest that in the
absence of structural model error this parameter may be estimable (Fu and Quinn 2000; Wang and
Liu 2006; Lee et al. 2011; Maunder and Wong 2011; Jiao et al. 2012; Johnson et al. 2015; Sippel
et al. 2017). Conversely, tag-recovery data are frequently used to estimate the natural mortality
rates of tagged cohorts of fish (Hoenig et al. 1998; Latour et al. 2001, 2003; Frusher and Hoenig
2003; Vandergoot and Brenden 2014). ITCAAN models that use both harvest age composition and
tag-recovery data may result in reliable estimates of natural mortality. Fishery reporting rates of
recovered tags are additional parameters that are seemingly estimable in ITCAAN models (Goethel
et al. 2015b). The extent that parameters such as movement, tag reporting, and natural mortality
rates can be reliably estimated in combination with each other or with additional parameters such
as abundance and fishing mortality for multiple stocks is not currently understood. It is possible,
even likely, that some of these parameters may be confounded and the accuracy and bias of some
parameters may be affected by the degree of movement among or differences in relative size of the

3

fish populations.
Tag-recovery data can be fit to different model frameworks depending on the parameters of
interest and the validity of assumptions. Tag-recovery data are most commonly modeled as the
number of tags recovered within a given time frame and region, divided by the total number of
tags released in a given tagging event (Hilborn 1990; Maunder 1998; Punt et al. 2000; Hulson
et al. 2011, 2013; Kerr et al. 2013; Goethel et al. 2015a). This framework for tag-recovery will be
referred to as the release-conditioned model and the multinomial likelihood distribution with the
scaling constants removed used to fit these data is:

"
#
Ö Ö Ö Rir y N R
L=
vir y wi i
r

i

y

(0.0.1)

where
vir y =

R̂ir y
Ti

and

wi =

NcRi
Ti

In this formula, the accented variables are those that are predicted by the model from other
parameters, for example R̂ir y is the predicted recoveries in year y and region r, for the release
group i and R is the observed recoveries. In the equations, Ti is the total number of tags released
in group i, N Ri is the number of tags that were never recovered, and L is the likelihood. The
denominator for the calculation of v and w gives the name for this analysis of tag-recovery data:
the release-conditioned framework.
The release-conditioned model requires assumptions regarding the rates of tag induced mortality, tag shedding, and tag reporting to limit the bias in parameter estimates, and allow the separation
of mortality into fishing and natural components (Brenden et al. 2010). Some common approaches
when analyzing tag-recovery data are to assume that these rates are negligible (Kleiber et al. 1987;
Hilborn 1990), make assumptions based on expert knowledge (Hampton 1997; Vandergoot and
Brenden 2014), or to conduct specialized experiments that allow these parameters to be estimated
internally or externally to the integrated assessment model (Pollock et al. 2001, 2002; Agnew et al.
2006; Vandergoot et al. 2012; Goethel et al. 2015a). Even with these experiments, biased results can
4

still occur due to small sample sizes or incorrect model-structure assumptions. Estimates of fishing
and natural mortality rates in tag-recovery studies have been found to be sensitive to inaccuracies
in reporting rates (Brenden et al. 2010). The tag-reporting rate has been considered one of the most
difficult variables to estimate in a tagging experiment (Denson et al. 2002; Miranda et al. 2002).
Thus, the modeling of tag-recovery data in terms of total number of tags released has the potential
of being suboptimal.
An alternative formulation for analyzing tag-recovery uses the number of tags returned within a
region and time period, divided by the total number of returns from a given release event (McGarvey
and Feenstra 2002). The multinomial likelihood for the recovery-conditioned model differs from
the likelihood for the release-conditioned model in two primary ways. First, tags that were never
recovered are not predicted by the model and are not included in the likelihood. Secondly, the
denominator for the predicted proportion is the total number of tags recovered (summed across
time and space) from a release group i:
LH =

Ö Ö Ö Rir y
vir y
r

i

y

(0.0.2)

where
vir y = Í

R̂ir y

ry

R̂ir y

.

Tagging-induced mortality, tag shedding, and non-reporting rate of tag-recoveries often require
additional costly experiments to estimate. With this formulation, tagging-induced mortality, tag
shedding, and non-reporting rate of tag recoveries cancel out of the likelihood equations for this
framework if they are assumed to be spatially and temporally constant, i.e. they do not need to be
estimated (McGarvey and Feenstra 2002; McGarvey et al. 2010). This is considered beneficial as
collection of data for estimating these factors can be expensive. There have been limited evaluations
of the performance of the recovery-conditioned model (McGarvey et al. 2010), and ITCAAN models
using a recovery-conditioned framework have not been fit to many real-world fisheries data. The
recovery-conditioned tag-integrated catch-at-age model has the potential to accurately estimate
important population dynamics parameters without the possible bias introduced by the nuisance
5

tagging parameters, if indeed they are spatially and temporally constant. This could result in
more accurate and precise tag-integrated models compared to the release-conditioned models, and
thus would be a preferable model. However, this model has not been tested under circumstances
where these nuisance parameters are not spatially constant; therefore, the robustness of recoveryconditioned ITCAAN models is not presently known.

Lakes Erie and Huron Walleye
Walleye (Sander vitreus) is a piscivorous keystone species, which aggregates during the early
spring in rivers and shallow rocky reefs for spawning (Busch et al. 1975). Walleye typically exhibit
spawning-site fidelity (Crowe 1962; Hayden et al. 2014), but genetic analyses have shown there may
be significant straying and interbreeding among spawning populations (Stepien and Faber 1998;
Strange and Stepien 2007; Brenden et al. 2015; Hayden et al. 2017). After spawning, walleye often
make directed and sometimes long-distance movements towards summer feeding grounds. Feeding
grounds are believed to be selected based on thermal conditions and prey availability (Wang et al.
2007; Zhao et al. 2011; Hayden et al. 2014; Vandergoot and Brenden 2014; Herbst et al. 2016).
Long distance movement by walleye between interconnected lakes has been shown throughout
their range (Smith et al. 1952; Rasmussen et al. 2002; Wang et al. 2007; Zhao et al. 2011; Hayden
et al. 2014; Vandergoot and Brenden 2014; Herbst et al. 2017). This dispersal of walleye after
spawning is recognized to be potentially problematic for management as fish can cross multiple
jurisdictional boundaries when moving between spawning and feeding grounds. Consequently,
fisheries for walleye may depend on spawning populations and systems over which managers have
no jurisdictional authority (Brenden et al. 2015; Herbst et al. 2017).
Both historical (jaw tag) and contemporary (acoustic telemetry) tagging studies, as well as
genetic analysis have found that movement of walleye within and between Lakes Erie and Huron
occurs frequently (Vandergoot and Brenden 2014; Brenden et al. 2015; Hayden et al. 2017). For
some walleye spawning populations in the western basin of Lake Erie, movement rates to Lake
Huron were estimated at around 1–2% (Wang et al. 2007; Vandergoot and Brenden 2014; Hayden

6

et al. 2017). Movement from the western basin to the eastern basin has been shown to be substantial
through jaw tag recoveries (Wang et al. 2007; Vandergoot and Brenden 2014) and telemetry studies
(Chris Vandergoot, personal communication). Lake Erie is generally regarded as consisting of
three basins (western, central, and eastern) that increase in depth moving eastward, but decrease
in walleye abundance. The western basin population is estimated to be on the order of tens of
millions of fish (Wills et al. 2016), whereas abundance for the eastern basin population of Lake
Erie is closer to tens of thousands of fish (Zhao et al. 2011). Abundance of walleye in Lake Huron
has been estimated to be approximately one to four million fish (Fielder and Bence 2014). Given
the differences in walleye abundance between the Lake Erie basins and Lake Huron, even the low
rate of movement means that a considerable amount of the harvest in this region is fish from the
western basin population (McParland et al. 1999; Brenden et al. 2015).
Walleye are exploited commercially and recreationally throughout the Great Lakes (Pandit et al.
2013; Fielder and Bence 2014; Wills et al. 2016). The two largest fisheries for walleye in the
Great Lakes region occur in Lakes Erie and Huron (Baldwin et al. 2009). In 2000, harvest of
walleye in Lake Erie was worth $9.8 million in dock side value from commercial fisheries, which
does not account for the economic value of the recreational fishery (Baldwin et al. 2009). The
recreational fishery for walleye in Ohio during 2013 was estimated to generate $67 million in
total direct expenditures (Sohngen et al. 2015). Management of walleye in Lake Erie is currently
facilitated by the Great Lakes Fishery Commission, which was formed by the 1954 Convention on
Great Lakes Fisheries between the United States and Canada. Specifically, a walleye management
plan was developed by the Lake Erie Percid Management Advisory Group, which is comprised
of stakeholders, fisheries managers, agency fishery biologists, and stock assessment scientists.
The WTG provides annual harvest recommendations to the Lake Erie Committee (LEC) based on
assessment estimates of population status and the harvest control rules set forth by the management
plan. The LEC determines the annual total allowable catch (TAC), with harvest quotas then allocated
to individual jurisdictions based on water area (Wills et al. 2016). The four U.S. states (Michigan,
New York, Ohio, and Pennsylvania) and the Canadian province (Ontario) manage the harvest

7

of walleye through regulations specific to the jurisdiction. Presently, separate SCAA assessment
models are used to estimate walleye population abundances and mortalities in Lakes Erie and Huron
to gauge the health of the populations and assist in setting harvest regulations (Fielder and Bence
2014; Wills et al. 2016). Walleye in Lake Erie are currently managed assuming limited movement
between management areas (Wills et al. 2016), whereas the assessment in Lake Huron attempts to
account for this intermixing (Fielder and Bence 2014). There has been increasing interest in the
development and use of spatially-explicit models for assessing the walleye populations in Lakes
Erie and Huron due to the economical and ecological importance of the species and the degree of
movement that has been estimated to occur both within and between the lakes.
The current assessment model for walleye estimates the abundance of the stock in the western
and central basins of Lake Erie (Wills et al. 2016). This assessment does not account for the
intermixing of populations from other regions or the emmigration of walleye out of this region.
Although the contribution of western basin origin walleye to the harvest in the eastern basin is
acknowledged, the assessment of the eastern basin does not explicitly account for immigration
from the western basin of Lake Erie. However, previous research has attempted to estimate the
population in the eastern basin of Lake Erie and account for intermixing of fish from different
populations (Zhao et al. 2011). The assessment model for Lake Huron walleye attempts to account
for the immigration of western basin walleye by incorporating abundance estimates from the western
basin of Lake Erie assessment and the 3-year average of annual proportion of jaw tags returned
from the western basin captured in Lake Huron (Fielder and Bence 2014). However, jaw-tagging
of walleye in western basin of Lake Erie has not occurred since 2010 and recent recoveries are
infrequent. Previous attempts to integrate tag-recovery data into the assessment model for Lake
Huron ultimately resulted in the selection of the model that did not incorporate this data (Fielder
and Bence 2014). The three assessment methods used to provide management advice assume
natural mortality is known and movement of walleye between management boundaries are not fully
accounted for. Therefore, assessments that attempt to estimate natural mortality and intermixing
may be useful for management of walleye in Lakes Erie and Huron.

8

Application of tag-integrated assessment models have become increasingly common in recent
years (McGarvey et al. 2010; Hulson et al. 2013; Goethel et al. 2015a). Though it is standard
practice in stock assessments to test new modeling techniques through simulations (Bence et al.
2008), evaluation of the performance of ITCAAN models through simulation has not been widely
conducted. A comparison of model performance of release-conditioned and recovery-conditioned
models would be beneficial to fisheries scientist interested in using a spatially-explicit ITCAAN
model. The overall goal of my dissertation is to evaluate performance (i.e., parameter estimability,
parameter sensitivity) of release- and recovery-conditioned ITCAAN models and determine appropriateness of the models for application to Lakes Erie and Huron walleye. Specific objectives for
each chapter are as follows:
1. Determine precision and accuracy of parameters in release-conditioned ITCAAN models
with increasing complexity incorporated into model scenarios.
2. Evaluate precision and accuracy of parameters in recovery-conditioned ITCAAN models with
increasing complexity incorporated into model scenarios and sensitivity to the assumption
of spatially constant nuisance parameters.
3. Evaluate the sensitivity of release-conditioned ITCAAN models to common assumptions
made when evaluating model performance.
4. Apply an ITCAAN model to data from Lakes Huron and Erie walleye and determine suitability
of the model to provide management advice.

9

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10

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17

CHAPTER 1
SIMULATION TESTING THE ROBUSTNESS OF A MULTI-REGION
TAG-INTEGRATED ASSESSMENT MODEL THAT EXHIBITS NATAL HOMING AND
ESTIMATES NATURAL MORTALITY AND REPORTING RATE

Abstract
The influence of model complexity on integrated tagging and catch-at-age analysis (ITCAAN)
parameter estimation is poorly understood for populations exhibiting natal homing. We investigated ITCAAN performance under varying levels of movement, degree of similarity in population
productivities, data quality, spatial complexity in parameterization, and whether natural mortality
and/or reporting rates were fixed at actual values, estimated, or misspecified. Dynamics of four
populations with natal homing that intermixed during periods of harvest were simulated based on
Lake Erie walleye (Sander vitreus). Our results suggest, when high-quality tagging data are available, ITCAAN models are able to simultaneously estimate movement rates, natural mortality, and tag
reporting rates, though accuracy and precision of model estimates will decrease with greater model
complexity and fewer tags released. Additionally, ITCAAN models may have difficulty estimating
individual population abundances under certain movement rates when population productivities are
vastly different. ITCAAN models that estimate natural mortality and reporting rates may perform
best with similar sized populations and when data are available to assist the estimation of reporting
rates.

Introduction
Fishery scientists and managers commonly assume fish harvested in a single management unit
originate from an isolated spawning population (Beverton and Holt 1957). The validity of this
assumption has come under increased scrutiny due to recognition of stock complexity (Cadrin
et al. 2004; Goethel et al. 2011; La Valley and Feeney 2013) and the migratory behavior exhibited
by both freshwater and marine species (Punt et al. 2000; Hayden et al. 2014; Goethel et al.
18

2015a). Numerous simulation studies have shown that ignoring spatial complexity of intermixed
populations can result in overexploitation of less productive populations (Ying et al. 2011; Guan
et al. 2013; Molton et al. 2013). The collapse of some high profile fish stocks such as Atlantic cod
(Gadus morhua; Fu and Fanning 2004; Hutchinson 2008) and many Pacific salmon populations
(Oncorhynchus spp.; Morishima and Henry 1999) are believed to have in part resulted from
inadequate accounting of spatial complexity arising from movement. This in turn led to the
development and use of assessment methods that account for the spatial complexity of migratory
behavior in order to reliably estimate abundances, mortality components, and/or movement rates
of multiple populations in mixed stocks (Hampton 1991; Goethel et al. 2011; Maunder and Punt
2013).
Some terms will be explicitly defined for clarity, because many definitions exist. A stock
is defined, following that of Cadrin et al. (2004), as an exploited fishery unit defined by the
region of harvest. A population is defined as a self-sustaining group of fish that interbreed and
share similar life history characteristics. Thus a stock may be composed of individuals from
multiple populations. An intermixed fishery is any fishery that harvests individuals from multiple
populations while operating within a single management unit.
Integrated tagging and catch-at-age analysis (ITCAAN) assessment models incorporate recovery
information from tagging studies as data components within statistical catch-at-age (i.e., integrated)
assessment models. These models have been used to estimate the abundance and mortality rates
of multiple species (Maunder 2001; Fielder and Bence 2014; Goethel et al. 2015a). However,
parameter estimability in ITCAAN models has not been rigorously tested, and studies conducted
have generally assumed a particular movement dynamic. Previous simulation analyses of ITCAAN
models have all assumed reproductive mixing of multiple subpopulations when testing model
performance (Maunder 2001; Hulson et al. 2011, 2013; Goethel et al. 2015b). Reproductive
mixing of multiple subpopulations occurs when individuals from a spawning populations move to
a new region and then spawn in the new region and stay there indefinitely (i.e., individuals become
part of the spawning population in the region; Goethel et al. 2011). Alternatively, populations

19

can mix among regions during periods of harvest but return to their natal regions to reproduce
each year. This type of movement has been referred to as population overlap (Porch et al. 2001)
and overlapping populations with natal homing (Goethel et al. 2011). Spatially-explicit models
that incorporate natal homing movement characteristics do not always perform the same as models
with reproductive mixing of multiple subpopulations (Ying et al. 2011; Guan et al. 2013; Li et al.
2014). Testing parameter estimability of ITCAAN models accounting for natal homing and other
movement dynamics is needed as differences in model structure may affect model performance.
The inclusion of tagging data in ITCAAN models ostensibly allows the estimation of parameters
beyond those generally estimated in traditional assessment models; however, the extent of parameterization that can accurately be estimated by incorporating tagging data is uncertain and requires
investigation. Mixing rates, natural mortality, and reporting rates are parameters that potentially
can be estimated in ITCAAN models. Estimation of mixing or movement rates of populations is an
essential process for a spatially-explicit catch-at-age assessment model, and incorporating tagging
data will likely inform the estimation of these rates. Catch-at-age models typically require an a
priori estimate of natural mortality (Doubleday 1976; Deriso et al. 1985), though attempts have
been made to estimate natural mortalities using information inherent in the age composition with
varied success (Wang and Liu 2006; Lee et al. 2011). However, tag-recovery data frequently are
used to estimate the natural mortality rates of tagged cohorts of fish (Latour et al. 2001, 2003;
Frusher and Hoenig 2003; Vandergoot and Brenden 2014). ITCAAN models that use both harvest
age composition and tag-recovery data may result in reliable estimates of natural mortality. Fishery
reporting rates of recovered tags are additional parameters that are seemingly estimable in ITCAAN
models (Goethel et al. 2015b). The extent that parameters such as movement, tag reporting, and
natural mortality rates can be reliably estimated in combination with each other or with additional
parameters such as abundance and fishing mortality for multiple stocks is not currently understood.
It is possible, even likely, that some of these parameters may be confounded and the estimability of
some parameters may be affected by the degree of movement among or differences in relative size
of the fish populations.

20

The goal of our research was to evaluate the estimability of model parameters within a releaseconditioned ITCAAN model under a range of conditions. We used information from walleye
(Sander vitreus) populations in the Laurentian Great Lakes of North America as the basis for
simulating population dynamics and associated time series of data. However, the operating model
was intended to be sufficiently generic with stochasticity in both annual recruitments and fishing
mortalities for the results to be applicable elsewhere. Simulations were conducted exploring how
bias and precision of parameter estimates were affected by the following: 1. movement rates and
whether movement, natural mortality, and/or reporting rates were estimated or treated as known and
fixed quantities; 2. misspecification of reporting rate or natural mortality when treated as known and
fixed quantities in the ITCAAN model; 3. varying levels of data quality, including tagged cohort
size; 4. assumptions as to spatial complexity of reporting rate and natural mortality parameters
estimated in the ITCAAN model; and 5. parity in productivities of the spawning populations (i.e.,
equal stock-recruitment relationships).

Lakes Erie and Huron walleye
Walleye is a piscivorous keystone species that is harvested commercially and recreationally throughout the Great Lakes (Pandit et al. 2013). Walleye spawn in early spring either in rivers or on
shallow rocky reefs. Postspawning walleye distribute throughout the lakes (Wang et al. 2007;
Vandergoot and Brenden 2014; Hayden et al. 2014) but display a high degree of natal homing each
year while spawning (Stepien and Faber 1998; Haponski and Stepien 2014; Hayden et al. 2014).
Two of the largest and most valuable walleye fisheries in the Great Lakes are in Lakes Erie
and Huron. Tagging studies have documented the movement of walleye between Lakes Erie and
Huron via the Detroit River, Lake St. Clair, and St. Clair River (Wang et al. 2007; Vandergoot and
Brenden 2014; Hayden et al. 2014). Lake Erie is generally regarded as consisting of three basins
(western, central, and eastern) that increase in depth moving eastward, but decrease in walleye
abundance. The western basin population is estimated to be on the order of tens of millions of fish
(Wills et al. 2016), whereas abundance for the eastern basin population of Lake Erie is closer to tens
21

of thousands of fish (Zhao et al. 2011). Abundance of walleye in Lake Huron has been estimated
to be approximately one to four million fish (Fielder and Bence 2014). For some walleye spawning
populations in the western basin of Lake Erie, movement rates to the eastern basin of Lake Erie and
Lake Huron were estimated at around 1–2% (Wang et al. 2007; Vandergoot and Brenden 2014).
Given the differences in walleye abundance between the Lake Erie basins and Lake Huron, even
this low rate of movement means that a considerable amount of the harvest in these other regions
is fish from the western basin population (McParland et al. 1999; Brenden et al. 2015). There is
developing interest in using ITCAAN models as the basis for management decisions for Lakes Erie
and Huron walleye because of the degree of movement between and within the lakes and the value
of the respective fisheries.

Methods
The simulation framework used in this research consisted of an operating model that generated
and tracked the true dynamics of fish populations and tagged cohorts. Given the true dynamics
from the operating model, observed time series of data (e.g., fishery harvest in numbers caught,
fishery harvest age composition, tag-recovery data) were generated. These data were then used in
a release-conditioned ITCAAN model to estimate dynamics of the fish populations. The spatial
framework of the simulation consisted of four spawning populations that overlapped with four
regions of harvest (Figure 1.A.1). After spawning at the beginning of the year, individuals from
each of the spawning populations could move to any of the harvest regions. For simplicity, a single
fishery was assumed to operate in each region. Catch-at-age models in the Great Lakes region are
generally based on abundance. Even species for which observed harvest is biomass based (e.g.,
yellow perch (Perca flavescens)), predicted harvest is calculated based on assumed mass-at-age or
mass-at-length values (i.e., growth is not dynamically modeled in the assessment models). Thus, for
our research both the operating and ITCAAN models were predominantly abundance-based. The
four spawning populations differed considerably with regards to productivity (i.e., stock-recruitment
steepness) and equilibrium spawning stock biomass, although as part of a sensitivity analysis we

22

explored how results changed when stock-recruitment parameters were identical among spawning
populations. Characteristics of the four spawning populations and harvest regions were based on
estimated parameters for Lakes Huron and Erie walleye populations and fisheries exploiting these
stocks. The first population had characteristics that were similar to the spawning population in
Saginaw Bay of Lake Huron. The second population was based on the very productive western
basin of Lake Erie, whereas the third and fourth populations were based respectively on the central
and eastern basins of Lake Erie (Figure 1.A.2). Mass and maturity at age were assumed to be
spatially and temporally constant in the operating and ITCAAN models.
The operating model generated a 40-year time period of observations, with the ITCAAN model
applied once at the end of the time period. Both the operating and ITCAAN models followed the
dynamics of age-2 to age-7 fish, with the last age class an aggregate group including age-7 and older
fish. The operating model was programmed in R version 2.15.1 (R Core Team 2016), whereas the
ITCAAN model was programmed in AD Model Builder version 11.5 (Fournier et al. 2012). Code
for the operating model and ITCAAN model can be found in Supplementary Material 1. Symbols
and equations used to model the dynamics for both the operating model and ITCAAN model
are presented in Appendix 1.B. Parameter values assumed in the operating model and likelihood
equations used within the ITCAAN model are presented in Supplementary Material 1.

Operating Model
Recruitment for the spawning populations assumed Ricker stock-recruitment functions with spawners equal to the spawning biomass 2 years prior to the year of recruitment. An autoregressive
recruitment deviation randomly generated for each population independently was also used to
calculate annual reproduction (Equation (1.B.2.1)). Consistent with information for walleye populations within Lakes Erie and Huron, recruitment steepnesses (i.e., productivities) of the individual
populations were chosen so there was considerable variation among populations (Figure 1.A.2;
Supplementary Material 1 Table 2). Spawning site fidelity was assumed to be 100% with instantaneous return annually at the time of spawning. Recruitment deviations on a loge scale for the
23

spawning populations were generated from a first-order autoregressive process (Equation (1.B.2.2)).
Thorson et al. (2014) used a hierarchical Bayesian approach to estimate posterior distributions of
mean autoregressive coefficients and innovations (uncorrelated errors) variances for a variety of
exploited taxonomic orders. Values of the autoregressive coefficient (ρ p ) and innovations variances
(σp2 ) for each spawning population and simulation iteration for this research were randomly generated from the posterior distribution estimated for Percidae (Thorson et al. 2014). The mean of the
autoregressive process (δ y ) was calculated such that it would have a mean of 1 when exponentiated
to give a mean unbiased process (Thorson et al. 2016) and the variance of the stationary distribution
would equal the variance randomly drawn from the posterior distribution estimated for Percidae.
Spawning was assumed to occur at the beginning of the year.
Abundances at age for the spawning populations were calculated using standard exponential population models. Underlying equations accounted for movement and harvest of populations in multiple harvest regions with the older ages accumulating in the oldest age group (Equations (1.B.2.4)
and (1.B.2.5)). The apical fishing mortality rates for the harvest regions were randomly generated
from first-order autoregressive processes (Equation (1.B.2.9)), where the means of the processes
were different for each region and were based on estimates from Lakes Erie and Huron (Supplementary Material 1 Table 2). Assumed selectivities and catchabilities were based on estimated
values for walleye in Lakes Erie (Wills et al. 2016) and Huron (Fielder and Bence 2014) and were
used to simulate fishing mortality (Supplementary Material 1 Tables 1 and 2). Movement was
based on a box-transfer process that assumed instantaneous movement to harvest regions, in which
fish remained for the rest of the year (Goethel et al. 2011). The proportion of the population that
moved to each harvest region varied depending on the examined scenario (see section on Simulation
Scenarios), but in all cases was assumed to be the same proportion to all non-natal regions for all
populations, which was temporally and age-invariant. Fishery effort data were generated assuming
a lognormal observation error (Equation (1.B.2.10)). A fishery-independent survey was assumed
to be conducted on each harvest region during October when fish were intermixed, which collected
a relative abundance time series and age-composition data (Equations (1.B.2.13) and (1.B.2.14)).

24

Cohorts of tagged fish from each spawning population were assumed to experience the same
dynamics as the at-large populations (i.e., tagged individuals were fully mixed with the at-large
populations). All tagging was conducted when fish were located in their spawning regions. Our
baseline tagging rate was 2000 fish per year and region, but lower tagging levels were considered for
some scenarios (Table 1.A.1). Tags were allocated to different ages based on the real-world average
proportion at age observed from tagged fish in Lake Erie (Supplementary Material 1 Table 1).
However, all ages were treated as a single release cohort in each year and region when simulating
the data for the number of tags recaptured (Equation (1.B.2.16)). Tagging-induced mortality and
tag shedding were assumed to not occur. Actual numbers of fish from a tagged cohort that moved
to each harvest region after spawning were randomly generated from multinomial distributions
with the underlying proportions equal to the assumed movement rates for that particular scenario
(Equation (1.B.2.17)). The probabilities of a tagged fish being harvested (Equation (1.B.2.18)),
surviving (Equation (1.B.2.19)), or dying (Equation (1.B.2.20)) in a harvest region were then
calculated based on the fishing, total, and natural mortalities in a region. These probabilities
(Equation (1.B.2.21)) were used in a multinomial random number generator to determine the
number of fish in each fate category (Equation (1.B.2.22)). A binomial random variable based
on an assumed fishery reporting rate with a sample size equal to the number of tags recovered
was then used to determine the number of harvested fish that were reported (Equation (1.B.2.24)).
A reporting rate of 50% was assumed in the operating model for all examined scenarios and
fisheries. The number of tagged fish that survived were then progressed to the next age and year
(Equation (1.B.2.23)). The number of tags never recovered was calculated as the number of tags
released minus the total tags returned summed across year, age, and region (Equation (1.B.2.25)).
A limitation that we imposed on our simulations was that abundances for any of the four
populations could not decrease to less than 40000 fish. If this occurred, that iteration was discarded
and another simulation created. An abundance of less than 40000 fish would mean that more than
5% of a population was tagged within a year at the baseline tagging rate of 2000 fish per year and
region, which seemed an unrealistic tagging rate even for fish that exhibit natal homing.

25

We simulated data that were subject to observation error and available for all regions every
year that were summed across populations (i.e., stock-specific not population-specific values). The
following data sources were used in the ITCAAN model: total harvest in number of fish, harvest age
composition, fishing effort, survey index of abundance, survey age composition, and tag recovery
data. The values and distributions assumed for each of the simulated data sources for examined
scenarios are summarized in Table 1.A.2.

ITCAAN Model
The ITCAAN model used in this research was similar to that of Goethel et al. (2015a), but differed in
that we modeled 100% natal homing, included more spawning populations and harvest regions, and
in at least some scenarios accounted for a more complex model parameterization (e.g., estimating
both natural mortality and reporting rates). The dynamics assumed in the ITCAAN model were
similar to assumptions in the operating model (e.g., box-transfer movement, 100% spawning site
fidelity, full mixing between tagged cohorts and at-large populations).
Annual recruitment in the ITCAAN model was estimated through a random-walk process in
which the multiplicative random-walk deviations were assumed to be from a lognormal distribution
(Equation (1.B.2.3)) with the log-standard deviation fixed at 4. The last 2 years of recruitment in the
ITCAAN model were set equal to the mean recruitment for the previous 3 years for each population,
which was necessary for the model to converge with a positive-definite Hessian matrix. Abundances
in the first modeled year for age-3 and older fish were estimated as the product of a mean abundance
and multiplicative age-specific deviations that were assumed to be from a lognormal distribution
and constrained to sum to 0 across ages (Equation (1.B.2.28)). Year-specific fishery catchabilities
were modeled using a random-walk process (Equation (1.B.2.12)), as advocated by Wilberg and
Bence (2006). Age-specific selectivities were estimated for ages 2 to 7 individually for each fishery
and were assumed constant through time. Depending on the examined scenario, natural mortality
and reporting rate were either estimated or set equal to assumed (sometimes misspecified) values
in the ITCAAN model. Region-specific survey catchabilities and age-specific survey selectivities
26

were assumed constant over time and were estimated parameters in all simulations. Movement rates,
including the proportion staying in the natal region, were estimated through a multinomial logit
transformation that constrained movement rates to be between 0 and 1 and to sum to 1 (Vandergoot
and Brenden 2014). The formulation is similar to that of Goethel et al. (2015a) except the parameter
for movement to region 4 for all populations was set equal to 0, instead of the residency parameter.
Three parameters for each population were then transformed into movement rates to the four regions
so that the model was identifiable (Equation (1.B.2.15)). As with the operating model, movement
rates were assumed to be temporally and age-invariant. When estimated, reporting rates were
modeled using a logistic function, which constrained the reporting rate to be between 0 and 1.
Numbers of recovered tags were predicted based on the known number of tags released by age
each year, estimated population movement rates, survival estimates, and a fishery-specific estimated
reporting rate (Equation (1.B.2.26)). Proportion of yearly regional tags recovered and tags never
recovered relative to the total number of tags released were assumed to be multinomially distributed
and were used in likelihood calculations.
Highest posterior density estimation, which is also referred to as maximum penalized likelihood,
was used to estimate the parameters of the ITCAAN model. Diffuse upper and lower bounds were
specified for all parameters to keep the optimization algorithm from flat parts of the likelihood
surface and to prevent unreasonable parameter estimates. The objective function was the sum of
multiple negative log-likelihood and log-penalty components. Age-composition and tag-recovery
data were modeled as multinomial distributions, while all other data and parameter penalties were
modeled as lognormal distributions (Supplementary Material 1 Table 4).
An ITCAAN model was assumed to have converged if the maximum gradient across all parameters was less than 0.05 and the model produced a positive-definite Hessian matrix. If the ITCAAN
model for an individual simulation did not converge based on these criteria, the results from that
simulation run were discarded. Additional simulations were conducted until 1000 iterations with
a converged ITCAAN model were obtained. The total number of simulations needed to reach a
sample size of 1000 for each scenario, percent convergence, and the number of simulations rejected

27

for the two conditions are presented in Table 1.A.1.

Simulation Scenarios
We evaluated ITCAAN model performance through scenarios grouped into five categories (Table 1.A.1). In the first group of scenarios, we explored how parameter estimates were affected
by variation in movement rates in combination with whether movement, natural mortality, and/or
reporting rates were estimated or treated as known quantities fixed at their correct values in the
ITCAAN model. In the second group of scenarios, we explored sensitivity of parameter estimates
to misspecification of reporting rates or natural mortalities when these parameters were assumed
known in the ITCAAN model. We used a third group of scenarios to examine the influence of
data quality on parameter estimates, and a fourth group to explore the ability to estimate spatially
varying reporting rates and/or natural mortalities. We simulated a fifth group of just one scenario to examine the influence of assuming the same productivity (i.e., Ricker parameters) for all
populations on parameter estimates.
Many parameters were consistent among simulation scenarios and differences are presented in
Table 1.A.2. All scenarios assumed a natural mortality rate of 0.32 in the operating model, and
if the parameter was not estimated it was correctly specified in the ITCAAN model, except under
scenarios RSensO and RSensU (reporting rate sensitivity to natural mortality over and under the
true value, respectively; Group 2). The reporting rate in the operating model was 50% for all
regions and years, which was correctly specified when not estimated except for scenario MSens
(natural mortality sensitivity; Group 2). While fish were aggregated for spawning each year,
2000 fish were tagged from each population every year, unless otherwise specified (Table 1.A.1;
Group 3). The variance of simulated data and the effective sample size was consistent for most
simulation scenarios but differed for a few scenarios (Table 1.A.2; Group 3). When the reporting
rate was estimated in the ITCAAN model, it was assumed to be a unique parameter for each region,
unless otherwise specified (Table 1.A.1; Group 4). When natural mortality was estimated within
the ITCAAN model, it was assumed to be a single parameter across all regions, unless specified
28

differently below (Table 1.A.1; Group 4).

Group 1: Varying Movement and Reporting Rate and Natural Mortality Estimation
We simulated a total of 20 scenarios to examine how assumed movement rates, and the estimation of
movement, natural mortality, and/or reporting rates affected ITCAAN performance: four movement
rates (the percentage of the populations that moved to each non-natal region: 1%, 5%, 10%, and
20%) were each crossed with five estimation approaches for the ITCAAN model (MvFix: fixed
movement, natural mortality, and reporting rate (only scenario with fixed movement); MRFix: fixed
natural mortality and reporting rate but movement estimated; MEst: estimated natural mortality
and movement but known reporting rate; REst: estimated reporting rates and movement but known
natural mortality; BEst: both natural mortality and reporting rate estimated along with movement).
When movement, natural mortality, or reporting rate were treated as known, they were fixed at
their correct value (i.e., the value assumed in the operating model) in the ITCAAN model. When
presenting the results for these scenarios, we use the abbreviations for each estimation approach
followed by the assumed movement rate (e.g., MRFix1 scenario refers to 1% movement rate where
movement is estimated but natural mortality and reporting rate are assumed known and fixed in the
ITCAAN model).

Group 2: Sensitivity to Misspecified Reporting Rate and Natural Mortality
Our second group of scenarios explored the consequences on parameter estimates of misspecifying
reporting or natural mortality rates in the ITCAAN model when these parameters were treated as
fixed and known. This group had three scenarios, all with data generated assuming the highest
movement rate (20%). In the first scenario, a reporting rate of 75% was assumed in the ITCAAN
model when the true reporting rate in the operating model was 50% for all fisheries. We conducted
this scenario (referred to as the MSens scenario) to determine the sensitivity of natural mortality
estimates and other parameter estimates to reporting rate misspecification. We used the two other
scenarios to explore the sensitivity of reporting rate and other parameter estimates when natural
29

mortality in the ITCAAN model was specified too low [RSensU scenario: reporting rate sensitivity
to natural mortality specified under the true value (i.e., 0.16 in the ITCAAN model versus 0.32 in
the operating model)] or specified too high [RSensO scenario: reporting rate sensitivity to natural
mortality specified over the true value (i.e., 0.48 in the ITCAAN model versus 0.32 in the operating
model)].

Group 3: Data Quality
The third group of scenarios examined sensitivity of parameter estimates to differing levels of data
quality, including fewer tags released per region and year, smaller effective sample size for age
composition data, and/or larger measurement error in fishing effort, harvest, and survey indices of
abundance data. In these scenarios, reporting rates and natural mortalities were always estimated
in the ITCAAN model and assumed a 20% movement rate in the operating model. We conducted
four scenarios with smaller annual tagged cohort size per region than in scenario Group 1: 1500,
1000, 500, and 250 tags per region and year. These scenarios were abbreviated by T, for tagging,
followed by the number of tags released per year and region (e.g., T1500 scenario refers to 1500
tags being released per year and region). We conducted a scenario in which the effective sample
size of the harvest and survey age compositions was reduced to 50 in the operating and ITCAAN
models but 2000 tags were still released per year and region. We refer to this as the ESS50 scenario.
The last scenario in this group was referred to as the high variance scenario (HighVar). For this
scenario, 2000 tags were released per year and region; however, the measurement error associated
with the effort and survey index data was double that of all other examined scenarios, and the
effective sample sizes of the harvest and survey age compositions were set to 50 in the operating
and ITCAAN models (Table 1.A.2).

Group 4: Spatial Complexity in Reporting Rates and Natural Mortalities
The fourth group of scenarios evaluated the consequences of estimating spatially varying natural
mortality and/or reporting rates in the ITCAAN model. Three scenarios were conducted for this
30

group that differed with respect to spatial complexity considered in the ITCAAN model, all with
a 20% movement rate. In the first scenario (RC_MC scenario: reporting rate constant and natural
mortality constant), a single natural mortality and reporting rate was estimated in the ITCAAN
model that was applied to all regions. In the second scenario (RC_MU scenario: reporting rate
constant and natural mortality unique), a single reporting rate was estimated that was applied to all
regions but unique natural mortality rates were estimated for each region in the ITCAAN model.
In the third scenario (RU_MU scenario: reporting rate unique and natural mortality unique),
unique natural mortality and reporting rates for each region were estimated in the ITCAAN model.
The results from these scenarios were compared with those from the BEst20 scenario because it
estimated a single natural mortality but spatially unique reporting rates. The RC_MC, BEst20,
RC_MU, and RU_MU scenarios represent a gradient in parameterization complexity to examine
ITCAAN model sensitivity to spatial complexity.

Group 5: Equal Productivity
The fifth group of scenarios consisted of just a single scenario (EqProd scenario: equal productivity)
that investigated how parity in productivities among the four populations affected ITCAAN performance. For this scenario, all populations were assigned the same stock-recruitment parameters
(i.e., Ricker ι and β parameters for population 2 in other scenarios; Figure 1.A.2). Unique autoregressive parameters (ρ p ) and innovations variance parameters (σp2 ) for each of the populations
were still generated as previously described.

Performance Metrics
The performance of the ITCAAN model was explored by comparing parameter estimates with the
true values assumed in the operating model. For the sake of brevity, we discuss the precision and
accuracy in estimates of annual recruitment, movement, natural mortality, reporting rates, and total
abundance (i.e., abundances summed over all regions); results for all other parameters are included
in the Supplementary Material 1. Parameters not presented showed either no bias in estimates or
31

biases similar to recruitment, though not always in the same direction. The percent relative error
estimate (REE) for all parameters except movement were calculated by subtracting the true value
from the estimate and then dividing by the true value and multiplying by 100. Error in movement
rate estimates was assessed (and presented) as actual error (i.e., estimate minus true) to facilitate
comparisons across scenarios, though movement REE are presented in the Supplementary Material
1. Errors in parameters that were age-specific (e.g., selectivity; results shown in Supplementary
Material 1) or year-specific (e.g., recruitment) were calculated for each age or year separately for
the 1000 simulations and then aggregated by region for summarization and plotting. For example,
the boxplots of recruitment show 40000 values (i.e., 40 years of recruitment times 1000 iterations).
The median and interquartile ranges (IQR) of the REE and actual error of the 1000 simulated data
sets were used to summarize model bias and precision, respectively, for the scenarios.

Results
Operating Model Trends in Abundance
To meet the condition that no more than 5% of a population was tagged (i.e., an abundance greater
than 40000 for all populations and years), approximately 7% of the simulations that were conducted
were discarded from the analysis. However, the number rejected are not included in the number of
runs required to reach 1000 simulations in Table 1.A.1 because this was a result of the operating
model and not the ITCAAN model. Abundance in the operating model varied widely among year,
population, operating model scenario, and simulation iteration. As a result, the proportion of the
population that was tagged also varied by these conditions. For scenarios that released 2000 tags
per population, the median proportion of the population tagged was 0.093%. For the scenario that
released 250 tags per population each year (T250), the median proportion of the populations tagged
was 0.013%.
Assumed movement level affected annual trends in abundance in the operating model for
the four populations (Figure 1.A.3). When averaged over all iterations, decreases in abundance
were observed for all populations under all movement rates, but the level of depletion varied by
32

movement rate and region. For populations 1, 2, and 3, median abundance generally stabilized after
approximately 10 years. However, for the least productive population (population 4), abundance
declined throughout the duration of the simulations, and the magnitude of depletion was greatest
under high movement. Mean exploitation rates were different for each region and were higher in
regions where the natal population was more productive. Therefore, at higher movement rates a
larger proportion of the population would be exposed to higher rates of exploitation, which lead
to greater declines in abundance. On a per simulation basis, interannual variability in abundance
levels could be quite large due to the autoregressive processes of recruitment and fishing mortality
(Figure 1.A.3). This variability matches observed walleye population dynamics in Lakes Erie (Zhao
et al. 2009, 2013; Wills et al. 2016) and Huron (Fielder and Bence 2014).

ITCAAN Model Convergence
The convergence rate of the ITCAAN model (i.e., proportion of simulations where both the
maximum gradient of the parameters was less than 0.05 and a positive-definite Hessian matrix
was produced) exceeded 95% for all scenarios except those assuming 1% movement rates, for
which the convergence rate was approximately 75% (Table 1.A.1). At the 1% movement rate, a
maximum gradient larger than 0.05 was the main factor causing non-convergence, though nearly
all iterations had a positive-definite Hessian matrix. At movement rates of 10% and 20%, failures
of the ITCAAN model to converge generally was a consequence of neither criteria being met.
Whether movement, natural mortality, and/or reporting rate were estimated by the ITCAAN model
did not appear to have a major influence as to whether ITCAAN models converged (Table 1.A.1).
Similarly, convergence rates of the ITCAAN model did not appear to be influenced by the conditions
assumed in scenario Groups 2 through 5, as failed convergence rates ranged from 1% to 5% across
the scenarios (Table 1.A.1).

33

ITCAAN Model Performance
Recruitment Relative Error
Movement rates had a large effect on both the bias and precision of recruitment estimates (Figure 1.A.4). Under a 1% movement rate when natural mortality and reporting rate were estimated
(BEst1 scenario), recruitment estimates for the four populations were mostly accurate and precise.
As movement rate increased, the level of imprecision increased and the magnitude of bias increased,
with the direction of bias depending on the size of the population. For population 2 (i.e., the largest
and most productive population), recruitment was generally negatively biased, whereas recruitment
estimates for the smaller populations were positively biased (Figure 1.A.4). The degree of bias
and imprecision were generally the greatest when reporting rates were estimated, either alone or
in conjunction with natural mortality. The precision of recruitment also decreased when reporting
rate was estimated and became more biased for some regions (Figure 1.A.4).
When reporting rates were specified (i.e., not estimated) too high in the ITCAAN model (1.5
times the true value), recruitment for population 2 was positively biased (MSens population 2:
median REE = 37.72%; Figure 1.A.5), which was the opposite direction of the bias observed in
either the MEst20 or BEst20 scenarios. When natural mortality was specified at 0.5 times the
true value, recruitment was strongly negatively biased for population 2 (RSensU population 2:
median REE = -64.38), which was nearly double the bias observed for the BEst20 scenario (BEst20
population 2: median REE -31.38%). When natural mortality was specified at 1.5 times the
true value, the median recruitment was strongly positively biased (RSensO population 2: median
REE = 125.24%), and one of the least precise among the evaluated scenarios for all populations
(Figure 1.A.5).
The effects of data quality on recruitment REE from the ITCAAN model depended on the
scenario under consideration. Releasing fewer tags per region and year magnified the bias and
decreased the precision in recruitment estimates for all populations (Figure 1.A.5). Reducing the
age composition effective sample size to 50 resulted in slightly larger negative bias of population

34

2 recruitment for the ESS50 scenario compared with the BEst20 scenario (ESS50 population 2:
median REE = -34.7%). Compounding a smaller effective sample size with greater levels of
measurement error had only a marginal effect on bias (HighVar population 2: median REE =
-37.6%). Reducing the amount of tags released had a much larger impact on recruitment estimates
than reducing the effective sample size or increasing the variance of data sources (Figure 1.A.5).
The degree of spatial complexity assumed for natural mortality and reporting rates in the
ITCAAN model affected bias and precision of recruitment estimates, with results most sensitive
to spatial complexity in reporting rates (Figure 1.A.5). When reporting rates were estimated
as spatially constant, median REE in recruitment for population 2 were approximately -14%.
Conversely, the median REE in recruitment for population 2 when reporting rates were estimated as
spatially unique was approximately two times greater. Similar patterns were observed for the other
populations. The precision of recruitment estimates for population 2 was relatively unaffected by
the degree of spatial complexity; however, for the three smallest populations precision decreased
as spatial complexity increased (Figure 1.A.5).
When all populations were assumed to have equal parameters in the Ricker stock-recruitment
functions, recruitment estimates were unbiased across all populations under a 20% movement rate
(EqProd populations 1–4: median REE = -2.3% to -4.6%). For population 2, the imprecision
in recruitment estimates was the second largest of the evaluated scenarios. However, for all other
populations, the recruitment estimates were the most precise among the evaluated scenarios (EqProd
populations 1–4: IQR REE ∼ 60%).

Movement Rate Actual Error
Estimates of the movement rate to regions were largely accurate regardless of the assumed movement
rate and whether reporting rates and/or natural mortality were estimated or treated as known
(Figure 1.A.6). Median actual errors were within -0.26 and 0.08 for all examined scenarios and
regions examined in Group 1 scenarios. Precision in the movement rate estimates decreased as the
level of assumed movement increased. A small bias in movement rate estimates into each of the
35

regions was observed when reporting rates were estimated but natural mortality in the ITCAAN
model was fixed at its true value for the highest movement rate (REst20). The direction of bias in
movement to each region was in the same direction as the bias in recruitment for natal populations
in that region. These biases were not observed when both natural mortality and reporting rates
were estimated for the high movement rate scenario (BEst20; Figure 1.A.6).
Estimates of movement to regions were also accurate and precise for simulations conducted
as part of scenario Groups 2 through 5. Some biases resulted in movement to regions 1 and 2
when either natural mortality or reporting rates were misspecified (Figure 1.A.7). The precision of
movement estimates was relatively consistent among scenarios when the number of tags released
in each region was 2000 (BEst20 region 2: IQR actual error = 1.47). However, when the number
of tags released was reduced to 250 in each region, the IQR of movement actual error nearly tripled
(T250 region 2: IQR actual error = 4.38). Despite this, the movement estimates from the examined
scenarios were precise and also remained relatively unbiased (Figure 1.A.7).

Natural Mortality and Reporting Rate Relative Error
When estimated in the ITCAAN model, natural mortality was generally accurate and precise across
each of the Group 1 scenarios (Figure 1.A.8). When natural mortality was estimated and reporting
rate was fixed at its true value, the estimates of natural mortality were very precise (MEst1, MEst5,
MEst10, and MEst20: IQR REE = 0.85% to 0.90%). However, estimating both reporting rates
and natural mortality decreased the precision of natural mortality estimates, with the degree of
imprecision increasing as movement rates increased. Similar results with respect to precision were
observed for reporting rate (i.e., precision decreased when both natural mortality and reporting rate
were estimated and movement rate increased; Figure 1.A.8). Unlike natural mortality estimates,
some bias in reporting rates occurred with bias generally increasing as movement rates increased.
The bias in reporting rate was most noticeable for region 2 under a 20% movement rate when
reporting rate was estimated alone or in conjunction with natural mortality (REst20 and BEst20
region 2: median REE ≈ -14%). Conversely, median relative errors in reporting rates for the other
36

regions were generally within Âą 5%.
Estimates of natural mortality were highly affected by incorrectly specifying the reporting rate
in the ITCAAN model (Figure 1.A.9). When reporting rate was misspecified at 1.5 times its
actual value, natural mortality estimates were positively biased (MSens: median REE = 20.64%).
Similarly, reporting rate estimates were affected when natural mortality was fixed at an incorrect
value in the ITCAAN model. When natural mortality was fixed at half of its true value (RSensU),
reporting rates were negatively biased. Conversely when the natural mortality value in the ITCAAN
model was fixed at 1.5 times the true value (RSensO), the estimated reporting rates for all regions
had median REEs near 100%. This would imply that the model was estimating that all tags
recaptured were reported (i.e., 100% reporting rate) for all regions.
The number of tags released per region and year affected the precision of the natural mortality and reporting rate estimates and had a slight influence on bias of reporting rate estimates
(Figure 1.A.9). Decreasing the number of tags released resulted in less precise estimates of natural
mortality and reporting rate. A slight negative bias was also observed for region 2 as fewer tags
were released. Reducing the effective sample size of the age compositions or doubling the error in
the other data sources had little influence on estimates of natural mortality and reporting rate.
Among the Group 4 scenarios, the largest biases in natural mortality and reporting rate were
observed for the scenario where both natural mortality and reporting rate were estimated as spatially
unique parameters (RU_MU). Natural mortalities and reporting rates were both negatively biased
in region 2 but positively biased in all other regions for scenario RU_MU (Figure 1.A.9). The least
amount of bias in reporting rate was observed among the Group 4 scenarios when the parameter
was assumed to be spatially constant in the ITCAAN model (RC_MC and RC_MU). IQR REE for
both natural mortality and reporting rate increased as the complexity (i.e., number of parameters)
of the estimation model increased for the respective parameters.
Reporting rate estimates were unbiased for the scenario with equal Ricker stock-recruitment
parameters (EqProd). The IQR REE of reporting rate were consistent across the four regions.
Estimation of natural mortality for the EqProd scenario was unbiased (median REE = -1.40%).

37

Total Abundance Relative Error
Bias and precision of total abundance estimates varied by examined scenario (Figure 1.A.10). For
all movement rates examined in the Group 1 scenarios, there was a slight negative bias in total
abundance estimates. The degree of bias increased with higher movement and when reporting
rates were estimated regardless of whether natural mortality was estimated or fixed in the ITCAAN
model at its true value. The precision in total abundance was relatively similar when reporting
rate was not estimated (MvFix, MRFix, and MEst scenarios) and was largest when both natural
mortality and reporting rate were estimated (BEst).
Examination of relative errors in annual abundances for some of the Group 1 scenarios identified
the source of the biases observed in total abundances. For the MRFix1 scenario, annual abundance
estimates for all populations and combined across populations were accurate and relatively precise,
except for the last few years of the simulations (Figure 1.A.11). However for the BEst20 scenario,
annual abundances were consistently biased for all populations; estimates for population 2 were
consistently negatively biased, and estimates for the other populations were positively biased. The
biases were consistent for the duration of the simulations for all populations except population 4, in
which bias increased throughout the time series. The strength of the bias varied by population size
(Figure 1.A.11); for population 2 (i.e., the largest population), the median REE in annual abundance
was consistently around -35%, whereas for some of the other populations median REE approached
500%. With respect to total annual abundance, these population-specific biases largely canceled
each other out (Figure 1.A.11). For population 2, precision of abundance decreased in the last few
years of the simulations. Conversely, for populations 1 and 3, the precision in annual abundances
were fairly consistent throughout the duration of the simulations, whereas for population 4 the
precision decreased annually throughout the simulations.
Large positive biases in total abundance estimates were observed when reporting rate was fixed
at 1.5 times the true value (MSens median REE 50.89%) and when natural mortality was fixed
at 1.5 times the true value (RSensO median REE 131%; Figure 1.A.10). Conversely, there was
negative bias in total abundance when natural mortality was fixed at half the true value (RSensU
38

median REE -48%). Simulations that tested different structural assumptions and data quality had
similar median REE values compared with the BEst20 scenario. However, when the number of
tags released was reduced to 250 per region the IQR REE of total abundance doubled (BEst20
total: IQR REE = 11%; T250 total: IQR REE = 21%).

Discussion
Simulation analysis is an important tool in fishery science for determining how well models
can accurately and precisely estimate parameters and the robustness/sensitivity to violations in
model assumptions, data quality, and/or structural uncertainties. Previous simulation analyses of
ITCAAN models had investigated reproductive mixing movement dynamics with natural mortality
fixed at the true value (Hulson et al. 2011, 2013; Goethel et al. 2015b). This study analyzed
the performance of an ITCAAN model with natal homing movement dynamics and more harvest
regions and populations than had previously been simulated, while testing the estimability of natural
mortality, movement rates, and tag reporting rates. Additionally, our operating model created data
sets by simulating stochastic first-order autoregressive annual fishing mortality and recruitment
processes and applied observation error for four populations with drastically different magnitudes
of spawning population size. These stochastic processes were included to create data sets that were
generic such that the results would be broadly applicable. Our study allowed for the estimation of
natural mortality and tag reporting rate simultaneously with other population dynamics parameters
internal to the ITCAAN model. The intent of this study was to establish a baseline of parameter
estimability performance for a four-region ITCAAN model with the movement dynamics modeled
as intermixed populations with natal homing, which expands on previous simulation analyses
(Hulson et al. 2011, 2013; Goethel et al. 2015b).
An issue we encountered when fitting the ITCAAN model was that different parameterizations
could have large consequences on model fit. For example, initial configurations of our ITCAAN
model estimated recruitment as a white-noise process that resulted in large systematic biases
in recruitment estimates. Specifically, the ITCAAN model underestimated recruitment early in

39

the time series and overestimated recruitment later in the time series. Conversely, estimating
recruitment through a random-walk process with a large assumed variance term removed these
systematic biases and greatly improved precision of the recruitment estimates. We suspect that the
key feature here is that we allowed for the mean recruitment to be non-stationary (Maunder and
Deriso 2003; Li et al. 2014). Similarly, issues were encountered in estimating initial abundances
and the last few years of recruitment, which affected whether the model could reliably produce
a positive-definite Hessian matrix for many simulated data sets. Ultimately, the ITCAAN model
parameterization that we used in our study was the best approach we could find to correct the
estimation complications we encountered. Such estimation issues could easily remain undiscovered
in empirical applications of ITCAAN models. We thus recommend that the sensitivity of alternative
parameterizations be routinely evaluated in real-world applications, and in agreement with Goethel
et al. (2015b) that simulations be used to evaluate the most appropriate approach when such
sensitivity exists.
Part of our motivation for this research was that we envisioned there could be confounding
among parameters that fishery scientists might be interested in estimating with an ITCAAN model.
Additionally, the estimation of reporting rates within an ITCAAN model is a recent proposal
(Goethel et al. 2015a,b). We found that natural mortality, tag reporting rates, and movement
rates can all be accurately and precisely estimated simultaneously in an ITCAAN model assuming
natal homing. Across the range of scenarios considered in this research, movement rates were
accurately and precisely estimated even at the lowest tagging level. Accuracy and precision of
natural mortality and reporting rates were largely unaffected by the degree of measurement error
assumed in the statistical catch-at-age data (Table 1.A.2). However, precision and bias of natural
mortality, movement rates, and reporting rates were appreciably affected by reductions in tagged
cohort sample size. This suggests that tag-recovery data are the primary source of information
that allows estimation of these parameters in ITCAAN models, and such data will typically be
necessary in order to estimate movement rates in spatial assessment models (Goethel et al. 2015b).
The ability to estimate these parameters is important because fixing them at incorrect values can

40

cause severe biases in all other model parameters.
Given the consequences on ITCAAN model parameter estimates from misspecifying reporting
rates and natural mortalities, we advocate initially attempting to estimate these parameters simultaneously rather than fixing them at assumed values. Admittedly, the ability to estimate reporting
rates and natural mortalities simultaneously might be more challenging than what we encountered because actual data will likely have greater uncertainty than generated data. Our simulation
scenarios that explored the consequences of data quality showed that greater levels of bias and
imprecision in parameter estimates resulted with lower quality data; however, the amount of bias
in parameter estimates were generally greater when reporting rates or natural mortalities were misspecified. The natal homing assumed for this study may influence the extrapolation of these results
to other movement types; nevertheless, we speculate that the specification of the natural mortality
rate may have been incorrect in the reproductive mixing movement ITCAAN model of Goethel
et al. (2015a) and likely led to biases in reporting rates and other parameters. Supporting this
speculation, Goethel et al. (2015a) noted that the region-specific reporting rates estimated by the
ITCAAN model were all lower than an estimate for all areas combined from a high-reward tagging
study (Cadrin 2006). In general, this issue can be addressed by both evaluating sensitivity of results
to specified natural mortality rates and evaluating whether the natural mortality parameter can be
estimated. If difficulty in estimating natural mortality and reporting rate concurrently exists, model
convergence may be improved by incorporating methods that normally are factored into tagging
studies. For example, the release of high-reward tags, using observers, or planted tags (Polacheck
et al. 2006; Eveson et al. 2007) could be incorporated in the likelihood of the ITCAAN model.
Bias and precision in reporting rates and natural mortality were affected by the degree of
spatial complexity assumed for reporting rate and natural mortality parameters in the ITCAAN
model. Our findings illustrate that caution should be used when considering the complexity
of parameterization within ITCAAN models, as greater model complexity may lead to greater
variability in parameter estimates. Model selection criteria, such as deviance information criteria,
may be useful to determine the spatial complexity that can be supported by observed data (Wilberg

41

and Bence 2008; Linton and Bence 2011). In some cases, it might be possible to estimate spatially
varying parameters by modeling rates as a function of some measured quantity, such as modeling
natural mortality as a function of temperature. However, fisheries scientists will need to consider
whether parameters should be modeled as an environmental characteristic of the region occupied
or a genetic feature of the originating population.
One of the main parameters of interest in an ITCAAN model is the estimation of movement
rates among the populations. Previous simulations of ITCAAN models under different movement
dynamics found that movement rate estimates were accurate even when movement varied as a
function of environmental variables (Hulson et al. 2013) or as a function of regional stock density
(Goethel et al. 2015b). Our findings in combination with these other studies suggest that unbiased
and precise estimation of movement is a robust feature of ITCAAN models. However, this conclusion may depend on the simplistic movement dynamics in the operating models used to generate
the tagging data. Our study, as well as those of Hulson et al. (2013) and Goethel et al. (2015b),
assumed movement occurred instantaneously and that after movement fish became sedentary. In
actuality, movement will not be instantaneous and may vary seasonally or across even shorter
time periods. Additionally, our estimates of precision may be conservative because we generated
tag recoveries assuming a multinomial process, but overdispersion relative to this distribution in
tagging data is often observed (Bacheler et al. 2008; Hanselman et al. 2015; Mayakoshi and Kitada
2016). We assumed tagged cohorts were fully mixed with the at-large population (i.e., both at-large
populations and tagged cohorts experienced the exact same dynamics). If the dynamics that the
tagged cohorts experience are different than the at-large populations, then parameter estimation
undoubtedly would have been affected. Future evaluations of ITCAAN models would benefit from
including more complex movement scenarios to determine whether the apparent robustness of
ITCAAN models for estimating movement is a general feature of the models or an artifact of the
simplified movement characteristics assumed in the operating model.
Although we attempted to incorporate a range of scenarios in this study, it is important to
acknowledge that our results are nevertheless influenced by assumed conditions, both in the ope-

42

rating and ITCAAN models. Our assumed 40-year time series of tagging and fishery harvest data
is perhaps an unlikely scenario of data availability and a shorter time series of data may encounter
different estimation issues. Our study did not include chronic tag loss and tag-induced mortality.
These processes would effectively reduce the sample size of tags released and could affect bias and
precision of parameter estimates if not accounted for in the ITCAAN model. We did not consider
the weighting of tagging data versus harvest and survey data in the ITCAAN model and there may
be situations where down-weighting of tagging data may be beneficial or necessary due to some
of the issues mentioned above (non-mixing, more complex movements, etc.) (Fielder and Bence
2014; Francis and McKenzie 2015; Goethel et al. 2015a). We did not investigate the model misspecification of incorrectly identifying spawning populations. Spawning population identification
is difficult (Cadrin et al. 2004) and could easily result in identifying a separate spawning population that does not exist or combining multiple spawning populations into one. How the estimates
obtained from a spatially-explicit ITCAAN model are influenced by model misspecification of the
spatial structure has yet to be evaluated for both natal homing and reproductive mixing ITCAAN
models. Similarly, simulations that incorporate harvest by multiple fisheries within a single region
may be useful to expand our understanding of ITCAAN models. Additional sources of uncertainty
that may be present in real data that were not explored include time-varying selectivity, selectivity
that is size-based with annually varying growth, fishing mortality that is not linearly related to fishing effort or changes over time, contradicting trends in multiple surveys, and time-varying natural
mortality and/or reporting rates. These types of model misspecification would likely make the
estimates of parameters more uncertain, and their influence could be evaluated through additional
simulation experiments.
One of the major motivators for incorporating spatially-explicit dynamics in assessment models
is the concern that less productive populations may be overexploited or even extirpated if spatially
varying dynamics are not incorporated in the management process (Stephenson 1999; Hutchinson
2008; Li et al. 2014). For fishery scientists and managers responsible for assessing and/or managing
fish populations exhibiting complex spatial structuring, ITCAAN models are likely an attractive

43

assessment approach. One of the key findings from our study was that under conditions of
high movement and large differences in spawning population size, ITCAAN models were biased
and imprecise estimators of individual population annual recruitment. Additionally, biases in
recruitment estimates become more pronounced when reporting rates were estimated, which may
indicate that the estimation of reporting rates within an ITCAAN model could lead to biased
estimates if large differences in population size are present. Likewise, the abundance in population
4 in the BEst20 scenario was increasingly overestimated as the population size declined, but this
was not observed for the EqProd scenario. This suggests that even a spatially-explicit ITCAAN
model may have difficulty estimating abundance for a population that is close to collapse, if a large
portion of the catch comes from other populations. An assumption of large differences in population
size and depletion level among the spawning populations, used in our simulations, may be more
reflective of actual conditions for many species than an assumption of equality in stock-recruitment
relationships. Consequently, the potential for overestimating recruitment of smaller populations
and underestimating recruitment of larger populations under conditions of high movement and large
differences in relative size of spawning populations is an important issue to consider for fishery
scientists looking to implement ITCAAN models. However, this overestimation of recruitment was
only severe when movement was at the 20% mixing rate. Real-world scenarios where more than half
of the population leave the natal region (i.e., for the 20% movement scenarios, 60% of populations
leave natal region) may be rare occurrences. Thus, a more thorough investigation is required into
what proportion or relative quantity of regional catch non-natal stocks must contribute such that
the natal population is overestimated. If movement rates among the populations are anticipated
to be high, the implementation of standardized surveys when populations are unmixed may be
beneficial for improving accuracy and precision of recruitment estimates from ITCAAN models.
Alternatively, the incorporation of genetic data to determine the population source of fish caught in
a mixed survey and/or fishery could improve the ability of ITCAAN models to accurately estimate
individual population abundance, but requires additional investigation.
In conclusion, we found that release-conditioned ITCAAN models yielded accurate and precise

44

parameter estimates under moderate to low movement rates. However, biases in some parameters
could result under conditions of high movement and large differences in stock-recruitment relationships among spawning populations. Misspecification of certain parameters, such as natural
mortalities and reporting rates, induced larger biases for tested misspecification levels than when
parameters were estimated; thus, we urge caution in fixing parameters at assumed values when
utilizing ITCAAN models. We recommend additional investigation of factors such as the inclusion
of additional data sources, greater levels of uncertainty in data sources, greater spatial complexity, weighting of tagging data relative to fishery harvest and survey data, temporal complexity of
parameters (e.g., natural mortality and reporting rate), alternative parameterizations (e.g., recruitment estimation as random walk or white noise), and model misspecification to gain additional
perspectives on the performance of ITCAAN models. Finally, we recommend the use of management strategy evaluations for specific situations to determine whether some combination of using
ITCAAN models and appropriate harvest policies can maintain desirable levels of biomass for all
spawning populations.

Acknowledgments
The authors thank three anonymous reviewers and Mark Maunder for comments that helped
improve the manuscript. This work was partially funded by grant 2012.1250 from the Great Lakes Fishery Trust and 2013_BRE_44025 from the Great Lakes Fishery Commission. Additional
funding support was provided by Supporting Partners of the Michigan State University Quantitative Fisheries Center. The authors acknowledge the support of Michigan State University High
Performance Computing Center and the Institute for Cyber-Enabled Research. This is publication
number 2017-13 of the Quantitative Fisheries Center at Michigan State University.

45

APPENDICES

46

APPENDIX 1.A
TABLES AND FIGURES

Table 1.A.1: Abbreviations used in figures and text, model characteristics, and convergence rates of the ITCAAN model for investigated
scenarios.
Scenario
Group

Abbrv.

1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1

MvFix1∗
MRFix1
MEst1
REst1
BEst1
MvFix5∗
MRFix5
MEst5
REst5
BEst5
MvFix10∗
MRFix10
MEst10
REst10
BEst10
MvFix20∗
MRFix20
MEst20
REst20

ITCAAN model
Reporting Natural
rate
mortality
Known
Known
Known
Known
Known
Est. RC
Est. RU
Known
Est. RU
Est. RC
Known
Known
Known
Known
Known
Est. RC
Est. RU
Known
Est. RU
Est. RC
Known
Known
Known
Known
Known
Est. RC
Est. RU
Known
Est. RU
Est. RC
Known
Known
Known
Known
Known
Est. RC
Est. RU
Known

Operating model
Emigration tags per
rate
region
1%
2000
1%
2000
1%
2000
1%
2000
1%
2000
5%
2000
5%
2000
5%
2000
5%
2000
5%
2000
10%
2000
10%
2000
10%
2000
10%
2000
10%
2000
20%
2000
20%
2000
20%
2000
20%
2000
47

# needed
for 1000
converged
1297
1250
1266
1310
1283
1014
1028
1015
1027
1035
1007
1012
1005
1006
1005
1028
1024
1023
1015

Percent
converged
77.1
80.0
79.0
76.3
77.9
98.6
97.3
98.5
97.4
96.6
99.3
98.8
99.5
99.4
99.5
97.3
97.7
97.8
98.5

NPD
Maximum
Hessian Gradient
> 0.05
1
296
5
249
4
265
2
310
0
283
2
13
4
28
2
15
3
26
3
35
6
2
12
4
5
0
6
2
4
3
27
4
24
1
23
2
15
3

1
2
2
2
3
3
3
3

BEst20
MSens
RSensU
RSensO
T1500
T1000
T500
T250

Est. RU
1.5×True
Est. RU
Est. RU
Est. RU
Est. RU
Est. RU
Est. RU

Est. RC
Est. RC
0.5×True
1.5×True
Est. RC
Est. RC
Est. RC
Est. RC

Table 1.A.1 (cont’d)
20%
2000
20%
2000
20%
2000
20%
2000
20%
1500
20%
1000
20%
500
20%
250

3

ESS50†

Est. RU

Est. RC

20%

2000

1022

97.8

22

7

3
4
4
4

HighVar†‡
RC_MC
RC_MU
RU_MU

Est.
Est.
Est.
Est.

Est.
Est.
Est.
Est.

RC
RC
RU
RU

20%
20%
20%
20%

2000
2000
2000
2000

1032
1017
1022
1006

96.9
98.3
97.8
99.4

32
17
22
5

1
0
3
4

5

EqProd§

Est. RU

Est. RC

20%

2000

1003

99.7

3

2

RU
RC
RC
RU

1024
1030
1012
1051
1010
1010
1018
1017

97.7
97.1
98.8
95.1
99.0
99.0
98.2
98.3

23
30
11
49
10
10
18
16

6
4
5
13
1
2
4
4

* Note: Est. = Estimated in ITCAAN; RC = Regionally constant; RU = Regionally unique; Known = Fixed at true value; NPD = Not positive-definite
* Movement rate fixed at true value; For all other scenarios movement is estimated
† Effective sample size of age composition set at 50
‡ CV of observation error of harvest=20%, effort=20% and survey=40%, double other scenarios
§ Ricker parameters for all populations set equal to population 2

48

Table 1.A.2: Distributions and variance or effective sample size (ESS) assumed to simulate different
data sources and stock-recruitment productivity assumptions for scenarios investigated.
Data Source

All Other Scenarios
Total Catch
Lognormal
CV 10%
Fishing Effort
Lognormal
CV 10%
Survey Catch Per Effort
Lognormal
CV 20%
Catch Age Composition
Multinomial
ESS 100
Survey Age Composition
Multinomial
ESS 100
Ricker Stock-Recruitment Different
Parameters (ι & β)
among
populations

HighVar

ESS50

EqProd

Lognormal
CV 20%
Lognormal
CV 20%
Lognormal
CV 40%
Multinomial
ESS 50
Multinomial
ESS 50
Different
among
populations

Lognormal
CV 10%
Lognormal
CV 10%
Lognormal
CV 20%
Multinomial
ESS 50
Multinomial
ESS 50
Different
among
populations

Lognormal
CV 10%
Lognormal
CV 10%
Lognormal
CV 20%
Multinomial
ESS 100
Multinomial
ESS 100
Same across
populations

49

Populations During Spawning

Population 1

Population Mixing During the Rest of the Year

Population 2

Population 1

Population 2

Harvest Region 1

Harvest Region 2

Harvest Region 1

Harvest Region 2

Harvest Region 3

Harvest Region 4

Harvest Region 3

Harvest Region 4

Population 3

Population 4

Population 3

Population 4

Figure 1.A.1: Movement dynamics simulated by the four-region operating model assuming natal
homing. The left half of the figure represents fish during spawning at the beginning of every year,
which are assumed to return to their natal population to spawn. The right half of the figure shows
the distribution of fish during the remainder of the year that mix to all harvest regions and stay for
the rest of the year.

50

Figure 1.A.2: Ricker stock-recruit relationships used to create the recruitment dynamics of the four
populations in the simulation. Note the large difference in axes scale between the two panels.

51

Figure 1.A.3: Total abundance trends of each population for two different scenarios in a spatiallyexplicit operating model for 1000 simulation iterations. The left column of figures is for populations
with 1% movement and the right column is for populations with 20% movement to non-natal regions.
The lines show three examples of simulated time series of abundance for each population. Whiskers
on the boxplots extend to 1.5 times the interquartile range or the most extreme observed data point,
whichever is less extreme. Relative errors outside the whisker range were not plotted.

52

Figure 1.A.4: Relative error (%) of annual recruitment estimates for each population of an ITCAAN
model under different movement rates and parameter estimation assumptions (scenario Group 1)
for 1000 simulation iterations. Table 1.A.1 lists the model abbreviations and corresponding model
components. Whiskers on the boxplots extend to 1.5 times the interquartile range or the most
extreme observed data point, whichever is less extreme. Relative errors outside the whisker range
were not plotted. Note the difference in y-axis scale among populations.

53

Figure 1.A.5: Relative error (%) of recruitment estimates for each population of an ITCAAN
model under scenarios investigating misspecfied natural mortality and reporting rates, data quality,
spatial complexities, and equal productivities (scenario Groups 2–5) for 1000 simulation iterations.
Table 1.A.1 lists the model abbreviations and corresponding model components. Whiskers on
the boxplots extend to 1.5 times the interquartile range or the most extreme observed data point,
whichever is less extreme. Relative errors outside the whisker range were not plotted. Note the
difference in y-axis scale among populations.

54

Figure 1.A.6: Actual error of movement rates from all populations to individual harvest regions of
an ITCAAN model under different movement rates and parameter estimation assumptions (scenario
Group 1) for 1000 simulation iterations. Table 1.A.1 lists the model abbreviations and differences
in operating and ITCAAN models. Whiskers on the boxplots extend to 1.5 times the interquartile
range or the most extreme observed data point, whichever is less extreme. Actual errors outside the
whisker range were not plotted.

55

Figure 1.A.7: Actual error of movement rate estimates from all populations to individual harvest
regions of an ITCAAN model under scenarios investigating misspecified natural mortality and
reporting rates, data quality, spatial complexities, and equal productivities (scenario Groups 2–5)
for 1000 simulation iterations. Table 1.A.1 lists the model abbreviations and corresponding model
components. Whiskers on the boxplots extend to 1.5 times the interquartile range or the most
extreme observed data point, whichever is less extreme. Actual errors outside the whisker range
were not plotted.

56

Figure 1.A.8: Relative error (%) of natural mortality and regional reporting rate estimates of an
ITCAAN model under different movement rates and parameter estimation assumptions (scenario
Group 1) for 1000 simulation iterations. Table 1.A.1 lists the model abbreviations and corresponding
model components. Whiskers on the boxplots extend to 1.5 times the interquartile range or the
most extreme observed data point, whichever is less extreme. Relative errors outside this range
were not plotted.

57

Figure 1.A.9: Relative error (%) of natural mortality (first plot in each pair) and reporting rate
(second in pair) estimates for each region of an ITCAAN model under scenarios investigating
misspecfied natural mortality and reporting rates, data quality, spatial complexities, and equal productivities (scenario Groups 2–5) with BEst20 plotted as a reference for 1000 simulation iterations.
Table 1.A.1 lists the model abbreviations and corresponding model components. Whiskers on
the boxplots extend to 1.5 times the interquartile range or the most extreme observed data point,
whichever is less extreme. Relative errors outside this range were not plotted. Circles indicate a
parameter specified in the ITCAAN model, and boxplots only presented in region 1 were estimated
as spatially constant.

58

Figure 1.A.10: Relative error (%) of total abundances for all years aggregated from an ITCAAN
model for all simulation scenarios described in Table 1.A.1 for 1000 simulation iterations. Whiskers
on the boxplots extend to 1.5 times the interquartile range or the most extreme observed data point,
whichever is less extreme. Relative errors outside the whisker range were not plotted. Note the
difference in scale between the top and bottom panel.

59

Figure 1.A.11: Relative error (%) of population-specific abundances and total abundances (summed
across populations) for 1000 simulation iterations of an ITCAAN model for a 1% movement with
natural mortality and reporting rate fixed at true values in the left column and in the right column
20% movement with natural mortality and reporting rate estimated. The lines show three examples
of time series of relative error in abundance estimates for a single simulation in each population.
Whiskers on the boxplots extend to 1.5 times the interquartile range or the most extreme observed
data point, whichever is less extreme. Estimates outside the whisker range were not plotted. Note
the difference in y-axis scale among populations.

60

APPENDIX 1.B
PARAMETER LIST AND MODEL EQUATIONS

Table 1.B.1: Symbols and descriptions of variables used in Operating and ITCAAN models.
Symbol
y
Y
a
A
p
r
l

δp

Description
Subscript for year
Last year in model
Subscript for age
Subscript for oldest modeled age
Subscript for spawning population
Subscript for region
Subscript for release cohort unique by year and
population
Population abundance
Parameter of Ricker stock-recruit function
Parameter of Ricker stock-recruit function
Mass at age
Maturity at age
Autoregressive annual deviation in recruitment
Autoregressive coefficient in autoregressive recruitment
White noise annual deviation in recruitment

Model
Both
Both
Both
Both
Both
Both
Both

Type
Index
Index
Index
Index
Index
Index
Index

Both
Operating
Operating
Operating
Operating
Operating
Operating

Derived Variable
Fixed values
Fixed values
Fixed values
Fixed values
Random variable
Random variable

Operating

Random variable

σp2

Recruitment innovation variance

Operating

Random variable

Λ
Îť
Tp,r

Recruitment in the first year
Annual recruitment deviation
Movement rate from population p to region r

ITCAAN
ITCAAN
Both

S
Z
M

Survival
Total mortality
Natural mortality

F
f
Âľ

Age-specific fishing mortality
Apical fishing mortality
Mean fishing mortality in autoregressive process

N
Îą
β
w
m

ρp

61

Estimated variable
Estimated variable
Fixed variable in operating model; Derived variable in ITCAAN*
Both
Derived Variable
Both
Derived Variable
Both
Fixed in Operating Model; Estimated in ITCAAN*
Both
Derived Variable
Operating Random variable
Operating Fixed values

Table 1.B.1 (cont’d)
σr2
ρr

v

Fishing mortality innovation variances
Autoregressive coefficient in simulated fishing
mortality
White noise annual deviation in fishing mortality
Age-specific fishery selectivity

E
q

Observed fishing effort
Fishery catchability coefficient

Îł

Observation error in effort

Fixed variable in operating model; estimated in
ITCAAN
Both
Simulated data
Both
Fixed variable in operating model; Derived variable in ITCAAN
Operating Random variable

σE2

Variance of effort data observation error

Operating

Fixed value

K
Îş
I
Q

Catchability parameter in the first year
Annual catchability deviation
Survey abundance index
Survey catchability coefficient

ITCAAN
ITCAAN
Both
Both

V

Age-specific survey selectivity

Both

τ

Observation error in survey index

Operating

Estimated variable
Estimated variables
Simulated Data
Fixed variable in operating model; Estimated
variable in ITCAAN
Fixed variable in operating model; Estimated
variable in ITCAAN
Random variable

σI2

Variance of survey index data observation error

Operating

Fixed value

ω p,r

Multinomial logit parameter for estimating movement from population p to region r
Number of tagged fish alive
Number of tagged fish released
Number of tags captured by fishery F, die naturally M, or survive S

ITCAAN

Estimated variable*

δr

n
R
t

Operating Fixed values
Operating Fixed values
Operating

Random variable

Both

Both
Derived variable
Both
Fixed values
Operating Random variable

φF

Expected proportion of tagged cohort harvested

Operating

Derived variable

φS

Expected proportion of tagged chort to survive

Operating

Derived variable

φM

Expected proportion of tagged cohort to die
from natural mortality
Vector of expected proportions of the fates of
tagged cohorts

Operating

Derived variable

Operating

Derived variables

Vector of tags captured by fishery F, die naturally M, or survive S

Operating

Random variables

ÎŚ
t F,S,M

62

Table 1.B.1 (cont’d)
d

Number of tags recovered

Both

ÎĽ

Angler reporting rate of tags

dl,N R

Number of tags never recovered

Γ
∆
C

Mean abundance for first model year
Age-specific abundance deviations in first year
Harvest in numbers caught

Îś

Observation error in harvest

Simulated data in operating model; Derived
variable in ITCAAN
Both
Fixed value in operating
model; Estimated variable in ITCAAN
Both
Simulated data in operating model; Derived
variable in ITCAAN
ITCAAN Estimated variable
ITCAAN Estimated variable
Both
Simulated data in operating model; Derived
variable in ITCAAN
Operating Random variable

σC2

Variance of harvest data observation error

Operating

Fixed value

P

Harvest age composition

ITCAAN

Simulated data in operating model; Derived
variable in ITCAAN

* When not fixed at true value for some scenarios

63

Table 1.B.2: Equations used to model and estimate population dynamics in Operating and ITCAAN models.
Equation Number
Recruitment

Equation

(1.B.2.1)

Ny+2,a=1,p = Îąp
(

(1.B.2.2)

y =

(1.B.2.3)

Abundance and Survival
(1.B.2.4)
(1.B.2.5)
(1.B.2.6)
(1.B.2.7)
Fishing Mortality and Effort
(1.B.2.8)

(1.B.2.9)

ρ p  y−1 +

Í

q
1 − ρ2 p δp,y

δp,y

a (ma wa Ny,a,p )e

for y > 1
for y = 1

Model
−β p

where

Í

Operating

a (ma wa Ny,a,p ) y

δp,y ∟ N

bp
by=1,a=1,p = Λ
N
by,a=1,p = N
by−1,a=1,p eλby,p
N
by,a=1,p = ( N
bY −2,a=1,p + N
bY −3,a=1,p + N
bY −4,a=1,p )/3
N

−σp2 (1−ρ p ) 2
q
, σp
2 1−ρ2p

for

y=1

for
for

1 < y ≤Y −2
y = Y − 1 or Y

Ny,a,p Tp,r Sy,a,r
where
a < A−1
r Ny,A,p Tp,r Sy,A,r + Ny,A−1,p Tp,r Sy,A−1,r
Z y,a,r = M + Fy,a,r

!
Operating

ITCAAN

Ny+1,a+1,p =

Í

Both

Ny+1,A,p =

Í

Both

r

Both

Sy,a,r = e−Z y,a,r

Both

Fy,a,r = fy,r va,r


fy=1,r ∼ Trunc. Normal µr , σr2, 0, ∞
for
y=1


fy+1,r = µr (1 − ρr ) + ρr fy,r + δr,y
for
1< y ≤Y


where
δr,y ∼ Trunc. Normal 0, σr2, −(ρr fy,r + µr (1 − ρr ) , ∞)

Operating

64

Operating

Table 1.B.2 (cont’d)
(1.B.2.10)
(1.B.2.11)
(1.B.2.12)

E y,r = fy,r Îł y,r /qr



γ y,r ∼ LN − σE2 /2, σE2
Fy,a,r = E y,r q̂ y,r v̂a,r
where

q̂ y=1,r = K̂r
q̂ y,r = q̂ y−1,r e κ̂ y,r

for y = 1
for 1 < y ≤ Y

Operating
ITCAAN
ITCAAN

Survey Calculations
(1.B.2.13)
(1.B.2.14)

Í
I y,a,r = Qr Va,r p Ny,a,p Tp,r e−Z y,a,r 10/12


Í
I y,r = τy,r a I y,a,r
where
τy,r ∼ LN − σI2 /2, σI2

Movement Estimation
(1.B.2.15)
Tag Dynamics
(1.B.2.16)
(1.B.2.17)

ω
br,p = Í e r,p ,
T
3
eωr,p

where ωr=4,p = 0

Both
Operating
ITCAAN

r=1

nl,y,a = Rl,a

for


y=l


Both
Operating

(1.B.2.18)

tl,y,a,r ∟ M N nl,y,a, Tp,r


Fy,a,r
F
φ y,a,r = Z
1 − Sy,a,r

Operating

(1.B.2.19)

φSy,a,r = Sy,a,r

Operating

(1.B.2.20)

M
φM
y,a,r = Z y,a,r (1 − Sy,a,r )


Φ y,a,r = φ Fy,a,r , φSy,a,r , φ M
y,a,r


F,S,M
t l,y,a,r
∟ M N tl,y,a,r , Ό y,a,r
Í S
nl,y+1,a+1 = r tl,y,a,r


F
dl,y,a,r ∟ BI N tl,y,a,r
, ÎĽr

Operating

(1.B.2.21)
(1.B.2.22)
(1.B.2.23)
(1.B.2.24)

y,a,r

65

Operating
Operating
Operating
Operating

(1.B.2.25)
(1.B.2.26)

(1.B.2.27)

Table 1.B.2 (cont’d)
Í
Í Í Í
dl,N R = a Rl,a − y a r dl,y,a,r


Í
F̂y,a,r
b
br
b
b
1 − Sy,a,r Υ
dl,y,r = a n̂l,y,a Tp,r

Both
ITCAAN

Ẑ y,a,r

n̂l,y,a
= Rl,a
Í
bp,r Sby,a,r
n̂l,y+1,a+1 = r n̂l,y,aT
Í
bp,r Sby,A,r + n̂l,y,A−1T
bp,r Sby,A−1,r
n̂l,y+1,A = r n̂l,y,AT

for
for
for

y=l
a < A−1
a=A

Initial Abundance Estimation
(1.B.2.28)

by=1,a,p = exp(b
N
Γp + b
∆ p,a )

for

a>2

Í
where a b
∆ p,a = 0.0

ITCAAN

ITCAAN

Catch Calculations
(1.B.2.29)
(1.B.2.30)

Cy,r = Îśy,r

Í

a Cy,a,r

Cy,a,r =

where

ζy,r ∼ LN(−σC2 /2, σC2 )

Í Fy,a,r

p Z y,a,r Ny,a,p Tp,r

(1.B.2.31)

Cy,r =

(1.B.2.32)

Py,r = Cy,a,r /Cy,r

66

Í

a Cy,a,r

(1 − Sy,a,r )

Operating
Both
ITCAAN
ITCAAN

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67

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Mol. Ecol. 7(12): 1757–1769. doi:10.1046/j.1365-294x.1998.00512.x.
Thorson, J.T., Jensen, O.P., and Zipkin, E.F. 2014. How variable is recruitment for exploited
marine fishes? A hierarchical model for testing life history theory. Can. J. Fish. Aquat. Sci.
71(7): 973–983. doi:10.1139/cjfas-2013-0645.
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Thorson, J.T., Jensen, O.P., and Zipkin, E.F. 2016. Corrigendum: How variable is recruitment for
exploited marine fishes? A hierarchical model for testing life history theory. Can. J. Fish. Aquat.
Sci. doi:10.1139/cjfas-2013-0645.
Vandergoot, C.S. and Brenden, T.O. 2014. Spatially varying population demographics and fishery
characteristics of Lake Erie walleyes inferred from a long-term tag recovery study. Trans. Am.
Fish. Soc. 143(1): 188–204. doi:10.1080/00028487.2013.837095.
Wang, H.Y., Rutherford, E.S., Cook, H.A., Einhouse, D.W., Haas, R.C., Johnson, T.B., Kenyon, R.,
Locke, B., and 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(2): 539–551. doi:10.1577/T06012.1.
Wang, Y. and Liu, Q. 2006. Estimation of natural mortality using statistical analysis of fisheries
catch-at-age data. Fish. Res. 78(2–3): 342–351. doi:10.1016/j.fishres.2005.11.020.
Wilberg, M.J. and Bence, J.R. 2006. Performance of time-varying catchability estimators in
statistical catch-at-age analysis. Can. J. Fish. Aquat. Sci. 63(10): 2275–2285. doi:10.1139/f06111.
Wilberg, M.J. and Bence, J.R. 2008.
Performance of deviance information criterion
model selection in statistical catch-at-age analysis.
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doi:10.1016/j.fishres.2008.04.010.
Wills, T., Robinson, J., Faust, M., Gorman, A.M., Belore, M., Cook, A., Drouin, R., MacDougall,
T., Zhao, Y., Murray, C., and Hosack, M. 2016. Report for 2015 by the Lake Erie walleye
task group. Technical report, Lake Erie Committee Great Lakes Fishery Commission. Available
from http://www.glfc.org/pubs/lake_committees/erie/WTG_docs/annual_reports/WTG_report_
2016.pdf [accessed 28 November 2017].
Ying, Y., Chen, Y., Lin, L., and Gao, T. 2011. Risks of ignoring fish population spatial structure in
fisheries management. Can. J. Fish. Aquat. Sci. 68(12): 2101–2120. doi:10.1139/f2011-116.
Zhao, Y., Einhouse, D.W., and MacDougall, T.M. 2011. Resolving some of the complexity of a
mixed-origin walleye population in the east basin of Lake Erie using a mark-recapture study. N.
Am. J. Fish. Manage. 32(2): 379–389. doi:10.1080/02755947.2011.571516.
Zhao, Y., Jones, M.L., Shuter, B.J., and Roseman, E.F. 2009. A biophysical model of Lake Erie
walleye (Sander vitreus) explains interannual variations in recruitment. Can. J. Fish. Aquat. Sci.
66(1): 114–125. doi:10.1139/F08-188.
Zhao, Y., Kocovsky, P.M., and Madenjian, C.P. 2013. Development of a stock-recruitment model
and assessment of biological reference points for the Lake Erie walleye fishery. N. Am. J. Fish.
Manage. 33(5): 956–964. doi:10.1080/02755947.2013.822442.

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CHAPTER 2
PARAMETER ESTIMATION PERFORMANCE IN A RECOVERY-CONDITIONED
INTEGRATED TAGGING CATCH-AT-AGE ANALYSIS MODEL

Abstract
Recovery-conditioned models are infrequently used in fisheries science to analyze recovery
data from tagging experiments, but were proposed as an alternative to release-conditioned models
when nuisance factors such as tag reporting or shedding rates were spatially constant. Integrated
tagging and catch-at-age analysis (ITCAAN) models incorporate tag-recovery information as data
components within statistical catch-at-age models for spatially-explicit assessment of fish stocks.
Through simulations, we investigated the performance of recovery-conditioned ITCAAN models
under a range of model complexities and different intermixing rate scenarios. We also investigated
how misspecification of natural mortality, parity in population productivities, and spatially varying
reporting rates affected ITCAAN model estimates. An operating model based on Lake Erie
walleye (Sander vitreus) with four populations that exhibited natal homing and intermixing during
harvest periods was used to simulate data. At low intermixing rates, ITCAAN model estimates
of total abundance and spawning population abundances were accurate and precise with median
relative error within Âą10% and inter-quartile ranges of relative errors between 5 and 42%, with
precision decreasing when natural mortality was estimated. Accuracy and precision of individual
spawning population abundance estimates declined with higher intermixing rates, with the largest
bias and imprecision occurring when estimating relative reporting rates. This bias was not evident
when simulated populations had similar productivity levels, even at high intermixing rates. The
accuracy and precision associated with estimating relative reporting rates depended on intermixing
and productivity levels of the associated spawning population. Natural mortality estimates were
accurate and precise for most examined scenarios, though precision generally decreased with higher
intermixing rates. Estimating relative reporting rates resulted in biased and less precise movement

73

rate estimates. Assuming reporting rates were spatially constant when they varied regionally caused
biased estimation of movement rates and spawning population abundances. Based on our results, we
recommend recovery-conditioned ITCAAN models only be used for spatially-explicit assessments
of intermixed fish stocks when there is high certainty that tag reporting rates are spatially constant
or when spawning populations can be assumed to have similar levels of productivity.

Introduction
Spatially-explicit population assessment models simultaneously estimate abundances, mortalities, and movement rates of populations that are exploited as mixed stocks during the fishing season
(Goethel et al. 2011). For our purposes, populations are defined as self-sustaining groups of fish
that interbreed and share similar life history characteristics. Stocks are defined as exploited fishery
units delineated by region of harvest (Cadrin et al. 2004). Therefore, a mixed stock is comprised of
individuals from two or more populations that are exploited as a single unit. Mixed stocks create
overharvesting risks for less productive populations depending on how stocks are managed (Ying
et al. 2011; Guan et al. 2013; Hulson et al. 2013; Molton et al. 2013; Li et al. 2014). Integrated
tagging and catch-at-age analysis (ITCAAN) models (Maunder 2001; Goethel et al. 2015b; Vincent
et al. 2017), which incorporate tag-recovery data within a statistical catch-at-age assessment model,
is one spatially-explicit assessment approach that has been used to assess and help manage mixed
stocks. Performance of ITCAAN models has been explored through simulations under a range
of model complexities and different movement dynamics of fish populations (e.g., reproductive
mixing, natal homing) (Hulson et al. 2013; Goethel et al. 2015b; Vincent et al. 2017).
Two contrasting approaches are used to analyze tag-recovery data. The most common approach
is for tag recoveries at different time periods or by different harvest methods to be conditioned
on the number of tags released (release-conditioned framework) (Brownie et al. 1987; Hoenig
et al. 1998; Frusher and Hoenig 2003; Latour et al. 2003; Jiang et al. 2007). With a releaseconditioned framework, the number of tags that are never recovered and the probability of tags
never being recovered are factored into analyses. The probability of never recovering a tag is

74

influenced by several nuisance factors including tag reporting, tagging mortality, and tag shedding;
these nuisance factors must be accounted for in recovery probabilities to prevent biased parameter
estimates (Hampton 1997; Denson et al. 2002; Cowen et al. 2009; Brenden et al. 2010; Vandergoot
et al. 2012). The other general approach for analyzing tag-recovery data is for tag recoveries at
different time periods and by different harvest methods to be conditioned on the total number of
recoveries (recovery-conditioned framework, also referred to as recapture-conditioned) (McGarvey
and Feenstra 2002; McGarvey 2009). The recovery-conditioned framework was proposed to
eliminate the need to account for nuisance factors (e.g., tag reporting) to estimate movement rates.
The framework for this formulation was derived from the following property: when nuisance factors
such as tag reporting are assumed to be spatially constant, they cancel out in likelihood equations and
thus do not influence model fit (McGarvey and Feenstra 2002). The assumption of spatially constant
nuisance parameters is commonly made for the recovery-conditioned framework (McGarvey et al.
2010), but whether this assumption will be met with actual fishery data is questionable. If nuisance
parameters are not spatially constant they do not cancel out in the likelihood and therefore need to
be accounted for in the model, either as parameters to be estimated or as assumed values, or else
parameter estimates may be biased.
The recovery-conditioned framework has been infrequently used for analyzing tag-recovery
data in fisheries science, although see McGarvey and Feenstra (2002) and McGarvey (2009). There
also has been limited application and simulation evaluation of ITCAAN models that incorporate a
recovery-conditioned framework, although see McGarvey et al. (2010). As a result of its limited use,
it is not presently known how complex of a parameterization (e.g. natural mortality estimation) can
be handled by a recovery-conditioned ITCAAN model. Additionally, it is unknown how sensitive
parameter estimates are to assuming nuisance parameters, such as reporting rates, are spatially
constant when the true dynamics are spatially variable.
The purpose of this research was to evaluate the accuracy, precision, and robustness of model
parameters for a recovery-conditioned ITCAAN model through simulations. Specifically, we
investigated how accuracy and precision of parameter estimates were affected by the following:

75

1. whether movement, natural mortality, and/or reporting rates were estimated or treated as known
and fixed quantities and how this was affected by the degree of intermixing of the populations;
2. spatial variability in reporting rates among regions and whether reporting rates were estimated
in the recovery-conditioned ITCAAN model or presumed to be constant; and 3. misspecification
of natural mortality when these parameters were treated as known within the recovery-conditioned
ITCAAN model and parity in productivities of the spawning populations. We were motivated to
explore the performance of recovery-conditioned ITCAAN models to spatially varying reporting
rates because reporting rates in actual systems are unlikely to be constant across space. Factors
that can lead to spatially varying reporting rates include differences in types of fisheries (e.g.,
commercial versus recreational fisheries) operating in different regions of the system, how well
the tagging study is advertised, degree of apathy toward the tagging study, or relationship with the
agency conducting the tagging study (Hoenig et al. 1998; Denson et al. 2002; Vandergoot et al.
2012). As a result, fishery managers and biologist choosing which tagging framework to use in an
ITCAAN model would benefit from knowing how recovery-conditioned ITCAAN models perform
when confronted with spatially-varying reporting rates.
Simulations were based on walleye (Sander vitreus) populations in the Laurentian Great Lakes
of North America. Walleye have been found to be highly migratory both in the Great Lakes (Wang
et al. 2007; Zhao et al. 2011; Vandergoot and Brenden 2014; Hayden et al. 2014) and in inland
systems (Smith et al. 1952; Rasmussen et al. 2002; Herbst et al. 2016). For both the Great Lakes and
inland systems, walleye migration has been identified as potentially problematic for management
(Brenden et al. 2015; Herbst et al. 2017).

Lakes Erie and Huron Walleye
Walleye are economically important in the Great Lakes region and are subject to both commercial
and recreational exploitation (Fielder and Bence 2014; Wills et al. 2016). Walleye spawn in rivers
or on shallow reefs during the early spring. After spawning, walleye disperse throughout the Great
Lakes (Wang et al. 2007; Zhao et al. 2011; Vandergoot and Brenden 2014; Hayden et al. 2014),
76

but typically return to their natal region to spawn each year (Stepien and Faber 1998; Haponski and
Stepien 2014; Hayden et al. 2014; Wilson et al. 2017).
The largest walleye fisheries in the Great Lakes region are in Lakes Erie and Huron, which are
connected via Lake St. Clair and the Detroit and St. Clair Rivers. Walleye abundance in Lake
Huron has been estimated to be between one and four million fish (Fielder and Bence 2014). In
Lake Erie, abundance of walleye in the eastern basin of the lake has been estimated on the order
of tens of thousands for fish (Zhao et al. 2011), whereas abundance in Lake Erie’s western basin
is closer to tens of millions of fish (Wills et al. 2016). Tagging studies have documented walleye
migrating between Lakes Erie and Huron (Wang et al. 2007; Hayden et al. 2014; Vandergoot and
Brenden 2014). Estimated intermixing rates of walleye from some spawning populations in Lake
Erie’s western basin to Lake Huron and the eastern basin of Lake Erie have been around 1 to
2% (Wang et al. 2007; Fielder and Bence 2014; Vandergoot and Brenden 2014). This rate of
intermixing may be low, but a considerable amount of the harvest in all regions may originate from
the western basin population given the large differences in population abundances between the
areas (McParland et al. 1999; Brenden et al. 2015). Interest in developing spatially-explicit models
to assist with the management of Lakes Erie and Huron walleye has increased in recent years due to
the recognition of the movement between the lakes and the value of the respective fisheries (Fielder
and Bence 2014; Wills et al. 2016).

Methods
An operating model was used to generate and track the true dynamics of simulated fish populations and tagged cohorts. From this operating model, observed time-series data were generated,
which were then fit in a recovery-conditioned ITCAAN model. The operating model used in this
research was identical to that presented in Vincent et al. (2017), but will be summarized here.
The operating model simulated the abundances and dynamics of four populations that intermixed
among four regions. Fish were assumed to aggregate in their natal region at the beginning of
each year to spawn (i.e., 100% spawning site fidelity was assumed). Recruitment was simulated

77

from population-specific Ricker stock-recruitment functions with a first-order autoregressive process error. Values for the first-order autoregressive process were randomly drawn from posterior
distributions for Percidae for each population (Thorson et al. 2014). The equilibrium stock size
and productivity (i.e., stock-recruit steepness) were assumed to differ among the four populations
for most scenarios (Table 2.A.1). The stock-recruit parameters for population 1 were based on
Lake Huron walleye, while the stock-recruit parameters for populations 2, 3, and 4 were based on
western, central, and eastern Lake Erie walleye, respectively.
After spawning, fish were assumed to instantaneously mix among the four regions using a
box-transfer model (Goethel et al. 2011), where they were assumed to remain for the rest of the
year and were subject to fishing. The exploitation rates experienced by the mixed stocks were
region-specific. Apical fishing mortality rates for the regions were generated using first-order
autoregressive processes with regionally unique means based on estimated fishing mortalities for
Lakes Erie and Huron (Table 2.A.1). Region-specific catchability coefficients and lognormal
multiplicative observation errors with a CV of 10% were used to simulate fishery-specific time
series of fishing effort. The natural mortality rate was assumed to be 0.32 year-1 in all populations
for the entire time series of the simulations. Age-specific selectivities for each fishery were assumed
to be temporally constant but regionally varying. Region-specific harvest data (i.e., summed across
populations) were generated from actual harvest multiplied by lognormal observation errors with a
CV of 10% for all 40-years. Observed harvest age composition for each fishery was simulated from
multinomial distributions that used the actual harvest age composition as the underlying proportions
and assumed a sample size of 100 fish. A fishery-independent survey was simulated to occur in each
region during October (i.e., during the intermixed period). Region-specific catchabilities and agespecific selectivities were used to simulate a survey catch per effort time series with multiplicative
lognormal observation errors with a CV of 20%. Age-composition data for all years were also
simulated for each survey from multinomial distributions based on the intermixed age distribution
present in October with a sample size of 100.
Two thousand fish were simulated to be tagged annually from each population at the beginning

78

of the year when fish were aggregated for spawning. The fate (i.e., survived, harvested, or died
due to natural causes) of tagged fish each year were generated from multinomial distributions with
expected proportions equal to the dynamics of the at-large populations (e.g., exploitation rate). Tag
reporting was assumed to be imperfect for all simulations, but the assumed regional reporting rates
varied among the different scenarios (see Simulation Scenarios). The number of tags recovered
were simulated using a binomial process based on the number of harvested tagged fish and the
regional reporting rate. Simulations that had an abundance for any of the four populations less than
40000 fish were automatically excluded and replaced with a new simulation, because we believed
that it was unlikely that more than 5% of a population would be tagged within a year.
Forty years of data were generated by the operating model; the full time series of observations
were then fit using the ITCAAN model. The data sources generated by the operating model were
region-specific fishery harvest in numbers, fishery harvest age composition, region-specific mixed
population survey catch per effort, survey age composition, tag-recovery data, and fishery effort
per region. Both the operating model and the ITCAAN model tracked the dynamics of walleye
between the ages of 2 and 7, with the last age group in the model aggregating all fish age 7 and
older. The operating model was programmed in R version 2.15.1 (R Core Team 2016), whereas the
ITCAAN model was programmed in AD Model Builder version 11.5 (Fournier et al. 2012). Code
for the operating model and ITCAAN model can be found in the Supplementary Material 2.

ITCAAN Model
The ITCAAN model used in this research was nearly identical to that used in Vincent et al. (2017).
The primary difference between these models was this study used a recovery-conditioned framework
to analyze the tag-recovery data. Therefore, the negative log likelihood equation for the tagging
component of the ITCAAN model in this research, ignoring scaling constants, was as follows:
L=−


dš
l,y,r
∗ dl,y,r
log Í Í
š
r
y r dl,y,r

ÕÕÕ
l

y



(2.0.1)

where d is the observed number of tags recovered and dˆ is the model predicted number of tags
79

recovered. The subscripts for d are the unique release event for each population and year (l), the
year of recovery (y) and the region of recovery (r). The predicted number of tags recovered from
a tagged cohort were calculated as
dš
l,y,r =

Õ

bp,r
n̂l,y,a T

a

F̂y,a,r 
Ẑ y,a,r


cr
1 − Sby,a,r Υ

(2.0.2)

where n̂l,y,a is the predicted number of tags alive in year y of age a from tag release year and
bp,r is the predicted movement rate from population p to region r, F̂ is the predicted
population l, T
instantaneous fishing mortality rate, Ẑ is the predicted instantaneous total mortality rate, Ŝ is
cr are the region-specific reporting rates. With a recovery-conditioned
the survival rate, and ÎĽ
framework, actual reporting rates for the regions are not estimable because unique solutions do not
exist given Equations (2.0.1) and (2.0.2). In other words, region-specific reporting rates of 10%,
20%, 30% and 40% would be expected to produce the same model fit as region-specific reporting
rates of 20%, 40%, 60%, and 80%. In this research, we explored the estimability of relative
reporting rates in a recovery-conditioned framework by fixing the reporting rate for one region to
a particular value and then estimating the reporting rates for the remaining regions. A relative
reporting rates formulation produces unique solutions, and in the above examples would equal 1.0,
2.0, 3.0, and 4.0 if scaled relative to region 1. However, the existence of unique solutions for relative
reporting rates does not guarantee that accurate and precise parameter estimates can be obtained
from a recovery-conditioned ITCAAN model, due to possible confounding with other parameter
estimates. For this research, we fixed the reporting rate for region 1 at a value of 1.0 and then
estimated the relative reporting rates for the other three regions as bounded parameters between
0.01 and 100. For scenarios where reporting rates were not estimated but were treated as fixed
values, region-specific reporting rates were still treated as relative values. Thus, if the operating
model assumed a reporting rate of 0.5 for all regions and the reporting rates were assumed known
in the ITCAAN model, the relative reporting rates were specified at 1.0 for all regions. Fixing
the relative reporting rates equal among regions was equivalent to assuming that reporting rates
canceled out of the likelihood equations.
ITCAAN models were fit to generated data from the operating model using highest posterior
80

density estimation, also referred to as maximum penalized likelihood estimation (Stewart et al.
2013). We assessed convergence of the ITCAAN model by whether the maximum gradient across
all parameters was less than 0.05 and the model produced a positive-definite Hessian matrix. This
cutoff for the maximum gradient was determined after preliminary results for the low movement
scenario showed that gradients much smaller than this were infrequent and estimates were within
the range of plausibility. Simulated datasets were fit by the ITCAAN model until 1000 datasets had
converged. Table 2.A.2 presents the number of simulations that were required to reach a sample
size of 1000, as well as the number of simulations that failed to converge for either criteria.

Simulation Scenarios
Three groups of scenarios were investigated to examine recovery-conditioned ITCAAN model
performance. The first group of scenarios evaluated the estimability of movement, natural mortality,
and/or relative reporting rates under different rates of population intermixing. The second group
of scenarios analyzed the influence of spatially varying reporting rates on parameter estimates
when either estimating relative reporting rates or assuming the reporting rates were regionally
constant (i.e., canceled out of likelihood). The third group of scenarios evaluated the influence of
misspecifying natural mortality in an ITCAAN model and the effect of equal productivities among
populations.

Group 1: Estimation of Movement, Relative Reporting Rates, and Natural Mortality Under Varying
Intermixing Rates
Simulations were conducted for a total of 20 scenarios to examine how the estimation of movement,
natural mortality, and/or relative reporting rates in the ITCAAN model and the intermixing rate
of the simulated populations influenced ITCAAN model performance. Four assumed intermixing
scenarios were crossed with five ITCAAN model parameterizations. The four intermixing scenarios
consisted of different rates of movement from natal region to each non-natal region. The examined
rates were 1%, 5%, 10%, and 20% of the population. For example, under a 20% intermixing

81

rate 40% of the populations would remain in their natal region and 20% of the populations would
move to each of the other three regions. The five ITCAAN parameterizations varied with regards
to whether movements, natural mortality, and/or relative reporting rates were estimated as part
of the model fitting process or fixed at the true values assumed in the operating model. The first
parameterization assumed that movements, natural mortality, and relative reporting rates were fixed
at their true values and this was the only parameterization where movement rates were not estimated
(MvFix). The second parameterization estimated movement rates, but assumed natural mortality
and relative reporting rates were fixed at their true values (MRFix). The third parameterization
estimated movement rates and natural mortality, but assumed relative reporting rates were fixed
at their true values (RFix). The fourth parameterization estimated movement rates and relative
reporting rates but fixed natural mortality at the true value (MFix). The final parameterization
estimated movement, natural mortality, and relative reporting rates (NoFix). The results are
presented using the estimation approach of the ITCAAN model followed by the intermixing rate in
the operating model. For example, MFix20 refers to the ITCAAN parameterization where relative
reporting rates and movement rates were estimated, but natural mortality was fixed in the ITCAAN
model and the operating model assumed a 20% intermixing rate.

Group 2: Regionally Varying Reporting Rates
The second group of scenarios investigated the influence of regionally varying reporting rates in
the operating model on different treatments of reporting rates in the ITCAAN model. All scenarios
in this group assumed a 20% intermixing rate for the simulated populations. We investigated
two scenarios of spatially varying reporting rates in the operating model. The first scenario with
reporting rates varying spatially (RV1) assumed that the reporting rates were the highest for regions
where the natal populations were the least productive (Table 2.A.1). The second scenario with
reporting rates varying (RV2) assumed that the reporting rate was the highest in regions where the
natal populations were the most productive and decreased with decreasing productivity. For both of
these reporting rate scenarios, we attempted to estimate the relative reporting rates for the regions
82

using the method described in the ITCAAN model section. We also explored the consequence
of assuming the reporting rates were constant in the ITCAAN model under these two scenarios
by fixing the relative reporting rates for all regions to 1.0. Scenarios in this group that estimated
relative reporting rates were referred to as Est scenarios (e.g., RV1Est); when relative reporting
rates were assumed to be spatially constant, we refer to these simulations as Canc scenarios (e.g.,
RV1Canc).

Group 3: Sensitivity to Misspecified Natural Mortality and Equal Productivity
The third group of simulations investigated the consequences of misspecifying natural mortality
in a recovery-conditioned ITCAAN model and the effect of assuming equal productivities among
spawning populations in the operating model. All scenarios in this group assumed a 20% intermixing rate in the operating model. The first scenario examined the influence of misspecifying the
natural mortality in the ITCAAN model at 0.5 times the true value (i.e., 0.16). This scenario was
referred to as SensU because it evaluated sensitivity to natural mortality that was specified to be
less than (under) the true value. The second scenario in this group examined the effect of specifying
the natural mortality in the ITCAAN model at 1.5 times the true value (i.e., 0.48). This scenario
was referred to as SensO because it evaluated the sensitivity of parameter estimates to specifying
natural mortality to be greater than (over) the true value. The third scenario in this group evaluated
how parity in productivities among the four populations affected ITCAAN parameter estimation.
This scenario was referred to as EqProd to stand for equal productivities among populations. For
this scenario, all populations were assumed to have the same stock-recruitment parameters in the
operating model (i.e., Ricker parameters for population 2 in other scenarios), and natural mortality
and relative reporting rates were estimated in the ITCAAN model.

Performance Metrics
ITCAAN model performance was evaluated by comparing parameter estimates to the true population dynamics in the operating model and the number of simulations that converged for each
83

scenario (Table 2.A.2). Model performance was assessed through percent relative error, which
was calculated by subtracting the true value from the estimate and then dividing by the true value
and multiplying by 100. For the sake of brevity, we discuss the precision and accuracy of model
estimates of total abundance (i.e., abundance summed over all populations), spawning population
abundance, relative reporting rate, natural mortality, and movement rates. Performance of all other
parameter estimates are presented in the Supplementary Material 2. Parameters not presented
either showed no bias in estimates or were biased similar to population abundances, though not
always in the same direction. Relative error was calculated for all parameters including those that
are age specific (e.g, selectivity, results shown in Supplementary Material 2) and year specific (e.g.,
abundance) for all converged simulations and then aggregated by region for plotting. For example,
the boxplots of population abundance summarizes 40 years of error in abundance estimates times
1000 simulations. The median of the relative errors was used as a metric of model accuracy and
the interquartile range (IQR) was used as a metric of estimate precision. Accuracy and precision of
parameter estimates were compared across scenarios to give a holistic view of recovery-conditioned
ITCAAN model performance.

Results
ITCAAN Model Convergence
Convergence of the recovery-conditioned ITCAAN model varied depending on the intermixing
rate of the operating model (Table 2.A.2). A convergence rate greater than 95% occurred for
simulation scenarios where the assumed intermixing rates were 5% or greater. Simulation scenarios
at the 1% intermixing rate had approximately 80% of simulations converged. Simulations at
the 1% intermixing rate typically failed to converge due to a maximum gradient greater than
0.05. A decrease in convergence as a result of failing both criteria was observed for one of the
scenarios where reporting rates were spatially varying but assumed constant in the ITCAAN model
(RV2Canc).

84

Model Performance
Total Abundance Relative Error
Accuracy and precision of total abundance summed across all populations, as measured by median
and IQR relative error, varied among the simulation scenarios. Median relative errors in total
abundance for Group 1 scenarios were between -0.13% and -7.99% suggesting a consistent negative
bias in total abundance estimates from a recovery-conditioned ITCAAN model. However, in all
cases the relative error IQR encompassed 0% (Figure 2.A.1). In scenarios where natural mortality
was estimated (i.e., RFix and NoFix scenarios), total abundance estimates had greater bias and
imprecision compared to scenarios where natural mortality was fixed at the true value (i.e., MvFix,
MRFix, and MFix) (Figure 2.A.1). Scenarios in which relative reporting rates were estimated,
but natural mortality was fixed (i.e., MFix) had levels of bias and imprecision similar to scenarios
where both natural mortality and reporting rates were fixed(i.e., MRFix) (Figure 2.A.1). Across all
scenarios in which natural mortalities were fixed at their true values, accuracy and precision of total
abundance estimates were fairly consistent across the evaluated intermixing levels. For scenarios
in which natural mortality was estimated, the highest (i.e., 20%) intermixing rates resulted in the
largest imprecision of total abundance estimates.
The influence of spatially varying reporting rates on total abundance depended on how reporting
rates were parameterized in the ITCAAN model. Median and IQR relative error for total abundance
estimates in the ITCAAN models with relative reporting rates and natural mortality estimated
(RV1Est and RV2Est scenarios) were similar to the RFix20 and NoFix20 scenarios. Conversely,
when reporting rates were assumed to be spatially constant in the ITCAAN model (RV1Canc
and RV2Canc scenarios), accuracy and precision of total abundance estimates worsened. Under
conditions where the reporting rates were the largest in the most productive natal region (RV1Canc),
the total abundance estimates were slightly positively biased, but imprecision was approximately 2
times greater than the RFix20 or NoFix20 scenarios. Total abundance was very negatively biased
for the scenario with reporting rate smallest in the most productive natal region (RV2Canc).

85

The misspecification of natural mortality at 0.5 times the true value resulted in an underestimation of the total abundance with a median relative error of approximately -50%. Conversely, setting
natural mortality at 1.5 times the true value in the ITCAAN model resulted in a positive bias in
total abundance with a median relative error equal to 385%. Specifying natural mortality above the
true value also resulted in the largest imprecision in total abundance observed among the examined
scenarios (Figure 2.A.1). When all populations were assumed to have equal productivity levels,
total abundance estimates from the ITCAAN model had bias similar to the NoFix20 scenario, but
were slightly more precise (Figure 2.A.1).

Population Abundances Relative Error
Estimates of individual population abundances were generally more imprecise and biased than
estimates of total abundance. Abundance estimates of population 2, the most productive population,
for Group 1 scenarios were generally negatively biased, while biases for all other populations were
positive (Figure 2.A.2). As intermixing rate increased, the bias and imprecision in population
abundance estimates generally increased. Among scenarios with low intermixing rates, the largest
bias and imprecision in population abundance for populations 2 and 4 occurred in when natural
mortality was estimated (RFix and NoFix) (Figure 2.A.2). For populations 1 and 3, the largest
amount of bias and imprecision occurred in scenarios where reporting rates were estimated (MFix
and NoFix) (Figure 2.A.2). Estimates for all populations were the most biased and imprecise
for high intermixing rate scenarios when reporting rates were estimated (MFix20 and NoFix20)
(Figure 2.A.2).
Individual population abundances were most biased for Group 2 scenarios when reporting
rates were assumed to be spatially constant (i.e., were not estimated). Bias and precision of
individual population abundance estimates for models that estimated relative reporting rates under
both spatially varying reporting rates scenarios (RV1Est and RV2Est) were similar to the NoFix20
scenario. The bias in individual population abundance estimates, for ITCAAN models that assumed
a spatially constant reporting rate, were greatly influenced by which region had the highest assumed
86

reporting rate. When the highest reporting rates occurred in regions associated with the most
productive populations (RV1Canc), abundance estimates for populations 2 and 4 were severely
underestimated, whereas abundance of population 3 was severely overestimated (median relative
error approximately 5000%) (Figure 2.A.3). When the highest reporting rates occurred in regions
associated with the least productive populations (RV2Canc) the abundance of populations 2 and 3
were underestimated, the abundance of population 4 was greatly overestimated, and the abundance
for population 1 was slightly overestimated (Figure 2.A.3).
Incorrect specification of natural mortality had large consequences on population estimates
(Figure 2.A.3). When natural mortality was specified at 0.5 times the true value in the ITCAAN
model (SensU), abundance estimates for population 1 and 3 were positively biases, whereas abundance estimates for population 2 were negatively biased (Figure 2.A.3). The absolute magnitude
of bias for populations 1, 3 and 4 was between that observed for the RFix20 and MFix20 scenarios.
However, for population 2 the absolute magnitude of bias was considerably greater than what was
observed from the RFix20 or MFix20 scenarios. When natural mortality was set at 1.5 times
the true value in the ITCAAN model, all population abundances were significantly overestimated
(Figure 2.A.3). When the productivities among the populations were equal, individual population
abundance estimates were accurate and precise, with precision consistent across populations.

Natural Mortality and Relative Reporting Rates Relative Error
Natural mortality estimates for Group 1 scenarios were accurate (within Âą5%), but precision varied
between scenarios (Figure 2.A.4). The IQR of the relative error for natural mortality was relatively
consistent for the 1%, 5% and 10% intermixing scenarios, but doubled for the 20% intermixing
scenario. Additionally, a slight negative bias in natural mortality estimates occurred when the
intermixing rates were 20%. Estimation of relative reporting rates concurrently with natural
mortality did not affect accuracy or precision of the natural mortality estimates (Figure 2.A.4). For
Group 2 scenarios, natural mortality estimates were also fairly accurate when the relative reporting
rates were estimated (RV1Est and RV2Est). When reporting rates were assumed constant in the
87

ITCAAN model, a positive bias in natural mortality estimates occurred in the scenario where
reporting rates were the greatest in the region associated with the most productive population
(RV1Canc). This bias was not observed under the scenario where reporting rates were the lowest in
the region associated with the most productive population (RV2Canc) (Figure 2.A.4). For both the
RV1Canc and the RV2Canc scenarios, precision of natural mortality estimates was poor compared
to Group 1 scenarios (Figure 2.A.4). For the Group 3 scenario in which spawning populations had
equal productivities, accuracy and precision of natural mortality estimates were similar to Group 1
scenarios under a 20% intermixing rate.
Accuracy and precision of relative reporting rates varied by intermixing rate scenario and
region (Figure 2.A.4). For Group 1 scenarios, relative reporting rates were fairly accurate for
regions 3 and 4 across the evaluated intermixing levels; conversely, relative reporting rates for
region 2 were negatively biased with the degree of bias increasing as the intermixing rate increased
(Figure 2.A.4). For all regions, precision of the relative reporting rates improved with higher
intermixing. For Group 2 scenarios, accuracy and precision of relative reporting rates varied
depending on the spatial pattern of reporting rates. When reporting rates were the highest in
the natal region for the largest population (RV1Est), the relative reporting rate parameter for this
region was negatively biased and was the least precise estimate for this region among scenarios
investigated. Conversely, when reporting rate was the lowest for the largest population (RV2Est),
the relative reporting rates for all regions were generally unbiased and precise. Misspecification
of natural mortality within the ITCAAN model had comparatively little influence on estimates of
relative reporting rates. Estimates of relative reporting rates were unbiased and accurate for the
scenario that assumed 20% intermixing and equal productivities among populations.

Movement Rate Relative Error
For Group 1 scenarios where reporting rates were assumed spatially constant, estimated movement
rates were accurate and precise when reporting rates were fixed at the true values, with the most
precise estimates at 5 and 10% intermixing rates (Figure 2.A.5). For scenarios where relative
88

reporting rates were estimated, imprecision in movement rates was generally greater than when
relative reporting rates were not estimated at the same level of intermixing. For all regions, accuracy
and precision declined as intermixing rates increased (Figure 2.A.5). For Group 2 scenarios,
spatially varying reporting rates had little influence on accuracy and precision of movement rates
when relative reporting rates were estimated, but had large influences when reporting rates were
assumed spatially constant. Scenarios with spatially varying reporting rates but assumed spatially
constant reporting rates resulted in larger biases and greater imprecision in movement estimates
compared to the NoFix20 scenario (Figure 2.A.5). As with other parameters, misspecification of
natural mortality at 0.5 times the true value did not have a large effect on accuracy or precision of
movement rates; however, misspecifying natural mortality at 1.5 times the true value had a large
effect on accuracy and precision of the movement rate estimates (Figure 2.A.5). Movement rates
for all regions were accurate and precise when spawning populations were assumed to have similar
productivity levels (Figure 2.A.5).

Discussion
Simulation studies are an essential tool for determining the effectiveness of a model to estimate
parameters and capture the population dynamics of a system. Simulations analyses have been
conducted for various ITCAAN models, but previous analyses have mostly been conducted assuming a release-conditioned framework for tag-recovery data (Hulson et al. 2011, 2013; Goethel
et al. 2015b; Vincent et al. 2017). This study analyzed the performance of a recovery-conditioned
ITCAAN model under an assumption of natal homing of the spawning populations and explored
different model complexities of parameter estimation. Our main purpose was to determine the utility of recovery-conditioned ITCAAN models and the feasibility of accounting for spatially-varying
reporting rates with this framework.
The data used in these simulation scenarios would be considered very high quality. The
operating model simulated 8000 tags released annually for 40 years, which may be an unrealistic
number of tags released for a prolonged period of time even for high-valued fisheries. Vandergoot

89

and Brenden (2014) reported that on average 6100 walleye were tagged annually in Lake Erie
between 1990 and 2017, with the number of tags released in some years exceeding 10000 (C.S.
Vandergoot, USGS, personal communication) so the tagging level assumed in our research was
not outside the realm of possibility. The dynamics of tagged fish in the operating model were a
simplistic representation of the processes that could happen in the real world and were constrained
by numerous assumptions. First, tagging induced mortality was not simulated and tagged fish never
lost or shed their tags. These two processes would reduce the amount of tagged fish alive and thus
the number of tags recovered would be less, which would decrease model precision (Dorazio and
Rago 1991). Additionally, if tag shedding is not accounted for by the model, then estimates will
be biased (Brenden et al. 2010). The operating model simulated the fates of tagged fish through a
multinomial process, yet overdispersion relative to a multinomial distribution in tag-recovery data
is often observed (Bacheler et al. 2008; Vandergoot and Brenden 2014; Hanselman et al. 2015;
Mayakoshi and Kitada 2016). This perfect match between the operating model and the estimation
likelihood in the ITCAAN model would lead to more precise estimates than if a mismatch occurred
between the processes. The operating model also assumed that tagged fish experienced the same
dynamics as the rest of the population. If a mismatch existed between the dynamics the tagged
cohorts experienced and the rest of the population, due to factors such as delayed mixing or altered
behavior as a consequence of tagging, then parameter estimation would undoubtedly have been
affected. Finally, tagged fish were simulated to move instantaneously and then remain sedentary for
the remainder of the year. This is a common assumption when simulation testing ITCAAN models
(Hulson et al. 2013; Goethel et al. 2015b; Vincent et al. 2017), but is unlikely to reflect actual fish
movement. Additional evaluations of ITCAAN models would benefit from loosening some of the
restrictions above to see how models performed with poorer-quality data, in addition to accounting
for alternative ecological dynamics in simulated populations.
The estimation of movement rates by the recovery-conditioned tag-recovery framework was
tested through simulations by McGarvey et al. (2010). Their simulation framework replicated the
dynamics of southern rock lobster (Jasus edwardsii) in south Australia and consisted of 2 regions in

90

which tagged lobsters were harvested. McGarvey et al. (2010) simulated tag-recovery data through
an individual-based model using a daily time step with simulated releases occurring at dates of
actual releases from empirical studies. Simulation of movement dynamics in the individual-based
model was not clear, but we assume was based on an instantaneous movement assumption once
during the year based on the estimation model. Likewise, McGarvey et al. (2010) did not indicate
what reporting rate was assumed to generate tag recovery data. Their simulation study found
that the recovery-conditioned tag-recovery framework produced unbiased estimates of movement
when mortality rates (both fishing and natural) were assumed at correct values. Conversely, they
found estimating movement rates as simple proportions of recoveries of tagged fish in a new region
divided by the total number of recoveries resulted in over-estimation of movement rates. However,
McGarvey et al. (2010) did not test the estimation of other ITCAAN model parameters, or the
estimation of movement rates when mortalities were not known precisely.
McGarvey et al. (2010) used a recovery-conditioned ITCAAN model to analyze empirical
southern rock lobster harvest and tag recovery data. The underlying population model was length
structured and sex dependent for two regions and estimated the mortality components. Estimates of
movement and mortality were obtained from the recovery-conditioned ITCAAN model. However,
the authors noted that movement rate estimates from the recovery-conditioned ITCAAN model
differed from estimates obtained from a recovery-conditioned tagging framework that was provided
mortality estimates from a catch-at-length model that did not incorporate movement. In other
words, the mortality and movement rate estimates changed when both processes were estimated
simultaneously as opposed to independently. Additionally, different weightings of the tag-recovery
data within the ITCAAN model resulted in noticeably different fits to the harvest and catch per
unit effort data. This research assumed the effective sample size of the multinomial distribution
to model the tag-recovery data was equal to the number of tags recovered. Other simulation
analysis have assumed different effective sample sizes of the tag-recovery data, such as equal to the
effective sample size of the age composition (Goethel et al. 2015a) or equal to the number of tags
released (Vincent et al. 2017). The weighting of tag-recovery data in an ITCAAN model influences

91

parameter estimates regardless of the tagging framework used, but guidelines for weighting of
tagging data in an ITCAAN model requires additional research.
The simulation framework used in this study was quite different from that of McGarvey et al.
(2010). Our simulations consisted of four populations that intermixed between four regions and
tested the accuracy and precision of movement rate estimates as well as other ITCAAN model parameters that are important for management of intermixed fish stocks (e.g., abundances, mortalities).
Tag recoveries were simulated using yearly time steps and movement was assumed to occur at the
beginning of the year. We also tested the effect that non-spatially constant reporting rates had on
model performance and whether relative reporting rates could be estimated by the model.
We found that a recovery-conditioned ITCAAN model performed adequately for some parameters under certain conditions, but poorly under others. Model parameter estimates were generally
unbiased and accurate when intermixing rates were low and the relative reporting rates and natural
mortality were correctly specified. Bias in individual population estimates at high intermixing rates
was due to the large difference in abundances between the populations, which were not present
when populations were assumed to have the same productivities. Accurate and precise estimation
of individual population abundances became more problematic as movement rates increased and
as the estimation models became more complex. A similar performance issue was observed for a
release-conditioned ITCAAN model (Vincent et al. 2017).
The recovery-conditioned ITCAAN model investigated in this simulation study was very sensitive to assumptions regarding the reporting rates. As previously indicated, actual reporting rates
cannot be estimated in a recovery-conditioned ITCAAN model. We attempted to estimate relative
reporting rates for regions under the belief that reporting rates are unlikely to be constant across
space. We found that a recovery-conditioned ITCAAN model had difficulty estimating relative
reporting rates particularly for the region that corresponded to the natal region where the largest
population spawned. Higher intermixing rates only exacerbated the difficulty in estimating relative
reporting rates for the regions. Estimation of relative reporting rates also resulted in biases in other
model parameters such as movement rates. Alternatively, assuming that the reporting rates were

92

spatially constant in the ITCAAN model when the reporting rates were spatially variable resulted in
large biases in individual population abundance estimates. When high reporting rates occurred in
the natal region corresponding to the least productive population the estimates of relative reporting
rates were generally unbiased and had slightly more precise estimates of relative reporting rates
than scenarios where reporting rates were spatially constant. These results suggest that recoveryconditioned ITCAAN models are somewhat able to estimate relative differences in reporting rates
between regions; however, when there are large differences among stock sizes some estimation
problems may arise. As with population abundances, when populations were simulated under an
assumption of equal productivity levels, precise and accurate relative reporting rates were estimated
from a recovery-conditioned ITCAAN model.
The recovery-conditioned ITCAAN model generally provided unbiased estimates of natural
mortality. However, when the natural mortality parameter was estimated in the ITCAAN model the
precision of total abundance estimates decreased severely. Additionally, the estimates of natural
mortality became less precise as movement levels increased. Misspecification of natural mortality
caused severe biases in abundance estimates, which were worse when specified above the true
value. The recovery-conditioned likelihood has some information that contributes to the estimation
of natural mortality, but a release-conditioned ITCAAN framework performed better (Vincent et al.
2017). Across Group 1 simulation scenarios, IQRs in total abundance estimates for the recaptureconditioned were 1.11 to 5.98 times larger than release-conditioned IQRs. The largest difference
in precision occurred when natural mortality was estimated by the ITCAAN models under high
intermixing. Additionally, median estimates of total abundance and population abundance were
more biased by up to 7%. In general, the release-conditioned ITCAAN model performed superior
to the recovery-conditioned ITCAAN model.
In conclusion, the recovery-conditioned ITCAAN model was able to estimate natural mortality
reasonably well but had biased estimates of relative reporting rates at high mixing rates. A recoveryconditioned ITCAAN model may be appropriate if there is high certainty that reporting rates are
spatially constant and intermixing rates are low or stocks are of similar size and productivity.

93

However, when different fisheries occur in different spatial regions it may not be reasonable to
assume that reporting rates are spatially constant and could result in biased estimates within an
ITCAAN model. The consequence of assuming spatially constant reporting rates when they are
not and the bias in reporting rate estimates at high intermixing rates, pose a quandary for stock
assessment scientists attempting to fit a recovery-conditioned ITCAAN model. We recommend
release-conditioned ITCAN models be preferred to recovery-conditioned models based on the
problems with treating reporting rates in the recovery-conditioned ITCAAN model, imprecision in
natural mortality estimates, and release-conditioned ITCAAN models providing more precise and
accurate model estimates.

Acknowledgments
This work was partially funded by grant 2012.1250 from the Great Lakes Fishery Trust and
2013_BRE_44025 from the Great Lakes Fishery Commission. Additional funding support was
provided by Supporting Partners of the Michigan State University Quantitative Fisheries Center.
The authors acknowledge the support of Michigan State University High Performance Computing
Center and the Institute for Cyber-Enabled Research. This is publication number 20XX-XX of the
Quantitative Fisheries Center at Michigan State University.

94

APPENDIX

95

APPENDIX 2.A
TABLES AND FIGURES

Table 2.A.1: Regional reporting rates, average fishing mortality, unfished spawning stock biomass,
and recruitment steepness specified in the operating model for investigated scenarios, where SSB
is spawning stock biomass.
Parameter
Steepness
Steepness

Scenario
EqProd
All Other Scenarios

Region 1 Region 2 Region 3 Region 4
0.849
0.849
0.849
0.849
1.255
0.849
0.619
0.267

Unfished SSB
Unfished SSB

EqProd
All Other Scenarios

5.903E7
1.778E6

5.903E7
5.903E7

5.903E7
1.412E6

5.903E7
1.285E7

Average Apical F

All Scenarios

0.438

0.194

0.232

0.194

Reporting Rate
Reporting Rate
Reporting Rate

RV1
RV2
All Others

0.3
0.5
0.5

0.7
0.1
0.5

0.1
0.7
0.5

0.5
0.3
0.5

96

Table 2.A.2: Abbreviations, model characteristics, and convergence rates of simulation scenarios
to investigate the influence of parameterization and movement (Group 1), spatially varying reporting rate (Group 2), and misspecification of natural mortality or reporting rate (Group 3), where
movement is estimated unless noted.
Scenario Abbrv.
Group
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
3
3
3

ITCAAN model
Relative Natural
reporting mortality
∗
MvFix1 Known Known
MRFix1 Known Known
RFix1
Known Est. RC
MFix1
Est. Rel Known
NoFix1 Est. Rel Est. RC
MvFix5∗ Known Known
MRFix5 Known Known
RFix5
Known Est. RC
MFix5
Est. Rel Known
NoFix5 Est. Rel Est. RC
MvFix10∗ Known Known
MRFix10 Known Known
RFix10 Known Est. RC
MFix10 Est. Rel Known
NoFix10 Est. Rel Est. RC
MvFix20∗ Known Known
MRFix20 Known Known
RFix20 Known Est. RC
MFix20 Est. Rel Known
NoFix20 Est. Rel Est. RC
RV1Canc Canc
Est. RC
RV1Est Est. Rel Est. RC
RV2Canc Canc
Est. RC
RV2Est Est Rel Est. RC
SensU
Est. Rel 0.5×True
SensO
Est. Rel 1.5×True
EqProd Est. Rel Est. RC

Operating model # needed
Intermixing
for
1000
converged
1%
1149
1%
1155
1%
1165
1%
1141
1%
1176
5%
1011
5%
1019
5%
1021
5%
1072
5%
1084
10%
1017
10%
1014
10%
1010
10%
1031
10%
1031
20%
1022
20%
1036
20%
1029
20%
1010
20%
1008
20%
1128
20%
1011
20%
1025
20%
1015
20%
1026
20%
1012
20%
1018

NPD
Hessian
3
3
5
2
2
2
4
10
2
6
17
14
10
8
12
22
36
29
10
7
109
11
25
11
26
12
18

Maximum
Gradient
> 0.05
147
155
164
141
175
10
19
19
71
82
4
4
5
27
23
4
3
10
3
2
94
3
12
7
5
3
8

* Note: NPD = Not Positive-Definite; Known = Fixed at true value; Est. = Estimated in ITCAAN; Rel = Reporting
rates relative to region 1; RC = regionally constant; Canc = Reporting rates assumed regionally constant
* Movement Rate Fixed at True Value

97

Figure 2.A.1: Relative error (%) of abundance summed across populations for a four region
ITCAAN model under different intermixing rates and parameter estimation assumptions (Group
1), spatially varying reporting rates (Group 2), and misspecification of natural mortality and equal
productivities (Group 3) for 1000 simulation iterations. The grey colored boxplot corresponds
to the y-axis on the right side of the bottom plot. Table 2.A.2 lists the model abbreviations and
corresponding model components. Whiskers on the boxplots extend to 1.5 times the inter-quartile
range or the most extreme relative error, whichever is less extreme. Relative errors outside the
whisker range were not plotted.

98

Figure 2.A.2: Relative error (%) of population abundance for a four region ITCAAN model under
different intermixing rates and parameter estimation assumptions. The grey colored boxplots
corresponds to the y-axis on the right side of the figure. Table 2.A.2 lists the model abbreviations
and corresponding model components. Whiskers on the boxplots extend to 1.5 times the interquatile
range or the most extreme relative error, which ever is less extreme. Relative errors outside the
whisker range were not plotted.

99

Figure 2.A.3: Relative error (%) of population abundance for a four region ITCAAN model under
spatially varying reporting rates (Group2) and misspecification of natural mortality and equal
productivities (Group 3) for 1000 simulation iterations. The grey colored boxplots corresponds
to the y-axis on the right side of the figure, note that only population 3 of scenario RV1Canc and
population 4 of scenario RV2Canc corresponds to the axis on the right. Table 2.A.2 lists the model
abbreviations and corresponding model components. Whiskers on the boxplots extend to 1.5 times
the interquatile range or the most extreme relative error, which ever is less extreme. Relative errors
outside the whisker range were not plotted.

100

Figure 2.A.4: Relative Error (%) of relative reporting rates and natural mortality for a four region
ITCAAN model under different intermixing rates and parameter estimation assumptions (Group
1), spatially varying reporting rates (Group2) and misspecification of natural mortality and equal
productivities (Group 3) for 1000 simulation iterations. Table 2.A.2 lists the model abbreviations
and corresponding model components. Dots indicate parameters that are fixed within the ITCAAN
model at incorrect values. Whiskers on the boxplots extend to 1.5 times the interquatile range or
the most extreme relative error, which ever is less extreme. Relative errors outside the whisker
range were not plotted.

101

Figure 2.A.5: Relative Error (%) of movement rates of all populations to a harvest region for a four
region ITCAAN model under different intermixing rates and parameter estimation assumptions
(Group 1), spatially varying reporting rates (Group2) and misspecification of natural mortality
and equal productivities (Group 3) for 1000 simulation iterations. Table 2.A.2 lists the model
abbreviations and corresponding model components. Dots indicate parameters that are fixed
within the ITCAAN model at the true value. Whiskers on the boxplots extend to 1.5 times the
interquatile range or the most extreme relative error, which ever is less extreme. Relative errors
outside the whisker range were not plotted.

102

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CHAPTER 3
TESTING COMMON ASSUMPTIONS USED IN SIMULATIONS OF MULTI-REGION
INTEGRATED TAGGING AND CATCH-AT-AGE ANALYSIS MODEL PERFORMANCE

Abstract
Integrated tagging and catch-at-age analysis (ITCAAN) models provide a means for estimating
spatially-varying population abundances, mortality rates, intermixing rates, and other important
parameters associated with fisheries that exploit mixed stocks and the populations that contribute
to these mixtures. Several simulation studies have been conducted investigating ITCAAN model
performance under various conditions; however, previous studies have made simple assumptions
about movement dynamics and the degree of temporal variation in important population and/or
fishery dynamics rates. Additionally, previous studies have not incorporated important features of
tagging studies, such as releases of high-reward tags or the possibility of tag shedding. The goal of
our research was to advance the understanding of ITCAAN model performance and sensitivity to
assumptions by conducting simulations incorporating more complicated (i.e., seasonal) movement
dynamics, temporally varying natural mortality and reporting rates, release of high-reward tags,
and imperfect tag retention. The simulations assumed four spatial regions and four spawning
populations with fishery characteristics and dynamics based on Lakes Erie and Huron walleye
(Sander vitreus) populations. We found that annual releases of high-reward tags increased the
precision of model estimates and reduced some, but not all, bias in individual population abundance
estimates. ITCAAN models performed best with estimation of natural mortality and reporting rates
in 5-year blocks and performed worst when estimating both parameters as temporally constant.
Temporal trends in reporting rate biases were evident when true reporting rates decreased linearly
but were estimated in 5-year blocks; estimating temporally constant reporting rates resulted in
the largest regional biases and imprecision when high-reward tagging was infrequent. Seasonal
movements resulted in more accurate population abundance estimates due to an overall average

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lower movement rate, but movement rates tended to be biased when compared to the average
movement rate across seasons. We caution that ITCAAN models may produce biased estimates of
population abundances when mixing rates are high and there are very large differences in the size
of the populations. Additionally, tagging studies intended for use in ITCAAN models should be
designed to estimate annual reporting rates and tag retention rates. We propose that reporting rates
and natural mortality parameters be estimated in ITCAAN models using multi-year time blocks or
whenever high-reward tags are released to reduce bias in population abundance estimates.

Introduction
Integrated tagging and catch-at-age analysis (ITCAAN) models (Maunder 2001; Hulson et al.
2011; Goethel et al. 2015a) incorporate tag-recovery data within a statistical catch-at-age (SCAA)
framework; these models are a spatially-explicit assessment approach used to estimate abundances,
mortalities, and intermixing rates of populations that are exploited as mixed stocks during the fishing
season (Hulson et al. 2013; Goethel et al. 2015b; Vincent et al. 2017). Herein, populations are groups
of fish that interbreed and share similar life-history characteristics. Stocks are fishery units that are
characterized by the region in which they are harvested (Cadrin et al. 2004). Therefore, a mixed
stock consists of fish from multiple populations that are harvested within a defined region, such as
a management unit. Several simulation studies have been conducted investigating ITCAAN model
performance under varying model complexities, movement strategies, and tag-recovery likelihood
frameworks (Hulson et al. 2011, 2013; Goethel et al. 2015b; Vincent et al. 2017, in preparation).
Such simulation studies have yielded valuable information concerning ITCAAN model performance
under various conditions. However, these simulations have made simple assumptions with regards
to fish movement, the degree of temporal variation in important population (e.g., natural mortality)
and fishery (e.g., tag reporting) dynamic rates, and have not considered important features of
tagging studies (e.g., release of high-reward tags, tag shedding). Consequently, there remains much
to learn about the performance and sensitivities of ITCAAN models.
ITCAAN model performance has been explored under both reproductive mixing (Goethel et al.

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2011; Hulson et al. 2013; Goethel et al. 2015a) and natal homing (Vincent et al. 2017) movement
strategies. Reproductive mixing occurs when individuals of a population move to a different region
and contribute to the spawning stock in the new region. Natal homing occurs when individuals
from multiple populations intermix at particular time periods, but return to separate areas to spawn.
Simulations indicated that movement rate estimates from ITCAAN models were highly precise and
accurate for both movement strategies (Hulson et al. 2011, 2013; Goethel et al. 2015a; Vincent et al.
2017). However, previous simulation studies assumed that movement occurred instantaneously at a
single point in time during the year and that fish then remained sedentary and were subject to regional
exploitation. Such movement dynamics are not realistic for actual fish populations. Although it
might be desirable to estimate movement rates at finer temporal scales, this has the potential to
greatly increase model complexity and could result in model estimation problems. Consequently,
it would be beneficial to understand the sensitivity to finer temporal scale movements for ITCAAN
models that assume annual movement dynamics.
Fishery managers and biologists are often interested in incorporating estimation of natural
mortalities into assessment methods, such as SCAA models, given that natural mortality can be
an important determinant of sustainable harvest policies. In actual systems, natural mortality
rates are unlikely to be temporally constant as factors such as predation, disease, starvation, and
environmental conditions are likely to change over time (Jiao et al. 2012; Johnson et al. 2015).
Ultimately, the ability to estimate time-varying natural mortalities within assessment models would
be highly desirable. For SCAA models, the estimation of natural mortality rates is highly dependent
on the quality of length- or age-composition data (Beverton and Holt 1957; Maunder and Wong
2011). According to Jiao et al. (2012), estimating time-varying natural mortalities within a SCAA
model may be possible, although based on the results of Fu and Quinn (2000) this has the potential
to result in biased estimates of other parameters. Currently, the benefit of estimating time-varying
natural mortality within an SCAA model is uncertain when weighed against the possibility of
the biases it may induce (Fu and Quinn 2000; Johnson et al. 2015). For ITCAAN models, the
inclusion of tag-recovery data within a SCAA framework provides additional information that

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can be used for estimating natural mortalities. Vincent et al. (2017) conducted simulations and
found that temporally constant natural mortalities could be estimated within an ITCAAN model,
although estimates were affected by the number of tags released and model complexity. Whether
time-varying natural mortalities can be estimated under any circumstances within an ITCAAN
model is presently unknown, but this information would be of immense value given the importance
of natural mortality estimates for management.
For tag-recovery studies, two important design features to consider are the rates that tags
are reported by anglers and the possibility that some tags may be shed while recoveries are still
being collected. Both tag non-reporting and shedding can result in positively biased natural
mortality estimates and negatively biased fishing mortality estimates if unaccounted for in analysis
of recovery data (Hearn et al. 1987; Dorazio and Rago 1991; Fabrizio et al. 1996; Hampton 1997;
Brenden et al. 2010). Within an ITCAAN model, tag non-reporting and shedding would ostensibly
lead to incongruences between estimated dynamics for tagged cohorts and at-large populations if
these factors were not incorporated into the model. In traditional tag-recovery studies, multiple
approaches have been used to estimate tag non-reporting rates, such as releasing high-reward tags,
placing observers on fishing vessels or cleaning stations, or conducting mail surveys (Pollock et al.
1991; Denson et al. 2002; Taylor et al. 2006; Konrad et al. 2016). Goethel et al. (2015b) found
that estimation of tag-reporting rates may be possible within an ITCAAN model without additional
sources of data; however, Vincent et al. (2017) found that reporting rate estimates could be biased
in cases of large differences in population productivities and high movement rates. Simultaneous
estimation of reporting rates and natural mortalities led to reduced accuracy and precision, but
were superior to estimates when one of the parameters was incorrectly assumed. Vincent et al.
(2017) suggested that inclusion of an additional data source, such as recoveries from high-reward
tagging release, might improve ITCAAN model estimation of tag reporting rates and perhaps
improve the accuracy and precision of other parameter estimates. Given that tag reporting rates
can vary temporally due to factors such as apathy towards the tagging study, how well a tagging
study is advertised, relationship with or trust in the tagging agency, and the relative harvest of

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different fisheries (e.g., commercial versus recreational fisheries) (Hoenig et al. 1998; Denson
et al. 2002; Vandergoot et al. 2012), the ability to estimate temporally-varying reporting rates
would be an attractive feature of ITCAAN models. To our knowledge, evaluations of ITCAAN
model performance have not considered the ability to estimate temporally-varying tag reporting
rates or natural mortalities. Furthermore, how accuracy and precision of parameter estimates may
be affected by tag shedding or the release and recovery of high-reward tags requires additional
investigation.
The goal of this research was to build upon previous studies of ITCAAN model performance by
conducting simulations incorporating more complicated movement dynamics, temporally-varying
natural mortality and reporting rates, release of high-reward tags, and imperfect tag retention for
the purpose of evaluating parameter estimability and robustness of release-conditioned ITCAAN
models. Simulations were based on walleye (Sander vitreus) populations in the Laurentian Great
Lakes (Zhao et al. 2009, 2011; Fielder and Bence 2014; Wills et al. 2016), which exhibit complex
movement patterns and large differences in population abundances (Wang et al. 2007; Vandergoot
and Brenden 2014; Hayden et al. 2014; Herbst et al. 2016). Specifically, we investigated how
accuracy and precision of ITCAAN model estimates were affected by the following: 1. whether
the operating and ITCAAN models incorporated tag loss and/or the release of high-reward tags;
2. simulation of time-varying natural mortality and/or reporting rates and estimation of these
parameters annually, in 5-year time blocks or temporally constant; 3. the frequency of high-reward
tag release; and 4. movement dynamics simulated as seasonally varying (4 seasons per year), but
estimated as an annual rate.

Lakes Erie and Huron Walleye
Walleye is a piscivorous species that is exploited by both recreational and commercial fishers in
the Great Lakes (Fielder and Bence 2014; Wills et al. 2016). Walleye aggregate during the early
spring in rivers and shallow rocky reefs for spawning (Busch et al. 1975). After spawning, walleye
often make directed and sometimes long-distance movements towards summer feeding grounds
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that are selected based on thermal conditions and prey availability (Wang et al. 2007; Zhao et al.
2011; Hayden et al. 2014; Vandergoot and Brenden 2014; Herbst et al. 2016). This dispersal of
walleye after spawning is recognized to be potentially problematic for management as fish can
cross multiple jurisdictional boundaries when moving between spawning and feeding grounds.
Consequently, fisheries may depend on spawning populations and systems over which managers
have no jurisdictional authority (Brenden et al. 2015; Herbst et al. 2017).
Lakes Huron and Erie contain two of the largest and most valuable fisheries in the Great Lakes
region (Baldwin et al. 2009). Presently, separate SCAA assessment models are used to estimate
walleye population abundances and mortalities in Lakes Erie and Huron to gauge the health of the
populations and assist in setting harvest regulations (Fielder and Bence 2014; Wills et al. 2016).
The abundance of walleye in Lake Huron has been estimated to be between one and four million
fish (Fielder and Bence 2014). Lake Erie is generally regarded to consist of three basins (western,
central, and eastern) that decrease in walleye abundance moving eastward. The abundance of
walleye in the western and central basin of Lake Erie has been estimated to be upwards of tens
of millions of fish (Wills et al. 2016), whereas walleye abundance in the eastern basin has been
estimated to be closer to tens of thousands of fish (Zhao et al. 2011). Estimates of intermixing
rates between Lake Huron and the western basin of Lake Erie have been around 1 to 2% (Hayden
et al. 2014; Fielder and Bence 2014; Vandergoot and Brenden 2014). Although this degree of
movement may seem inconsequential, given the difference in population abundances it may mean
a considerable number of walleye are migrating from Lake Erie to Lake Huron (Fielder and Bence
2014). A larger movement rate (∟ 10%) has been estimated for fish moving from the western
basin of Lake Erie into the Huron Erie Corridor (Wang et al. 2007; Vandergoot and Brenden
2014). Movement from the western basin to the eastern basin has been shown to be substantial
through jaw tag recoveries (Wang et al. 2007; Vandergoot and Brenden 2014) and telemetry studies
(Chris Vandergoot, USGS, personal communication). There has been increasing interest in the
development and use of spatially-explicit models for assessing the walleye populations in Lakes
Erie and Huron due to the species’ economic and ecological importance and the estimated degree

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of movement both within and between the lakes.

Methods
Fish populations and tagged cohorts were simulated through an operating model with specified
recruitment functions, population dynamic rates, and intermixing rates. A 40-year time-series
of data were generated from the operating model, which were then fit by a release-conditioned
ITCAAN model. The operating and ITCAAN model used in this research were similar to those
described in Vincent et al. (2017, in preparation). Summaries and alteration from previous analyses
(Vincent et al. 2017, in preparation), are provided below for the operating and ITCAAN models
used in this research. Both the operating and ITCAAN models tracked the dynamics of age-2
through age-7 fish, with the last age class an aggregate group of age-7 and older fish. Code for
the operating and ITCAAN models can be found in the Supplementary Material 3. The ITCAAN
model was programed in ADMB version 11.5 (Fournier et al. 2012), while the operating model was
programmed in R version 2.15.1 (R Core Team 2016). Parameter values assumed in the operating
model can be found in the Supplementary Material 3.

Operating Model
The operating model simulated the dynamics of four independent spawning populations that intermixed among four harvest regions. Recruitments were simulated using population-specific Ricker
stock-recruitment curves with annual error simulated from a first-order autoregressive (AR1) process. Parameters of the AR1 process for each population and investigated scenario were generated
from the posterior distribution for Percidae from Thorson et al. (2014). The Ricker stock-recruitment
functions were based on perceived conditions of walleye populations in Lakes Huron and Erie and
had very different unfished spawning stock biomasses and productivities. Stock-recruit parameters
for population 1 were chosen to mimic Lake Huron walleye, while the stock-recruit parameters
for populations 2, 3, and 4 were based on estimates from the western, central, and eastern Lake
Erie walleye populations, respectively (Supplementary Material 3 Table 3). After spawning, a box-

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transfer model (Goethel et al. 2011) was used to simulate movement of the spawning populations
to different regions. For most scenarios, intermixing was simulated where 20% of the population
moved to each non-natal region for all scenarios (i.e., 40% of each spawning population was assumed to remain in their natal region). In previous analyses, this rate of intermixing resulted in
biased reporting rates and population abundances for ITCAAN models Vincent et al. (2017, in preparation). Part of the impetus for this study was to determine whether recoveries from high-reward
tagging would rectify these regional biases. For a few scenarios (see Simulation Scenarios section)
movement was simulated to occur immediately after spawning and at three other evenly spaced
time periods within a year (i.e., seasonally) to test the impact such dynamics had on parameter
estimation.
One difference in the operating model used in this research from that described in Vincent et al.
(2017) was that two fisheries were assumed to operate in each harvest region, similar to what occurs
in Lakes Huron and Erie. Annual apical fishing mortality rates for each region-specific fishery were
simulated using a truncated AR1 process, which constrained values to be greater than zero. The
average fishing mortality and selectivity-at-age parameters for each fishery and region are presented
in the Supplementary Material 3 and are based on commercial and recreational fishery estimates
from Lakes Erie and Huron. The instantaneous natural mortality rates assumed in the operating
model varied by scenario (see Simulation Scenario section) but in all cases had a mean value of
0.32 year-1 and were invariant over ages and regions.
The operating model also tracked the fates of tagged cohorts of fish and included some processes
that were not included in the simulations of Vincent et al. (2017, in preparation). Annually 2000
fish were assumed to be tagged with standard-reward tags and released from each population at
the beginning of the year when fish were aggregated for spawning. The age of tagged fish at the
time of release were assumed known in the operating model based on a temporally constant set
of proportions at age (Supplementary Material 3 Table 2). The fate of tagged fish were simulated
from age-specific mortality rates, but simulated tag-recovery data were pooled across ages. If the
simulated abundance for any of the four populations was less than 40000 fish at any point in time,

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the simulation was discarded from further analysis and replaced with a new simulation because we
believed it was unlikely that more than 5% of a population would be tagged within a year. For some
investigated scenarios, the fates of 200 fish tagged with high-reward tags from each population were
also tracked in the operating model; the frequency of releases of high-reward tagged fish was one
of the factors evaluated as part of this research. Tagged fish were assumed to intermix immediately
with the at-large populations, meaning that both standard and high-reward tagged fish experienced
the same dynamics (e.g., mortalities and movements) as the at-large populations. However, 100%
of recaptures of fish tagged with a high-reward tag were reported, but reporting rates of standard
tags varied by simulation scenario (see Simulation Scenarios and Supplementary Material 3 Table
1).
Most investigated scenarios assumed some level of tag shedding. The probability of tag
retention given the number of years after release were calculated from parameters estimated by
Vandergoot et al. (2012) for Lake Erie walleye and are presented in Table 4 of the Supplementary
Material 3. The numbers of fish that retained their tags from each tagging cohort were generated
by multiplying the number of tags alive at the beginning of the year by the tag retention probability
given the number of years after release and rounding to the nearest number. In essence, tag shedding
was assumed to occur instantaneously at the beginning of the year, when simulated. For scenarios
with annual movement rates, movement of tagged fish to different regions were generated from
multinomial distributions with 20% of the tags moving to each non-natal region. Whether standardor high-reward tagged fish survived, were harvested, or died due to natural causes in each region
were simulated from multinomial distributions with expected proportions equal to the dynamics of
the stock within the region (e.g., exploitation rate). For scenarios with seasonal movement, each
year was evenly divided into four time periods or seasons. At the beginning of each season, tagged
fish were simulated to move based on seasonal movement parameters and then exploited at region
specific mortalities. Seasonal instantaneous mortality rates were assumed to be one quarter of the
annual instantaneous mortality rate for all seasons (i.e., equal mortality rate throughout the year).
The number of recovered tags were generated from multinomial distributions in each season; these

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recoveries were summed across age and season to determine annual recovery counts. The at-large
populations for these seasonal scenarios experienced the same movement and regional mortalities
as tagged fish.
Data used by the ITCAAN model were generated from the operating model with assumed
levels of observation error. Fishery-specific time-series of fishing effort were generated from the
apical fishing mortalities using fishery-specific catchability coefficients (Supplementary Material
3 Table 1) and lognormal multiplicative observation errors with a CV of 10%. Observed regionspecific harvest data were created from actual harvests summed across populations within a region
multiplied by annual random errors with a CV of 10%. During October (i.e., during intermixing),
a fishery-independent survey was simulated to occur within each region. A survey catch per effort
time-series for each region was simulated using intermixed stock abundance multiplied by regionspecific catchability coefficients, age-specific selectivity parameters, and lognormal observation
error with a CV of 20%. Annual age-composition data of fish captured by fisheries and surveys
were simulated independently using multinomial distributions based on the true age compositions
and a sample size of 100. The number of reported tags by fishery and year of recapture for
each release event (i.e., by region and year of release) were simulated using a binomial process.
Reporting of harvested fish equipped with standard tags by commercial and recreational fisheries
was assumed to be imperfect for all investigated scenarios. The numbers of tags reported by each
fishery were generated from binomial distributions based on the number of tags harvested by fishery
and fishery-specific reporting rates, the values of which depended on the scenario of investigation
(see Simulation Scenarios and Supplementary Material 3 Table 1).

ITCAAN Model
The release-conditioned ITCAAN model used in this research was nearly identical to that used in
Vincent et al. (2017). The primary modifications in the ITCAAN model from previous work were
that 1. release and recovery of high-reward tags were included as data components in the model for
scenarios that assumed high-reward tagging; 2. the predicted number of tags reported incorporated
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tag shedding rates for scenarios that evaluated tag shedding; and 3. fishing mortality was expanded
to estimate dynamics for both recreational and commercial fisheries. The recovery-probability
equations for high-reward tags were the same as those for standard tags with the exception that
tag reporting was assumed to be 100% for high-reward tags. For the purpose of this research, we
assumed that tag-shedding rates were precisely known and therefore tag shedding rates were fixed
at known values in calculations of the predicted number of tags recovered.
The ITCAAN model was fit to generated data and estimated parameters using maximum
penalized likelihood in ADMB (Stewart et al. 2013). Lognormal likelihoods were assumed for the
harvest, effort, and survey catch per effort data, whereas multinomial distributions were assumed
for tag-recovery data and age compositions of each fishery and survey. Regional variances of the
harvest data were estimated. Variance for effort and survey catch per effort data sources were
calculated based on assumed ratios of their variances relative to the estimated variances of the
harvest data. The assumed ratios were equal to the actual ratios in variances from the operating
model. Effective sample sizes for age compositions were assumed equal to 100 for both the
fisheries and surveys, whereas for the tag-recovery data the effective sample size was the number
of tags released each year. ITCAAN model convergence criteria was based on whether the model
produced a positive-definite Hessian matrix and the maximum gradient for all parameters was
less than 0.05, as in (Vincent et al. 2017, in preparation). Simulations were conducted until 1000
ITCAAN estimates had converged. Table 3.A.1 reports the number of simulations required to reach
a sample size of 1000, the percent convergence, and the number of simulations that failed based on
the different criteria.

Simulation Scenarios
Seven groups of simulation scenarios were conducted exploring ITCAAN model estimation performance. The first group of scenarios explored the influence of incorporating tag shedding and
high-reward tagging on ITCAAN model performance. Four groups of scenarios simulated different
combinations of time-varying natural mortalities and reporting rates crossed with three approaches
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for estimating these time varying rates. One group of scenarios investigated the influence of releasing high-reward tags at frequencies of 5 or 10 years. The final group of scenarios explored the
sensitivity of ITCAAN models to seasonal movement dynamics.

Tag Shedding and Release of High-Reward Tags
The first group of scenarios investigated the consequences of tag shedding and release of highreward tags on ITCAAN model performance. These scenarios assumed that natural mortality
and reporting rates were temporally constant in the operating model and estimated with the same
assumption in the ITCAAN model. Reporting rates were unique for each fishery, but in all regions
the reporting rates for commercial fisheries were lower than recreational fisheries (Supplementary
Material 3 Table 1). These scenarios assumed that movement occurred once during the year after
returning to the natal region to spawn. The first scenario in this group assumed that no highreward tags were released and no tag shedding occurred (NoRwrdNoLoss). The second scenario
assumed that no high-reward tags were released, but tag shedding was included in the operating
and ITCAAN models (NoRwrdLoss). The final scenario assumed that 200 high-reward tags were
released annually in each region and both the operating and ITCAAN models incorporated tag
shedding (RwrdLoss).

Time-Varying Natural Mortality
The second group of scenarios investigated how well an ITCAAN model could estimate timevarying natural mortalities. Annual natural mortalities in the operating model were simulated
using a AR1 process that was truncated such that natural mortalities could not be less than or
equal to zero. The AR1 process assumed a mean of 0.32, a standard deviation of 0.05, and an
autocorrelation coefficient of 0.8 (Figure 3.A.1). Natural mortalities were estimated using three
different methods: annually, in 5-year time blocks (i.e., one parameter for 5 years), and temporally
constant. The annual natural mortality model estimated a free parameter for each model year
and was referred to in the scenario names as Ann. The block estimation of natural mortality
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also estimated each parameter freely for eight 5-year segments and was referred to as Block in
the scenario abbreviations. Natural mortality was also estimated as temporally constant and these
scenarios were referred to as Const. Given this group of scenarios investigated time-varying
natural mortality, the three scenarios in this group were referred to as TVMAnn, TVMBlock, and
TVMConst. Both the operating and ITCAAN models assumed that reporting rates were temporally
constant but varied by fishery for these scenarios (Supplementary Material 3 Table 1). Tag shedding
was incorporated in both the operating and ITCAAN models. Additionally, all simulations in this
group incorporated annual releases of high-reward tags and assumed annual movement dynamics
similar to Vincent et al. (2017).

Time-Varying Reporting Rates
The third group of scenarios investigated how well an ITCAAN model could estimate time-varying
reporting rates. Annual reporting rates for each fishery in the operating model were generated
using an AR1 process that was constrained between 0 and 1 with fishery-specific means (43%
for recreational fisheries; 15% for commercial fisheries), a standard deviation of 0.05, and an
autocorrelation coefficient of 0.7 (Figure 3.A.1). As with the time-varying natural mortality
group of scenarios, three different approaches for estimating reporting rates were considered: 1.
estimating annually varying reporting rates (TVRRAnn), 2. estimating reporting rates in 5-year time
blocks (TVRRBlock), and 3. estimating a constant reporting rate for each fishery (TVRRConst).
Annual estimates of reporting rates were estimated through a logit-transformed random walk (i.e.,
constrained to be between 0 and 1). The reporting rates in the first year were estimated as logit
transformed parameters, while subsequent years were estimated using the equations:
Reporting Rate y =
where

1
1 + exp(−(RRy ))

(3.0.1)

RRy =RRy−1 +  y .

In the equation above, the estimated parameters are the deviations from the previous year’s
reporting rate,  y , which were constrained by a normal penalty with an assumed standard deviation
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of 2. The block parameterization ITCAAN model estimated eight 5-year blocks of reporting
rates for each fishery, while the constant parameterization estimated a single temporally constant
parameter for each fishery. In the simulations for this group of scenarios, natural mortality was
assumed to be temporally constant with a value of 0.32 year-1 in the operating model and was
estimated as a temporally constant parameter in the ITCAAN model. Simulations in this group
integrated tag shedding and annual release of high-reward tags in both the operating and ITCAAN
models, which assumed annual movement dynamics similar to Vincent et al. (2017).

Time-Varying Natural Mortality and Reporting Rates
The fourth group of scenarios investigated how well ITCAAN models could simultaneously estimate
time-varying natural mortalities and reporting rates. Annual natural mortalities and reporting rates
were generated using the AR1 processes previously described (Figure 3.A.1). All simulations in this
group assumed annual releases of high-reward tags and tag shedding in the operating and ITCAAN
model while assuming a single annual movement. As with the previous two groups of scenarios,
three different approaches for estimating natural mortalities and reporting rates were considered:
1. estimating natural mortalities and reporting rates as both annually varying (BothTVAnn), 2.
estimating natural mortalities and reporting rates in 5-year time blocks (BothTVBlock), and 3.
estimating constant parameters for both natural mortalities and reporting rates (BothTVConst).

Decreasing Reporting Rates
The fifth group of scenarios investigated how well an ITCAAN model could estimate reporting
rates that declined over time. In the operating model, natural mortality was simulated using the
AR1 process previously described. Reporting rates were generated assuming a constant linear
decline; the values at the start and end of the time series for the reporting rates are presented in
Table 1 of the Supplementary Material 3. Similar to the other scenarios, commercial reporting
rates were assumed to be lower than the recreational fisheries and were region-specific. The
ITCAAN model was parameterized to estimate natural mortalities and reporting rates as either
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annual (DecrRRAnn), in 5-year time blocks (DecrRRBlock), or constant values (DecrRRConst).
These simulations assumed a single annual movement and incorporated tag shedding and annual
releases of high-reward tags in both the operating and ITCAAN model.

High-Reward Releases Every 5 or 10 Years
The sixth group of scenarios evaluated the effects of less frequent (every 5 years or every 10 years)
releases of fish tagged with high-reward tags. We assumed that 200 fish were tagged with highreward tags when releases occurred. For both groups of scenarios, time-varying natural mortalities
in the operating model were generated using the AR1 process previously described. Time-varying
reporting rates for these scenarios were generated assuming a linear decrease identical to that
described in the Decreasing Reporting Rates group of scenarios. We again tried estimating natural
mortalities and reporting rates as either annual (Rwrd5Ann and Rwrd10Ann), 5-year time blocks
(Rwrd5Block and Rwrd10Block), or constant values (Rwrd5Const and Rwrd10Const). Both the
operating and ITCAAN models assumed annual movement dynamics similar to Vincent et al.
(2017) and tag shedding for all scenarios in this group.

Seasonal Movement
The final group of scenarios investigated the influence of seasonal movement on the performance of
ITCAAN model estimation. Natural mortality was simulated through an AR1 process and reporting
rates were assumed to decrease linearly throughout the time-series. For the operating model, each
year was separated into four seasons that had unique movement matrices (Figure 3.A.2). Movement
rates were chosen to simulate all fish returning to their natal regions at the beginning of the year,
followed by population intermixing increasing throughout the year to a maximum during the third
season, with fish beginning to return to their natal regions to spawn in the fourth season.
Movement was simulated to occur at the beginning of the season after which the fish experienced
region-specific mortality rates. In the operating model, the annual instantaneous mortality rates
were evenly divided between the four seasons and were simulated to occur after movement for each
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season. The mixing rate averaged over the year for this scenario was less than the movement rate
investigated for all other simulation scenarios (Figure 3.A.2). We again tried estimating natural
mortalities and reporting rates either as annual (SeasonAnn), in 5-year time blocks (SeasonBlock),
or as constant values (SeasonConst), where mortalities and movement rates were assumed constant
within a year. The ITCAAN and operating models incorporated tag shedding and high-reward tags
were released every 10 years.

Performance Metrics
The performance of the ITCAAN model was evaluated using percent relative error of estimated
model parameters. Percent relative error compares parameter estimates to true values in the
operating model by subtracting true values from their estimates, then dividing by the true values
and multiplying by 100. The precision and accuracy of total abundance (i.e., abundances summed
over all populations), population abundances, movement, natural mortality, and reporting rates
are presented here for the sake of brevity; precision and accuracy of other model parameters are
presented in the Supplementary Material 3. Parameters not presented either showed no bias in
estimates or biases similar to other model parameters, though not always in the same direction.
Errors in parameters that were year-specific (i.e. abundance) or age-specific (e.g. selectivity, results
in Supplementary Material 3) were calculated for each age or year for each of the 1000 simulations
and then aggregated by region or population for summarization and plotting. For example, the
boxplots of total abundance show 40000 values (i.e., 40 years of total abundance times 1000
iterations). The interquartile ranges (IQR) and medians of the relative error of the 1000 iterations
were used to summarize precision and bias of parameter estimates for the scenarios, respectively.

Results
ITCAAN Model Convergence
Across all simulation scenarios, the average convergence rate of the ITCAAN models was 80%.
Among scenarios where natural mortality and reporting rates were estimated annually, the conver124

gence rates were generally greater than 90%, whereas when these parameters were estimated in
5-year blocks the convergence rate was around 70%. The 5-year time block and constant ITCAAN
models failed to converge primarily as a result of a maximum gradient larger than 0.05. About
two-thirds of the iterations that failed to converge due to a large maximum gradient for the 5-year
time block and constant ITCAAN models had maximum gradients that were between 0.05 and 0.1.
The inclusion of annual high-reward tag releases increased the convergence rate by approximately
10% (i.e., from 70% to 80%; Table 3.A.1).

ITCAAN Model Performance
Total Abundance
The accuracy and precision of total abundance estimates were affected by the inclusion of highreward tag releases, the true dynamics of natural mortality and reporting rates, and the parameterization of the ITCAAN model. Across all examined scenarios, median relative errors of
total population abundance were between Âą 5%, except for the Rwrd5Const, Rwrd10Const, and
SeasonConst scenarios (Figure 3.A.3). Tag shedding without the release of high-reward tags (NoRwrdLoss) decreased precision in total population abundance by 1.4 times when compared to the
scenario where no tag shedding occurred (NoRwrdNoLoss; Figure 3.A.3). Scenarios that did
not simulate high-reward tag releases (NoRwrd Scenarios) resulted in median estimates of total
abundance that were negatively biased by 4% and were less precise than scenarios that simulated annual high-reward tag releases. However, the combination of tag shedding and high-reward
tag releases (RwdLoss) improved both the accuracy and precision of total population abundances
(Figure 3.A.3). Among the scenarios where natural mortalities and/or reporting rates were timevarying in the operating model, the estimation of these parameters as temporally constant (Const)
resulted in the most imprecise total abundance estimates compared to when these parameters were
estimated annually or in 5-year time blocks (Figure 3.A.3). For the scenario where natural mortality
was simulated as time-varying and reporting rate was constant, the estimation of natural mortality

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in 5-year time blocks (TVMBlock) resulted in marginally more precise estimates of total abundance
compared to annual estimation, though accuracies of the estimation approaches were equivalent.
For scenarios where only reporting rates were time-varying, the estimation of annual reporting
rates (TVRRAnn) had similar precision compared to 5-year time block estimation, but was slightly
more negatively biased (TVRRAnn: median relative error = -1.4%; TVRRBlock: median relative
error = -0.88%). Relative errors of total abundance estimates for scenarios where both natural
mortalities and reporting rates were simulated by AR1 processes (BothTV) were more similar to
the Time-Varying Natural Mortality group of scenarios than to the Time-Varying Reporting Rate
group of scenarios. Scenarios that simulated the release of high-reward tags at a frequency of either
5 years or 10 years and estimated reporting rates and natural mortalities as temporally constant in
the ITCAAN model had large imprecision and positive median bias in total abundance estimates
greater than 10% (Figure 3.A.3). Simulating the movement as a seasonal process resulted in relative
error in total abundance estimates similar to Rwrd10 scenarios (Figure 3.A.3).

Population Abundance
Estimates of population abundances were more biased and imprecise compared to estimates of
total abundance. Median estimates of abundance for the largest population (i.e., population 2)
were negatively biased across all scenarios, except for the SeasonConst scenario, while estimates
of abundance for all other populations were positively biased (Figure 3.A.4). The largest bias
and imprecision in abundance estimates for populations 2 and 3 manifested when tag shedding
occurred and no high-reward tags were released (NoRwrdLoss) and was similar to the scenario
where high-reward tags were released every 10 years and natural mortality and reporting rate
parameters were estimated as temporally constant (Rwrd10Const). Bias and imprecision in all
populations were halved when high-reward tags were released annually (RwrdLoss) compared to
when no tags were released and tag loss was present (NoRwrdLoss). Simulation of time-varying
natural mortality and/or reporting rates resulted in marginally less precise estimates compared to the
tag shedding and high-reward tagging scenario for all populations. Within the same simulation type
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when high-reward tags were released annually, the median relative error of estimates were similar
between the three ITCAAN parameterizations, though constant estimation of natural mortality and
reporting rate was less precise (Figure 3.A.4). Estimation of reporting rates and natural mortalities
as temporally constant generally resulted in increased bias and imprecision of population abundance
estimates, especially for populations 2 and 4 when high-reward tag releases were less frequent than
annual (Rwrd5Const and Rwrd10Const scenarios). However, median relative error in abundance
estimates for population 2 when estimating constant reporting rates and natural mortalities with
high-reward tags released less frequently than annual (Rwrd5Const and Rwrd10Const) were less
biased compared to annual and block estimation, though estimates were two times as imprecise.
As the frequency of high-reward tag releases decreased, the bias and imprecision for all population
abundance estimates increased for annual and block parameterizations of reporting rates and natural
mortalities. Population abundance estimates were the most precise and accurate when movement
and other dynamics were simulated in four seasons, except for population 2 when natural mortality
and reporting rates were estimated as temporally constant (Figure 3.A.4).

Movement Rate
Movement estimates were precise and accurate for most scenarios investigated. A marginal decrease
in precision in movement estimates was observed for all regions when tag shedding occurred and no
high-reward tags were released (NoRwrdLoss) compared to the scenario without tag shedding and
no release of high-reward tags (NoRwrdNoLoss). Conversely, the scenario that incorporated tag
shedding and annual releases of high-reward tags (RwdLoss) had precision similar to the scenario
where no reward tags were released and no tag loss (NoRwrdNoLoss; Figure 3.A.5). Simulation
of natural mortality or reporting rates through AR1 processes had little influence on movement
estimates, though these parameters were estimated as constant in the ITCAAN model, movement
rate estimates were marginally less precise (TVMConst, TVRRConst, and BothTVConst) compared
to scenarios when natural mortality and reporting rate parameters were estimated annually or in
5-year time blocks. Movement rate estimates with linearly decreasing reporting rates and natural
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mortalities and reporting rates estimated annually or in 5-year time blocks (DecrRRAnn and
DecrRRBlock) were similar in precision and bias compared to estimates when natural mortality and
reporting rates were simulated by AR1 processes. Median absolute relative errors between 1.7 and
6.1% were observed in scenarios with linearly decreasing reporting rates and constant estimation of
natural mortality and reporting rates (DecrRRConst, Rwrd5Const, Rwrd10Const), where bias was
positive in regions 2 and 4 and negative in regions 1 and 3. Precision in movement rate estimates
decreased when the frequency of high-reward tag releases decreased to 5 and 10 years for all three
ITCAAN parameterizations (Figure 3.A.5). When movement was simulated to occur seasonally in
the operating model, movement rate estimates were negatively biased for all populations; median
relative errors in movement rates ranged from -0.6 to -8.6% using the seasonal-average movement
rate as the true value for calculations. The largest biases under seasonal movement were for
movement rates of all populations into regions 2 and 3.

Natural Mortality
Natural mortality estimates were generally accurate, but precision varied by simulation scenario and
ITCAAN model parameterization. Median relative error of natural mortality estimates were within
Âą 1.5% of zero, with the exception of the DecrRRConst, Rwrd5Const and Rwrd10Const scenarios
(Figure 3.A.6). Imprecision in natural mortality estimates was 1.6 times larger for the models that
incorporated tag shedding (NoRwrdLoss) versus those that did not (NoRwrdNoLoss). Precision of
natural mortality estimates was considerably better when high-reward tags were released annually
(RwrdLoss) compared to the scenario without high-reward tags (NoRwrdLoss; Figure 3.A.6). The
simulation of natural mortality through an AR1 process greatly decreased precision in natural
mortality estimates compared to scenarios where natural mortality was simulated and estimated
as temporally invariant, although estimates remained relatively unbiased. Estimation of annual
natural mortality parameters resulted in imprecision of estimates 1.7 times greater than when
natural mortality was estimated in 5-year time blocks (Figure 3.A.6). Simulation of both natural
mortality and reporting rates as AR1 processes (BothTV scenarios) resulted in precision and bias
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of natural mortality estimates similar to when only natural mortality was simulated as an AR1
process (TVM scenarios). When reporting rates decreased linearly over time, a small negative bias
(median relative error = -7.0%) resulted when natural mortalities were estimated as temporally
constant (DecrRRConst). A decrease in the frequency of high-reward tag releases caused an
increase in imprecision of natural mortality estimates among all ITCAAN parameterizations, and
slight changes to accuracy of estimates when natural mortality and reporting rates were estimated as
temporally constant (Rwrd5Const and Rwrd10Const; Figure 3.A.6). Seasonal movement dynamics
had little influence on the accuracy and precision of natural mortality parameters for the annual and
block estimations.
For scenarios where high-reward tags were released less frequently than annually, natural
mortality estimates were most precise in years when high-reward tags were released (Figure 3.A.7,
Rwrd10Ann scenarios). Additionally, the precision in natural mortalities greatly decreased in the
last few years of the time-series when estimated annually. Similarly, precision in natural mortality
estimates was worst in the last 5-year time block (Block scenarios). Within a 5-year time block
natural mortality estimates in the second, third, and fourth years were generally more precise than
the first and last year (Figure 3.A.7). Imprecision and bias in natural mortality was fairly consistent
across the time series when this parameter was estimated as temporally constant.

Reporting Rate
Accuracy and precision in reporting rate estimates varied greatly between fisheries, ITCAAN
parameterizations, and scenarios. The most precise estimates of reporting rates occurred when
high-reward tags were released annually and reporting rates were simulated as temporally constant
(RwrdLoss and TVM scenarios; Figure 3.A.6). The largest imprecision and bias in reporting rate
estimates occurred when high-reward tags were released every 10 years, reporting rates decreased
linearly throughout the time-series, and the ITCAAN estimated reporting rates as temporally
constant (Rwrd10Const and SeasonConst). When reporting rates were temporally constant, no
high-reward tags were released, and the model did not include tag loss (NoRwrdNoLoss), reporting
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rate estimates were biased with the direction of bias inversely related to population size (i.e.,
negatively biased in region 2, but positiviely biased in other regions). The occurrence of tag
shedding amplified the bias and imprecision in reporting rates.
When reporting rates were simulated by an AR1 process, the reporting rate estimates were four
times less precise compared to scenarios where reporting rates were temporally constant, though
estimates generally remained unbiased (Figure 3.A.6, TVRR and BothTV scenarios). Estimates
of reporting rates for commercial fisheries, which were assumed to have lower reporting rates
than recreational fisheries in the operating model for each region, were less precise compared to
recreational fisheries in the same region for most scenarios and regions. Estimation of annual
reporting rates resulted in the most precise estimates of reporting rates when this parameter was
simulated by an AR1 process (TVRRAnn and BothTVAnn), whereas estimation of reporting rates
as temporally constant were the least precise and most biased (TVRRConst and BothTVConst).
When reporting rates were simulated to decrease linearly throughout the time-series, estimation
of reporting rates in 5-year time blocks resulted in the most precise estimates (DecrRRBlock,
Rwrd5Block, and SeasonBlock); alternatively, estimating reporting rates as temporally constant
resulted in the least precise estimates (Figure 3.A.6). However, systematic trends of underestimating
the first two years and over estimating the last two years in the 5-year time block were observed for
scenarios with linearly decreasing reporting rates (Figure 3.A.8). Temporal trends were consistent
between recreational and commercial fisheries, but the level of bias and imprecision varied by
fishery (Figures 3.A.6, 3.A.8 and 3.A.9). Region-specific biases in reporting rates when highreward tags were released less frequently than annually and reporting rates were estimated annually
or in 5-year time blocks were similar to estimates for the scenario with tag shedding and no
high-reward tags released (NoRwrdLoss). Positive bias in all estimates occurred when reporting
rates were estimated as temporally constant and high-reward tags were released less frequently
than annually (Figure 3.A.6). Precision and bias of reporting rate estimates did not appear to be
influenced by seasonal movements.

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Discussion
Simulation studies are beneficial for testing how well assessment models can estimate parameters
of interest. Additionally, simulations can test how sensitive models are to violations of assumptions,
including mismatches between assumed and actual underlying dynamics. While ITCAAN models
have been in use since the late 1990s (Maunder 1998, 2001), to date there have been relatively
few simulation studies conducted that have explored ITCAAN model performance (Hulson et al.
2011, 2013; Goethel et al. 2015b; Vincent et al. 2017, in preparation). Studies that have been
conducted assumed the population and fishery dynamics were relatively simple. Our goal for this
research was to improve understanding of ITCAAN model performance by incorporating additional
complexities in the simulation analyses and including some mismatches between operating and
estimation model processes. We found that inclusion of tag shedding processes in the operating
and ITCAAN models decreased accuracy and precision of parameter estimates. Conversely,
accuracy and precision of parameter estimates improved with high-reward tag releases, although
the frequency that high-reward tags were released did affect ITCAAN model performance. Large
biases in abundance estimates were present when the operating model simulated reporting rates as
linearly decreasing and natural mortality through an AR1 process, but the ITCAAN model estimated
natural mortality and reporting rates as constant. The estimation of an annual movement rate when
the underlying movements were seasonal resulted in biased estimates of movement rates, whereas
all other scenarios showed unbiased movement estimates. Comparison of the results from our no
tag shedding and no high-reward tag releases with results from Vincent et al. (2017) showed similar
precision and bias of total abundance estimates, but this study had lower convergence rates compared
to when only a single fishery was assumed to operate in each region. Although all simulation models
are simplifications of the actual system they are attempting to replicate, previous simulation studies
of ITCAAN models may have been oversimplifications. By assuming instantaneous movement
occurs once at the beginning of the year, temporally constant natural mortality and reporting rates,
and no tag shedding previous simulation analyses of ITCAAN performance likely overestimated
the precision and accuracy of parameter estimates.
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In our non-seasonal simulations, we assumed that 20% of the population moved to each nonnatal region for all scenarios (i.e., 40% of each spawning population was assumed to remain in
their natal region). This was the highest movement rate evaluated in the simulations conducted by
Vincent et al. (2017) and resulted in the largest bias and imprecision in abundance estimates from the
ITCAAN model. We chose this high movement rate partly to determine whether the incorporation
of high-reward tags could remove bias observed in population estimates and reporting rates. Similar
to the results from Vincent et al. (2017), the ITCAAN model generally overestimated population
abundances for the less productive population and underestimated the population abundance for
the most productive population (i.e., region 2). Accuracy was improved with annual releases of
high-reward tags, but some bias was still evident. Therefore, fisheries scientists should keep in mind
that even when attempting to account for the intermixing of stocks in an ITCAAN model, small
populations may be overestimated and at risk of overharvest if populations are of very different size
and intermixing rates are high. Accuracy in estimates for smaller populations may be improved
by including fishery independent survey data that capture juvenile fish as a metric of recruitment
in each region. Similarly, fishery-independent surveys that measure catch per effort while the fish
are separated by population during spawning could improve estimation. Non-extractive sampling
methods, such as cameras or hydroaccoustic methods may be ideal methods to provide such data to
limit interference with reproduction. Whether an ITCAAN model, a spatially aggregated catch-atage model, or independent catch-at-age models provide better management advice will ultimately
depend on the specific scenario and we recommend conducting a management strategy evaluation
(Butterworth and Punt 1999; Punt et al. 2001).
Simulating movement in four seasons affected the estimation of movement and individual
population abundance, but did not have a large influence on total abundance estimates. The bias in
individual population abundance estimates was reduced likely due to the lower average emigration
rate (Vincent et al. 2017). The movement rates were generally underestimated compared to the
annual average and were much lower compared to peak mixing rates. In general, this seasonal
movement scenario showed that the ITCAAN model is sensitive to how movement is simulated in the

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operating model. This also suggests that previous analyses of ITCAAN models may overestimate the
precision and accuracy of movement rate estimates in ITCAAN models (Hulson et al. 2011, 2013;
Goethel et al. 2015b; Vincent et al. 2017). Given that the magnitude of movement rates assumed in
the operating model can influence ITCAAN model performance, it is difficult to determine whether
seasonal movement would ultimately result in greater imprecision or bias in parameter estimates
of interest to managers such as abundance and mortality rates. Further investigation of ITCAAN
model sensitivity to the assumed movement dynamics is required. Additionally, how ITCAAN
model performance changes as a result of seasonal movement paired with fishing mortalities that
are not evenly divided between seasons is an area of needed research. Investigation of ITCAAN
sensitivity to other methods that simulate the intermixing of fish beyond multiple box-transfer
processes are recommended, such as individual (or agent) based models (Railsback et al. 1999;
Scheibe and Richmond 2002).
When high-reward tags were released annually, estimates of total abundance were generally
unbiased and much more precise compared to estimates without this data when simulated as
temporally constant. Similarly, bias in total abundance and population abundances increased as
the frequency of high-reward tag releases decreased. Therefore, we recommend that high-reward
tags be released annually to provide accurate estimates of reporting rates thereby providing more
accurate and precise estimates of population abundance. Imprecision and bias in total abundance
estimates were largest under scenarios where linear trends in reporting rates were not accounted for.
We recommend that applications of ITCAAN models attempt to estimate reporting rates as either
annual parameters or in time blocks and estimate natural mortality in time blocks. The size of these
time blocks should coincide with the release of high-reward tags throughout the time-series, when
releases occur less frequently than every 5-years. Additionally, a larger time-block for the terminal
years of the model for natural mortality is recommended because parameter estimates were highly
uncertain at the end of the time-series. We recommend avoiding the estimation of reporting rates
and natural mortality as temporally constant, when possible, as large biases in abundance estimates
are likely to occur in the presence of temporal trends.

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Estimation of natural mortality within a statistical catch at age model has been shown to be
possible through simulations (Wang 1999; Wang and Liu 2006; Lee et al. 2011; Johnson et al.
2015; Vincent et al. 2017); however, the estimation of this parameter in assessment models remains
a controversial topic (Francis 2012). The estimation of natural mortality in catch-at-age models
may be affected by recruitment variability, the selectivity pattern, and the fishing mortality history
(Fu and Quinn 2000; Wang and Liu 2006; He et al. 2011; Lee et al. 2011). When estimated, natural
mortality is commonly assumed to be temporally constant within the model (Wang 1999; Wang
and Liu 2006; Lee et al. 2011; Johnson et al. 2015), except see Jiao et al. (2012). The results of this
simulation analysis showed that the incorporation of tag-recovery data could assist the estimation
of time-varying natural mortality, where a 5-year time block provided the most precise estimates.
The results of this simulation also suggest that the variability of natural mortality has a larger
influence on the accuracy and precision of ITCAAN model abundance estimates compared to the
variability of the reporting rates. This simulation study did not evaluate the impact or estimation
of age- or region/population- specific natural mortalities within the ITCAAN model and additional
evaluation of the estimability and importance of such rates relative to temporal variability are
required. Estimation of natural mortality as temporally constant or as non-stationary in catch-atage and ITCAAN models will likely remain a debated topic as uncertainty in real data are likely
greater than simulation analyses depict, which can make the estimation of reporting rates and natural
mortalities in an ITCAAN model difficult to estimate regardless of the parameterization. Therefore,
simulation analyses should attempt to investigate a wide range of assumptions and uncertainties to
provide a holistic understanding of accuracy and precision in assessment methods.
A variety of assumptions were made when conducting this research and it is important to
consider our results in the context of these assumptions. In our simulations, we did not account
for tagging-induced mortality, although it is reasonable to expect that its consequences would be
similar to that of tag shedding. We also assumed that the rates of tag shedding in the operating
model were precisely known and the exact values could be incorporated in the ITCAAN model. In
actuality, tag shedding rates will never be known precisely and errors in tag shedding rates would

134

be anticipated to affect accuracy and precision of ITCAAN model estimates. We additionally
assumed that dynamics of the tagged cohorts matched the at-large population. Future research
examining the consequences of a mismatch between the dynamics of the tagged cohorts and the
at-large populations would be beneficial for diagnosing whether such a mismatch occured with real
data. The variance ratios of catch data relative to the survey data were assumed known. The results
of this study may be subject to change if the models were tuned to the data and the weightings of the
data sources differed from the simulated true dynamics (Maunder and Wong 2011; Johnson et al.
2015). Previous simulation analyses have assumed the effective sample size of tag recovery data
was equal to the age composition with a value of 100 (Goethel et al. 2015b) or equal to the number
of tags released (Vincent et al. 2017, in preparation). The weighting of tagging data, presumed
either implicitly or explicitly, relative to other data sources and the assumed distribution of tagrecovery data (Maunder 2001; Hulson et al. 2011, 2013; Goethel et al. 2015b; Vincent et al. 2017)
in ITCAAN models is an area of research that should be conducted. Finally, the operating model
and ITCAAN model were created with the same number of populations and harvest regions, which
may not be a realistic assumption for real fish populations. Therefore, we recommend additional
investigations into the influence of incorrectly identifying the number of populations within an
ITCAAN model.
In conclusion, tag-shedding will reduce the precision of parameter estimates even when this
process is correctly accounted for in the ITCAAN model. The inclusion of high-reward tag releases
in an ITCAAN model will increase the precision and accuracy in parameter estimates, especially if
released annually. Population abundance estimates were less biased when high-reward tag-recovery
data were incorporated into the ITCAAN model, but bias was still present under the high intermixing
rates simulated. Imprecision and bias in natural mortality and reporting rate parameters increased
with lower frequency of high-reward tag releases, especially when estimated as temporally constant.
Therefore, we recommend that high-reward tags be released as frequently as possible to increase the
precision of model estimates. The estimation of natural mortality performed best when estimated
in 5-year time blocks, whereas reporting rates estimated through a logit transformed random-walk

135

process and as 5-year time blocks performed best under different assumption of the true reporting
rate. We suggest estimation of time-varying natural mortality and/or reporting rate parameters be
attempted in ITCAAN models. The ITCAAN model underestimated the annual average movement
rate when movement was simulated to occur through box-transfer movement over 4 seasons within
a year. Other simulation frameworks, such as individual based models, should be evaluated to
determine how sensitive the ITCAAN model is to the assumption of movement occuring as a boxtransfer process in the operating model. We reiterate the conclusion of Vincent et al. (2017) that
ITCAAN models should only be used where spawning stock sizes are similar between populations
or intermixing rates in stocks are low to prevent biased population estimates.

Acknowledgments
This work was partially funded by grant 2012.1250 from the Great Lakes Fishery Trust and
2013_BRE_44025 from the Great Lakes Fishery Commission. Additional funding support was
provided by Supporting Partners of the Michigan State University Quantitative Fisheries Center.
The authors acknowledge the support of Michigan State University High Performance Computing
Center and the Institute for Cyber-Enabled Research. This is publication number 20XX-XX of the
Quantitative Fisheries Center at Michigan State University.

136

APPENDIX

137

APPENDIX 3.A
TABLES AND FIGURES

Table 3.A.1: Abbreviations used in figures and text, operating and ITCAAN model characteristics, number of iterations need to reach
1000 converged estimates, and convergence rates of the ITCAAN model for investigated scenarios.
Scenario
name
NoRwrdNoLoss
NoRwrdLoss
RwrdLoss
TVMAnn
TVMBlock
TVMConst
TVRRAnn
TVRRBlock
TVRRConst
BothTVAnn
BothTVBlock
BothTVConst
DecrRRAnn
DecrRRBlock
DecrRRConst
Rwrd5Ann
Rwrd5Block
Rwrd5Const
Rwrd10Ann

ITCAAN model
Reporting
M
rates
Const
Const
Const
Const
Const
Const
Const
Annual
Const
Block
Const
Const
Annual
Const
Block
Const
Const
Const
Annual
Annual
Block
Block
Const
Const
Annual
Annual
Block
Block
Const
Const
Annual
Annual
Block
Block
Const
Const
Annual
Annual

Operating model
High- Tag Reporting
Reward Loss
rates
Never
No
Const
Never Yes
Const
Annual Yes
Const
Annual Yes
Const
Annual Yes
Const
Annual Yes
Const
Annual Yes
AR1
Annual Yes
AR1
Annual Yes
AR1
Annual Yes
AR1
Annual Yes
AR1
Annual Yes
AR1
Annual Yes
Decr
Annual Yes
Decr
Annual Yes
Decr
5 Year Yes
Decr
5 Year Yes
Decr
5 Year Yes
Decr
10 Year Yes
Decr
138

M
Const
Const
Const
AR1
AR1
AR1
Const
Const
Const
AR1
AR1
AR1
AR1
AR1
AR1
AR1
AR1
AR1
AR1

# needed
for 1000
converged
1373
1362
1216
1128
1229
1261
1077
1399
1209
1086
1375
1236
1057
1311
1201
1044
1320
1200
1027

Percent
convergence
72.8
73.4
82.2
88.7
81.4
79.3
92.9
71.5
82.7
92.1
72.7
80.9
94.6
76.3
83.3
95.8
75.8
83.3
97.4

NPD
Maximum
Hessian Gradient
> 0.05
16
364
12
356
28
200
23
115
24
210
26
244
67
76
21
385
18
198
70
83
25
363
29
214
56
55
19
299
18
188
40
43
24
305
14
190
23
21

Rwrd10Block
Rwrd10Const
SeasonAnn
SeasonBlock
SeasonConst

Block
Const
Annual
Block
Const

Block
Const
Annual
Block
Const

10 Year
10 Year
10 Year
10 Year
10 Year

Table 3.A.1 (cont’d)
Yes
Decr
Yes
Decr
Yes
Decr
Yes
Decr
Yes
Decr

AR1
AR1
AR1
AR1
AR1

1396
1211
1162
1469
1420

71.6
82.6
86.1
68.1
70.4

21
22
12
6
4

381
198
158
466
418

* Note: M = Natural Mortality; NPD = Not Positive-Definite; Const = temporally constant; AR1 = simulated as a first order autoregressive process; Decr= reporting
rates decreased linearly over the time-series; and Block = estimation in 5-year time blocks

139

Figure 3.A.1: Examples of annual natural mortalities and reporting rates for the commercial fishery
in region 1 simulated by a truncated first-order autoregressive process.

140

From \To

Reg 1

Pop 1
Pop 2
Pop 3
Pop 4

1
0
0
0

Pop 1
Pop 2
Pop 3
Pop 4

0.4
0.2
0.2
0.2

Pop 1
Pop 2
Pop 3
Pop 4

0.650
0.125
0.100
0.075

Reg 2

Reg 3

Reg 4

Season 1: Spawning
0
0
0
1
0
0
0
1
0
0
0
1
Season 3: Fully Mixed
0.2
0.2
0.2
0.4
0.2
0.2
0.2
0.4
0.2
0.2
0.2
0.4
Annual Average
0.175
0.100
0.075
0.650
0.125
0.100
0.125
0.650
0.125
0.100
0.175
0.650

Reg 1
0.60
0.15
0.10
0.05
0.60
0.15
0.10
0.05

Reg 2

Reg 3

Reg 4

Season 2: Dispersal
0.25
0.10
0.05
0.60
0.15
0.10
0.15
0.60
0.15
0.10
0.25
0.60
Season 4: Return to Spawn
0.25
0.10
0.05
0.60
0.15
0.10
0.15
0.60
0.15
0.10
0.25
0.60

Figure 3.A.2: Matrices used to simulate seasonal movement and the average annual movement
rates for the Season scenario, where the rows are the natal population the fish come from and the
columns are the region to which the fish move.

141

Figure 3.A.3: Relative error (%) of abundance summed across populations for a four region
ITCAAN model under differing assumptions of tag loss, frequency of high-reward tag releases,
whether movement was simulated annually or seasonally, the true dynamics of natural mortality
and reporting rates, and parameterization in the ITCAAN model. Table 3.A.1 lists the model
abbreviations and corresponding model components. Whiskers on the boxplots extend to 1.5 times
the inter-quartile range or the most extreme relative error, whichever is less extreme. Relative errors
outside the whisker range were not plotted.

142

Figure 3.A.4: Relative error (%) of population abundance for a four region ITCAAN model
under differing assumptions of tag loss, frequency of high-reward tag releases, whether movement
was simulated annually or seasonally, the true dynamics of natural mortality and reporting rates,
and parameterization in the ITCAAN model. Table 3.A.1 lists the model abbreviations and
corresponding model components. Whiskers on the boxplots extend to 1.5 times the interquartile
range or the most extreme relative error, which ever is less extreme. Relative errors outside the
whisker range were not plotted.

143

Figure 3.A.5: Same as Figure 3.A.4 but for the movement rate for all populations into the region.

144

Figure 3.A.6: Same as Figure 3.A.4 but for natural mortality (top plot) and reporting rate parameters
(bottom 4 plots), where the boxplot on the left of each pair for the bottom 4 plots is the relative
error for the commercial fishery and the boxplot on the right is for the recreational fishery.

145

Figure 3.A.7: Relative Error (%) of annual natural mortality for varying frequencies of highreward tag releases and when natural mortality was estimated annually, in 5-year time blocks, or as
temporally constant. Scenario abbreviations and model components are presented in Table 3.A.1.
Whiskers on the boxplots extend to 1.5 times the interquartile range or the most extreme relative
error, which ever is less extreme. Relative errors outside the whisker range were not plotted.

146

Figure 3.A.8: Relative Error (%) of annual reporting rates of the commercial fishery in region
1 for scenarios where reporting rates were simulated as linearly decreasing and high-reward tags
were released annually or every 5 or 10 years, crossed with reporting rates estimated annually, in
5-year time blocks, or as temporally constant. Scenario abbreviations and model components are
presented in Table 3.A.1. Whiskers on the boxplots extend to 1.5 times the interquartile range or
the most extreme relative error, which ever is less extreme. Relative errors outside the whisker
range were not plotted.

147

Figure 3.A.9: Same as Figure 3.A.8, but for the recreational fishery in region 1.

148

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walleye (Sander vitreus) explains interannual variations in recruitment. Can. J. Fish. Aquat. Sci.
66(1): 114–125. doi:10.1139/F08-188.

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CHAPTER 4
A MULTI-REGION INTEGRATED TAGGING CATCH-AT-AGE ANALYSIS OF LAKE
ERIE AND HURON WALLEYE

Abstract
Walleye (Sander vitreus) are economically important piscivores in the Laurentian Great Lakes.
This species exhibits long distance migrations between spawning sites and feeding grounds and
intermixing among spawning populations occurs frequently. Movement of walleye from the western
basin of Lake Erie into Lake Huron and the eastern basin of Lake Erie has been shown through
tagging, telemetry, and genetic studies. The contribution of walleye from the western basin of Lake
Erie to harvest in these other regions has been identified as potentially problematic for management;
consequently, assessment methods that can account for the intermixing of walleye to provide
management advice are sought. Integrated tagging and catch-at-age analyses (ITCAAN) models
are an assessment approach intended for estimating the dynamics of intermixing populations,
including the natural mortality of populations and reporting rates of fisheries. We applied a threeregion ITCAAN model to walleye in Lake Huron, the western and central basins of Lake Erie, and
the eastern basin of Lake Erie for the time period 1993 to 2015. The ITCAAN tag-recovery data
were from a jaw-tagging study conducted on Lakes Erie and Huron starting in 1993 and lasting
through 2007 in the eastern basin of Lake Erie (ELE), 2010 in the western basin of Lake Erie
(WLE), and 2015 in Lake Huron (HUR). The ITCAAN model incorporated harvest, effort and agecompositions from the fisheries, fishery-independent survey catch per effort and age compositions,
tag recoveries by fisheries, and age-0 trawl catch in WLE to estimate movement, abundance,
reporting rates, fishing mortalities and regional natural mortalities. To produce a fit to the data
with no apparent biases in residuals and reasonable parameter estimates, we assumed a temporally
constant reporting rate across all recreational fisheries and reduced the weighting of tag-recovery
data. Estimates of natural mortality were within reasonable ranges, though the reporting rate for the

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recreational fisheries was higher than estimates from previous studies. For Lake Huron, estimates
of natural mortality (0.24) and abundances from the ITCAAN model closely matched estimates
from assessment models used to provide management advice. For WLE, the estimates of natural
mortality (0.15) and abundance were lower compared to the current assessment. ITCAAN model
abundance and natural mortality estimates for ELE were higher than the current assessment model
that did not account for movement. Additionally, the ITCAAN model estimated abundance in
ELE to increase following a high recruitment in 2005, where as the current assessment estimated
abundance to return to abundance prior to the large recruitment. We recommend that future tagging
studies involving walleye in Lakes Huron and Erie include high-reward and double-tagged fish to
provide accurate estimation of both reporting rates and tag shedding, which ultimately should
improve estimates of natural mortality and population abundance.

Introduction
An integral component of sustainable management of harvested fish species is accurate estimation of current and historic population abundance and exploitation (Quinn and Deriso 1999).
Abundance estimates allow for estimation of the productivity (i.e. stock-recruitment relationship)
of fishery stock, which in turn can be used to determine harvest regulations. The estimation of
population size and productivity is difficult when multiple populations intermix during periods of
harvest (Goethel et al. 2011). Throughout this paper we will refer to a population as an interbreeding
group of fish that reproduce in a self-sustaining manner with similar life history characteristics.
A stock will be referred to as fish within a defined harvest area (Cadrin et al. 2004), such as a
management unit. Therefore, an intermixed stock is composed of multiple populations that are
harvested in the same region. Incorrect estimation of abundance and productivity can easily lead
to populations being overexploited. When intermixing rates are high, less productive stocks are
susceptible to overharvest if management actions and assessment methods do not account for the
spatial dynamics of the species (Ying et al. 2011; Guan et al. 2013; Hulson et al. 2013; Molton et al.
2013; Li et al. 2014). The collapse of some economically important fish stocks has been partly

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attributed to inadequately accounting for the spatial dynamics that arise from movement, such as
Atlantic cod (Gadus morhua; Fu and Fanning 2004; Hutchinson 2008) and many Pacific salmon
populations (Oncorhynchus spp.; Morishima and Henry 1999). Therefore, the incorporation of
spatial dynamics into population assessment models may be a critical component of sustainable
management when populations intermix.
Walleye (Sander vitreus) are economically important native piscivores in the Laurentian Great
Lakes that spawn in rivers and shallow reef complexes. Walleye are typically considered to exhibit
spawning-site fidelity (Crowe 1962; Hayden et al. 2014), although genetic and telemetry studies
have shown some straying and interbreeding can occur (Stepien and Faber 1998; Strange and Stepien
2007; Brenden et al. 2015; Hayden et al. 2017). In Lake Erie, the majority of recruits to the western
and central basin are believed to come from the Maumee and Sandusky Rivers and the mid-lake
reef complex (Busch et al. 1975). Spawning populations of walleye in the Thames River, Ontario
and Tittabawassee River, Michigan contribute large amounts of individuals to the populations in
Lake St. Clair and Lake Huron, respectively (McParland et al. 1999; Fielder and Bence 2014). Van
Buren Bay and Grand River, Ontario are major spawning locations in the eastern basin of Lake Erie
(Stepien and Faber 1998; Strange and Stepien 2007). Despite these local spawning populations,
individuals from the western basin of Lake Erie are believed to compose a significant proportion of
the harvested stock in both Lake Huron and the eastern basin of Lake Erie (McParland et al. 1999;
Haponski and Stepien 2014; Brenden et al. 2015). Long distance movement by walleye between
interconnected lakes has been shown in Lakes Erie and Huron (Wang et al. 2007; Zhao et al. 2011;
Hayden et al. 2014; Vandergoot and Brenden 2014) and elsewhere (Smith et al. 1952; Rasmussen
et al. 2002; Herbst et al. 2017). The dispersal characteristics of walleye has been identified as a
potentially vexing problem for the management of this species, as fisheries may be dependent on
spawning populations that are not under the jurisdictional authority of managers (Brenden et al.
2015; Herbst et al. 2016).
The two largest fisheries for walleye in the Great Lakes are in Lakes Erie and Huron (Baldwin
et al. 2009). In 2000, harvest of walleye in Lake Erie was worth $9.8 million in dock-side value from

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commercial fisheries, which does not account for the economic value of the recreational fishery
(Baldwin et al. 2009). The recreational fishery for walleye in Ohio during 2013 was estimated to
generate $67 million in total direct expenditures (Sohngen et al. 2015). Management of walleye in
Lake Erie is currently facilitated by the Great Lakes Fishery Commission, which was formed by
the 1954 Convention on Great Lakes Fisheries between the United States and Canada. Specifically,
a walleye management plan was developed by the Lake Erie Percid Management Advisory Group,
which integrated stakeholders, fisheries managers, agency fishery biologist and stock assessment
scientists. The Walleye Task Group (WTG) is a sub-committee of the Lake Erie Committee (LEC),
which consists of fisheries scientist from state, provincial and federal agencies responsible for the
management of walleye in Lakes Erie and St. Clair and connecting waters. The WTG provides
annual harvest recommendations to the LEC based on assessment estimates of population status
and the harvest control rules set forth by the management plan. The LEC determines the annual
total allowable catch (TAC), with harvest quotas then allocated to individual jurisdictions based on
surface area (Wills et al. 2016). The four U.S. states (Michigan, New York, Ohio, and Pennsylvania)
and the Canadian province (Ontario) manage the harvest of walleye through regulations specific to
their jurisdiction. The current assessment model (Wills et al. 2016) estimates the abundance of the
stock in the western and central basins of Lake Erie, hereafter WLE (Figure 4.A.1). This assessment
does not account for the intermixing of populations from other regions or the emmigration of walleye
out of this region. Although the contribution of WLE walleye to the harvest in the eastern basin
of Lake Erie (hereafter ELE) is acknowledged, the assessment model of ELE walleye does not
explicitly account for immigration of WLE walleye and is not formally used to set harvest policies
in this region. Previous research has attempted to estimate the population in ELE and account for
intermixing of fish from different populations (Zhao et al. 2011). The assessment model for Lake
Huron walleye attempts to account for the immigration of western basin walleye by incorporating
abundance estimates from the WLE walleye assessment and the 3-year average of annual proportion
of jaw tags recovered in Lake Huron from the western basin of Lake Erie (Fielder and Bence 2014).
However, jaw-tagging of walleye in WLE has not occurred since 2010 and recent recoveries are

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infrequent. Previous attempts to integrate tag-recovery data into the assessment model for Lake
Huron ultimately resulted in the selection of the model that did not incorporate this data (Fielder
and Bence 2014). The three assessment methods currently used to provide management advice do
not fully account for movement of walleye between management boundaries and assume natural
mortality is known. Therefore, assessment models that attempt to estimate natural mortality and
intermixing of populations may be useful for management of walleye in Lakes Erie and Huron.
Integrated tagging and catch at age analysis (ITCAAN) assessment models were developed
to account for the spatial dynamics of intermixing populations that result from fish movement
(Maunder 2001; Goethel et al. 2011, 2015a; Fielder and Bence 2014; Vincent et al. 2017). ITCAAN models combine the information from tag-recovery studies, fishery-independent surveys,
creel surveys, and commercial harvest monitoring to estimate the movement, mortality rates, and
abundance of multiple populations. A traditional stock assessment model estimates the size of
the stock within management boundaries defined by the data collected. By accounting for the
movement dynamics and intermixing of populations, ITCAAN models attempt to estimate population abundances rather than the abundances in a region of harvest. Simulation analyses have
evaluated the precision and accuracy of ITCAAN model estimates for populations that experience
movement dynamics characterized as reproductive mixing (Hulson et al. 2011, 2013; Goethel et al.
2015a) and overlapping populations with natal homing (Vincent et al. 2017). Reproductive mixing
occurs when individuals move to a new region and contribute to the reproduction in the new region.
Alternatively, overlapping populations with natal homing occurs when populations intermix for
portions of the year but return to natal regions to spawn. ITCAAN models were shown to reliably
estimate the movement rates, natural mortalities and fishing dynamics under low mixing rates or
similar population abundances (Hulson et al. 2011, 2013; Goethel et al. 2015a; Vincent et al. 2017).
However, estimates of population abundance and reporting rates were biased when there were large
differences in stock size and intermixing rates were high (i.e. the majority of each population left
the natal region) (Vincent et al. 2017, in preparation). The ITCAAN model generally overestimated
the smaller and less productive populations under conditions of high intermixing, even though the

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model accurately estimated the intermixing of populations. An ITCAAN model may be appropriate to use for Walleye in Lakes Erie and Huron because movement between and within Lake
Erie and Huron has been shown to be considerable, but the majority of the populations remain in
the natal region (Wang et al. 2007; Vandergoot and Brenden 2014). Additionally, there is a trawl
survey conducted in WLE targeted at age-0 fish, which may aid in the estimation of recruitment
although this is not guaranteed since it is only conducted in one region. Although ITCAAN models
may not be a panacea for assessing intermixing populations with spatially complex dynamics, this
assessment method can provide alternative estimates to compare against assessments that do not
account for movement dynamics of the populations (Goethel et al. 2011; Hulson et al. 2011, 2013;
Goethel et al. 2015a). Therefore, accounting for the movement of fish when assessing intermixed
populations is difficult, but imperative for the sustainable management of all populations.
The goal of this research was to fit a spatially-explicit ITCAAN model to harvest, survey,
age-composition and tag-recovery data from Lakes Erie and Huron. Our intent was to evaluate the
utility of estimating population abundances through an ITCAAN model to assist the management of
walleye in Lakes Huron and Erie. The population assessment component of the ITCAAN model was
largely based on the catch-at-age models used to assess the stocks in Lake Huron, western/central
Lake Erie and the eastern basin of Lake Erie. Tag recovery data from jaw-tagged walleye released
in Lakes Huron, Erie, and St. Clair and various connected rivers were incorporated assuming the
mortality components were identical to the rest of the population.

Methods
Data
Data from fisheries, surveys, and tag-recoveries were separated into three regions: Lake Huron and
the Huron-Erie Corridor (HUR), WLE, and ELE. (Figure 4.A.1). The HUR region incorporated
the Lake Huron basin and the Huron-Erie Corridor (HEC) north of 42.074 °N (Figure 4.A.1). This
boundary was chosen because it is the boundary for the Michigan recreational fishery between the
Detroit River and Lake Erie. The WLE region encompassed the western and central basins of Lake
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Erie and also included harvest and tag recoveries in the Huron, Sandusky, and Maumee Rivers.
The ELE region incorporated harvest data and tag recoveries in the eastern basin of Lake Erie and
the Niagara and Grand Rivers (Figure 4.A.1). Walleye harvest, fishing effort, and tag-recovery
data between 1993 and 2015 were obtained from Ohio Department of Natural Resources (ODNR),
Ontario Ministry of Natural Resources and Forestry (OMNRF), Michigan Department of Natural
Resources (MDNR), New York State Department of Environmental Conservation (NYSDEC), and
Pennsylvania Fish and Boat Commission (PFBC). A summary of the data availability for each
region is provided in Table 4.A.3 and a detailed description of all data sources used in the analysis
is provided in Appendix 4.B.

ITCAAN Model
The ITCAAN model assumed there were three harvest regions and three spawning populations
(Figure 4.A.1). Though there are multiple spawning locations within each region, we assumed
that walleye within a region were sufficiently mixed to be considered a single population. The
model assumed that walleye returned to their natal region each year to spawn with 100% fidelity.
Abundances of the three populations were estimated by the number of individuals recruiting to
the population at age two and the abundance at age in 1993 and projected forward based on
estimated mortalities by fitting predicted catch to observed catch data. The model used the
general approach for statistical catch-at-age models with auxiliary information outlined by (Deriso
et al. 1985) with the inclusion of a box-transfer intermixing process (Goethel et al. 2011). The
recruitment for each population was estimated by a random-walk process from the previous year
(Equation (4.C.2.1)) and an assumed lognormal penalty on recruitment deviates with a standard
deviation of 4 (Equation (4.C.3.1)). The initial abundance for ages 3 through 7 were estimated
as an average value with age-specific deviations that summed to zero (Equation (4.C.2.2)), which
were assumed to be lognormally distributed with a standard deviation of 4 (Equation (4.C.3.2)).
Intermixing of the populations was modeled through a box-transfer process (Goethel et al. 2011),
which estimated the proportion of the population that moved to each region (Equation (4.C.2.3)).
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Movement was assumed to occur instantaneously after spawning at the beginning of the year and
was temporally constant. Walleye were modeled to remain in the region for the entire year and
were subject to region specific survival (Equations (4.C.2.4) and (4.C.2.5)). Regional survival was
modeled by the sum of region-specific natural mortality and total fishing mortality (i.e., summed
across fisheries; Equations (4.C.2.6) and (4.C.2.7)).
Fishing mortalities for most fisheries were modeled by estimating annual catchabilities and
age-specific selectivity components multiplied by observed fishing effort and an indicator variable,
which equaled one if a fishery was active in a region or zero otherwise (Equation (4.C.2.8)).The
fisheries modeled by catchability and age-specific selectivity parameters were: the Michigan recreational fisheries in HUR and WLE, HUR trapnet, HUR gillnet, WLE gillnet, Ohio Recreational,
ELE gillnet, and the combined NY/PA recreational fishery (Table 4.A.2). For these fisheries,
annual catchability coefficients were modeled using a random-walk process (Equation (4.C.2.9))
and selectivity-at-age parameters were estimated relative to an age that was assumed to be fully
selected. To adjust for an increase in the minimum legal size in 2004 in the Ohio and WLE Michigan
recreational fisheries, selectivity at age two prior to 2004 were estimated as additional parameters.
Annual fishing mortalities for the bycatch fishery in Lake Huron were calculated by multiplying
the observed fishing effort by an estimated catchability coefficient. The catchability coefficient for
the bycatch fishery was assumed to be temporally constant and all ages were assumed to be fully
selected to the fishery. Annual fishing mortalities were estimated for the three recreational fisheries
in Ontario waters of the three regions and the HEC and all ages were assumed to be fully selected
by the fisheries (Table 4.A.2). Catch at age was predicted for each fishery in a region using the Baranov catch equation for the fraction of each population present in the region (Equation (4.C.2.10)).
Predicted annual total catch for each fishery was obtained by summing across ages, while the
proportion at age were obtained by dividing the catch at age by total catch (Equation (4.C.2.11)).
Fishery-independent surveys were modeled to occur on the mixed stocks within each region at
specific times during the year. The surveys for HUR MDNR, WLE OMNRF, WLE ODNR/MDNR,
ELE NYSDEC, and ELE OMNRF were assumed to sample the population after it had experienced

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8.5/12, 9.5/12, 10/12, 9/12 and 9/12 of the mortality in that year, respectively. Predicted CPE
by age were calculated by survey-specific estimated catchability and selectivity-at-age parameters
multiplied by the abundance alive for the specific region (Equation (4.C.2.12)). Annual survey
catchability coefficients were modeled through a random-walk process (Equation (4.C.2.13)). Total
predicted CPE was calculated by summing over ages and proportions at age were obtained by
dividing predicted age-specific CPE by total CPE (Equation (4.C.2.14)). The predicted CPE of age0 walleye by the interagency trawl was calculated by multiplying an estimated annual catchability
coefficient by the number of recruits to the fishery at age-2 raised to the power of a scaling factor
parameter (Equation (4.C.2.15)). Therefore, the first year of data used by the model for the age-0
trawl was collected in 1991 and compared against estimated recruitment to the fishery at age-2 in
1993. The catchability coefficients of the age-0 trawl survey were estimated using a random-walk
process (Equation (4.C.2.15)).
Predicted tag recoveries were calculated using the known number of tags released at age and
estimated total fishing and natural mortality parameters that also were used in the catch-at-age
components of the model (Equation (4.C.2.16)). In total, there were ten fisheries tracked by the
ITCAAN model that recovered tags. The three fisheries in HUR were the Michigan recreational
fishery, a combined commercial fishery, and a recreational fishery for tags recovered in Ontario and
the HEC. The combined commercial fishery in HUR was modeled as the sum of the mortalities for
the Saginaw Bay bycatch, trapnet and gillnet fisheries with a single estimated reporting rate. Tag
recoveries in the WLE were assigned to one of four fisheries based on the reported gear of recovery
and location of recovery; recoveries in the region by commercial gear were assigned to the WLE
gillnet, whereas recreational recoveries were separated between the Ohio recreational, Michigan
recreational and Ontario recreational fisheries based on the reported location of recovery and state
and international boundaries. In ELE, recovered tagged walleye were caught either by the ELE
gillnet fishery, the recreational fishery in Ontario, or the combined recreational fishery for NY/PA.
All recreational fisheries in all regions were assumed to share an estimated reporting rate that was
temporally constant. Temporally constant reporting rates for the HUR commercial combined, WLE

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gillnet, and ELE gillnet fisheries were also estimated. Tag loss was accounted for using parameters
estimated by Vandergoot et al. (2012), where each tagging agency had different shedding rates
(Table 4.A.1). The formulation of tag retention used in this model was slightly different from
that of Vandergoot et al. (2012) because this model predicted number of tags recovered through
calculating the number of tags alive each year instead of calculating the recovery probabilities times
the number of tags released. Tag retention during the first year of release was calculated by the
initial probability the jaw tag was retained multiplied by a half year of chronic tag shedding. Tag
retention in all subsequent years after release were assumed to be a full year of chronic tag loss
specific to the agency of release (Equation (4.C.2.17)). Tag shedding rates for OMNRF were not
estimated by Vandergoot et al. (2012), but this agency used the same tagging technique as ODNR
and thus were assumed to have the same shedding rates.
The ITCAAN model was fit by penalized maximum likelihood using ADMB version 11.5
(Fournier et al. 2012). The error structure of observed harvest, survey, and penalties on randomwalk parameters were assumed to be lognormally distributed (Equations (4.C.3.1) to (4.C.3.7)). A
standard deviation parameter for one data source from each region was estimated as a free parameter
(HUR trapnet fishery harvest, WLE OMNFR survey CPE, and ELE OMNRF survey CPE); standard
deviations for all other data sources in a region were calculated using assumed variance ratios.
Variance ratios for each data source or parameter penalty are presented in Table 4.A.2, which
were used to calculate the standard deviation of the likelihood component by Equation (4.C.2.18).
We attempted to fit the model based on the ratios of variances estimated by Fielder and Bence
(2014), but the resulting model poorly fit the HUR MI recreational harvest data. Therefore, we
assigned variance ratios that were on a similar scale as the eastern and western basins of Lake
Erie. These ratios were somewhat arbitrary but were assigned based on the confidence in the data
source. For WLE, variance ratios were the values used by the WTG as determined from expert
opinion by Berger et al. (2012). Variance ratios for data sources in ELE were obtained from the
assessment model used by the WTG (Wills et al. 2016). Age compositions for surveys and fisheries
in all years were assumed to be multinomially distributed with an effective sample size of 100

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(Equations (4.C.3.8) and (4.C.3.9)). This effective sample size was chosen because it was less than
the effective sample size predicted by the western basin assessment through iterative reweighting
(McAllister and Ianelli 1997) and the sample size of fish aged was greater than this for all years,
fisheries, and surveys. The standard and reward tag recoveries by year of release, agency of release,
fishery of recovery and year of recovery and tags that were never recovered were assumed to be
multinomially distributed (Equation (4.C.3.10)).
We attempted to estimate reporting rates for each fishery, but estimates for the recreational
fisheries in New York and Michigan (both Huron and WLE) were consistently estimated to be
100%, which was deemed to be highly unlikley. Therefore, we estimated a single reporting rate
parameter for all recreational fisheries that was temporally constant. However, we found that
when the effective sample size for the tag-recovery data equaled the number of tags released major
discrepancies occurred between observed and predicted values for some data sources (results below).
Consequently, we tested multiple weightings of the tag-recovery data by dividing the number of
tags released by a weighting factor of 5, 10, 20, or 50. Sensitivity of some parameter estimates
to the weighting factor are presented below. Parameter estimates, fits to data, and comparison of
abundance estimates to assessment models currently used for WLE and ELE walleye assessments
are presented for the ITCAAN model that assumed a tag-recovery weighting factor of 10 because
this model resulted in no noticeable bias in all data sources.

Results
The scale of the population abundance estimates were very sensitive to the assumed structure
of the reporting rates and the weighting of the tag-recovery data. Reporting rate estimates of 100%
for multiple recreational fisheries were determined to be a result of a large number of standard tags
recovered in 2003 by these fisheries, but few or no reward tags were recovered from the year 2000
high-reward tag release. Estimates of reporting rates for the WLE and ELE recreational fisheries in
2003 using the method described by Pollock et al. (1991) exceeded 100% (Vandergoot et al. 2012).
The ITCAAN model thus fit these data and estimated the reporting for these fisheries near 100%

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due to the lack of other high-reward tag releases. By assuming all recreational fisheries shared a
common reporting rate the estimated parameter was less than 100%; however, this subsequently
resulted in the Ohio recreational harvest being severely underestimated.
The estimated reporting rate for recreational fisheries in all regions was sensitive to the tagrecovery weighting factor, with reporting rates exponentially decreasing as the weighting factor
increased in size (Figure 4.A.2). Natural mortalities were also influenced by the tag-recovery
weighting factor with estimates for HUR and WLE decreasing as the weighting factor increased.
Conversely, natural mortalities for ELE increased as the weighting factor increased. Across the
evaluated weighting factors, movement rate estimates from the WLE population to HUR were
generally low and inversely related to the tag-recovery weighting factor. Population abundance
estimates were also influenced by the tag-recovery weighting factor (Figure 4.A.3). Abundance
estimates for the HUR and ELE populations generally decreased as the tag-recovery weighting factor
decreased, with the exception of a weighting factor of 50 for the ELE population. Conversely, the
estimates of abundance for the WLE population were the lowest for the unweighted tag-recovery
data and the highest with a tag-recovery weighting factor of 5. Abundance estimates for the WLE
population decreased as the weighting factor increased for factors of 10, 20, and 50 (Figure 4.A.3).
Based on the quality of fit to input data sources we chose to use a tag-recovery weighting factor of
10 and all subsequent reported results are based on this weighting factor.
Harvest and survey data were fit well by the ITCAAN model. Observed and predicted fisheryindependent survey CPE matched closely, although there was less agreement between observed
and predicted values for the western basin age-0 trawl (Figure 4.A.4). Harvest data were not as
well predicted as survey data (Figure 4.A.5), but there did not appear to be systematic bias in
the residuals for any of the harvest data. Harvest estimates for the HUR bycatch fishery generally
decreased throughout the time-series, with the exception of an increase in harvest between 2004 and
2006. Walleye harvest, estimated by tag recoveries only, from the recreational fisheries in Ontario
varied greatly between years and ranged between 0 and 155 thousand walleye captured, with an
average of 44 thousand walleye per year (Figure 4.A.5). There was little difference in average

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number of walleye captured between the Ontario recreational fisheries in HUR, WLE and ELE, but
fishing mortality rates varied between the regions. The average apical fishing mortality estimated
from tag returns between 1993 and 2015 for the recreational fishery in Ontario waters of HUR
and the HEC was 0.0130; average apical fishing mortalities for the Ontario recreational fisheries in
WLE and ELE were 0.0023 and 0.0080, respectively. Average apical fishing mortality in HUR was
highest for the gillnet fishery (0.02408) followed by the recreational fishery in Michigan (0.08961).
The average apical fishing mortality for the trapnet fishery in HUR (0.05057) was more than four
times the rate of the bycatch fishery (0.011624). In WLE, the average apical fishing mortality
for the gillnet fishery (0.16882) was approximately double that of the Ohio recreational fishery
(0.07986) and almost seventeen times larger than the Michigan recreational fishery (0.010252). For
ELE, the recreational fishery in New York and Pennsylvania had an average apical fishing mortality
(0.05978) more than double that of the gillnet fishery (0.022095).
Selectivity at age for the fisheries varied considerably among the regions (Figure 4.A.6). In
HUR, the trapnet fishery was fully selective for age-2 fish and then decreased at older ages, whereas
the selectivity of the gillnet and recreational fisheries generally increased with age (Figure 4.A.6).
The HUR MDNR survey was nearly fully selective for ages less than 5 but decreased for the oldest
ages. For WLE, the fisheries were fully selective for ages 3 and 4, but selectivity declined for older
ages. Fishery-independent surveys in WLE were fully selective for age-2 and selectivity decreased
as walleye got older. Both commercial and recreational fisheries in ELE had the lowest selectivity
for age-2 walleye, with selectivity increasing nearly linearly with age until fully selective for the
age 7 and older walleye. The fishery-independent survey by NYSDEC was fully selective for age-2
fish, but ages-4 and older walleye were much less selected by the survey. The OMNRF survey in
the ELE region was highly selective for at age 7 and older walleye (Figure 4.A.6).
Natural mortality was estimated to be 0.23 (SE=0.018), 0.15 (SE=0.019), and 0.31 (SE=0.032)
in the HUR, WLE, and ELE regions respectively. The reporting rate for the recreational fisheries
was estimated to be 58.8% (SE=6.5%). Reporting rates for all commercial fisheries in HUR (0.6%,
SE=0.30%), and the commercial gillnet fisheries in WLE (6.4%, SE=0.99%) and ELE (15.4%,

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SE=4.63%) were much lower than the estimate for the recreational fisheries. Movement from the
HUR population to WLE and ELE was estimated to be 0.25% (SE= 0.20%) and 0.016% (SE =
0.050%) of the population. Movement of walleye from the WLE population to HUR was 3.6%
(SE=0.32%) and to ELE was 6.2% (SE=0.89%). Estimates of movement for walleye from the ELE
population to WLE was 3.5% (SE =1.5%) and to HUR was 0.12% (SE=0.23%).
Instantaneous total mortality estimates in HUR between 1993 and 2005 were relatively stable
between 0.35 and 0.42 year-1 for ages 4 and older (Figure 4.A.7). After 2005 the rate of total
mortality increased for age 4 and older fish but decreased for walleye ages 2 and 3. The decrease
in total mortality on ages 2 and 3 walleye occurred as a result of decreasing fishing mortality by
the trapnet fishery from 2005 to 2015. In WLE, mortality varied among ages with the highest
mortality on ages 3 and 4. Total mortality estimates in the WLE were highest between 1995 and
2000, relatively low and stable between 2001 and 2011, and increased between 2012 and 2015.
Total mortality in ELE was the lowest among the three regions and was greatest on walleye age 7
and older (Figure 4.A.7). Total mortality in the ELE region on the oldest fish generally decreased
throughout the time series with a sudden increase during 2006 and 2007 (Figure 4.A.7).
Abundance estimates for the WLE population were nearly an order of magnitude larger than
abundance for the HUR and ELE populations (Figure 4.A.8). WLE abundance estimates between
1993 and 2004 were relatively stable around 25 to 30 million walleye followed by a peak abundance
in 2005 of 62.6 million walleye (SE = 7.6 million walleye). After the peak in 2005, abundance
of the WLE population was estimated to decrease until reaching the lowest abundance at the end
of the time series of 15.2 million walleye (SE = 2.2 million walleye). Abundance estimates for
HUR and ELE populations were approximately 3 million walleye in 1993 and abundance decreased
slightly until 2004. Walleye abundance increased in the HUR and ELE populations between 2005
and 2007, where the abundance for the HUR population peaked at 3.5 million walleye (SE =
0.47 million walleye) and the ELE population peaked at 8.7 million walleye (SE = 1.8 million
walleye). Following this increase, abundance of the ELE population was relatively stable, whereas
abundance of the HUR population decreased to 2.2 million walleye in 2015 (SE = 0.39 million

168

walleye) (Figure 4.A.8). Increases in population abundance in 2005 were due to abnormally
large recruitment events for both Lake Erie populations, whereas the HUR population experienced
multiple years of high recruitment between 2005 and 2007 (Figure 4.A.9).
Agreement in abundance estimates from the ITCAAN model and the assessment models currently used to provide management advice for Lakes Huron and Erie varied depending on the
population (Figure 4.A.8). Estimates of walleye abundance age-2 and older for the HUR population were very similar to estimates of abundance from Fielder and Bence (2014). Total abundance
estimates by the ITCAAN model for WLE were approximately 20 million walleye less than estimates from the currently used assessment model. The largest difference in the abundance estimates
between the two WLE models of nearly 73 million walleye occurred in 2005 at the highest estimated
abundance in the time series (Figure 4.A.8). Estimates of total abundance for the ELE population
from the ITCAAN model were higher in all years by an average of 600000 walleye compared to the
assessment model currently used in that region. Additionally, after the large recruitment in 2005
the general trend estimated by the two models diverged (Figure 4.A.8). The assessment model
currently used in ELE estimated an abundance in 2015 of approximately 1.3 million walleye (SE
= 0.38 million walleye). Conversely, the ITCAAN model estimated the abundance in the eastern
basin in 2015 to remain at abundance consistent with the high recruitment year at nearly 5.2 million
walleye (SE = 1.4 million walleye) (Figure 4.A.8). The largest difference in estimated abundance
between the two models for ELE of 5.5 million walleye occurred in 2014.

Discussion
The ITCAAN model produced reasonable estimates of natural mortality and reporting rates
and no systematic biases in fits to observed data when a single reporting rate was assumed for all
recreational fisheries and weighting of the tag-recovery data was reduced by a factor of 10. Estimates
of reporting rates from the ITCAAN model differed from a previous analysis (Vandergoot et al.
2012), even though both studies used portions of the same database of tagged walleye for the eastern
and western basins of Lake Erie. Vandergoot et al. (2012) estimated reporting rates of 10% for

169

the commercial fishery in the western basin, 33% for the recreational fisheries in WLE, and 39%
for recreational fisheries in ELE based on model averaging of fits to standard and high-reward tag
recoveries tagged in the year 2000. High-reward tag-recovery data that were tagged in 1990 were
also used to estimate reporting rates for WLE recreational fishery of 55% and for WLE commercial
fishery of 17% (Vandergoot et al. 2012). Though our analysis did not include the high-reward tag
release in 1990, the estimate of recreational reporting rate from the ITCAAN model (58%) was
closest to estimates for the recreational fishery during this time period. On average, 1650 more
tags were released each year in WLE between 1993 and 1999 compared to between 2000 and
2010. Therefore, it is reasonable that the reporting rate is closer to the 1990 estimates than the
2000 estimates. Estimates of reporting rate for the recreational fisheries were more than double the
estimate of 24.8% obtained from returns of reward tags by all fisheries from a telemetry study on
the Tittabawassee River (Fielder 2014a), but this data were not included in the ITCAAN model.
The estimate of reporting rate for the recreational fishery from the ITCAAN model was within the
realm of possibility, but was larger than previous estimates for the region (Vandergoot et al. 2012;
Fielder and Bence 2014; Fielder 2014a). Reporting rate estimates from the ITCAAN model for the
commercial fishery in the western basin (6.4%) were marginally lower compared to estimates by
(Vandergoot et al. 2012). The estimate of reporting rate by the ITCCAN model for the combined
commercial fisheries in HUR was very low. This low reporting rate was expected given the very low
number of returns from commercial fisheries in this region compared to returns by the recreational
fishery. Similarly low estimates of reporting rates were obtained from another ITCAAN model
for commercial fisheries on yellowtail flounder in the Atlantic Ocean (Goethel et al. 2015a). The
reporting rates estimated by the ITCAAN model for the commercial fisheries were relatively stable
across the different modeling assumptions explored. The estimation of reporting rates in this model,
especially for the recreational fisheries, would greatly benefit from additional years of high-reward
tag releases (Vincent et al. in preparation).
Vandergoot and Brenden (2014) analyzed the Lake Erie jaw tag database and estimated agespecific natural mortality and movement rates in Lake Erie for ages 2, 3, 4, and 5 and older. That

170

analysis used the reporting rates and tag shedding rates estimated in Vandergoot et al. (2012) and
assumed that ages 3 and older were fully selected. Estimates of natural mortality for the western
basin of Lake Erie ranged between 0.13 and 0.40 and were lowest for the age-5 and older group.
Our estimate of natural mortality for the WLE, which was assumed constant over all ages, of 0.15
was most similar to the estimate for ages 5 and older from Vandergoot and Brenden (2014). More
than half of the tagged walleye used in the ITCAAN model were age 5 or older, which likely
influenced these estimates. The natural mortality estimate from the ITCAAN model in the western
and central basin of Lake Erie was less than half of the value used by the current assessment for
walleye of 0.32 (Wills et al. 2016). An analysis of tag recoveries in the eastern basin of Lake
Erie estimated natural morality for this region to be 0.22 (Zhao et al. 2011). Zhao et al. (2011)
used a similar database as what was used in this analysis, but included the recoveries of tagged
walleye by NYSDEC during the tagging process every year. Future analysis of Lake Erie walleye
ITCAAN models could attempt to incorporate such data. The natural mortality estimate for the
ELE region from the ITCAAN of 0.31 was larger than the estimate by Zhao et al. (2011) or the
value used in the current assessment of 0.19. There is much uncertainty in the estimate of natural
mortality for the eastern basin given that the New York/PA recreational fishery had great difficulty
estimating reporting rates below 100% and the large influence of the tag-recovery weighting factor.
The estimate of natural mortality from the ITCAAN model for HUR of 0.23 was nearly identical
to a constant value of 0.24 used in a sensitivity analysis for Lake Huron (Fielder and Bence 2014).
Estimates of natural mortality from the ITCAAN model for all regions were within the realm of
plausibility, but varied in terms of agreement with values used in current assessments.
To our knowledge, this is the first ITCAAN model using empirical harvest, survey, and tagrecovery data to estimate both reporting rates and natural mortality parameters within the assessment
model. Previous ITCAAN models have assumed natural mortality was known and estimated
reporting rates (Goethel et al. 2015b; Punt et al. 2000), assumed reporting rate was known and
estimated natural mortality (Eveson et al. 2012b; Siddeek et al. 2016), or pre-specified both
natural mortality and reporting rates (McGarvey et al. 2010). The model was sensitive to the

171

parameterization of the reporting rate and the weighting of the tag-recovery data. Difficulty in
estimating reporting rates that were not 100% was due to the small sample size of reward tags,
which were only released in 2000. The results of this study show that estimation of reporting rates
likely require large sample sizes of high-reward tags released more frequently than once during the
time series. Selection of appropriate weighting of the tag-recovery data in a multi-region ITCAAN
model is an area of needed research and beyond the scope of this manuscript. However, estimation
of weighting of data with conflicting information has been an area of recent research and has been
used for size-structured models that integrate tagging information to estimate growth (Punt et al.
2017). Additionally, determination of the effective sample size through various iterative weighting
methods for age composition data relative to other data sources has been explored (Truesdell
et al. 2017). Such methods could ostensibly be applied to weighting both the tag-recovery and
age-composition data simultaneously.

Model Assumptions and Limitations
The ITCAAN model used in this analysis made numerous assumptions and it is important to
consider our results in the context of these assumptions. Data for ELE were the limiting factor for
this analysis, specifically data from the commercial gillnet fishery in Ontario and the recreational
fishery in Pennsylvania. Tag-recovery data in Lake Erie were available starting in 1990 and include
high-reward tag releases in 1990. The model may be expanded to include this data, but would
require an assumption and extrapolation regarding the harvest of these two fisheries for the period
of 1990-1992. No high-reward tags were released in the eastern basin and thus would likely not
influence the estimation of reporting rate for this fishery, but releases in other regions may influence
the estimation for other recreational fisheries. Creel surveys to measure the recreational effort and
age composition of harvest in the Huron-Erie corridor were sporadically available for the time series
and thus were not feasible for the model. For this study, the HEC was combined with Lake Huron
to match the current Lake Erie assessment and management boundaries. However, a boundary that
incorporates walleye in Lake St. Clair with the population in the western basin of Lake Erie is both
172

possible and plausible (Strange and Stepien 2007). Though a spawning population exists in the
HEC (McParland et al. 1999), we did not attempt to estimate this region as a separate population
given the lack of available data. Similarly, the central basin of Lake Erie may contain a separate
spawning population from the western basin populations, but we did not attempt to estimate its
size given infrequent and small quantities of walleye tags released. Therefore, the model structure
of the ITCAAN model used in this analysis are reflective of available data and various simplifying
assumptions.
The ITCAAN model assumed that movement of walleye was constant across ages and over time.
Additionally, the model assumed that movement occurred once during the year instantaneously
after spawning. Therefore, estimated movement proportions between the regions are in terms
of the proportion of the population that would reside in that region for the entire year. Though
the regions of analysis between this study and Vandergoot and Brenden (2014) are not identical,
movement estimates from WLE to the other two regions from the ITCAAN with a weighting
factor of 10 appear to be lower. This difference in movement rate estimates is in part due to the
tag-recovery weighting-factor assumed, given that movement estimates decreased with lower tagrecovery weighting. Simulation analysis showed that when movement occurs as a seasonal process
the ITCAAN model generally underestimates the movement rate (Vincent et al. in preparation).
Wang et al. (2007) found that mean length at tagging of walleye of western basin Lake Erie origin
recovered in the eastern basin of Lake Erie were larger than those recovered in the western basin
or Lake St. Clair. They inferred that walleye moving eastward from the western basin were
generally older or larger in length at age. However, movement rate estimates for age-2 through
4 were found by Vandergoot and Brenden (2014) to be similar to movements for age-5 and older
walleye. Estimates of selectivity at age from the ITCAAN model for the eastern basin suggest
that older fish were more vulnerable to fishing in this region, whereas the western basin walleye
were fully selected at ages-3 and 4. Such a difference in selectivity could explain the difference
in mean size between the regions in the absence of age- or size- based movement. Yet genetic
analysis of contributions of Lake St. Clair and western Lake Erie origin walleye to the Saginaw

173

Bay stock showed that older walleye were found more frequently during the summer than during
the late winter and spring (Brenden et al. 2015). Contributions of age-3 and age-4 walleye from
the Lake Erie and Lake St. Clair populations were fairly similar among seasons, suggesting that
movement may vary seasonally among ages (Brenden et al. 2015). In our preliminary analyses, we
attempted to estimate biennial movement when tagging data were available, but estimates became
unreasonably high for the eastern basin in some years when the weighting of the tag-recovery data
was reduced. These preliminary model fits suggest that movement may vary over time, especially
for the western basin. Similarly, Zhao et al. (2011) showed that the movement of walleye from
the western basin to the eastern basin was correlated with the total abundance of walleye in the
western basin population, suggesting density-dependent movement. Therefore, the assumption that
movement is constant over ages, within a year, and among years is a simplification of reality.
There were many assumptions made with regards to the dynamics of tagged walleye. First,
we assumed no tagging-induced mortality, which is a common assumption for jaw tagged walleye
(Wang et al. 2007; Zhao et al. 2011; Vandergoot et al. 2012; Vandergoot and Brenden 2014). We
also assumed that the parameters for the tag shedding process estimated by Vandergoot et al. (2012)
were correct. We were required to extrapolate the estimates beyond the time period analyzed by
Vandergoot et al. (2012) to account for tag shedding for the entire time series. If the tag shedding rate
estimates were higher than the true value then natural mortality rates would be underestimated. We
also assumed that the reporting rate was temporally constant across all fisheries and all recreational
fisheries shared a single reporting rate. Estimates of reporting rates from a high-reward tag study
in 1990 and 2000 in the western basin of Lake Erie showed that reporting rates for the recreational
fishery decreased between these two time periods and were different between the western and
eastern basin (Vandergoot et al. 2012). An implicit assumption made by this tagging model was
that the reporting rate for a fishery was the same for all recovered walleye. It is possible that
recovered walleye have a higher reporting for fish that are tagged in a state different from the state
in which they are recaptured. For example, recreational fishers in New York may be more inclined
to report a tagged walleye from Michigan or Canada because it is a more memorable experience

174

compared to catching a tagged walleye from New York. We did not attempt to estimate such a
formulation of reporting rate as this would increase the number of this type of parameter estimated,
which were already poorly estimated. However, if such characteristics of reporting rates do occur it
would cause a mismatch between the true dynamics and the estimation model, which could cause
estimation problems.
The ITCAAN model assumes that the dynamics experienced by tagged fish and the population
at large were the same (Maunder 1998; Goethel et al. 2011). However, the large population of
walleye that spawn on WLE shallow water reef complex may not have been adequately represented
in the tagging studies. The population of fish tagged in the rivers of Lakes Erie and Huron may
have experienced a higher recreational fishing mortality compared to the rest of the population due
to easier access to rivers compared to the lake, and potentially lower exploitation by commercial
fisheries as they may not be in areas fished commercially as frequently as walleye from the shallow
reefs. Additionally, the tagging in these regions occurred mostly on the U.S. side of Lake Erie
and tag-recovery data were not available for the Ontario side of the ELE region. Likewise, a catch
at-age model for the western and central basin of Lake Erie provided a superior fit to data when the
catch-at-age data were modeled with basin specific catchability and selectivity parameters (Berger
et al. 2012). However, the ITCAAN model assumed the central and western basin of Lake Erie
were a single uniform area. It is possible that the assumption of identical dynamics between the
catch-at-age data and the tag-recovery data was violated. We recommend future tagging studies in
Lake Erie and Lake Huron be designed to tag walleye that come from a wide variety of spawning
locations including the mid-lake reef complexes.
The ITCAAN model assumed a single spawning population occured within each region. Within
each of the three model regions there are multiple known spawning locations (McParland et al.
1999; Stepien and Faber 1998; Strange and Stepien 2007), especially within the western basin of
Lake Erie such as the Huron, Maumee and Sandusky Rivers, and numerous shallow water reef
complexes. There is genetic evidence to suggest that populations intermix to a large degree in the
western basin of Lake Erie (Stepien and Faber 1998; Strange and Stepien 2007) and may be a single

175

metapopulation, which is often assumed (Berger et al. 2012; Wills et al. 2016). The model assumed
that within a region, walleye returned to their natal population with 100% fidelity. This assumption
may be realistic for some populations, such as the Tittabawassee River where returns to spawning
site of tagging were 95%; however, this assumption may be more tenuous for other populations,
such as the Mauamee River where spawning site fidelity was estimated to be 70% (Hayden et al.
2017). The influence of incorrectly identifying the number of spawning stocks within a region or
individuals not returning to their natal population with 100% fidelity has not been evaluated within
an ITCAAN model and is an area of needed research.
Natural mortalities were estimated as independent parameters for the three regions of the
ITCAAN model. This formulation implicitly assumes that the rate of natural mortality is based
on the environmental conditions in which the walleye resides. We assumed that natural mortality
would be most strongly influenced by the temperature, availability of prey and other characteristics
of the region the walleye inhabits. Thus we assumed that natural mortality was not a genetic factor,
which would be different between the different populations. The validity of this assumption is
uncertain.
The ITCAAN model assumed 100% reporting rate for walleye tagged with high-reward tags. A
$100 (USD) reward was offered for the recovery and reporting of high-reward tags, but no analysis
has been conducted to determine if this amount is sufficient to elicit a 100% reporting rate. If a
reward tagging study, such as described by Taylor et al. (2006), elucidates that the $100 value was
insufficient to garner a 100% reporting rate, then estimates of mortality using these data would be
biased (Pollock et al. 1991). Tags were occasionally reported by fish processors, implying that the
commercial fisher that caught the fish either failed to see the tag or recognized the tag but did not
remove it (Vandergoot et al. 2012). Estimates of jaw tag reporting rates have also been obtained
by comparing proportion of standard jaw tags returned to proportion of walleye implanted with
telemetry tags returned, which had a $100 reward. These walleye are also tagged with an external
t-bar anchor or external loop tags that are highly visible (Hayden et al. 2014). Estimates of reporting
rates from the acoustic tag studies have been lower for Tittabawasee River (Fielder and Bence 2014)

176

and Van Buren Bay (Jason Robinson, NYSDEC pers. comm.) than estimates from the high-reward
study in 2000. This difference in reporting rate estimates of jaw-tagged walleye between these
studies could be a result of temporal changes in reporting rates or differences in visibility between
jaw and other external tags. However, preliminary returns for a 2016 study conducted in the Thames
River Ontario of walleye tagged with anchor tags and jaw tags had a higher return rate compared
to walleye tagged with only jaw tags (Andy Cook, OMNRF pers. comm.). If the jaw reward tags
are reported at less than 100%, this would be violation of a key modeling assumption.
In this analysis we assumed that the incidental catch from the Pennsylvania commercial fishery
was a negligible source of mortality for walleye in ELE. Prior to 1996 the commercial fishery in
PA was a gillnet operation and the bycatch of walleye was much greater than the current trapnet
fishery. Therefore, the estimates of fishing mortality in ELE are an underestimate of the true
fishing mortality, especially during the first 3 years of the model. Yet the average harvest from the
commercial bycatch by PA between 2010 and 2015 was 770 pounds, which is small compared to
other harvests in the region. Additionally, no tags were reported for this fishery indicating that either
the fishing mortality was very low or the reporting rate was very low. Therefore, this assumption
perhaps was reasonable, but future analyses should attempt to incorporate this source of mortality.

Comparison to Existing Models
The estimates of abundance in HUR of the ITCAAN model matched almost exactly with estimates
from the model described by Fielder and Bence (2014). This was a surprising result as the ITCAAN
model incorporated the walleye population in the Huron-Erie corridor into the estimates for the
rest of Lake Huron. Estimates of abundance from an ITCAAN model that assumed the effective
sample size of the tag-recovery likelihood equal to the number of tags released were nearly double
the estimates from the currently used assessment. Therefore, there is a large degree of uncertainty
surrounding the estimates of population abundance in the Lake Huron and HEC region. Abundance
of the ELE population could potentially be overestimated because simulation studies showed that
populations that are much smaller than a large population will generally be overestimated by the
177

ITCAAN model under high movement rates (Vincent et al. 2017, in preparation). Bias in population
abundance estimates increased with an increase in intermixing and at a rate of 10% of the population
median relative error in abundance estimates could be as large as 50% for some small populations.
Though the model that assumed a weighting factor of 10 for the tag-recovery data estimated
movement to be less than 10% from WLE to ELE, the movement rate was highly sensitive to the
assumed weighting of the tag-recovery data and previous estimates of movement between these
regions were as high as 12% (Vandergoot and Brenden 2014). Additionally, estimates of abundance
in the ELE region were larger than estimates from the current assessment. Therefore, we caution
against using estimates of abundance in the eastern basin of Lake Erie for management purposes
without further exploration of appropriate weighting of the tag-recovery data and parameterizations
of the tag reporting rate. Additionally, analyses that incorporate tags recaptured during the tagging
process could provide additional information to estimate spawning population sizes (Zhao et al.
2011). Estimates of population abundance for the western basin were much lower compared
to estimates from the assessment model used by the WTG (Wills et al. 2016). This difference
is attributed to a large difference in the natural morality assumed in the WTG model and that
estimated by the ITCAAN model. Estimates of natural mortality in WLE for all weighting factors
of tag-recovery data were much lower than the value assumed in the current model used to provide
management advice. Therefore, it is highly possible that natural mortality in the western basin of
Lake Erie is lower than 0.32.

Management Recommendations
Although the ITCAAN model described in this paper has many assumptions and limitations,
insights to the dynamics of walleye in Lakes Erie and Huron can be gained from this analysis. First,
in gathering data for this model we identified a general lack of available data from the Huron-Erie
corridor region. However, estimated recreational fishery harvest from the HEC was on the same
scale as exploitations from the trapnet fishery in HUR. Harvest in this region is not accounted
for in assessment models for neither Lake Huron nor western Lake Erie. As a quarter of walleye
178

harvested in Saginaw Bay are from populations in Lake St. Clair and western Lake Erie (Brenden
et al. 2015) the HEC is an important connection between Lakes Huron and Erie. Management of
walleye populations in the region will require additional data in the HEC region to provide accurate
estimates of all sources of exploitation. Therefore, we recommend that annual creel surveys be
conducted in the Huron-Erie corridor to quantify the recreational fishing harvest and effort by both
MDNR and OMNRF.
The reporting and tag shedding rates are necessary components of tag-recovery data to accurately estimate the exploitation and natural mortality rates (Brenden et al. 2010), which in turn
will influence abundance estimates (Schnute and Richards 1995; Johnson et al. 2015). Therefore,
the design of tag studies to be used in ITCAAN models should include ways to estimate both tag
shedding rates and reporting rates. Tag shedding can be estimated through double tagging individuals with the same or different tag types (Fabrizio et al. 1996; Hampton 1997; Vandergoot and
Brenden 2014). Reporting rates can be estimated through various methods, including high-reward
tags (Pollock et al. 1991, 2001, 2002; Denson et al. 2002; Frusher and Hoenig 2003). Designing
tag-recovery studies to allow for estimation of both the reporting rates and tag shedding may be
more costly and complex, but is necessary to provide accurate and precise estimates of the mortality
rates of the population. As both reporting rates and tag shedding have the potential to change over
time, design components of tagging studies to estimate both rates should be included every year
that tags are released. We also recommend conducting a study to determine the necessary level of
tagging required to illicit a 100% tag reporting rate (Taylor et al. 2006). Similarly, a comparison
study of the reporting rates between jaw tags and Floy tags would be beneficial for choosing the
higher reported tag. A higher tag reporting would yield a more accurate estimate of exploitation,
natural mortality, and ultimately population abundances. However, given that tagging in the western
basin has not been conducted since 2010, the resumption of any tagging would be beneficial for
providing more accurate model estimates in the future.
Additional tag-recovery data are available for the region, which could be integrated in the
ITCAAN model to provide more accurate estimates. For example, walleye were tagged with PIT

179

tags and portions of the commercial harvest were scanned for the presence of these tags. It is
uncertain whether this tag-recovery dataset would aid the estimation of commercial mortality or
complicate the model due to changes in the amount of the harvest scanned for PIT tags each year
and/or faulty scanners which would influence reporting rates. Walleye tagged with telemetry tags
as a part of the Great Lakes Acoustic Telemetry Observation System could be incorporated into the
ITCAAN models in two ways (Hayden et al. 2014, 2017). First, tag recoveries of walleye implanted
with telemetry tags could be used as an additional high-reward tag release in the model to aid in
the estimation of tag reporting rates. Second, the data from the telemetry receivers could be used
to aid the estimation of movement rates and more realistic movement models could be estimated
(e.g. seasonal movement) (Eveson et al. 2012a). Finally, future analyses of ITCAAN models for
Lake Erie walleye could attempt to incorporate observations of tagged fish that are recovered and
released during the tagging processes in each region (Zhao et al. 2011).
Estimation of natural mortality is difficult in catch-at-age models (Wang and Liu 2006; Lee
et al. 2011) . However, this parameter is essential for accurately estimating the abundance of a
population. The ITCAAN model presented in this work estimated natural mortality rates for the
three regions modeled by accounting for tag shedding and tag non-reporting. The estimate of
natural mortality for the western basin of Lake Erie was less than half the value currently used
in the assessment model of 0.32. Our estimate of natural mortality aligns with the estimates of
ages 5 and older by Vandergoot and Brenden (2014). Therefore, it is probable that the value of
natural mortality currently used in the assessment model is too high. We recommend using a
lower value within the assessment model as an overestimate of natural mortality will generally
lead to the overestimation of abundance (Schnute and Richards 1995; Vincent et al. 2017). Future
investigations could attempt to estimate age-specific natural mortality parameters.
In conclusion, we were able to use an ITCAAN model to estimate natural mortality, reporting
rates, abundance and mortalities for walleye in Lake Huron, the Huron-Erie Corridor and Lake Erie.
Estimates of natural morality were reasonable, though estimates of recreational reporting rates were
higher than previous estimates. Walleye abundance estimates in the western basin from the ITCAAN

180

model were much lower compared to the models currently used to provide management advice; this
difference was attributed partly to the large difference in natural mortality estimates. The estimates
of abundance in the eastern basin of Lake Erie should be used with caution as results of simulations
showed that estimates of smaller populations could be positively biased when intermixing rates
were 10% or higher and there were large differences in population abundances. We recommend
that future tagging studies release high-reward tags and double tag individuals annually to provide
more precise estimates of tag shedding and reporting rates. Additional studies to determine if Floy
tags provide a higher reporting rate would be beneficial. The estimates of abundance for walleye
in Lake Erie and Huron from this study are not intended as a replacement to current assessments
used for management decisions. We recommend conducting a management strategy evaluation
to determine the performance of this model compared to currently used assessment models and
appropriate harvest policies to account for the intermixing of walleye populations (Butterworth and
Punt 1999; Punt et al. 2001).

Acknowledgments
The authors would like to thank member agencies of the WTG for access to the data, specifically
Dave Fielder, Matt Faust, Jason Robinson and Andy Cook greatly assisted understanding the
databases and provided knowledge of Lake Erie and Lake Huron walleye. This work was partially
funded by grant 2012.1250 from the Great Lakes Fishery Trust and 2013_BRE_44025 from the
Great Lakes Fishery Commission. Additional funding support was provided by Supporting Partners
of the Michigan State University Quantitative Fisheries Center. This is publication number 20XXXX of the Quantitative Fisheries Center at Michigan State University.

181

APPENDICES

182

APPENDIX 4.A
TABLES AND FIGURES

Table 4.A.1: Number of standard (S) and reward (R) tags released from 1993 to 2015 and tag retention parameters for Ontario Ministry
of Natural Resources (OMNRF) in the Lake Huron region and in western basin of Lake Erie, Michigan Department of Natural Resources
(MDNR) in the Lake Huron region and in the western basin of Lake Erie, Ohio in the western basin of Lake Erie, New York State
Department of Environmental Conservation (NYSDEC) and Pennsylvania Fish and Boat Commission combined in the eastern basin of
Lake Erie and the instantaneous retention (ι) and chronic shedding (β) parameters for each agency.
Year
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009

HUR OMNRF
S
R
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
40
3
89
9
139
12
0
0
0
0
0
0
0
0
0
0

HUR MDNR
S
R
2991
0
3429
0
3165
0
2992
0
2993
0
5484
0
5997
0
5986
300
3042
0
3234
0
3171
0
3143
0
3262
0
3107
0
2966
0
3031
0
3094
0

WLE OMNRF
S
R
1647
0
454
0
835
0
0
0
2784
0
378
0
0
0
1091
115
765
0
0
0
0
0
0
0
1520
0
0
0
0
0
0
0
0
0

183

WLE MDNR
S
R
1958
0
2544
0
965
0
2268
0
1740
0
1290
0
1630
0
1874
208
94
0
2822
0
1511
0
2849
0
1926
0
2388
0
396
0
1292
0
818
0

WLE ODNR
S
R
4149
0
2723
0
4021
0
3494
0
1735
0
0
0
0
0
1656
166
2318
0
2703
0
2132
0
1005
0
2330
0
2030
0
1711
0
0
0
0
0

ELE NYSDEC
S
R
1906
0
1475
0
1312
0
892
0
1144
0
459
0
1084
0
999
121
1061
0
1136
0
630
0
268
0
1630
0
1497
0
1327
0
0
0
0
0

2010
2011
2012
2013
2014
2015
Îąt
βt

0
0
0
261
204
271

0
0
0
138
49
69
0.95
0.28

3063
2988
2994
2993
2700
2699

0
0
0
0
300
300
0.99
0.08

0
0
0
0
0
0

Table 4.A.1 (cont’d)
0
1008
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.95
0.99
0.28
0.08

184

0
0
0
0
0
0

0
0
0
0
0
0
0.95
0.28

0
0
0
0
0
785

0
0
0
0
0
0
0.99
0.07

Table 4.A.2: Region of activity, variance ratios for observed values and processes error of catchability coefficients for fisheries and surveys modeled. An X in the selectivity, catchability, reporting
rate or annual F column indicates these parameters were estimated for this fishery/survey. Reporting
rates with the same superscript were assumed to have the same values.
Fishery / Survey

Region

Penalty
Var.
Ratio

Selectivity

Catchability

HUR
HUR
HUR

Data
Var.
Ratio
2.0
1.0
0.9

HUR Comm Bycatch
HUR Comm Trapnet
HUR Comm Gillnet
HUR MI Rec

Reporting Annual
Rate
F

1.0
0.9

X
X

Constant X ∗
X
X∗
X
X∗

HUR

0.85

0.85

X

X

X†

HUR ON and HEC Rec HUR
HUR MDNR Survey
HUR
WLE Comm Gillnet
WLE

0.91
0.91

1.07
0.89

X
X

X
X

X

WLE Ohio Rec
WLE MI Rec

0.85
0.76

0.86
0.8

X
X

X
X

X†
X

WLE
WLE

WLE ON Rec
WLE
WLE OMNRF Survey WLE
WLE ODNR/MDNR WLE
Survey
WLE Age-0 Trawl
WLE

1.0
0.86

2.0
2.0

X
X

X
X

1.0

2.0

X

X

ELE NY/PA Rec
ELE Comm Gillnet

ELE
ELE

0.9
1.0

1.0
0.4

X
X

X
X

ELE ON Rec
ELE NYSDEC Survey
ELE OMNRF Survey

ELE
ELE
ELE

0.4
1.0

2.0
2.0

185

X
X

X
X

X†

X†

X

X

X†
X
X†

X

Table 4.A.3: Data availability for fisheries and surveys modeled in a three region ITCAAN model
for Lakes Erie and Huron Walleye, where § indicates tag recoveries were combined and modeled
as a single fishery.
Fishery / Survey
HUR Comm Bycatch
HUR Comm Trapnet
HUR Comm Gillnet
HUR MI Rec
HUR ON and HEC Rec
HUR MDNR Survey
WLE Comm Gillnet
WLE Ohio Rec
WLE MI Rec
WLE ON Rec
WLE OMNRF Survey
WLE ODNR/MDNR Survey
WLE Age-0 Trawl
ELE NY/PA Rec
ELE Comm Gillnet
ELE ON Rec
ELE NYSDEC Survey
ELE OMNRF Survey

Age Composition

Total Harvest

Effort

X
X
X

X
X
X

X
X
X
X

X
X
X
X

X
X
X

X
X
X

X
X

X
X

X
X
X
X
X
X

186

Tag Reco- CPE
veries
§
§
§
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X

Figure 4.A.1: Boundary lines of the three regions modeled by the ITCAAN Model and location of
tag releases indicated by triangles (A). Tag recovery locations for tags that were released in HUR
(B), the WLE (C), and the ELE region (D) between 1993 and 2015 indicated by circles.

187

Figure 4.A.2: Estimates and 95% confidence interval of reporting rate for the recreational fisheries
across all regions, natural mortality for the Huron, WLE, and ELE regions and movement rates from
WLE population to HUR, where the x-axis is the value the weighting factor for the tag-recovery
data.

188

Figure 4.A.3: Estimated total walleye abundance in the three regions of the ITCAAN model for the
time period 1993 through 2015 for five weighting factors of the tag-recovery data, where the tag
weighting factor is the value that the multinomial likelihood was divided by.

189

Figure 4.A.4: Observed (open circles) and predicted (solid line) catch per effort of walleye of the
six fishery-independent surveys used in a three region ITCAAN model for Lake Huron and Lake
Erie.

190

Figure 4.A.5: Observed (open circles) and predicted (solid line) number of walleye harvested by
fishery from a three region ITCAAN model for Lake Huron and Lake Erie.

191

Figure 4.A.6: Selectivity at age for fisheries and surveys operating in the three regions of a tag
integrated catch-at-age model for walleye in Lake Huron and Lake Erie.

192

Figure 4.A.7: Total instantaneous regional mortality at age experienced in the three regions estimated by a tag integrated catch-at-age model for Lake Erie and Huron walleye.

193

Figure 4.A.8: Estimated population abundance from assessment models currently used to manage
the walleye fisheries in Lakes Huron and Erie (solid line) with 95% confidence interval (green
hashed region) and from a three region tag integrated catch-at-age model that estimates intermixing
of the populations (dashed line) with the 95% confidence interval (shaded region).

194

Figure 4.A.9: Recruitment of age-2 walleye to the Lake Huron, western and eastern basin Lake
Erie populations as estimated by a three region tag-integrated catch-at-age assessment model and
the 95% confidence interval shown by the shaded region.

195

APPENDIX 4.B
DATA SOURCES

Many datasets were available extending as far back as 1978, but data for the commercial fishery
in ELE and the Pennsylvania recreational fishery were available starting in 1993, which is why we
excluded earlier data. Total harvest of walleye in number of fish were available for the Ontario
trapnet fishery in Lake Huron, the Michigan recreational fishery in Lake Huron, the Ontario gillnet
fishery in Lake Huron, the tribal gillnet fishery in Lake Huron, Ontario gillnet fishery in WLE
and ELE, Ohio recreational fishery in WLE, Michigan recreational fishery in WLE, New York
recreational fishery in ELE and Pennsylvania recreational fishery in ELE. In Lake Huron, harvest
and age composition for the Ontario commercial gillnet and the Michigan tribal gillnet fisheries
were combined and modeled as a single fishery. Data for the commercial gillnet fisheries in Ontario
waters of WLE and ELE were modeled as two separate fisheries (Figure 4.A.1). Consistent with
the current assessment in the eastern basin of Lake Erie, the New York and Pennsylvania (NY/PA)
recreational fisheries were combined and treated as a single fishery in the model.
Commercial harvest for each fishery was reported in biomass. Following methods used to
assess Lake Huron, WLE, and ELE walleye, harvested biomass for each fishery was converted into
number of walleye based on weighed and aged fish from subsamples of harvested fish every year.
Fishing effort for the Lakes Huron and Erie commercial gillnet fisheries in km of gillnet set and for
the Lake Huron trapnet fishery in number of lifts were used as a component of the fishing mortality
sub-model. Fishing effort of an additional commercial trapnet fishery that operates in Saginaw
Bay of Lake Huron and captures walleye as bycatch was also incorporated into the model. An
estimate of 23500 walleye killed by the HUR bycatch fishery in 2010 (MacMillan and Roth 2012)
was used to scale the trapnet effort and provide an estimate of bycatch for the entire time series. We
were unable to reliably convert the incidental harvest of walleye reported in weight captured by the
Pennsylvania commercial yellow perch fishery into number of walleye because age composition
and average weight data of the catch were unavailable. Therefore, the harvest by this fishery was
196

not included in the model, which is consistent with the current assessment of the ELE; additionally,
the harvest by the PA commercial fishery was relatively small.
Recreational harvest and fishing effort in angler hours from New York, Pennsylvania, Ohio,
and Michigan (in HUR and WLE separately) were obtained from annual creel surveys and charter
boat reporting. Recreational catch-at-length data were converted into catch-at-age using annual
age-length keys (Wills et al. 2016). Harvest and effort data for the Ohio recreational fishery were
the sum of estimates obtained from creel surveys for Lake Erie and the Sandusky and Maumee
rivers. Missing years of harvest and effort data for the Sandusky River (1994-1996, 1999, and 2000)
and the Maumee River (1994-1996 and 1998-2000) were estimated through linear interpolation.
Recreational fishing data for Michigan in Lake Huron included harvest from Lake Huron open
water and in the Saginaw and Tittabawassee Rivers. Harvest and effort for the recreational fishery
differed from data described by Fielder and Bence (2014) in that we used harvest within a calender
year, whereas they assumed a fishing year (i.e., April 1st to March 31). Creel surveys of recreational
fishing in all three regions of Ontario and the HEC (both Ontario and Michigan) were infrequently
conducted between 1993 and 2015 and were not included in the ITCAAN model. However,
recreational fisheries in Ontario and the HEC did recover and report jaw-tagged walleye and we
used these recoveries to estimate fishing mortalities associated with these fisheries. The model
estimated separate annual fishing mortalities for recreational fisheries in the HEC and Ontario
waters of Lake Huron, WLE and ELE.
Multiple fishery-independent catch-per-effort time series were incorporated in the ITCAAN
model. A gillnet survey in Saginaw Bay was conducted each September by MDNR. In Canadian
waters of WLE, a depth-stratified random-site gillnet survey was conducted jointly by the OMNRF
and the Ontario Commercial Fisher’s Association during September through mid-October. A depth
stratified fixed-site gillnet survey was conducted in the western basin of Lake Erie jointly by ODNR
and MDNR in late September through November. An interagency age-0 trawl in WLE was used
as an index of recruitment to the population. A gillnet survey conducted by NYSDEC during
September in U.S. waters of ELE was also included in the ITCAAN model. The gillnet survey in

197

Ontario waters of ELE was conducted in late August to early September and data were available
starting in 1998. Fishery-independent surveys, with the exception of the age-0 trawl, captured
walleye while they were assumed to be intermixed. All walleye captured by the Canadian surveys
were weighed, measured for length and aged. Weight and length were measured for all walleye
captured by U.S. surveys, but only a subsample were aged and age-compositions for these surveys
were calculated using age-length keys. The age composition data for the surveys and the fisheries
include walleye age-2 through 7 and all fish older than age-7 were aggregated into an age-7 and
older age group.
Tag release and recovery databases were obtained for Lake Erie from the WTG and for Lake
Huron from MDNR and OMNRF. Mature walleye were collected and tagged from tributaries and
open-water reef spawning locations during the spring by MDNR and OMNRF in HUR from 1993
to 2015, by ODNR, OMNRF, and MDNR in WLE from 1993 through 2010 and by NYSDEC
in ELE from 1993 to 2007 and in 2015 (Table 4.A.1). Walleye that were tagged during March
through May at tagging sites throughout Lakes Huron and Erie were used in the analysis (i.e.,
walleye tagging after May were not included in this study; Figure 4.A.1). Walleye were tagged
by affixing a hard metal Monel butt-end band to the mandible or maxillary that was inscribed
with agency-specific fish identification numbers and tag reporting information and then released
(Wang et al. 2007; Fielder 2014b; Vandergoot et al. 2012; Vandergoot and Brenden 2014). Some
walleye were also implanted with Passive Integrated Transponder (PIT) tags, but our analysis did
not include walleye tagged with only a PIT tag. High-reward tags inscripted with “Reward $100”
were released by agencies in both regions of Lake Erie in 2000, by MDNR in HUR in 2000, 2014,
and 2015, and by OMNRF in HUR in all years walleye were tagged (Table 4.A.1). The release
of tagged walleye were modeled separately by agency as past research indicated that tag shedding
rates differed among agencies (Vandergoot and Brenden 2014). Walleye tagged and released by
OMNRF and MDNR in HUR and WLE were modeled separately. The PFBC released 72 tags in
2001, which were modeled as tags from NYSDEC. The age of tagged walleye at the time of release
were determined differently depending on the database. For tags released by MDNR in HUR,

198

the number of tags released at age were determined by the total number of tags released and the
proportion at age obtained from a subsample of tags aged each year during peak spawning (David
Fielder, MDNR pers. comm.). Age at release of tagged walleye in Lake Erie were estimated using
year-, sex-, and tagging-basin specific age-length keys applied to the observed length and sex of
the tagged fish (Vandergoot and Brenden 2014). Age-length keys were derived from aged walleye
samples collected from fishery-independent surveys conducted the fall prior to tagging based on
the assumption that growth during the winter was limited (Vandergoot and Brenden 2014). Age
at release of tagged walleye from Ontario in 2013 to 2015 were determined by a combination of
dorsal fin spines and age-length keys. The age of tagged walleye at release were incorporated into
the model and the predicted number of tags recovered were calculated from age-specific fishing
mortalities. However, we did not explicitly separate the recoveries by cohorts of age at release, but
instead modeled the recoveries summed across ages for each fishery.
We restricted our analysis of tag recoveries to those released and recovered between 1993 and
2015. More than half of the tag recoveries in the database from MDNR for Lake Huron did not
have gear information. Of the 6643 tags for which recovery gear was indicated in the recovery
database only 27 (0.4%) were reported as recovered from commercial fisheries. Therefore, the
tag recoveries for this database that did not have a recovery gear were randomly assigned to either
the recreational fishery (with a probability of 99.6%) or commercial fishery. Ten of the 6643 tags
were randomly assigned to be recovered by the commercial fishery from the Lake Huron database
and the rest were assumed to be recreational recoveries. With the exception of the Lake Huron
recovery gear, tags were considered not reported if they did not have a recovery location sufficient
to assign to one of the three model regions, a recovery gear, or were missing the year of release
or recovery. Tags that were recovered by assessment gear were removed from the number of tags
that were released. Tagged fish that were found dead were not explicitly incorporated into the
analysis. A total of 15600 standard tag recoveries and 318 high-reward tag recoveries were used in
the ITCAAN model. These recovered tags were distinguishable based on the year and agency of
release, and the year, region, and fishery of recovery. The total number of tags returned separated

199

by these five factors were incorporated in the ITCAAN model. Recovered tags were assigned to
one of the harvest regions (Huron, WLE, or ELE) based on the reported location of recovery.

200

APPENDIX 4.C
PARAMETER LIST AND MODEL EQUATIONS

Table 4.C.1: Symbols and descriptions of variables used in Operating and ITCAAN model.
Symbol
Index
y
Y
a
A
t
p
r
ty
ry
g
Diacritic
˜
ˆ
none
Parameters
Ñ

Description
Year
Last year modeled
Age
Oldest modeled age
Tagging agency
Spawning population
Harvest region
Year of tag release
Year of tag recapture
Fishing or survey gear
Variable derived from estimated parameters
Estimated Parameter
Observed Data or assumed value
Population abundance

Λ̂

Recruitment in the first year 1993

λ̂
Γ̂
∆ˆ

Annual recruitment deviation
Mean abundance for 1993
Abundance at age deviations in 1993

T̃p,r
ω̂ p,r

Percent of population p moving to region r
Estimated movement parameter from population p to region r

S̃
Z̃

Survival
Total mortality

F̃

Age-specific fishing mortality

M̂
v̂
q̃
E

Natural mortality
Age-specific fishery selectivity
Fishery catchability coefficient
Observed fishing effort
Indicator if fishery is active in region

1

201

Table 4.C.1 (cont’d)
K̂
κ̂
C
PC
I
ÎĽ

Fishery catchability parameter in 1993
Annual fishery catchability deviation
Harvest in numbers caught
Fishery proportion at age
Survey abundance index
Survey specific mortality fraction

V̂

Age-specific survey selectivity

Q̃

Survey catchability coefficient

Φ̂

Survey catchability parameter in 1993

φ̂
PI
R
ñ
L
Îą
β
d
ρ̂

Annual survey catchability deviation
Survey proportion at age
Number of tagged fish released
Number of tagged fish alive
Tag retention probability
Immediate tag retention probability
Instantaneous rate of chronic shedding
Number of tags recovered
Fishery reporting rate

θ̃

Tag recovery proportions

θ̃ N R
Κ̃
ε̂
ξˆ

Proportion of tags never recovered
Age 0 trawl annual catchability
Age 0 trawl catchability in 1993

Ρ̃
ζˆ
ψg
σ̂r
VR
ψN
ψR
N LL
W

Annual deviation of Age 0 trawl catchability
CPE from Age 0 trawl
Exponent of age 0 trawl W Erie
Standard deviation of specific data source
estimated standard deviation specific to each region
Data source specific variance ratio
Standard deviation for abundance deviations in 1993 = 4
Standard deviation for recruitment deviations random walk =4
Negative Log Likelihood
Tag-recovery data weighting factor

202

Table 4.C.2: Equations used to model and estimate population dynamics in ITCAAN models.
Eq. Number
(4.C.2.1)
(4.C.2.2)
(4.C.2.3)

Equation
Ñy,a=1,p = Λ̂ p

Ñy,a=1,p = Ñy−1,a=1,p eλ̂ y,p
ˆ

Ñy=1993,a,p = e Γ̂p +∆ p,a

(4.C.2.4)

Ñy+1,a+1,p =

Í

(4.C.2.5)

Ñy+1,A,p =

Í
r

y = 1993

for

y > 1993

a>2

eω̂r,p ,
2 ω̃
Í
e r,p
r=1

T̃r,p =

r

for

for

where

where

(4.C.2.7)
(4.C.2.8)

F̃y,a,r,g = q̃ y,g E y,g v̂a,g 1r,g

g

q̃ y,g = K̂g
q̃ y,g = q̃ y−1,g e κ y,g
C̃y,a,g =

Í F̃y,a,r,g
p Z̃ y,a,r

for
for

y = 1993
y > 1993

Ñy,a,p T̃p,r (1 − S̃y,a,r )

C̃y,a,g
g
PC y,a,g = Í

(4.C.2.11)

a

(4.C.2.12)

a < A−1

Ñy,A,p T̃p,r S̃y,A,r + Ñy,A−1,p T̃p,r S̃y,A−1,r
S̃y,a,r = e− Z̃ y,a,r
Í
Z̃ y,a,r = M̂r + F̃y,a,r,g

(4.C.2.10)

a

where ωr=3,p = 0

Ñy,a,p T̃p,r S̃y,a,r

(4.C.2.6)

(4.C.2.9)

͈
∆ p,a = 0.0

C̃y,a,g

Í
I˜y,a,g = Ñy,a,p T̃p,r e− Z̃ y,a,r Υ̂g Q̃ y,g V̂a,g
p

203

Table 4.C.2 (cont’d)
Q̃ y,g = Φ̂g
Q̃ y,g = Q̃ y−1,g e φ̂ y,g

(4.C.2.13)

for
for

y = 1993
y > 1993

˜
f y,a,g = ÍI y,a,g
PI
I˜y,a,g

(4.C.2.14)

a

(4.C.2.15)

ι̃ y = ε̂

for

y = 1993

Κ̃ y =

for

y > 1993

Ρ̃ y =



Í
F̃r y,a,r,g
1 − S̃r y,a,r ρˆg
dˆt y,t,r y,r,g = ñt y,t,r y,a T̃p,r

(4.C.2.16)

Z̃r y,a,r

a

Lt,r y = αt e−βt ∗0.5
Lt,r y = e−βt

for r y = t y
for r y > t y
p
ψg = σ̂r ÷ V Rg

(4.C.2.17)
(4.C.2.18)

(4.C.2.19)

ˆ
ι̃ y−1 eξ y
ζˆ
Κ̃ y Ñy,a=1,r=2

ñt y,t,r y,a
= Rt y,t,a
Í
ñt y,t,r y+1,a+1 = ñt y,t,r y,a T̃p,r S̃r y,a,r L̃t,r y
r
Í
ñt y,t,r y+1,A = ñt y,t,r y,A T̃p,r S̃r y,A,r + ñt y,t,r y,A−1 T̃p,r S̃r y,A−1,r L̃t,r y
r

(4.C.2.20)

Í
ÍÍÍ ˜
d˜t y,t,N R = Rt y,t,a −
dt y,t,r y,r,g
ry r g

a

d˜

(4.C.2.21)

t y,t,r y,r,g
θ̃ t y,t,y,g = Í R
t y,t,a
a

(4.C.2.22)

t y,t,N R
θ̃ t y,t,N R = Í R
t y,t,a

d˜
a

204

for
for

y = ty
a < A−1

for

a=A

Table 4.C.3: Likelihood Equations and penalties used in the ITCAAN model.
Equation Number

Likelihood Equation and Penalty

(4.C.3.1)

N LLRec =

ÍÍ

(4.C.3.2)

N LLN0 =

ÍÍ

y p

ln ψR 2π + 0.5



√

ln ψN 2π + 0.5

a p




λ̂ y,p
ψR
∆ˆ p,a
ψN

√ 

Îş y,g
ln ψg 2π + 0.5 ψg
N LLq =
y g

(4.C.3.3)

!2

!2

!2

ÍÍ

(4.C.3.4)

N LLQ =

ÍÍ
y g

(4.C.3.5)

N LLHarvest =

(4.C.3.6)

N LLSurvey =

ÍÍ

(4.C.3.7)

N LLTrawl =

Í
y

ln ψg 2π + 0.5



ln ψg 2π + 0.5

y g

y g

√

√

ÍÍ




(−φ y,g )
ψg

!2

ln(Cy,g )−ln(Ĉy,g )
ψg

ln ψg 2π + 0.5

ln(I y,g )−ln( Iˆy,g )
ψg

√ 

ln ψg 2π + 0.5

ln(η y )−ln(η̂ y )
ψg

√






(4.C.3.8)

N LLCP = −100

(4.C.3.9)

N LLSP = −100

(4.C.3.10)

√

ÍÍÍ
y g a

c y,a,g
PCy,a,g ln PC

ÍÍÍ
y a r

c y,a,g
ICy,a,g ln IC


 !2


 !2


 !2






N LLTag =

!

#
ÍÍ Í Í Í
−
dt y,t,r y,r,g ln b
θ t y,t,r y,g +dt y,t,N R ln b
θ t y,t,N R /W
"

ty t





ry

g

r

205

BIBLIOGRAPHY

206

BIBLIOGRAPHY

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Berger, A.M., Jones, M.L., Zhao, Y., and Bence, J.R. 2012. Accounting for spatial population structure at scales relevant to life history improves stock assessment: The case for Lake Erie walleye
Sander vitreus. Fish. Res. 115–116(complete): 44–59. doi:10.1016/j.fishres.2011.11.006.
Brenden, T.O., Scribner, K.T., Bence, J.R., Tsehaye, I., Kanefsky, J., Vandergoot, C.S., and Fielder,
D.G. 2015. Contributions of Lake Erie and Lake St. Clair walleye populations to the Saginaw
Bay, Lake Huron recreational fishery: evidence from genetic stock identification. N. Am. J. Fish.
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CONCLUSIONS

1. Both release- and recovery-conditioned ITCAAN models yielded accurate and precise parameter estimates under low to moderate movement rates.
2. Abundance and reporting rate parameters were largely biased for both the release- and
recovery-conditioned ITCAAN frameworks under conditions of high movement and large
differences in stock-recruitment relationships among spawning populations.
3. For the release-conditioned ITCAAN framework under high movement rates and similar
stock-recruitment functions, population abundances and reporting rate estimates were unbiased.
4. Misspecification of natural mortality or reporting rate for both the release- and recoveryconditioned ITCAAN frameworks induced larger biases, for tested misspecification levels,
than when both parameters were estimated. Therefore, I recommend that both natural
mortality and reporting rates be estimated within an ITCAAN model, when possible.
5. Precision of natural mortality and abundance estimates in a release-conditioned ITCAAN
model were sensitive to the number of tags released annually.
6. For recovery-conditioned ITCAAN models, estimates of population abundance were extremely biased when the reporting rate was assumed to be spatially-constant in the ITCAAN
model but varied in the operating model.
7. Model performance for the release-conditioned ITCAAN model was superior to the recoveryconditioned ITCAAN model for similar scenarios, especially for the natural mortality parameter. Therefore, I recommend that fisheries scientists use the release-conditioned ITCAAN
model and attempt to estimate both natural mortality and reporting rates within the model.

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8. Bias and imprecision of model estimates were greater when tag-shedding was incorporated
into the operating model and ITCAAN models compared to ignoring this process. Inclusion
of tag shedding in operating models of future analyses of ITCAAN models is recommended.
9. Performance of release-conditioned ITCAAN models improved greatly when high-reward
tags were released annually. However, some biases in population abundance estimates
remained under simulation conditions of high movement and large differences in population
abundances.
10. Estimation of natural mortality and reporting rates in 5-year blocks performed the best when
these parameters varied over the time series. Conversely, estimation of reporting rate and
natural mortality as temporally constant in the ITCAAN model resulted in large biases in
model parameters, and bias increased as the frequency of high-reward tag releases decreased,
when the operating model simulated natural mortality as an AR1 process and reporting rate
as linearly decreasing.
11. Movement rates were underestimated compared to the annual average when movement was
simulated to occur seasonally. I recommend that additional simulation frameworks, such as
individual based models, be conducted to determine how sensitive the ITCAAN model is to
the assumption of a box-transfer process.
12. I recommend that tag-recovery studies release high-reward tags annually to increase the
precision and accuracy of reporting rate, natural mortality, and abundance estimates.
13. ITCAAN abundance estimates of walleye from the eastern basin of Lake Erie should be
used with caution as simulations suggests that small populations can be overestimated under
moderate to high movement rates.
14. Estimates of natural mortality and abundance for the western/central basin of Lake Erie from
the ITCAAN model suggest that the value of natural mortality, 0.32, used in the current
assessment model to provide management advice may be too high.
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15. I recommend that future tagging studies of Lake Erie and Lake Huron walleye be designed such that they can estimate reporting and tag shedding rates annually. Additionally,
experiments to determine the value of high-reward tags necessary to elicit a perfect (100%)
reporting rate should be conducted.
16. Walleye harvest data from the Huron-Erie corridor are generally lacking, but harvest in this
region by recreational fishers is substantial; thus annual creel surveys should be conducted
to better quantify the amount of harvest and fishing effort on this system.
17. I recommend additional simulation analyses be conducted to investigate how ITCAAN model
performance changes as a result of including additional fishery independent surveys that
occur when walleye are aggregated during spawning or including region specific indices of
recruitment.
18. I recommend conducting a management strategy evaluation to determine the performance of
the ITCAAN model compared to the independent assessment models currently used for the
management of walleye in Lakes Erie and Huron.

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