THE INFLUENCE OF ALTERNATIVE ASSESSMENT APPROACHES ON YIELD AND
POPULATION STATUS OF INTERMIXING LAKE WHITEFISH POPULATIONS
By
Yang Li

A THESIS
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
Fisheries and Wildlife ― MASTER OF SCIENCE
2013

ABSTRACT
THE INFLUENCE OF ALTERNATIVE ASSESSMENT APPROACHES ON YIELD AND
POPULATION STATUS OF INTERMIXING LAKE WHITEFISH POPULATIONS
By
Yang Li
Recent evidence suggests that lake whitefish (Coregonus clupeaformis) populations in
lakes Huron and Michigan now intermix considerably during non-spawning periods, while lake
whitefish stocks continue to be largely treated as discrete, independent units for management and
assessment purposes, and stock status is usually assessed in each unit annually. The goals of my
thesis were to: 1) compare fishery management performance and assessment estimation
performance based on the current spatial structure for assessments (assuming non-mixing unit
stocks) and two alternative approaches to addressing mixing among stocks, and 2) evaluate
changes in performance that might results from less frequent assessments. The current target
mortality rate (65%) was maintained in both chapters. I modeled the dynamics of four
intermixing, age-structured populations using a management strategy evaluation framework to
evaluate assessment approaches and frequencies. In chapter 1, I found that the relative
performance of pooled and separate population assessments depends on mixing rates and
productivity. While pooling can sometimes be advantageous, it can also sometimes lead to
substantial overfishing, likely due to bias or inappropriate allocation among areas. In chapter 2,
the results showed that compared to other things, like the actual mixing among areas and the
choice of how to account for spatial structure, the frequency of assessment had modest effects.
When conducting an annual assessment, removing the 1-year lag had little influence. My results
suggest that conducting assessments every three or five years should be considered as part of a
management strategy and may allow analytical efforts to be directed in other ways.

Copyright by
YANG LI
2013

ACKNOWLEDGEMENTS

I am extremely grateful to many people who provided help to me throughout my master
program. I especially want to thank my advisor, Dr. James Bence, for providing me well-directed
guidance whenever I had questions and whatever the questions were. As an international student,
I feel so lucky to have such a wonderful advisor who teaches me not only quantitative analysis,
but also writing skill. I thank other members of my graduate committee, Dr. Brain Roth and Dr.
Juan Pedro Steibel, for raising my interest in fisheries and statistics. They both contributed their
thoughts and guidance throughout my academic study. I also want to thank Dr. Travis Brenden,
for bringing great ideas about my second chapter. Faculty and staff of the Department of
Fisheries and Wildlife provided assistance to make my master life much easier. I thank the
Michigan DNR Fisheries Division, the Great Lakes Fishery Commission, and the Great Lakes
Fishery Trust for financial support of this research. In addition I acknowledge computational
support and technical computing assistance from the High Performance Computing Center at the
Institute for Cyber-Enabled Research at MSU. The modeling subcommittee of the Technical
Fisheries Committee for 1836 Treaty Waters also provided some input on my research.
Lastly, I would like to thank all of my family and friends. My parents Jiajun Li and
Hongping Li, have supported and inspired me in so many ways. Thanks to them, I had the
chance to study abroad and see a totally different world. My boyfriend, Zhen Zhang, gave me a
lot of help and support to my life and study. He is also my important programing teacher,
provided me useful guidance about how to use R and the high performance computer. Thank you
all.

iv

PREFACE

The two chapters of this thesis following the Introduction and Summary were drafted as
manuscripts that will be submitted for publication in peer-review journals. When submitted, both
manuscripts will include Drs. James Bence and Travis Brenden as co-authors. Consequently,
both chapters were written with first person, plural narratives, even though I am listed as the sole
author of the thesis.

v

TABLE OF CONTENTS

LIST OF TABLES ...................................................................................................................... viii
LIST OF FIGURES ...................................................................................................................... ix
INTRODUCTION AND SUMMARY ............................................................................................1
The simulation framework ........................................................................................................1
Chapter 1: Evaluation of alternative assessment methods .......................................................3
Chapter 2: How alternative assessment frequency influenced the fishery performance .........5
Overall conclusions and future directions.................................................................................6
REFERENCES ........................................................................................................................9
CHAPTER 1
EVALUATING ALTERNATIVE ASSESSMENT APPROACHES FOR INTERMIXING
LAKE WHITEFISH POPULATIONS ..........................................................................................11
Abstract .......................................................................................................................................11
Introduction .................................................................................................................................12
Methods.......................................................................................................................................15
The “true” system ............................................................................................................16
The “perceived” system ...................................................................................................20
Experimental design.........................................................................................................23
Performance statistic ........................................................................................................24
Results .........................................................................................................................................25
Discussion ...................................................................................................................................29
REFERENCES ...........................................................................................................................35
CHAPTER 2
DOES STOCK ASSESSMENT FREQUENCY REALLY MATTER? A CASE STUDY FOR
INTERMIXING LAKE WHITEFISH POPULATIONS IN 1836 TREATY CEDED WATER ..57
Abstract .......................................................................................................................................57
Introduction .................................................................................................................................58
Methods.......................................................................................................................................61
Overall simulation framework .........................................................................................61
Four simulated populations ..............................................................................................61
The “true” system ............................................................................................................63
The “perceived” system ...................................................................................................66
Experimental design.........................................................................................................71
Performance statistic ........................................................................................................72
Results .........................................................................................................................................73
Comparison of annual assessment quotas with and without 1-year lag ..........................73
Comparison of annual and multiannual assessments ......................................................73
Comparison of three rules for setting TACs for the years between assessments ....74
Comparison among assessment frequencies ............................................................74
vi

Comparison of the relative magnitude of effects due to assessment frequency and
assessment model under different mixing scenarios ........................................................75
Discussion ...................................................................................................................................77
REFERENCES ............................................................................................................................83
APPENDIX .................................................................................................................................109

vii

LIST OF TABLES

Table 1.1: Four different levels of productivity for lake whitefish used in simulations and
associated steepness, equilibrium yield (tonnes), and the corresponding standard Ricker
parameters α and β. ........................................................................................................................48
Table 1.2: Equations used in stochastic simulation model ............................................................49
Table 1.3: Simulation scenarios. In all scenarios each of the four populations had different
productivity, with one population taking each of the four alternative productivity levels (Table 1)
........................................................................................................................................................55
Table 1.4: The convergence rate and Hessian warning percentage for the “meta” assessment
method under each scenario ...........................................................................................................56
Table 2.1: Four different levels of productivity for lake whitefish. Simulated populations have
different levels of productivity and steepness values. Their population indexes were defined
based on their productivities, from low productivity (LP) to high productivity (HP). Alpha and
beta are the Ricker stock–recruitment coefficients that were adjusted by different steepness levels
for lake whitefish spawning populations. . ....................................................................................98
Table 2.2: Equations used in stochastic simulation model ...........................................................99
Table 2.3: Design of assessment process based on different timetable and frequency of
assessment, and harvest limit setting rules for rotation years ......................................................105
Table 2.4: Mixing scenarios. In all scenarios each of the four populations had different
productivity, with one population taking each of the four alternative productivity levels (Table 1)
......................................................................................................................................................106
Table 2.5: The relative change of the median of LP SSB due to assessment frequency and
assessment model under different mixing scenarios ...................................................................107
Table 2.6: The relative change of the median of total yield due to assessment frequency and
assessment model under different mixing scenarios ....................................................................108

viii

LIST OF FIGURES

Figure 1.1: Structure of a simulation framework for evaluating stock assessment models
performance. ................................................................................................................................. 40
Figure 1.2: A conceptual diagram of stock intermixing for four hypothetical lake whitefish
populations that are spatially segregated during spawning, but subsequently intermix during the
non-spawning period when exploitation takes place. For interpretation of the references to color
in this and all other figures, the reader is referred to the electronic version of this thesis.............41
Figure 1.3: Mean annual spawning stock biomass (SSB) for each population and fishery yield for
fishing areas surrounding each spawning area over the last 25 years of simulations. The X-axis of
each section in Figure 1.3a represents all four simulated populations, from the low productivity
(LP) population to the high productivity (HP) population. The dashed line is at 20% of unfished
SSB (B20%). In Figure 1.3b, the X-axis identifies the four fishing areas surrounding the
spawning areas of the LP to HP populations separately. The box tops and bottoms cover the
interquartile range; the horizontal middle line represents the median value of all simulations for
each scenario ..................................................................................................................................42
Figure 1.4: As for Figure 1.3b, except y-axis is mean inter-annual percent variation in fishery
yield ...............................................................................................................................................45
Figure 1.5: Probability of SSB for each population being less than 20% of the unfished SSB level
........................................................................................................................................................46
Figure 1.6: Median relative error (MRE) and Median absolute relative error (MRE) of estimating
SSB for each assessment method over the last 25 years ...............................................................47
Figure 2.1: Structure of a simulation framework for evaluating stock assessment models
performance. ..................................................................................................................................87
Figure 2.2: A conceptual diagram of stock intermixing for four hypothetical lake whitefish
populations that are spatially segregated during spawning, but subsequently intermix during the
non-spawning period when exploitation takes place. ....................................................................88
Figure 2.3: Influence of one year lag. Shown are mean annual spawning stock biomass (SSB)
for each population (Figure 2.3a), fishery yield for fishing areas surrounding each spawning area
over the last 25 years of simulations (Figure 2.3b), the percentage of years SSB falling below
B20% for each population (Figure 2.3c), and inter annual variation of yield(Figure 2.3d). The Xaxis of each section indicates whether there was no lag (L0) or a one year lag (L1). The
horizontal section name represents the assessment model and population information (for 2.3a
and 2.3c) from the low productivity (LP) population to the high productivity (HP) population.
The dashed line is the 20% of unfished SSB (B20%). In Figure 2.3b and 2.3d, the horizontal
section name identifies the assessment model names and the four fishing areas surrounding the
spawning areas of the LP to HP populations separately. The box tops and bottoms cover the
ix

interquartile range; the horizontal middle line represents the median value of all simulations for
each scenario. .................................................................................................................................89
Figure 2.4: The influence of assessment frequency and harvest limit setting rule. Shown are
mean annual spawning stock biomass (SSB) for each population (Figure 2.4a), fishery yield for
fishing areas surrounding each spawning area (Figure 2.4b). The X-axis of each section
represents six annual and multiannual quotas: “CT3”, “CT5”, “TF3”, “TF5”, “AY3”, and
“AY5”. The horizontal section name represents the assessment model and population
information (for 2.4a) from the low productivity (LP) population to the high productivity (HP)
population. The dashed line is the 20% of unfished SSB (B20%). In Figure 4b, the horizontal
section name identifies the assessment models and the four fishing areas surrounding the
spawning areas of the LP to HP populations separately. The box tops and bottoms cover the
interquartile range; the horizontal middle line represents the median value of all simulations for
each scenario. .................................................................................................................................94
Figure 2.5: The influence of assessment frequency and harvest limit setting rule. Shown are the
proportion of years SSB falling below B20% for each population (Figure 2.5a), and inter annual
variation of yield (Figure 2.5b) under mixing scenario “SR=0.5”. All results are for the last 25
years of simulations. The X-axis of each section represents six annual and multiannual quotas:
“CT3”, “CT5”, “TF3”, “TF5”, “AY3”, and “AY5”. The horizontal section name represents the
assessment model and population information (for 2.5a) from the low productivity (LP)
population to the high productivity (HP) population. In Figure 2.5b, the horizontal section name
identifies the assessment models and the four fishing areas surrounding the spawning areas of the
LP to HP populations separately. The box tops and bottoms cover the interquartile range; the
horizontal middle line represents the median value of all simulations for each scenario..............96
Figure 3.1: Mean annual spawning stock biomass (SSB) for each population over the last 25
years of simulations. The X-axis of each section indicates the assessment design scenarios. The
horizontal section name represents the five mixing scenarios. The horizontal section name
represents the five mixing scenarios. The labels in X-axis showed two assessment models. For
each assessment model, four boxes represent four populations from the low productivity (LP)
population to the high productivity (HP) population. The dashed line is the 20% of unfished SSB
(B20%). The box tops and bottoms cover the interquartile range; the horizontal middle line
represents the median value of all simulations for each scenario. ..............................................111
Figure 3.2: As for Figure 3.1, except y-axis is mean annual fishery yield for fishing areas
surrounding each spawning area. .................................................................................................113
Figure 3.3: As for Figure 3.1, except y-axis is probability of SSB for each population being less
than 20% of the unfished SSB level. ..........................................................................................114
Figure 3.4: As for Figure 3.1, except y-axis is mean inter-annual percent variation in fishery
yield. ............................................................................................................................................115

x

INTRODUCTION AND SUMMARY

Lake whitefish generally reproduce during the late fall and demonstrate natal philopatry
(Ebener et al. 2010). It was once believed that during the harvest season most lake whitefish
near each spawning area were from that spawning area. Recent evidence shows that lake
whitefish populations in lakes Huron and Michigan are now intermixing considerably during
non-spawning periods (Ebener et al. 2010), possibly as a result of fish expanding their foraging
areas to meet nutritional needs. Current management of lake whitefish in 1836 Treaty-Ceded
waters of the upper Great Lakes is based on separate assessments and harvests calculations for
nominally distinct unit stocks that are assumed to not mix (Ebener et al. 2005; Caroffino et al.
2012). In northern Lake Huron one of these assessment units was formed by combining several
previously used units, in response to evidence of intermixing.
I simulated four lake whitefish spawning populations that have differing levels of
productivity and varying degrees of mixing during the fishing season, but are spatially
segregated during spawning. I assumed that the current approach of managing harvest to avoid
exceeding a target total mortality rate of 65% was retained. I explored the influence, over the
long term, of alternative spatial structure in the assessment models and different frequencies of
assessments on population sustainability and the success of the lake whitefish commercial
fishery.
The simulation framework
The simulation framework in both chapter 1 and 2 was based on management strategy
evaluation methods (Kell et al. 2005, Punt 2008). This framework modeled the “true” system
and “perceived” system (data collection, stock assessment, and harvest control rule application).

1

The “true” system is represented as “real” stock and fishery dynamics, from which the simulated
data were sampled each year. These data were then used in a periodically (annually or less often)
assessment procedure. The assessment procedure involved fitting a model to the (simulated) data,
and the target yield was set each year based on applying the current treaty-water harvest control
rule (constant 65% mortality) based on the most recent assessment result. The target yield, which
we refer to as total allowable catch (TAC), was then fed back into the corresponding "real
system", thereby influencing actual yield and the fishery performance in the next year.
Performance statistics based upon the stock and fishery dynamics model were eventually used to
evaluate the robustness of each assessment method.
The basic structure of my model for the "true" system is based on the approach developed
by Molton et al. (2012). I used an age- structured forward-projection model, consisting of four
hypothetical populations with a simulation length of 100 years, but used only results from the
final 25 years to evaluate performance. Recruits were added as the youngest age each year based
on the current stock size for the population and a stochastic Ricker stock recruitment function.
During the fishing season fish from each population mixed with fish from other populations in
four fishing grounds, which each surrounded the four spawning areas, but returned to the
spawning area for an instantaneous spawning period. During the fishing season fish died due to
natural mortality and fishing mortality. Fishing mortality in each area (fishing ground) was
partially determined based on perceived stock size based on a stock assessment that was done
each year during the simulations, in an attempt to achieve a defined annual target yield (referred
to as TAC for "total allowable catch"). The four populations were assumed to have differing
levels of "productivity" to mimic the likely range in productivity found in actual intermixing lake
whitefish populations. We equated "productivity" with steepness, and set unfished equilibrium

2

spawning biomass to be equal across the populations, so that differences between the populations
were due only to our assumed productivity differences.
The annual TAC for each fishing ground was the means by which the real system was
impacted by the perceived system. This TAC was set each year based on stock assessment
results. My model generated observed data each year that included annual yield, fishing effort,
and harvest age-compositions, and these differed from the true underlying values due to
observation error. Within the simulation frame-work an age-structured stock assessment model
was fit based on the observed data, either annually (Chapter 1) or sometimes less frequently
(Chapter 2). TACs were calculated based on assessment estimates with the intent that this
amount of yield would cause the target mortality of 65%. In the simulations I assumed that the
full TAC was utilized, although I allowed actual yield to vary above or below this each year
because of assumed implementation error.
Chapter 1: Evaluation of alternative assessment methods
In chapter 1, I evaluated the performance of three assessment methods with the current 65%
total mortality target under different intermixing scenarios. Deroba et al. (2012) and Molton et al.
(2012) previously used simulations to evaluate the status quo constant mortality rate target (65%
annual mortality), as well as alternative rates and control rules (e.g., fishing mortality being a
function of stock size), for lake whitefish. Deroba et al. (2012) used the existing assessment
approach and evaluated alternative harvest control rules and concluded that the status quo
mortality rate target was reasonable. Their analysis, however, assumed that the assumption of
unit stocks used in the assessments was correct. Molton et al. (2012) concluded that the 65%
mortality rate could put some lower productivity stocks at risk when population mixed, but
assumed that assessments would continue to be done assuming unit stocks surrounding each

3

spawning area. My work builds upon the previous studies by exploring both the influence of
mixing and how that mixing is accounted for in assessments.
The main goal for this chapter is to evaluate how the choice among three assessment
models, differing in how spatial structure was incorporated, would affect long-term fishery
performance metrics (yield, spawning stock biomass, et al.). The assessment models are all
variants of a statistical catch-at-age model (e.g., Fournier and Archibald 1982). The first
assessment model is the current separate assessment approach, where data collected in the
fishing grounds surrounding each spawning areas is taken as representing a distinct reproductive
population, or unit stock. I refer to the first alternative to this as a “pooled assessment”, with all
fish that might mix considered to be in one unit stock occupying a larger spatial area. As noted
above, to some extent this approach has already been implemented in northern Lake Huron,
where four assessment areas were merged into one. The second alternative approach, “metapopulation assessment”, explicitly accounts for intermixing. This assessment approach keeps
track of each population and how many of each population are present in each area during the
harvest season. For the “pooled assessment”, only a pooled TAC could be calculated directly
from the assessment and this needed to be allocated to fishing grounds. This was done according
to two rules: a constant allocation rule with the pooled TAC separated in proportion to
equilibrium yield for each of the four populations, and an annually varying allocation rule, with
pooled TAC separated in proportion to the annual area-specific catch per effort (CPE) observed
from the “true” system. All those assessment models were annually updated.
Scenarios consisting of different intermixing rates were examined to assess and compare the
performances of three assessment methods with current 65% total annual mortality control rule. For

one set of the scenarios, all populations mixed to the same extent, but a range of different mixing
rates were evaluated, from low to high. For the other set of scenarios, different mixing rate were
4

set for different populations based on the different assumption about how mixing and
productivity were related. The last scenario assumed no consistent relationship between
productivity and mixing. For this scenario each population had one of four distinct mixing rates.
There were 24 possible combinations of how the four mixing rates and productivities were
matched, and we equally weighted these possibilities.
I found that the “meta” population model could not provide useful assessment results
when mixing rates were high, in the absence of population-specific data, which are currently
unavailable as all assessment data represent the mixture present during the harvest season. My
results showed that the choice between pooled and separate population assessments depends on
mixing rates and productivity. While pooling can sometime provide advantages, in my
simulations it led to substantial population depletion when actual mixing was very high. I also
found that the separate assessment model could lead to extirpation or near extirpation of low
productivity populations with a low mixing rate, which suggests that the current harvest control
rule might be too aggressive for low productivity populations. That clearly reinforces a point
made by Molton et al. (2012), that the current 65% total mortality control rule may be not
conservative enough for the low productivity populations. Different TAC allocation rules for
pooled methods performed quite differently from one another. In particular a pooled method that
allocated yield among areas in proportion to equilibrium yield for the population spawning in
that area did poorly in terms of protecting low productivity populations when mixing was high.
This is likely because the population present in an area deviated from the assumed equilibrium
populations when mixing was high.
Chapter 2: How alternative assessment frequency influenced the fishery performance

5

In chapter 2, I explored how changing the assessment frequency to less often than annual
would affect long-term fishery performance metrics (yield, spawning stock biomass, etc.). I also
explored the influence of how annual yield targets were set for years between assessments done
less often than annually. These factors were applied using two of the alternative assessment
models described for Chapter 1: separate and pooled. For the pooled assessment, the TAC for
each area was based on the annual area-specific CPE observed from the “true” system.
I found that the influence of assessment frequency was modest compared to choices
about how to account for spatial structure in the assessment model. In addition, the frequency of
assessment had more impact on resulting levels of spawning biomass and yield when the
separate assessment method was used than when the pooled method was used. Lake whitefish
assessments are generally done with a one year lag between when data are collected and when
assessment results using those data are available for management, but some fisheries strive to
rapidly turn around assessments and avoid such a lag. I compared the performance of annual
assessments with and without the 1 year lag, and found that only when mixing rate were low for
all populations, did removal of the lag improve the performance of assessment. In the case
where some improvement was seen this was with respect to higher yield and lower annual
variation of yield across all areas, and lower risk of depletion of the low productivity population.
Overall conclusions and future directions
Our results clearly reinforce a point made by Molton et al. (2012), that the current 65%
total mortality control rule may be not conservative enough for the low productivity populations.
These results contrast with one overall conclusion of Deroba and Bence (2012), that the 65%
mortality rate produces acceptable results. This contrast appears to be due to the fact that Deroba
and Bence (2012) evaluated the probable performance of a management strategy applied to any

6

single unit stock, and not what might happen to a low productivity stock among a collection of
plausible populations ranging in productivity (Molton et al. 2012). As Molton et al. (2012)
argued, when mixing is ignored the LP population can be falsely assessed to have high
abundance and harvest. With substantial mixing, the harvest from the area surrounding the
spawning grounds of the LP population is likely to be composed largely of fish from other more
productive populations. This is clearly evident in our results, where yield for the area associated
with the low productivity population increased as mixing rates increased. We reiterate Molton et
al.'s (2012) point, that such mixing would also influence estimates of productivity, so that the
productivity of low productivity stocks could be overestimated. To the extent to which such
mixing influenced historical stock assessments, this in turn tends to make the lowest productivity
values we assumed even more plausible.
We found this risk of depleting low productivity populations is still present for the pooled
assessment method and can even be more severe for pooled methods when the mixing rate is
high. When the mixing rate for each population was moderate, the “pooled” assessment method
with TAC allocated by proportion of equilibrium yield was superior to the “separate” method.
Specifically, the “pooled (EY)” method provided more protection for the SSB of the low
productive population, with higher aggregate yield across the areas and the lowest annual
variation in yield. Initially it was surprisingly to us that when the mixing rate was high, this
“pooled” method lost its advantages. With high mixing, the “separate” method could provide the
lowest risk for the SSB of LP populations below B20%. In retrospect this deterioration of the
pooled (EY) with higher mixing makes sense. With higher mixing, the actual allocation of
biomass among the fishing areas increasingly deviates from being in proportion to equilibrium
yield for the populations.
7

In general, the differences in performance metrics due to assessment model (between
separate versus pooled) were larger than the differences due to assessment frequency and
approach to setting TACs during rotational periods. This finding should be useful to fishery
managers as they consider where the right place is to put their time and resources. While our
results are based on lake whitefish, this species has is not dissimilar to many harvested fishes,
and may in fact be more prone to rapid changes in abundance than many. Consequently, we
suspect that calls for annual assessments (e.g., Mace et al, 2001) may often be misplaced, and
that it may make more sense to work on developing a correct assessment structure.

8

REFERENCES

9

REFERENCES

Caroffino, D.C. and Lenart, S.J. 2012. Executive Summary in Caroffino, D.C., and Lenart, S.J., eds.
Technical Fisheries Committee Administrative Report 2012: Status of Lake Trout and Lake
Whitefish Populations in the 1836 Treaty-Ceded Waters of Lakes Superior, Huron and Michigan,
with recommended yield and effort levels for 2012.

Deroba, J.J., Bence, J. R., 2012. Evaluationg harvestcontrol rules for lake whitefish in the Great
Lakes: accounting for variable loge-history traits. Fish. Res. 94:210-223.
Ebener, M. P., J. R. Bence, K. Newman, and P. J. Schneeberger. 2005. Application of statistical
catch-at-age models to assess lake whitefish stocks in the 1836 treaty-ceded waters of
the upper Great Lakes. Pages 271-309 in L. C. Mohr, and T. F. Nalepa, editors.
Proceedings of a workshop on the dynamics of lake whitefish (Coregonus clupeaformis)
and the amphipod Diporeia spp. in the Great Lakes. Great Lakes Fishery Commission
Technical Report 66. Ann Arbor, Michigan.
Ebener, M. P., T. O Brenden, G. M. Wright, M. L. Jones, and M. Faisal. 2010. Spatial and
temporal distributions of lake whitefish spawning stocks in Northern lakes Michigan and
Huron, 2003-2008. Journal of Great Lakes Research 36:38-51.
Kell, L. T., Pilling, G. M., Kirkwood, G. P., Pastoors, M., Mesnil, B., Korsbrekke, K., Abaunza,
P. et al. 2005. An evaluation of the implicit management procedure used for some ICES
roundfish stocks. ICES Journal of Marine Science, 62: 750–759.
Mace P. M., N.W. Bartoo, A. B. Hollowed, P. Kleiber, R. D. Methot, S. A. Murawski, J. E.
Powers, and G. P., Scott. 2001. Marine Fisheries Stock Assessment Improvement Plan.
NOAA Technical Memorandum NMFS-F/SPO-56.
Molton, K. J., Brenden, T.O., Bence, J.R., 2012. Control rule performance for intermixing lake
whitefish populations on the 1836 Treaty waters of the Great Lakes : A simulation-based
evaluation. Journal of Great Lakes Research, 38: 686-698.
Punt, A. E. 2008. Refocusing Stock Assessment in support of policy evaluation. Pages 139-152
in K. Tsukamoto, T. Kawamura, T. Takeuchi, T. D. Beard, and M. J. Kaiser, editors.
Fisheries for Global Welfare and Environment, 5th World Fisheries Congress.
TERRAPUB,Tokyo.

10

CHAPTER 1
EVALUATING ALTERNATIVE ASSESSMENT APPROACHES FOR INTERMIXING
LAKE WHITEFISH POPULATIONS
Abstract
Recent evidence suggests that lake whitefish populations in lakes Huron and Michigan
intermix considerably during non-spawning periods, possibly from fish expanding foraging areas
to meet nutritional needs. Simulations have shown that ignoring spatial structure can lead to
unexpected risks of overexploitation, especially for low productivity populations. Currently,
management of lake whitefish in the 1836 Treaty ceded waters of the upper Great Lakes is based
on separate assessments and harvest calculations for nominally distinct unit stocks that are
assumed to not mix. In northern Lake Huron one of these assessment units was formed by
combining several previously used units, in response to evidence of intermixing. We simulated
four lake whitefish spawning populations with differing levels of productivity and mixing rates
during the fishing season, but which were assumed to be spatially segregated during spawning.
We evaluated how alternative assessment methods performed with respect to supporting a
thriving commercial fishery and ensuring long-term stock sustainability. Our first assessment
approach treated each population and the region surrounding its spawning grounds as a unit stock
(“separate populations”). The second approach lumped together the regions and populations into
a “pooled population”, so that all intermixed fish were treated as single unit stock occupying a
larger area. The third assessment approach incorporated actual mixing rates and treated several
populations as a “meta population”. Our results show that the choice between pooled and
separate population assessments depends on mixing rates and productivity. While pooling can
sometimes be advantageous, it can lead to substantial overfishing when actual mixing is low or
very high. The meta population assessment method can only work when rates of intermixing
11

between spawning populations were low. In order to improve this method, additional populationspecific data, such as genetic information allowing the catch in an area to be allocated to source
population, is needed.
Introduction
Stock-based assessment of exploited fish populations has long been used to estimate
demographic rates (e.g., age-specific mortality) and population sizes, and these in turn have been
used to establish appropriate levels of harvest. This management approach is typically
implemented inside of each spatial management unit, which is commonly assumed to be
composed of a single, rather than multiple spawning populations. Ignoring complex-population
structure in management could lead to poor estimation of abundance and unintended depletion of
local subunits, with unknown ecological consequence (Stephenson 1999, Hutchings 1996, 2000,
Frank et al. 2000, Molton et al. 2012). When mixtures of multiple spawning populations occur
on fishing grounds, a common response from assessment groups has been to modify boundaries
of management units such as lumping areas among which substantial movement is known to
occur (Powers et al. 2004, Kell et al. 2009, Ying et al. 2011). More complex assessment
approaches that allow for movement among the areas could be an alternative, but this may
require more information.
Management of lake whitefish in the 1836 Treaty-ceded waters of the upper Great Lakes
has been based on separate SCAA assessments and calculation of harvests for nominally distinct
unit stocks that are assumed to not mix (Ebener et al. 2005; Caroffino et al. 2012). Historically,
managing lake whitefish as distinct management units began in the 1970s in order to protect
distinct naturally reproducing populations. Management unit boundaries were designed to

12

encompass the spatial distribution of either individual stocks or a fishery that exploited a stock
(Ebener et al. 2010).
Recent evidence, however, has shown that many lake whitefish populations in the
northern parts of lakes Huron and Michigan are intermixing considerably during non-spawning
periods (Ebener et al. 2010), possibly as a result of fish expanding their foraging areas to meet
nutritional needs in the face of environmental changes. Recent decline in benthic prey of lake
whitefish -Diporeia, and increasing abundance of invasive dreissenid mussel (Nalepa et al., 1998,
2007, 2009a) may both influence the foraging behavior of lake whitefish populations (Nelepa et
al. 2009b, Porthoven and Madenjian, 2008). Despite this observed increase in mixing, lake
whitefish still exhibited strong spawning site fidelity (Ebener et al. 2010), which suggested that
despite widespread mixing during periods of exploitation, strong genetic structuring of lake
whitefish stocks within the Great Lakes should still exist. This assumption has been confirmed
by studies of stock genetic diversity (VanDeHey et al. 2009; Stott et al. 2010).
Despite the widespread mixing now known to occur, many lake whitefish stocks in the
vicinity of recognized spawning areas continue to be treated as discrete independent units for
management purposes. For example, the statistical catch-at-age (SCAA) assessment models
used to estimate year- and age-specific abundances and mortality rates for lake whitefish of lakes
Huron, Michigan, and Superior do not allow for the possibility of fish moving between
assessment areas. Stock assessment scientists have responded to information about the
movement of lake whitefish in northern Lake Huron, by combining four formerly distinct
assessment areas into one larger area (Caroffino et al. 2011). The assumption, however, remains
that fish within this newly defined area do not move to other areas. This approach also assumes
that fish in the new larger area are completely mixed. The mismatch between how fish actually

13

move, and what is assumed in the assessments undoubtedly affects the SCAA estimates of
mortality and abundance. Responses to knowledge about movement among spawning
populations has so far been ad hoc for lake whitefish. Fishery managers in other systems have
similarly lumped assessment areas when confronted with information about movement among
areas. Our research aims to compare fishery management and assessment estimation
performances based on the current “separate assessment” approach with two alternatives that
attempt to take intermixing into consideration. They are all variants of the SCAA model. We
refer to the first alternative as a “pooled assessment”, with all fish that might mix considered to
be in one unit stock occupying a larger spatial area. As noted above, to some extent this
approach has already been implemented in northern Lake Huron, where four assessment areas
were merged into one. The second alternative approach, “meta-population assessment”,
explicitly accounts for intermixing.
The current study is a simulation-based evaluation of the above three assessment
approaches. Rather than simply looking at how well the estimation methods work at estimating
stock size and mortality, we also consider resulting fishery performance metrics (e.g., yield,
spawning biomass). Based on the information about lake whitefish in 1836 Treaty-ceded waters,
we simulated four lake whitefish spawning populations that have differing levels of productivity
and varying degrees of intermixing during the fishing season, but are spatially segregated during
spawning. We then evaluated how assessment methods performed with respect to the trade-off
between whitefish commercial fishery metrics and long-term population sustainability. Deroba et
al. (2012) and Molton et al. (2012) previously used simulations to evaluate the status quo
constant mortality rate policy (65% annual mortality) for lake whitefish. Deroba et al. (2012)
concluded that the status quo mortality rate was reasonable, but they assumed that the actual fish

14

population dynamics were consistent with the unit stock dynamics used in the current
assessments. Molton et al. (2012) concluded that the 65% mortality rate could put some lower
productivity stocks at risk when populations mixed, but their analysis assumed that assessments
would continue to be based on the existing unit stock assessments for applied to fishing grounds
surrounding spawning areas. Our work builds upon the previous studies by exploring both the
influence of mixing and how that mixing is accounted for in assessments. Our approach to
evaluating the alternative assessment approaches used management strategy evaluation (MSE)
methods (Kell et al. 2005a, Punt 2008). Most MSE evaluations have compared different control
rules (e.g., constant fishing rate or constant escapement) or different parameters for the rules, but
keep the assessment constant (Kell et al. 2005b, Kell et al. 2006). Our study illustrates using
MSE to compare different assessment approaches.
Methods
The simulation framework used to evaluate assessment approaches was based on
management strategy evaluation (MSE) methods (Kell et al. 2005a, Punt 2008) (Figure 1.1). This
framework modeled the “true” system and “perceived” system (data collection, stock assessment,
and harvest control rule application). The “true” system was represented as “real” stock and
fishery dynamics, from which the simulated data were sampled. These data were then used in an
assessment procedure that establishes the status quo for resources. The three assessment methods
were fitted separately and the current treaty-water harvest control rule was applied to each
specific assessment result. The target yield, which we refer to as total allowable catch (TAC),
was then fed back into the corresponding "real system" (in our simulations) thereby influencing
actual yield and the fishery performance in the next year. Performance statistics based upon the
stock and fishery dynamics model were eventually used to evaluate the robustness of each

15

assessment method. The flexibility of this framework allowed us to incorporate a series of
uncertainties, including process, sampling, estimation, and model error, as described below.
The “true” system
The basic structure of our model for the "true" system was based on the approach
developed by Molton et al. (2012). We used an age- structured forward-projection model,
consisting of four hypothetical populations with a simulation length of 100 years. Only the final
25 years were summarized to evaluate performance. Our intent here was to evaluate the longterm performance of the alternative approaches, independent of the starting conditions. Recruits
were added as the youngest age each year based on the current stock size for the population and a
stock recruitment function. During the fishing season fish from each population mixed with fish
from other areas in four fishing grounds, which each surrounded the four spawning areas (Figure
1.2), but returned to the spawning area for an instantaneous spawning period, based on the
known natal philopatry of the species. During the fishing season fish died due to natural
mortality and fishing mortality. Fishing mortality was partially determined based on perceived
stock size based on a stock assessment that was done each year during the simulations, in an
attempt to achieve the TAC.
These populations were assumed to have differing levels of "productivity". Differences in
productivity among the four spawning populations were incorporated via adjustment of the
recruitment function coefficients (Table 1). We used a stochastic Ricker recruitment model (Eq.
(T.2.1)) because of strong evidence for over-compensation in lake whitefish populations (Healey
1978; Henderson et al. 1983; Kratzer 2006). The stochastic errors were multiplicative and
lognormal. Given information on life history (maturity and weight at age schedule) the Ricker
function can be parameterized in terms of steepness and the unfished spawning stock size. We

16

equated "productivity" with steepness (NOAA Pacific Islands Fisheries Center, 2011), and chose
four steepnesses for our simulated populations that were plausible for lake whitefish and
produced meaningful differences in equilibrium yield. We set unfished equilibrium stock sizes to
be equal, so that differences between the populations were due only to our assumed productivity
differences. The steepness and equilibrium yield parameterization was then converted to the
standard Ricker parameterization (Table 1). Calculations of equilibrium yield and spawning
stock sizes to define the productivity of the populations in the simulations assumed unit stocks
(no movement) and followed methods outlined by Quinn and Deriso (chapter 6 page 239, 1999).
The values of life-history parameters were based on the most recent 1836 Treaty-ceded water
assessment conducted by the Modeling Subcommittee (MSC) of the Technical Fisheries
Committee (TFC) and our claim of plausible steepnesses is based on review of the last five years
annual assessment of stock status [ftp://glpd.fw.msu.edu/MSCFTP/Assessment_models/]. The
unfished spawning biomass was also based on assessment results, but this only sets the scale of
results and otherwise does not influence the outcomes of our work. Each of the four simulated
lake whitefish spawning populations was assigned one of the four levels of productivity so that
there was a LP, MLP, MHP and HP population for each simulation.
Fish from a spawning population either remain in their natal area during the nonspawning season or move to one of the other three areas (Figure 1.2). Movement rate, θij (i ≠ j),
is the proportion of fish belonging to spawning population i (i.e., they spawned in area i) that
move to and live in area j during the non-spawning season. We refer to θii as the stay rate, which
is the proportion of fish belonging to spawning population i that stay in area i during the nonspawning season. The movement rates were calculated based on the stay rates, which was set
based on results from ongoing and published studies (Ebener et al.2010, Stott et al. 2010, Stott et
17

al. 2012). We assumed that a higher stay rate indicated a high quality habit, and that a high
proportion of whitefish would tend to move to that area. The movement rate θij (i ≠ j) is:

𝜃ij = (1 − 𝜃 𝑖𝑖 )

𝜃 𝑗𝑗

∑ 𝑘≠𝑖 𝜃 𝑘𝑘

(1)

where (1 − 𝜃 𝑖𝑖 ) is the total proportion of fish from population i that live in other areas
during the non-spawning season, and

𝜃 𝑗𝑗

∑ 𝑘≠𝑖 𝜃 𝑘𝑘

is the proportion of those fish residing in each

destination area j. This approach of specifying movement rates diverges from the approach of
Molton et al. (2012), who assumed that fish that did not stay in their natal area moved to other
areas in equal proportions.

𝑁 𝑖,𝑦+1,𝑎+1 = 𝑁 𝑖,𝑦,𝑎 ∑ 𝑗 𝜃 𝑖𝑗 exp(−𝑀 − 𝐹𝑗,𝑦,𝑎 )

We projected abundance-at-age after recruitment using an exponential mortality model:
(2)

where Ni,y,a is equal to the number of fish from spawning population i of age a in year y;
M is the natural mortality rate; and Fj,y,a is the year- and age-specific instantaneous fishing
mortality rate of fish occurring in area j during harvest season. This instantaneous fishing

𝐹𝑗,𝑦,𝑎 = 𝑠 𝑎 𝑓𝑗,𝑦

mortality rate was calculated as:
(3)

where sα is the age specific selectivity (equal for all four stocks), and fj,y is the fully
selected fishing mortality occurring in area j in year y. Thus the fishing mortality rate
experienced by a population was a weighted sum of the fishing rates occurring in the different
areas, with weights set by the θ. The fully selected fishing mortality rate for each area was

18

calculated using a Newton-Raphson algorithm so that the true yield for each area was produced
using the Baranov’s catch equation (Equation T.1.2.7) and assumed harvest weight at age. The
true yield was set equal to the Total Allowable Catch (TAC) (i.e., target yield) multiplied by a
lognormal implementation error (Equation T.1.2.8). The TAC was determined via the stock
assessment procedure described in the perceived system section.
Constant values of natural mortality, female proportion, and catchability were used.
Selectivity-, length-, weight-at-age, and annual spawning stock biomass (SSB) were determined
by deterministic functions. Selectivity was set as 0 for age-2 and younger whitefish because they
are rarely harvested in treaty waters. Selectivity for other age classes was simulated by a gamma
probability density function (Equation T.1.2.6) scaled by setting the fully selected age class (age
10) equal to 1.0; length-at-age was assumed to follow a Von Bertalanffy growth model (Equation
T.1.2.3); weight-at-age was determined by a power function of length (Equation T.1.2.4); and the
SSB (Equation T.1.2.2) was calculated as a function of abundance-at-age, maturity-at-age
(Equation T.1.2.5), and weight-at-age. The four populations shared the same selectivity-, length-,
and weight-at-age patterns.
The initial state of for each simulation in year 1was based on equilibrium recruitment and
target mortality rates and calculated based on deterministic models with no mixing. The actual
harvest policy and management process requires a twenty year time-series of data, which was not
available during the initial 20 year period of each simulation. Within this "burn-in" period,
population abundance at age was assumed to be known exactly before applying the harvest
control rule and thus the assessment model step was skipped during the burn-in period of
simulations. The intent here is merely to move the system closer to steady-state conditions
during this period. Stochastic recruitment errors were still included during this period.

19

The “perceived” system
In the perceived system (Figure 1.2), the management procedure for the treaty water
whitefish was duplicated, including data collection, stock assessment, and application of the
harvest control rule. When generating the data we assumed that total catch was observed with
error, and that observed age compositions also differed from actual age compositions due to
sampling error. Observed proportions-at-age in the simulated data arose from a multinomial
distribution with probabilities equal to the true age proportions of the harvest sample and an
effective sample size of 200 for “separate” and “meta” approaches or of 800 for the “pooled”

𝐸𝑗,𝑦 =

𝐹 𝑗,𝑦

𝑒𝑥𝑝(𝜇 𝑗,𝑦 − 0.5𝜎 2 𝐹 )

method. Observed fishing effort was calculated as:
𝑞

𝜇 𝑗,𝑦 ~ 𝑁(0, 𝜎 2 𝐹 )

(4)

𝜎2 𝐹 = 4 𝜎2 𝑐

where Fj,y is the fully-selected fishing mortality rate for area j and year y; q is the
-6

catchability coefficient of 1.50×10e ; and μj,y is the an normally distributed random variable
2

with expectation of 0 and variance of σ F (Equation T.1.2.10), which was assumed to equal to
2

0.04 (four times of σ C).
The above data was collected annually and used as the input for stock assessments. The
stock assessments were assumed to have knowledge of the true natural mortality rate and lifehistory parameters.
In the stock assessment process, three different assessment models were compared:
separate population, meta-population, and pooled population assessment models. All models
20

were variants of the SCAA model, which involves fitting a population dynamics model to
observed data to estimate the parameters used to summarize stock status and determine TAC for
each simulated population of the assessment year.
The first approach, the “separate population assessment”, assumed no movement among
areas. We applied the model to data from each fishing ground separately. An age-specific fishing
mortality was predicted by the same equations used in the population dynamics model. This is
the most commonly used approach for assessing lake whitefish in treaty waters.
The second approach, the “meta-population assessment”, assumed that the actual rates of
mixing were known. One combined assessment model for all four stocks was developed because
movement was included in the process of tracking estimated abundance-at-age for each
population and predicted catch-age-age for each area during the fishing season. Compared with
the first approach, stay and movement rates were an additional input for this assessment model.
The objective function was the summation of the negative log-likelihood components over the
four areas.
The third approach, the “pooled population assessment”, treated all lake whitefish across
the areas modeled as part of one well mixed population. This led to an exponential model for the
pooled population, rather than for each stock (Equation T.1.2.1).
For all three assessment models, recruitment (area specific or pooled), the initial
abundance-at-age for the first year, selectivity-at-age, and fishing mortality were estimated as
free parameters during model fitting. Best fit parameters were estimated via iterative methods so
as to minimize the negative penalized log-likelihood (i.e., the objective function). We assumed
lognormal distributions of errors for annual fishery catch, a lognormal prior component
associated with the fishing mortality-effort relationship, and the age compositions of the fishery

21

were assumed to follow multinomial distributions. The objective function was the sum of above
three negative log-likelihood or log prior components (T.2.9., T.2.10, T.2.11). Iterations
proceeded until the maximum absolute value of the gradient (derivatives of objective function
with respect to parameters) was below a specified criterion (0.001), although sometimes
iterations stopped before reaching the criterion either because no further progress was being
made in reducing the objective function or a maximum number of iterations (1000) were
completed. Fits that ended without reaching the gradient criterion were classified as failing
convergence. A second test of whether the solution after iterations was a minimum (i.e., true
maximum for the penalized likelihood) was whether the Hessian was negative definite. If this
was not the case we termed this a Hessian problem. A record was kept for each assessment on
whether there was convergence failure or a Hessian problem. The negative log likelihood
component for the age composition of the fishery harvest was weighted by effective sample size
(800 for the pooled method and 200 for the separate and the “meta” methods). The 20 years of
data prior to any given assessment year were included in the assessment model.
We mimicked the actual timing of assessments and setting of harvest guidelines based on
them in lake whitefish fisheries. These assessments are done in a given year, based on data
through the previous year, and are used to establish harvest targets for the next year. The stock
assessment thus produces abundance-at-age for the start of the year when the assessment is done.
Projections through the assessment year were based on an exponential population model, in
which total mortality rate was assumed to be the mean of the last three years’ values and
recruitment were assumed to be the mean of the last ten years’ values. For the year for which the
TAC was set, the same level of recruitment was assumed but fishing mortality was adjusted so
the target mortality rate was achieved (assuming the assessment point estimates were correct).

22

The current harvest control rule and policy parameter for lake whitefish in treaty waters, which
equates to a constant fishing mortality rate policy, were used in the simulation. The control rule
sets the maximum total annual mortality rate experienced by any age of fish at 65%. We used the
same methodology to determine the TAC as the one applied by the MSC to determine the target
maximum yield. This TAC was calculated from assessment-based estimates of abundance-at-age
at the start of the year the TAC applies to and target fishing mortality-at-age using the Baranov
catch equation. The age-specific fishing mortality rates were based on the estimated selectivityat-age from assessment multiplied by the target fishing mortality rates, which was the target
instantaneous total mortality rate minus the natural mortality rate as assumed in the assessment
model. For the “separate” and “meta” assessment methods, a TAC for each area was calculated
separately because the assessment results were area-specific for those methods. For the pooled
population assessment, only a pooled TAC could be calculated and this was allocated to the areas
according to two rules: a constant allocation rule and an annually varying allocation rule. The
first allocated the TAC in proportion to equilibrium yield for the population that spawned within
a given area. The assumption was that we had pre-assessment knowledge about how productive
each population was, and the allocation remained constant over time. The second allocation rule
was based on the annual area-specific CPE observed from the “true” system. The higher the CPE,
the more TAC was allocated to each area. To reduce annual variation of yield, we used the
average CPE over the last three years of available data (preliminary simulations suggested this
averaging outperformed alternative averaging periods).
Experimental design
For four hypothetical populations with differing productivity (Table 3), we evaluated how
assessment methods performed under different intermixing scenarios. Scenarios 1 to 4

23

(“SR=0.9”, “SR=0.75”, “SR=0.5”, “SR=0.25”) represented the cases where all areas shared the
same stay rate ordered from high to low (so the case of less mixing is first). We referred to
scenarios 1 to 4 as “same mixing” scenarios. Scenario 5 (i.e., “po-cor”) assumed that
productivity and stay rate for each area were positively correlated (fish from higher productivity
populations tended to stay in natal areas). Scenario 6 (i.e., “ne-cor”) assumed a negative
correlation between productivity and stay rate for each population. Scenario 7 (i.e.,
“unpredictable”) assumed no consistent relationship between productivity and stay rate. For this
scenario each population had one of four distinct stay rates. There were 24 possible combinations
of how the four stay rates and productivities were matched, and we equally weighted these
possibilities. In order to conduct approximately 1000 total simulation for this scenario, 42
simulations were conducted for each combination.
Within each mixing scenario, four assessment and management methods were examined:
1. The separate population model (“separate”); 2. the pooled model with TAC allocated by CPE
(“pooled (CPE)”); 3. the pooled model with TAC allocated by a constant ratio of equilibrium
yields (“pooled (EY)”); and 4. the meta-population model (“meta”).
Performance statistics
For each method under Scenarios 1 to 6, a 100-year simulation was performed 1000
times by using AD Model Builder (Fournier et al., 2012). For scenario 7, we conducted 1008
simulations for each method. Performance statistics were generated from the “true” system,
which was used to describe the real status of stock and fishery. The statistics allowed us to
compare the performance of alternative assessment and management methods under different
mixing scenarios with respect to the management objectives (i.e., long-term sustainability, high
and stable yield, and the trade-off between them) and the accuracy of SSB estimation. Given

24

that most performance statistics appeared to approach a long-term mean by year 75, we based
our evaluation of performance on the last 25 years of the simulations. Under different scenarios,
the performance statistics were:
1.

Average yield over the last 25 years for each area.

2.

Average SSB over the last 25 years for each population.

3.

Inter annual variation of yield over the last 25 years for each area.

4.

Proportion of years spawning stock biomass (SSB) being less than 20% of the unfished

SSB level
5.

Median relative error (MRE) and median absolute relative error (MRE) of estimating

SSB for each assessment method over the last 25 years.
Results
The “meta” assessment model is only included in model comparisons under Scenarios 1
and 2, when the stay rate for each area was high or medium-high. For other assessment models,
the convergence rates for the optimization were all above 99.95% among all scenarios (results
not shown), while for the “meta” assessment model, the convergence rate became low once
higher mixing occurred (Table 4). This indicates that the assessment model cannot always
minimize the objective function. In Scenario 4, the well-mixed case in which all areas shared the
same population composition, all simulations ran into problems calculating the Hessian for the
meta population assessment model. All of these results are likely a consequence of populationspecific data not being available. The area specific data in addition to the mixing rate were not
enough for the model to distinguish which population was actually producing recruits, especially
in Scenario 4 where all areas have the same population composition at the start of each year
because of complete mixing.

25

The performance statistics of assessment methods differed depending on the mixing rate
of spawning populations. For each assessment model under each mixing scenario, the expected
average annual SSB and yield (Figure 1.3a and 1.3b, respectively) over the last 25 years are
summarized by modified boxplots to represent its long-term performance. The relative
performance of “separate” and “pooled (CPE)” models was similar across all “same mixing”
scenarios (Scenarios 1 to 4). The major difference was the SSB of the LP population. With
increasing mixing rate, the “pooled (CPE)” method was more likely to drive the SSB of the LP
population below B20%, while the “separate” method tended to allow SSB to be above B20%.
This same trend was also observed in the “ne-cor” scenario. However, the opposite happened in
the “po-cor” scenario, in which “pooled (CPE)” was superior to the “separate” and “pooled (EY)”
methods, in that it had both the greatest SSB and high yield.
The first row in Figure 1.3 (SR=0.9) shows that the “pooled (CPE)” method
outperformed the others with respect to greater SSB of LP population and higher yield among all
areas, followed by the “separate” method. The “meta” method had the highest risk of overexploitation of the LP population. The “pooled (EY)” method surprisingly provided the greatest
SSB for the LP population across all populations, and the SSB of the other three populations
were much lower than the results obtained by the other three assessment methods, especially for
the MLP population.
In the second row in Figure 1.3 (SR=0.75), median SSB fell to less than B20% only for
the “meta” method, without significant yield benefit. In contrast, the “pooled (EY)” method
outperformed the others by maintaining high levels of biomass for the LP population and highest
yields among all areas. Even losing some yield in the LP area (Figure 1.2), more yields was
attained in the other three areas by this method, with acceptable levels of biomass. The third row
26

(SR=0. 5) illustrates similar results to those from Scenario 2. In Scenario 4 (SR=0. 25), however,
the “pooled (EY)” method showed high risk of median SSB falling to less than B20% for the LP
population, with yield from the LP area being negligible. This is not unexpected given that,
during the fishing season under the high mixing scenario, only 25% of the LP population stayed
in the LP area while most fish moved out and experienced high exploitation in the other areas.
Except for the “pooled (CPE)” method, in the “ne-cor” scenario (the fifth row of Figure
1.3) there were high risks of median SSB of the LP populations being below B20%. Especially
for the “pooled (EY)” method, almost all of our simulations for the SSB of the LP population
were below B20%, and the SSB of the MLP population were also substantially lower than for the
other two methods. The “pooled (CPE)” were superior to other methods, with the greatest SSB
of LP population and high yield across all areas. In the “po-cor” scenario (scenario 6), the
“separate” method outperformed the others by providing higher yield and greatest SSB across all
areas. In the unpredictable scenario (the last row of Figure 1.3), the “separate” and the “pooled
(CPE)” performed equally and better than the “pooled (EY)”. The median SSB and yield varied
in a larger range compared with the other scenarios, likely because this scenario includes all the
24 combinations of mixing rate and productivity.
The inter-annual variation (IAV) of yield ranged from 10 to 25% across most scenarios.
The “pooled (EY)” method provided the least IAV of yield under all mixing scenarios except the
unpredictable mixing relationship to productivity scenario (Figure 1.4). Under all “same mixing”
scenarios (scenarios 1 to 4), for the “separate” and “pooled (EY)” methods, the IAVs of yield
across all simulations decreased with increases in mixing rate. Not surprisingly, for the two
“pooled” methods, all four areas shared almost the same level of IAV of yield. For the “Separate”

27

method at low (SR=0.9) and mid low (SR=0.75) mixing scenarios, larger IAV of yield was
observed in the area with higher productivity.
For the “Separate”, “Pooled (EY)”, and “Meta” methods, only the LP populations had a
substantial risk of being below B20% (Fig. 5) For the “pooled (EY)” methods under the low
mixing (SR=0.9), correlated and random scenarios, there is some risk of being below B20% for
MLP as well as LP populations. For the “separate” method across all the same mixing scenarios
(Scenarios 1 to 4), there was an inverse relationship between the risk of SSB being lower than
B20% for the LP population and the mixing rates. For the “pooled (CPE)” method, the risk was
similar across all same mixing scenarios. The “pooled (EY)” method provided substantially
lower risk under scenarios 2 and 3, compared with other methods.
We used median relative error (MRE) to evaluate median bias, and median absolute
relative error (MARE) to characterize the magnitude of errors for SSB estimation over the last 25
years. The “pooled (CPE)” method was the most median-unbiased method, with median value of
MRE close to zero. The “separate” method had negative median-bias in estimating SSB
(underestimated the real total SSB) under all scenarios; while for the “pooled (EY)”, the negative
bias decreased and the estimator approached being unbiased as stay rate went from high to
medium high, and then increased to positive bias with higher mixing. The meta method was
negatively median-biased for SSB for those scenarios it was feasible. Under unpredictable
productivity versus mixing scenarios, the two pooled method both were essentially medianunbiased estimators of SSB.
The “separate” method had the lowest MARE, followed by “pooled (CPE)”, “meta”, and
“pooled (EY)”. For the “pooled (CPE)”, “meta”, and “pooled (EY)” methods, the MARE of SSB

28

decreased as mixing rate increased. Under the correlated and random scenarios, the MAREs for
“pooled (EY)” method were at least two times larger than those for the other two assessment
methods.

Discussion
Our goal was to evaluate different assessment methods for use with intermixing lake
whitefish populations under the current constant mortality control rule. The “separate”
assessment method, based on a SCAA model, has been used for the assessment of lake whitefish
in 1836 Treaty-Ceded water since 1998. The “pooled” method, also based on an SCAA model, is
essentially the response that was taken by the Technical Fisheries Committee and Modeling Sub
Committee in northern Lake Huron for lake whitefish in response to information about high
levels of mixing. Our study was not attempting to make tactical advice for specific lake whitefish
populations because actual mixing rates and productivity for each population are unknown in the
real world. Instead, we used the lake whitefish case as an example to address the more general
problem about how to deal with intermixing fish populations, and to evaluate whether there
might be some overriding messages applicable to whitefish or other species regardless of the
exact mixing and productivity values. Previously for lake whitefish, Jacobson and Taylor (1985)
and Deroba and Bence (2012) evaluated different harvest control rules based on simulation
studies without considering intermixing and alternative assessment methods. Later, Molton et al.
(2012) found that with mixing low productivity populations had high risk to be overfished under
the current constant mortality control rule, although they only applied the “separate” assessment
method. They found that mixing had little influence on either aggregate yield or the population
specific status in terms of SSB, but did have a large influence on area specific yield, with higher

29

yields in areas near low productivity populations when mixing was high. The “true” system in
the management strategy evaluation process in our study was based on the approach developed
by Molton et al (2012). We extended the work of Molton et al. by again considering the
performance of the current 65% mortality target for lake whitefish, but now considering three
alternative assessment approaches, rather than just the single separate approach they used. We
also refined the overall MSE approach (e.g., our assumption that the movement rates into an area
would be related to the tendency of fish from that areas' spawning population to remain in that
area).
High levels of intermixing tended to make sub populations effectively a pooled one,
while low intermixing tended to make them close to unit stocks. Our study illustrated some
results matching our prior expectations based on this and some surprises. For the scenarios with
low mixing rate (SR=0.9), consistent with the results from previous study for other species
(Crurtis et al. 2008, Kell et al. 2009, Ying et al. 2011), the “separate” assessment method
performed better than the “pooled” assessment method, when for the latter TAC allocated by
constant proportion based on the equilibrium yields. But the “pooled” assessment method with
TAC allocated by varying proportion based on area specific CPE performed even better than the
“separate” method, with regard to greater SSB for the low productivity area. This result was
surprising and we do not fully understand it, although the explanation likely rests with depletion
resulting from sequences of correlated assessment errors and inappropriate TACs, which may be
avoided with the pooled assessment and use of CPE for allocation, due in part to its conservative
bias.
Our observation that low productivity populations are at risk of depletion is consistent
with Molton et al (2012)’s results, although counter to their results, we found the risk of

30

depletion was actually higher for the lowest mixing rates for the separate assessment approach.
This difference may stem from the specific productivity levels we chose and our equating
productivity with steepness, while keeping unfished stock sizes the same across populations, a
somewhat different approach than that used by Molton et al. (2012). Perhaps more importantly,
we found this risk of depleting low productivity populations is still present for the pooled
assessment method and can even be more severe for pooled methods when the mixing rate is
high. When the mixing rate for each population was moderate, the “pooled” assessment method
with TAC allocated by proportion of equilibrium yield was superior to the “separate” method.
Specifically, the “pooled (EY)” method provided more protection for the SSB of the low
productive population, with higher aggregate yield across the areas and the lowest annual
variation in yield. Initially it was surprisingly to us that when the mixing rate was high, this
“pooled” method lost its advantages. With high mixing, the “separate” method could provide the
lowest risk for the SSB of LP populations below B20%. In retrospect this deterioration of the
pooled (EY) with higher mixing makes sense. With higher mixing, the actual allocation of
biomass among the fishing areas increasingly deviates from being in proportion to equilibrium
yield for the populations.
Our results clearly reinforce a point made by Molton et al. (2012), that the current 65%
total mortality control rule may be not conservative enough for the low productivity populations.
These results contrast with one overall conclusion of Deroba and Bence (2012), that the 65%
mortality rate produces acceptable results. This contrast appears to be due to the fact that Deroba
and Bence (2012) evaluated the probable performance of a management strategy applied to any
single unit stock, and not what might happen to a low productivity stock among a collection of
plausible populations ranging in productivity (Molton et al. 2012). As Molton et al. (2012)
31

argued, when mixing is ignored the LP population can be falsely assessed to have high
abundance and harvest. With substantial mixing, the harvest from the area surrounding the
spawning grounds of the LP population is likely to be composed largely of fish from other more
productive populations. This is clearly evident in our results, where yield for the area associated
with the low productivity population increased as mixing rates increased. We reiterate Molton et
al.'s (2012) point, that such mixing would also influence estimates of productivity, so that the
productivity of low productivity stocks could be overestimated. To the extent to which such
mixing influenced historical stock assessments, this in turn tends to make the lowest productivity
values we assumed even more plausible.
Differences in the bias in estimating stock status may be one of the explanations for the
relative performances of different assessment methods. The pooled methods regarded the four
populations to be one pooled population and this misspecification led to substantial negative bias
when mixing was low. The assessment bias for the separate model was negative across all
mixing scenarios, which could help to explain the conservative performance of the separate
assessment models under medium-high mixing (SR=0.9) and positive correlation (pocor)
scenarios. Kell et al. (2009) reported that, overall, pooling stocks together can provide a less
biased estimation of total spawning stocks than a separate assessment, which corresponds to our
results when mixing was moderate to high and for the unpredictable scenarios. We found that
without knowing the relationship between mixing rate and productivity, pooling stocks together
can provide an essentially unbiased estimator of SSB, while the separate method led to a
significant negative bias. Thus the advantages sometimes seen for the separate approach may
stem from it being accidentally more conservative than intended. This argues for future research
comparing a range of target mortality rates, to see if these occasional advantages could be more

32

than made up by using the less biased pooled method and a lower target mortality rate. Unlike
when allocating by CPE, positive bias arose as the mixing rate became quite high for the pooled
method that allocated based on equilibrium yield. We do not fully understand what led to this
result, but in this case fishing mortality is varying substantially among areas, and this is being
ignored in the assessment. This bias too may in part explain the higher depletion for the pooled
population when allocating this way in the face of high mixing.
Accurately quantifying mixing rate remains important for managing mixing lake
whitefish populations. Even if we can identify strategies that are robust to mixing rates, it is clear
that appropriate mortality rates depend upon the productivity of the populations. Without
information on the population source of fish caught in different areas, population productivity
levels cannot be refined nor can it be assessed if they are changing. The current critical task for
managing mixing populations, such as the pooled management unit for northern Lake Huron, is
to collecting data to identify the intermixing among the four spawning populations and how this
might be associated with population productivity. If the mixing rate were high, a low
productivity population has high risk to be overfished and there could be adverse ecological
consequences of loss of spawning components in terms of stock sub-structure and in terms of
preserving specific genes or genetic variations (Stephenson 1999).
We also considered a modification of the current SCAA model that used assumed known
mixing rates. Unfortunately this method did not produce useable estimates except when mixing
rates were relatively low. This emphasizes the need for collecting population-specific data, such
as genetic information that would allow separating catch from each area by its population source
(Porch, 1997). These problems arise because even with known mixing rates the SCAA still has
problems identifying which population was producing the recruits in a given year. Power and

33

Porch (2004) and Kell (2009) both emphasized that misinterpretations of mixing rate could lead
to even higher bias than just ignoring mixing. We believe further investigation is warranted, but
at this point it does seem clear that at least additional population specific data is required in
addition to prior information on mixing rates to apply the meta approach.
Our simulation framework for each assessment model can be considered as a variant of
management strategy evaluation (Kirkwood, 1992, 1996). We incorporated multiple assessment
models and applied the current harvest control rule with assessment and implementation error.
But like Irwin et al. (2008) said, “not all uncertainty can be captured by any model and
unexpected changes could occur”. Like other simulation studies (Irwin et al. 2008, Deroba and
Bence 2012), we made a number of simplifying assumptions and choices, such as mixing pattern,
different levels of mixing rate and productivity of each population and which levels of
productivity were most representative. Likewise, we ignored the temporal variation in
parameters such as catchability and natural mortality. These assumptions and choices may
influence the final results. Our application of the “pooled (EY)” method assumed that the ratio of
equilibrium yields between populations is known without uncertainty, and similar assumptions
are commonly used in other studies (Deroba and Bence 2012, Irwin et al. 2008, Punt et al. 2008).
In general, we based our simplifications on previous studies suggesting that qualitative results
would be robust to the simplifications, or as an initial evaluation to see if an approach would
even be effective at the limit of perfect information. While the assumptions and simplifications
deserve scrutiny, we believe that the necessary simplifications we made are of secondary
importance, in comparison with the large uncertainties regarding productivity and mixing.

34

REFERENCES

35

REFERENCES

Caroffino, D.C. and Lenart, S.J. 2011. Executive Summary in Caroffino, D.C., and Lenart, S.J.,
eds. Technical Fisheries Committee Administrative Report 2011: Status of Lake Trout
and Lake Whitefish Populations in the 1836 Treaty-Ceded Waters of Lakes Superior,
Huron and Michigan, with recommended yield and effort levels for 2011.
Caroffino, D.C. and Lenart, S.J. 2012. Executive Summary in Caroffino, D.C., and Lenart, S.J.,
eds. Technical Fisheries Committee Administrative Report 2012: Status of Lake Trout
and Lake Whitefish Populations in the 1836 Treaty-Ceded Waters of Lakes Superior,
Huron and Michigan, with recommended yield and effort levels for 2012.
Curtis, J.M.R., and Naujokaitis-Lewis, I. 2008. Sensitivity of population viability to spatial and
nonspatial parameters using GRIP. Ecol. Appl. 18(4): 1002–1013. doi:10.1890/071306.1. PMID:18536258.
Deroba, J.J., Bence, J. R., 2012. Evaluationg harvestcontrol rules for lake whitefish in the Great
Lakes: accounting for variable loge-history traits. Fish. Res. 94:210-223.
Ebener, M. P., J. R. Bence, K. Newman, and P. J. Schneeberger. 2005. Application of statistical
catch-at-age models to assess lake whitefish stocks in the 1836 treaty-ceded waters of
the upper Great Lakes. Pages 271-309 in L. C. Mohr, and T. F. Nalepa, editors.
Proceedings of a workshop on the dynamics of lake whitefish (Coregonus clupeaformis)
and the amphipod Diporeia spp. in the Great Lakes. Great Lakes Fishery Commission
Technical Report 66. Ann Arbor, Michigan.
Ebener, M. P., T. O Brenden, G. M. Wright, M. L. Jones, and M. Faisal. 2010. Spatial and
temporal distributions of lake whitefish spawning stocks in Northern lakes Michigan and
Huron, 2003-2008. Journal of Great Lakes Research 36:38-51.
Ebener, M.P., R.E. Kinnunen, L.C. Mohr, P.J. Schneeberger, J.A. Hoyle, and P. Peeters. 2008.
Management of commercial fisheries for lake whitefish in the Laurentian Great Lakes of
North America. Pages 99-143 in M. G. Schechter, W. W. Taylor, and N. J., Leonard,
editors. International governance of fisheries ecosystems: learning from the past, finding
solutions for the future. American Fisheries Society Symposium 62, Bethesda, Maryland.
Fournier, D.A., Skaug, H.J., Ancheta, J., Ianelli, J., Magnusson, A., Maunder, M.N., Nielsen, A.,
Sibert, J.,
2012. AD Model Builder: using automatic differentiation for statistical
inference of highly parameterized complex nonlinear models. Optim. Methods Softw.
27:233–249.
Frank, K.T., and Brickman, D. 2000. Allee effects and compensatory population dynamics
within a stock complex. Can. J. Fish. Aquat. Sci. 57(3): 513–517. doi:10.1139/f00-024.

36

Healey, M.C. 1978. Fecundity changes in exploited populations of lake whitefish (Coregonus
clupeaformis) and lake trout (Salvelinus namaycush). Canadian Journal of Fisheries and
Aquatic Sciences 35:945-950.
Henderson, B.A., J.J. Collins, and J.A. Reckahn. 1983. Dynamics of an exploited population of
lake whitefish (Coregonus clupeaformis) in Lake Huron. Canadian Journal of Fisheries
and Aquatic Sciences 40:1556-1567.
Hutchings, J. 1996. Spatial and temporal variation in the density of northern cod and a review of
hypotheses for the stock’s collapse. Can. J. Fish. Aquat. Sci. 53(5): 943–962.
doi:10.1139/f96-097.
Hutchings, J.A. 2000. Collapse and recovery of marine fishes. Nature, 406(6798): 882–885.
doi:10.1038/35022565. PMID:10972288.
Irwin, B.J., Wilberg, M.J., Bence, J.R., Jones, M.L., 2008. Evaluating Alternative Harvest
Policies for Yellow Perch in Lake Michigan. Fish. Res. 94:267–281.
Jacobson, P.C., Taylor, W.W., 1985. Simulation of harvest strategies for a fluctuating population
of lake whitefish. N. Am. J. Fish. Manag., 5:537–546.
Kell, L.T., Dickey-Collas, M., Hintzen, N.T., Nash, R.D.M., Pilling, G.M., Roel, B.A., 2009.
Lumpers or splitters? Evaluating recovery and management plans for metapopulations of
herring. ICES J. Mar. Sci. 66, 1776–1783.
Kell, L. T., Pilling, G. M., Kirkwood, G. P., Pastoors, M., Mesnil, B., Korsbrekke, K., Abaunza,
P. et al. 2005a. An evaluation of the implicit management procedure used for some ICES
roundfish stocks. ICES Journal of Marine Science, 62: 750–759.
Kell. L.T., Pastoors. M.A., Scott. R.D., Smith. M.T., Van Beel, F.A., O'Brien. C.M., and Pilling.
G.M., 2005b. Evaluation of multiple management objectives for Northeast Atlantic
flatfish ctocks: sustainability vs. stability of yield. ICES J. Mar. Sci. 62, 1104–1117.
Kirkwood, G. P. 1992. Report of the Scientific Committee. AnnexI. Background to the
development of revised management procedures. Reports of the International Whaling
Commission, 42:236–243.
Kirkwood, G. P. 1996. Assessing the precautionary nature of fishery management strategies.
FAO Fisheries Technical Memorandum, 350/2: 141–158.
Kratzer, J.F. 2006. Changes in growth, condition, fecundity, and egg lipid content of lake
whitefish in the upper Great Lakes between 1986-87 and 2003-05. Doctoral dissertation,
Michigan State University, East Lansing.
Molton, K. J., Brenden, T.O., Bence, J.R., 2012. Control rule performance for intermixing lake
whitefish populations on the 1836 Treaty waters of the Great Lakes : A simulation-based
evaluation. Journal of Great Lakes Research, 38: 686-698.

37

Nalepa, T.F., Schloesser, D.W., Pothoven, S.A., Lozano, S.J., 1998. Declines in benthic
macroinvertebrate populations in southern Lake Michigan, 1980–1993. Can. J. Fish.
Aquat. Sci. 55, 2402–2413.
Nalepa, T.F., Fanslow, D.L., Pothoven, S.A., Foley, A.J.I.I.I., Lang, G.A., 2007. Long-term
trends in benthic macroinvertebrate populations in Lake Huron over the past four
decades. J. Great Lakes Res. 33, 421–436.
Nalepa, T.F., Pothoven, S.A., Fanslow, D.L., 2009a. Recent changes in benthic
macroinvertebrate populations in Lake Huron and impact on the diet of lakewhitefish
(Coregonus clupeaformis). Aquat. Ecosyst. Health Manage. 12, 2–10.
Nalepa, T.F., Fanslow, D.L., Lang, G.A., 2009b. Transformation of the offshore benthic
community in Lake Michigan: recent shift from the native amphipod Diporeia spp. to the
invasive mussel Dreissenia rostriformis bugensis. Freshwater Biol. 54, 466–479.
NOAA Pacific Islands Fisheries Science Center. Quarterly Research Bulletin. 2011. Estimating
“steepness” of the stock-recruitment relationship, a key measure of fish stock
productivity. http://www.pifsc.noaa.gov/qrb/2011_06/article_08.php.
Pothoven, S.A., Madenjian, C.P., 2008. Changes in consumption by alewives and lake whitefish
after Dreissenid mussel invasions in lakes Michigan and Huron. N. Am. J. Fish. Manag.
28, 308–320.
Powers, J. E., and Porch, C. E. 2004. Approaches to developing management procedures which
incorporate mixing. Collective Volume of Scientific Papers ICCAT, 56: 1144–1152.
Punt, A. E. 2008. Refocusing Stock Assessment in support of policy evaluation. Pages 139-152
in K. Tsukamoto, T. Kawamura, T. Takeuchi, T. D. Beard, and M. J. Kaiser, editors.
Fisheries for Global Welfare and Environment, 5th World Fisheries Congress.
TERRAPUB, Tokyo.
Quinn, II, T. J., and Deriso. R. B., 1999. Quantitative Fish Dynamics. Oxford Univ. Press, New
York, NY, 542 p.
Stephenson, R., L. 1999. Stock complexity in fisheries management: a perspective of emerging
issue related to population sub-units. Fisheries Research, 43: 247-249.
Stott, W. L., J.A. VanDeHey, and B.L. Sloss. 2010. Genetic diversity of lake whitefish in lakes
Michigan and Huron: sampling, standardization, and research priorities. Journal of Great
Lakes Research, 36: 59-65.
Stott, W., Ebener, M.P., Mohr, L., Schaeffer, J., Roseman, E.F., Harford, W.J., Johnson, J.E.,
Fietsch, C.-L., 2012. Genetic structure of lake whitefish, Coregonus clupeaformis,
populations in the northern main basin of Lake Huron. Fundam. Appl. Limnol. Adv.
Limnol. 63, 241–260.

38

Van De Hey, J. A., B.L. Sloss, P.J. Peeters, and T.M. Sutton. 2009. Genetic structure of lake
whitefish (Coregonus clupeaformis) in Lake Michigan. Canadian Journal of Fisheries
and Aquatic Sciences 66: 382-393.
Ying, Y., Chen Y., Lin, L., Gao, T..2010. Risks of ignoring fish population spatial structure in
fisheries management. Can. J. Fish. Aquat. Sci., 68, p. 2101—2120.

39

Figure 1.1: Structure of a simulation framework for evaluating stock assessment models’ performance.
40

Figure 1.2: A conceptual diagram of stock intermixing for four hypothetical lake whitefish populations that are spatially segregated
during spawning, but subsequently intermix during the non-spawning period when exploitation takes place. For interpretation of the
references to color in this and all other figures, the reader is referred to the electronic version of this thesis.
41

Figure 1.3

42

Figure 1.3 (cont’d)

43

Figure 1.3(cont’d): Mean annual spawning stock biomass (SSB) for each population and fishery
yield for fishing areas surrounding each spawning area over the last 25 years of simulations. The
X-axis of each section in Figure 1.3a represents all four simulated populations, from the low
productivity (LP) population to the high productivity (HP) population. The dashed line is at 20%
of unfished SSB (B20%). In Figure 1.3b, the X-axis identifies the four fishing areas surrounding
the spawning areas of the LP to HP populations separately. The box tops and bottoms cover the
interquartile range; the horizontal middle line represents the median value of all simulations for
each scenario.

44

Figure 1.4: As for Figure 1.3b, except y-axis is mean inter-annual percent variation in fishery
yield
45

Figure 1.5: Proportion of years spawning stock biomass (SSB) being less than 20% of the
unfished SSB level
46

Figure 1.6: Median relative error (MRE) and Median absolute relative error (MRE) of estimating SSB for each assessment method
over the last 25 years.

47

Table 1.1: Four different levels of productivity for lake whitefish used in simulations and associated steepness, equilibrium yield
(tonnes), and the corresponding standard Ricker parameters α and β.
Population index

Productivity Steepness α

β

Equilibrium Yield

level
-4

LP population

Low

0.7

5.23×10

MLP population

Mid-low

1.1

9.19×10

MHP population

Mid-high

1.5

1.35×10

HP population

High

1.9

1.82×10

-4
-3
-3

48

-10

80

-10

219

-10

278

-10

312

1.51×10
2.06×10
2.43×10
2.72×10

Table 1.2: Equations used in stochastic simulation model

Equation

Description of

index

equation

(T.1.2.1)

Ricker stockrecruitment

Equation

Parameter

𝑅 𝑖,𝑦 = 𝛼 𝑖 𝑆𝑆𝐵 𝑖,𝑦−1 𝑒 −𝛽 𝑖 𝑆𝑆𝐵 𝑖,𝑦−1 𝑒 𝜀 𝑅,𝑖,𝑦

𝛼: see Table 1
𝛽: see Table 1

𝜀 𝑅,𝑖,𝑦 ~ N(0,

function by year

𝜎 𝑅 2)

(y) and
population (i)

𝜎 𝑅 = 0.6

49

Table 1.2 (cont’d)

(T.1.2.2)

age-specific SSB
by year (y)

(T.1.2.3)

(T.1.2.4)

Length at age

Weight at age

𝑆𝑆𝐵 𝑦 = � 𝐹𝑒𝑚 𝑁 𝑦,𝑎 𝑚 𝑎 𝑊𝑎
𝑎

𝐿 𝑎 =𝐿∞ (1 − exp(−𝜅(𝑎 − 𝑡0 )))

𝑊𝑎 = 𝛾𝐿 𝑎

𝐹𝑒𝑚 =0.5

𝐿∞ =60.9

𝜅=0.1686

𝑡0 =0.0

𝛾= 8.06 × 10−5

𝜓

𝜓=2.45

50

Table 1.2 (cont’d)

(T.1.2.5)

Maturity at age

(T.1.2.6)

Selectivity at
age

𝑚𝑎 =

𝑚∞
1 + exp(−𝜗(𝐿 𝑎 − 𝛿))

𝑎 𝜂 exp(−𝜏𝛼)
𝑠𝑎 =
10 𝜂 exp(−𝜏10)

51

𝜗=0.315

𝛿=37.9

𝜂= 13.074

𝜏= 1.26

Table 1.2 (cont’d)

(T.1.2.7)

Actual catch by
Baranov’s catch
equation by year
(y) and

𝐶 𝑖,𝑦

𝐹𝑖,𝑦,𝑎
=�
(1
𝑀 + 𝐹𝑖,𝑦,𝑎
𝑛

𝑎=1

− 𝑒 −𝑀−𝐹 𝑖,𝑦,𝑎 ) 𝑁 𝑖,𝑦,𝑎

population (i),
given fishing
mortality rates
and abundance

52

𝑀= 0.25

Table 1.2 (cont’d)

(T.1.2.8)

Actual catch by
year (y) and

𝐶

𝑗,𝑦

= 𝑇𝐴𝐶𝑗,𝑦 𝑒𝑥𝑝(𝜐 𝑖,𝑦 − 0.5𝜎 𝑐 2 )

population (i)
given the TAC.

(T.1.2.9)

likelihood
component for
total catch

𝑐̂ 𝑦
1
ℓ 𝑐 = 𝑛 𝑐 𝑙𝑜𝑔 𝑒 ( � 𝑐 ) + (
𝜎
) � 𝑙𝑜𝑔 𝑒 ( )2
̂𝑦
𝑐̃
2𝜎 𝑐 2 𝑦
�
𝑛 𝑐 = 𝑐̂ 𝑦 − ̂ 𝑦
𝑐̃

53

𝜐 𝑖,𝑦 ~ N(0, 𝜎 𝑐 2 )
𝜎 𝑐 = 0.1

�𝑐
𝜎

Table 1.2 (cont’d)

(T.1.2.10) Likelihood
component for

ℓ 𝜀𝐹 = 𝑛 𝜀𝐹 𝑙𝑜𝑔 𝑒 �
+(

fishing
mortality-effort
relationship

(T.1.2.11) Likelihood
component for
age composition

√0.25

0.25

�

)�
2𝜎 𝑐 2 𝑦
�

𝑙𝑜𝑔 𝑒 (𝜀𝐹)2

ℓ 𝑝 = − � 200 �(𝑝 𝑦,𝑎 𝑙𝑜𝑔 𝑒 � 𝑦,𝑎 )
�
𝑝
𝑦

𝑎

of the fishery
harvest

54

Table 1.3: Simulation scenarios. In all scenarios each of the four populations had different productivity, with one population taking
each of the four alternative productivity levels (Table 1).
Scenario

Description

Scenario 1

All populations have same high stay rate (0.9)

Scenario 2

All populations have same medium high stay rate (0.75)

Scenario 3

All populations have same medium-low stay rate (0.5)

Scenario 4

All populations have same low stay rate (0.25)

Scenario 5

Positive-correlated stay rates and productivity. Four stay rates (0.25, 0. 5, 0.75, 0.9)
matched in rank order to productivity of four populations

Scenario 6

Negative-correlated stay rates and productivity. Four stay rates (0.25, 0. 5, 0.75, 0.9)
matched in reverse rank order to productivity of four populations

Scenario 7

Unpredictable stay and productivity relationship. Four stay rates attached to populations of
different productivities using all possible combinations

55

Table 1.4: The convergence rate and Hessian warning percentage for the “meta” assessment method under each scenario.

Scenario 1 Scenario 2 Scenario 3 Scenario 4 Scenario 5 Scenario 6 Scenario 7
(SR=0.9)

(SR=0.75) (SR=0.5)

(SR=0.25) (po-cor)

(ne-cor)

(Unpredictable)

Convergence rate (%) 95.4

94.8

81.6

99.8

88.8

21.0

52.9

Hessian warning (%)

0

0

100

0

0

0.03

0

56

CHAPTER 2
DOES STOCK ASSESSMENT FREQUENCY REALLY MATTER? A CASE STUDY FOR
INTERMIXING LAKE WHITEFISH POPULATIONS IN 1836 TREATY CEDED WATER
Abstract
Stock assessment resources are limited and need to be focused in an efficient manner.
One tradeoff faced by assessment groups is the frequency with which to update assessments
versus investing efforts in identifying improvements in assessment model structure. We address
this issue using Management Strategy Evaluation type simulations for a spatially structured stock,
based on characteristics of lake whitefish in the Laurentian Great Lakes of North America.
Populations of lake whitefish exhibit philopatry, returning to spawning grounds in the fall and
winter, but often moving into areas near spawning grounds of other populations during the
harvest season. These populations are managed with the equivalent of a constant fishing
mortality rate policy. We modeled a hypothetical set of four populations, with proportions of
each reproductive population moving to areas surrounding the spawning grounds of the other
populations during the harvest season, and applied the status quo harvest policy. We explored
how assessment frequency (every year, every three years, and every five years) and lag between
data collection and use (with and without lag) influenced fishery performance as measured by
average yield, average spawning biomass, frequency of low stock sizes, and inter-annual
variation in yields. We also considered several alternative ways of setting harvest limits during
the years between assessments. The results showed that compared to other things like the actual
mixing among areas and the choice of how to account for spatial structure, the frequency of
assessment had modest effects. When conducting an annual assessment, removing the 1-year lag
had little influence. Our results suggest that conducting assessments every three or five years

57

should be considered as part of a management strategy and may allow analytical efforts to be
directed in other ways.
Introduction
Conducting stock assessments soon enough after the most recent data that are included
were collected and at an appropriate frequency is of great importance to establishing an effective
and sustainable fishery management system. Human resources that can be devoted to stock
assessment are limited, thus the optimal stock assessment process should be both provide highquality science information to managers while saving as much assessment resources as possible.
One trade-off faced by assessment groups is the frequency with which to update assessments
versus investing more efforts on identifying improvements in assessment model structure or
perhaps turning attention to another population that is completely unassessed. Some stock
assessment groups, such as ICES Study Group on Multiannual Assessment Procedures
(SGMAP), Modeling Subcommittee (MSC) of the Technical Fisheries Committee (TFC) of 1836
Treaty Ceded waters, and National Marine Fisheries Service (NMFS) National Task Force for
Improving Fish Stock Assessments, have already included “identifying appropriate assessment
frequency” or similar topics as their objects of discussions (Mace et al., 2001, Woldt et al. 2005,
ICES 2012). Some fishery scientists have suggested that the high frequency of assessment could
increase our capacity of monitoring fish populations and prevent early overfishing (Mace et al.,
2001). Other scientists have suggested the possibility of a rotation of stock assessments (i.e.
doing assessments at less than an annual frequency) because they thought the time and resources
saved from not annually assessment could be used for doing something else such as improving
models and verifying model performance (Woldt et al. 2005). Furthermore, maintaining the

58

amount and quality of assessment work when each assessment is done annually can be a
challenge in some circumstances (ICES 2012).
ICES (2012) suggested that the appropriate time period between stock assessments, in
theory, can be determined by two main factors: (a) biological attributes of the assessed
population that determine the rate of change in stock size that is possible, and (b) the current and
anticipated fishing pressure. These factors will clearly influence how much change is likely to
occur over a given time period, and this will clearly influence the amount of beneficial
information that can be obtained by doing an assessment sooner rather than later. We addressed
this issue using Management Strategy Evaluation (MSE) simulations for spatially structured
populations, based on characteristics of lake whitefish in the Laurentian Great Lakes of North
America. We explored how the lag between data collection and establishing a harvest
recommendation (the lag) and the frequency of assessments affected long-term fishery
performance metrics (yield, spawning stock biomass, et al.) for intermixing lake whitefish
populations. We chose lake white fish as an example because lake whitefish harvest across that
region has been well below established harvest limits in at least the most recent 9 years from
2005 to 2013 (Woldt et al. 2006, 2007, 2008, Caroffino et al. 2009a, 2009b,2011a, 2011b, 2012),
which illustrates that past and current fishing pressure was low. However, the current stock
assessment models are annually updating with a one-year time lag.
Most MSE-style simulation studies have focused on evaluation of alternative harvest
control rules. Our study uses an MSE-style simulation approach but is distinguished from most
others in that we emphasized the influence of how the assessment step of fishery management
was conducted. During simulations, data is generated on observed yield, harvest at age, and
fishing effort and stock assessments are done periodically (annually or less frequently). Each

59

year target yield levels are set based on the most recent assessment, and actual yield deviates
from this due to implementation error. Our research objective was to compare fishery
management and assessment estimation performances based on the current annual assessment
(with a 1-year lag) with alternative timings of the assessments.
An additional consideration for the assessments is recent evidence that has shown that
many lake whitefish populations in the northern parts of lakes Huron and Michigan are
intermixing considerably during non-spawning periods, and this may be a change from past
spatial distributions (Ebener et al. 2010). Nevertheless, lake whitefish stocks continue to be
largely treated as discrete, independent units for management purposes, whereas our results
(Chapter 1) show that using a pooled procedure can sometimes be superior in the face of mixing,
at least with an annual assessment and a 1 year lag. This may reflect a specific situation where
time spent improving the current assessment model in response to intermixing information, such
as by lumping assessment areas when confronted with information that there is substantial
movement among areas, may deserve higher priority than maintaining an annual assessment
frequency. Given these considerations we have incorporated spatial structure in our simulations
and applied both the pooled (all areas combined) and separate (by area) stock assessment
procedures for each frequency/lag scenario we considered. Thus, our study can not only provide
quantitative evaluation of proposed alternative assessment frequencies for management decision
making of intermixing lake whitefish population as well as other mixing species, but also weight
the relative importance between the assessment frequency and the choice of assessment models.

60

Methods
Overall simulation framework
The simulation framework used to evaluate the design of assessment process was based
on management strategy evaluation (MSE) methods (Kell et al. 2005, Punt 2008) (Figure 2.1).
This framework modeled the “true” system and “perceived” system (data collection, stock
assessment and harvest control rule application). The “true” system is represented as “real”
stock and fishery dynamics, from which the simulated data were sampled. These data were then
used in an assessment procedure that establishes the status quo for resources. During each
assessment year, the two assessment methods (i.e., “separate” and “pooled”) were fitted
separately and the current treaty-water harvest control rule was applied to each specific
assessment result. As for multiannual assessments, there were three way to calculate harvest
limits for rotation years, as described later. Each total allowable catch (TAC) was then fed back
into the corresponding real system, by its influence on the harvest in the next-year. Performance
statistics based upon the stock and fishery dynamics model were eventually used to evaluate the
robustness of each assessment frequency and assessment model. The flexibility of this
framework allowed us to incorporate a series of uncertainties, including process, sampling,
estimation, and model error, as described below.
Four simulated populations
Four lake whitefish populations were assumed to have differing levels of "productivity".
Differences in productivity among the four spawning populations were incorporated via
adjustment of the recruitment function coefficients (Table 1). We used a Ricker recruitment
model because of strong evidence for over-compensation in lake whitefish populations (Healey
1978; Henderson et al. 1983; Kratzer 2006). Given information on life history (maturity and

61

weight at age schedule) the Ricker function can be parameterized in terms of steepness and the
unfished spawning stock size. We equated "productivity" with steepness (NOAA Pacific Islands
Fisheries Science Center, 2011), and chose four steepnesses for our simulated populations that
were plausible for lake whitefish and produced meaningful differences in equilibrium yield. We
set unfished equilibrium stock sizes to be equal so that differences between the populations were
due only to our assumed productivity differences. The steepness parameterization was then
converted to the standard Ricker parameterization. Calculations of spawning stock sizes to
define the productivity of the populations in the simulations assumed unit stocks (no movement)
and followed methods outlined by Quinn and Deriso (chapter 6 page 239, 1999). The values of
life-history parameters were based on the most recent 1836 Treaty- Ceded water assessment
conducted by the Modeling Subcommittee (MSC) of the Technical Fisheries Committee (TFC)
and our claim of plausible steepnesses is based on review of the annual assessment models of
lake whitefish harvest recommendations from 2001 to 2012
[ftp://glpd.fw.msu.edu/MSCFTP/Assessment_models/]. The unfished spawning biomass was
also based on assessment results, but only sets the scale of results and otherwise does not
influence the outcomes of our work.
Each of the four simulated lake whitefish spawning populations was assigned one of the
four levels of productivity so that there was a LP, MLP, MHP and HP population for each
simulation. The dynamics of four hypothetical lake whitefish spawning populations had varying
degrees of intermixing during the fishing season, but were spatially segregated during the
spawning season (Figure 2.2). Intermixing was assumed to occur immediately after spawning,
with varying fractions of each population either staying within their natal areas or moving to

62

areas where the other stocks spawn. Fish residing in each area (a “stock”) were exploited during
the rest of the year and surviving fish then moved back to their natal area to spawn.
The “true” system
The basic structure of our model for the "true" system is based on the approach developed
by Molton et al. (2012). We used an age- structured forward-projection model, consisting of
four hypothetical populations with a simulation length of 100 years. Only the final 25 years were
summarized to evaluate performance. Our intent here was to evaluate the long-term performance
of the alternative approaches with different timetables and frequency of assessment, independent
of the starting conditions. Recruits were added as the youngest age each year based on the
current stock size for the population and a stock recruitment function. During the fishing season
fish from each population mixed with fish from other areas in four fishing grounds, which each
surrounded the four spawning areas (Figure 2.2), but returned to the spawning area for an
instantaneous spawning period, based on the known natal philopatry of the species. During the
fishing season fish died due to natural mortality and due to fishing mortality, and the latter was
set based on perceived stock size based on a stock assessment that was done periodically
(annually or less often) as part of the simulations.
Fish from a spawning population either remain in their natal area during the nonspawning season or move to one of the other three areas (Figure 2.2). Movement rate, θij (i ≠ j),
is the proportion of fish belonging to spawning population i (i.e., they spawned in area i) that
move to and live in area j during the non-spawning season. We refer to θii as the stay rate, which
is the proportion of fish belonging to spawning population i that stay in area i during the nonspawning season. The movement rates were calculated based on the stay rates, which was set
based on results from ongoing and published studies (Ebener et al.2010, Stott et al. 2010, Stott et
63

al. 2012). We assumed that a higher stay rate indicated a high quality habit, and that a high
proportion of whitefish would tend to move to that area. The movement rate θij (i ≠ j) is:

𝜃ij = (1 − 𝜃 𝑖𝑖 )

𝜃 𝑗𝑗

∑ 𝑘≠𝑖 𝜃 𝑘𝑘

(1)

Where (1- θii ) is the total proportion of fish from population i that live in other areas

during the non-spawning season, and

𝜃 𝑗𝑗

∑ 𝑘≠𝑖 𝜃 𝑘𝑘

is the proportion of those fish residing in each

destination area j. This approach of specifying movement rates diverges from the approach of
Molton et al. (2012), who assumed that fish that did not stay in their natal area moved to other
areas in equal proportions.

𝑁 𝑖,𝑦+1,𝑎+1 = 𝑁 𝑖,𝑦,𝑎 ∑ 𝑗 𝜃 𝑖𝑗 exp(−𝑀 − 𝐹𝑗,𝑦,𝑎 )

We projected abundance-at-age after recruitment using an exponential mortality model:
(2)

where Ni,y,a is equal to the number of fish from spawning population i of age a in year y;
M is the natural mortality rate; and Fj,y,a is the year- and age-specific instantaneous fishing
mortality rate of fish occurring in area j during harvest season. This instantaneous fishing

𝐹𝑗,𝑦,𝑎 = 𝑠 𝑎 𝑓𝑗,𝑦

mortality rate was calculated as:
(3)

where sα is the age specific selectivity (equal for all four stocks), and fj,y is the fully
selected fishing mortality occurring in area j in year y. Thus the fishing mortality rate
experienced by a population was a weighted sum of the fishing rates occurring in the different
areas, with weights set by the θ. The fully selected fishing mortality rate for each area was
64

calculated using a Newton-Raphson algorithm so that the true yield for each area was produced
using the Baranov’s catch equation (Equation T.2.2.7) and assumed harvest weight at age). The
true yield was set equal to the Total Allowable Catch (TAC) (i.e., target yield) multiplied by a
lognormal implementation error (Equation T.2.2.8). The TAC was determined via the stock
assessment procedure described in the perceived system section.
Constant values of natural mortality, female proportion, and catchability were used.
Selectivity-, length-, weight-at-age, and annual spawning stock biomass (SSB) were determined
by deterministic functions. Selectivity was set as 0 for age-2 and younger whitefish because they
are rarely harvested in treaty waters. Selectivity for other age classes was simulated by a gamma
probability density function (Equation T.2.2.6) scaled by setting the fully selected age class (age
10) equal to 1.0; length-at-age was assumed to follow a Von Bertalanffy growth model (Equation
T.2.2.3); weight-at-age was determined by a power function of length (Equation T.2.2.4); and the
SSB (Equation T.2.2.2) was calculated as a function of abundance-at-age, maturity-at-age
(Equation T.2.2.5), and weight-at-age. The four populations shared the same selectivity-, length-,
and weight-at-age patterns.
The initial state of for each simulation in year 1was based on equilibrium recruitment and
target mortality rates and calculated based on deterministic models with no mixing. The actual
harvest policy and management process requires a twenty year time-series of data, which was not
available during the initial 20 year period of each simulation. Within this "burn-in" period,
population abundance at age was assumed to be known exactly before applying the harvest
control rule and thus the assessment model step was skipped during the burn-in period of
simulations. The intent here is merely to move the system closer to steady-state conditions
during this period. Stochastic recruitment errors were still included during this period.

65

The “perceived” system
In the perceived system (Figure 2.2), the management procedure for the treaty water
whitefish was duplicated, including data collection, stock assessment, and application of the
harvest control rule. When generating the data we assumed that total catch was observed with
error, and that observed age compositions also differed from actual age compositions due to
sampling error. Observed proportions-at-age in the simulated data arose from a multinomial
distribution with probabilities equal to the true age proportions of the harvest sample and an
effective sample size of 200 for “separate” and “meta” approaches or of 800 for the “pooled”

Ej,y =

Fj,y

exp(𝜇 𝑗,𝑦 − 0.5𝜎 2 𝐹 )

method. Observed fishing effort was calculated as:
q

𝜇 𝑗,𝑦 ~ 𝑁(0, 𝜎 2 𝐹 )

(4)

𝜎2 𝐹 = 4 𝜎2 𝑐

where Fj,y is the fully-selected fishing mortality rate for area j and year y; q is the
-6

catchability coefficient of 1.50×10e ; and μj,y is the an normally distributed random variable
2

with expectation of 0 and variance of σ F (Equation T.1.2.10), which was assumed to equal to
2

0.04 (four times of σ C).
The above data was collected annually and used as the input for stock assessments. The
stock assessments were assumed to have knowledge of the true natural mortality rate and lifehistory parameters.
In the stock assessment process, two different assessment models were compared:
separate population, and pooled population assessment models. Both models were variants of
66

the SCAA model, which involves fitting a population dynamics model to observed data to
estimate the parameters used to summarize stock status and determine TAC for each simulated
population of the assessment year.
The first approach, the “separate population assessment”, assumed no movement among
areas. We applied the assessment model to each stock. An age-specific fishing mortality was
predicted by the same equations used in the population dynamics model. This is the most
commonly used approach for assessing lake whitefish in treaty waters.
The second approach, the “pooled population assessment”, treated all lake whitefish
across the areas being assessed as part of one well mixed population. This led to an exponential
model for the pooled population, rather than for each stock (Equation T.2.2.1).
For the two assessment models, recruitment (area specific or pooled), the initial
abundance-at-age for the first year, selectivity-at-age, and fishing mortality were estimated as
free parameters during model fitting. Best fit parameters were estimated via iterative methods so
as to minimize the negative penalized log-likelihood (i.e., the objective function). We assumed
lognormal distributions of errors for annual fishery catch, a lognormal prior component
associated with the fishing mortality-effort relationship, and the age compositions of the fishery
were assumed to follow multinomial distributions. The objective function was the sum of above
three negative log-likelihood or log prior components (Equations T.2.2.9., T.2.2.10, T.2.2.11).
Iterations proceeded until the maximum absolute value of the gradient (derivatives of objective
function with respect to parameters) was below a specified criterion (0.001), although sometimes
iterations stopped before reaching the criterion either because no further progress was being
made in reducing the objective function or a maximum number of iterations (1000) were
completed. Fits that ended without reaching the gradient criterion were classified as failing

67

convergence. A second test of whether the solution after iterations was a minimum (i.e., true
maximum for the penalized likelihood) was whether the Hessian was negative definite. If this was
not the case we termed this a Hessian problem. A record was kept for each assessment on whether

there was convergence failure or a Hessian problem. The negative log likelihood component for
the age composition of the fishery harvest was weighted by effective sample size (800 for the
pooled method and 200 for the separate and the “meta” methods). The 20 years of data prior to
any given assessment year were included in the assessment model.
We mimicked the actual timing of assessments and setting of harvest guidelines based on
them in lake whitefish fisheries and three alternative frequencies. We refer to the current
assessment timetable and frequency as “L1”, in which the assessments have been updated
annually, with a one-year lag of data availability. More specifically, these assessments are done
in a given year, based on data through the previous year, and are used to establish harvest targets
for the next year.
The first alternative called “L0” was also an annual assessment, but without a 1-year lag.
So data from year y are available in time to conduct an assessment and use the assessment results
to manage the fishery during year y+1. The other two multiannual alternatives did assessments
every 3 years and every 5 years, with a 1-year lag. During the simulations, harvest targets (which
we will refer to as TACs) were established for each year, even though assessments may not have
been, and in the case multiannual assessments these are based on projections from the most
recent assessment.
The details of how TACs are set for multiple year assessments can become complex. As
a starting point we describe how the TAC is set for the L1 and L0 scenarios, and then turn to the
more complex rotational scenarios. For L1, the stock assessment produces abundance-at-age for

68

the start of the year when the assessment is done (the lag year). Projections through the
assessment (lag) year were done based on an exponential population model, in which total
mortality rate was assumed to be the mean of the last three years’ values and the recruits were
assumed to be the mean of the last ten years’ values. During the year for which the TAC was set
the projections assumed the same level of recruitment but fishing mortality was adjusted so the
target mortality rate was achieved (this was also done for L0 where projection through a lag year
was not required). The current harvest control rule for lake whitefish in treaty waters, which
equates to a constant fishing mortality rate policy, were used in the simulation. The control rule
sets the maximum total annual mortality rate experienced by any age of fish at 65%. We used the
same methodology to determine the TAC as the one applied by the MSC to determine the target
maximum yield. This TAC was calculated from assessment-based estimates of abundance-at-age
at the start of the year the TAC applies to and target fishing mortality-at-age using the Baranov
catch equation. The age-specific fishing mortality rates were based on the estimated selectivityat-age from assessment multiplied by the target fishing mortality rates, which was the target
instantaneous total mortality rate minus the natural mortality rate as assumed in the assessment
model. For the “separate” assessment methods, TAC for each area was calculated separately
because the assessment results were area-specific for those methods. For the pooled population
assessment, only a pooled TAC could be calculated and was allocated according to an annually
varying allocation rule, which was based on the annual area-specific CPE observed from the
“true” system. The higher the CPE, the more TAC was allocated to each area. To reduce annual
variation of yield, we used the average CPE of the last three years.
For three and five year assessment frequencies, there are actually many ways to set the
TACs in the years between assessments, and we evaluated three different ways in our

69

simulations. First a “Constant TAC” or “CT” approach was to apply the same total allowable
catch (TAC) determined based on the last full assessment projected through the "lag" year.
Second, a “Target F” or “TF” approach was based on multiyear projections after the 1-year data
lag, and assumed fish populations experienced the target fishing mortality during subsequent
years before the next assessment results were available for use in management. Third, an “Add
yield information” or “AY” approach was to project annually in the years between assessments
to set the next year's TAC, taking into account each additional year of yield information. In this
case, the estimated fully selected fishing mortality was calculated using a Newton-Raphson
algorithm so that the projection predicted an amount of yield equal to the observed yield for each
area. For a given level of fully selected fishing mortality, the predicted yield was generated from
Baranov’s catch equation (Equation T.2.2.7) and assumed harvest weight at age). Then that
estimated fully selected fishing mortality could be used to project abundance to the start of the
next year and thus the TAC for that year could then be calculated in the same way as for annual
assessments.
For the CT and TF approaches for setting TACs in the years between assessments, the lag
year occurred immediately prior to the first year the TAC was set for, and TACs could be set at
one time for the entire period until new assessment results would be available. Projections
through the lag year were based on an exponential population model, again using a total
mortality rate of the mean of the last three years of values from the assessment and recruitment
were assumed to be the mean of the last ten years of values from the assessment. For the CT
method the TAC was calculated by projecting an additional year assuming the same level of
recruitment but with fishing mortality adjusted so the target mortality rate was achieved
(assuming the assessment point estimates were correct). This same TAC was then used in

70

subsequent years until the next assessment results were available. For the TF method,
projections were done over the entire period that TACs were set. Over the entire period the
same level of recruitment was used as for the L1 and CT projections, but the target fishing
mortality rate assumed to occur each year after the lag year. Thus, in contrast with the CT
method, the TF method produced different TACs for each year.
For the AY method, the TAC was set in an identical manner to the way the TAC was set
for the CT and TF methods for the first year that TACs were needed after the most recent
assessment. However, to set the TAC for the second year the projection for the initial lag was
first replaced with a projection that matched the observed yield for that year as described above,
and then from that starting point the lag procedure and the projection during the second TAC
year were done in the same way as when the TAC in the first year was set. For each subsequent
year a TAC was needed this same updating procedure was repeated, with the previous lag year
replaced with a projection based on a fishing mortality rate that now matched the observed yield.
For each combination of assessment frequency and harvest limit setting approach for the
rotation years, we denote it with a name that captures information on both aspects of the
approach. Say when we used the “Constant TAC” method to set the harvest limit between
assessments of a 3-year assessment frequency scenario, we referred it as “CT3”. In all we
compared the eight scenarios denoted: “L0”, “L1”, “CT3”, “CT5”, “TF3”, “TF5”, “AY3”, and
“AY5” (Table 3) .
Experimental design
For four hypothetical populations with differing productivity (Table 1), we evaluated how
assessment methods performed with respect to different frequencies of assessment as well as lag
choices, and alternative ways of setting harvest limits for the rotation years (Table 3). Within

71

each assessment scenario, five mixing scenarios were examined as listed in table 4: Scenarios 1
to 3 (“SR=0.9”, “SR=0.5”, “SR=0.25”) represented the cases that all areas shared the same stay
rate ordered from high to low (so the case of less mixing is first). We referred scenarios 1 to 3 as
four “same mixing” scenarios. Scenario 4 (“po-cor”) assumed that productivity and stay rate for
each area were positively correlated (fish from higher productivity populations tended to stay in
natal areas). Scenario 5 (“ne-cor”) assumed a negative correlation between productivity and stay
rate for each area. Under each mixing scenarios, the MSE model was run at each combination of
assessment models (separate population model (“separate”) or pooled model with TAC allocated
by CPE (“pooled”) and eight assessment timetable and frequency choices (“L0”, “L1”, “CT3”,
“CT5”, “TF3”, “TF5”, “AY3”, and “AY5”). Each of the total 16 combinations of assessment
model and timing are referred to below as “assessment process designs” because fishery
managers can affect those two characters during assessment.
Performance statistics
For each “assessment process design” under five mixing scenarios, a 100-year simulation
was performed 1000 times by using AD Model Builder (Fournier et al., 2012). Performance
statistics were generated from the “true” system, which was used to describe the real status of
stock and fishery. The statistics allowed us to compare the performance of alternative assessment
and management methods under different mixing scenarios with respect to the management
objectives (i.e., long-term sustainability, high and stable yield, and the trade-off between them)
and the accuracy of SSB estimation. Since most performance statistics appeared to approach a
long-term mean by year 75, all performance statistics were calculated based on the last 25 years
of the simulations. Under different mixing scenarios with different assessment
method/frequency/lag, the performance statistics were:

72

1. Average yield over the last 25 years for each area.
2. Average SSB over the last 25 years for each population.
3. Proportion of years spawning stock biomass (SSB) was less than 20% of the unfished SSB
level.
4. Inter-annual variation of yield over the last 25 years for each area.
5. Total average yield over the last 25 years for four populations.
Results
Comparison of annual assessment quotas with and without 1-year lag
Overall, compared with L1, there was no substantial or obvious advantage of “L0”, when
the one year lag was removed (Figure 2.3). There were some slight differences with respect to
SSB (Figure 2.3a) and yield (Figure 2.3b). For example, for the LP population, when stay rates
were high for all populations (SR=0.9), for the separate method SSB was slightly higher for L0
than for L1 (first row of Figure 2.3a). For the same population and approach, when stay rate was
positively correlated with productivity of populations, yield was slightly higher for L0 than L1
(fourth row in Figure 2.3b). Patterns for probability of SSB being less than 20% tended to be an
inverse mirror of those for SSB, albeit more variable (Figure 2.3c). Generally, the inter-annual
variation (IAV) of yield for L1 is slightly higher than L0 with a separate assessment model,
especially when all populations shared the same mixing rate (L0 versus L1, Figure 2.3b). That
difference in IAV decreased with the mixing rates increased. As for the pooled assessment
method, there was no clear difference between the IAVs of yield with and without a lag.
Comparison of annual and multiannual assessments
Here we present only results for the stay rate of 0.5, which reasonably illustrates the
impact of assessment frequency across the full experimental design (see Appendix).

73

Comparison of three rules for setting TACs for the years between assessments
For the same assessment frequency (annual, 3 year or 5 year in Figure 4a and 4b), three
rules (CT, TF, and AY) performed differently with separate assessment method. TF was the most
conservative rule among the three with respect to the highest SSB and the lowest probability of
SSB being less than 20% (Figure 2.4a and Figure 2.5a). The AY rule had relatively better fishery
performance in terms of higher yield and lower IAV of yield across all areas (Figure 2.4b and
Figure 2.5b), but with the cost of increasing risk of the depletion of the low productive (LP)
population (Figure 2.5a). The CT rule showed no obvious advantage compared with the others
with respect to SSB and yield, and could sometimes produce the highest IAV of yield across all
areas. As for the pooled assessment method, there was no clear difference between the
performances of the three harvest setting rules.
Comparison among assessment frequencies
The pattern of differences among an assessment frequency of annual, 3 years and 5 years
was quite similar for the different methods of setting TACs between assessments, although the
illustrated differences for the Constant TAC tended to be larger than for the Target F and Add
Yield approaches (Figure 2.4a, Figure 2.5a). More specifically, for CT rule, increasing
assessment frequency led to some modest increases in SSB with the separate assessment model,
while for other rules, there was no obvious benefit for SSB when increased assessment frequency
from annual to 5 year. For both assessment models with all three rules for setting TACs during
rotation years, higher assessment frequency could slightly improve the fishery performance
(higher yield and lower IAV of yield), but the improvements were much smaller for the pooled
model than the separate model (Figure 2.4a and Figure 2.4b).

74

Among the three rules for setting TACs during rotation years with the separate
assessment method, the TF rule was always the most conservative rule and performed about the
same with either annual or multiannual assessment frequencies. For example, for the 5 year
assessment with TF rule, the median value of the proportion of years spawning stock biomass
(SSB) being less than B20% was very similar compared with annual assessment(Figure 2.5a).
By increasing assessment frequency, with the separate model, the inter-annual changes in
area-specific yield within a set of simulations was decreased (Figure 2.5b), suggesting that a
constant exploitation rate was more closely adhered to with more frequent assessment, and both
median yield and IAV increased. For the pooled assessment model when increasing assessment
frequency to annual from 5 years, only the median yield of each area increased very slightly,
while the range of variation in yield were similar for the two frequencies. The IAV of yield
increased with the TF and AY rules and decreased with the CT rule. For both assessment
methods with the CT and AY rules, increasing assessment frequency led to a lower risk for LP
populations of falling below B20% (Figure 2.5a).
Comparison of the relative magnitude of effects due to assessment frequency and assessment
model under different mixing scenarios
Assessment frequency and assessment model (separate versus pooled) both influenced
the performance of the assessments. One of our goals was to investigate whether the impacts of
assessment frequency were large enough to warrant annual assessments at the potential expense
of efforts to choose the most appropriate assessment model. We found that in most mixing
scenarios, the difference between assessment models for a given frequency of doing assessments
(or approaches for setting TACs in the years between assessments) were larger than the

75

differences due to frequency or TAC setting approach for a given model (Table 2.2 and Table
2.3).
We included the current annual assessment (L1) and 5 year assessment with TACs setting
for rotation years based on TF rule (TF5) to represent the effect of assessment frequency, and
incorporated two assessment models (separate and pooled) across all mixing scenarios to explore
the effect due to assessment model. We compared which effect had a larger influence by looking
at the SSB of the LP population and the total yield aggregated over areas. We focused on SSB
for the LP population because this population had the highest risk of population depletion in all
cases (Figure 2.3c and Figure 2.5a).
The relative change of the median of the SSB of LP population (Table 2.5) due to the
decrease of assessment frequency were almost all negative across all mixing scenarios, and
varied from -0.163 to 0.034 across all mixing scenarios with both assessment models. The
negative value illustrates that decreases of assessment frequency from L1 to TF5 led to the slight
depletion of LP populations. When switching the assessment model from separate to pooled, the
relative changes across all mixing scenarios ranged from -0.293 to 0.514. The pooled method led
to a positive relative change in the SSB of the LP population in some scenarios, when stay rates
for populations were high (SR=0.9) or positively correlated with productivity (po-cor), while in
the other scenarios, the relative changes were negative. For each mixing scenario, the absolute
relative changes of the SSB of LP populations caused by assessment models were much larger
than those caused by assessment frequency (Table 2.5). We interpret this to mean that the
overall effect of assessment method was consistently larger than the influence of assessment
frequency.

76

The relative changes of the median of total yield across all areas due to the decrease of
assessment frequency (Table 2.6) were at the same scale compared with the changes caused by
different assessment models. All those absolute relative changes were below 0.08. Decreasing
assessment frequency from annual to 5 year could slightly decrease the median of total yield
across all mixing scenarios (with negative relative change), while pooled assessment methods
could provide a slightly higher total yield across almost all mixing (with positive relative change)
(Table 2.6).
So the overall effects due to the assessment model were larger than those due to
assessment frequency; because although both factors (assessment model and frequency) have
similar magnitude of effects on total yield, whereas the choice of assessment model influenced
the SSB of the LP population more than assessment frequency did. For example, in the first two
rows of Table 6 (SR=0.9), the pooled method performed markedly better than separate method,
no matter which assessment frequency was applied, with higher SSB of the LP populations, and
higher yield across all areas. In contrast, only slight differences can be detected within a method
when comparing the results among varying assessment frequencies and approaches to setting
TACs for rotation years.
Discussion
Our goal was to evaluate how various factors in the design of the assessment process
affect intermixing lake whitefish populations and fishery outcomes under the current approach of
attempting to limit total mortality to a constant 65% for the fully selected ages. Those factors
included whether to use area specific or a pooled assessment model, whether there would be a
one year or no lag between the end of the last year for which data were included and when the
assessment results were available for management, assessment frequency (every year, three years

77

or five years), and the approach to setting TACs in rotation years for multi-annual assessment. In
our application we simulated four lake whitefish populations based on biological data, stock
assessment results, and management practices in 1836 Treaty-Ceded waters of Lakes Michigan,
Huron and Superior. The assessment of lake whitefish in that region has been largely based on a
“separate” statistical catch at age assessment (SCAA) method since 1998. The pooled method
aggregates data over areas known to contain distinct spawning grounds, and treats the
populations within the larger area like it was a single population, also using an SCAA. After
increased mixing between management units was observed, the Modeling Subcommittee (MSC)
of the Technical Fisheries Committee (TFC) combined four nominal populations in North Lake
Huron into one single assessment unit beginning in 2011 (Caroffino et al. 2011). They thus
implemented an assessment model similar to our pooled method, although in the real system fish
can still move into and from the pooled region. As of 2013 these assessments are updated
annually with 1-year lag between the year data are available and when assessment results are
available for use in management. Based on recommendations from the MSC the TFC had
implemented a rotation plan for three management units of lake trout in 1836 treaty ceded water
since 2011, by switching from annual assessments to assessments every three years in those units
(Caroffino et al. 2009b). We are not aware of published peer-reviewed studies where the
performance of different assessment frequencies has been evaluated. This topic is clearly of
interest to fishery management, and the topic is discussed in several reports from workshops and
in improvement plans for assessment models (Mace et al. 2001, Woldt et al. 2005, ICES 2012).
One such workshop report provides results from a management strategy evaluation approach to
evaluating the risk engendered by doing a multiannual assessment instead of annual assessment
(ICES 2012). That study found that when starting conditions for the populations suggested a

78

downward trend (weak year classes in age-structure), there could be significant depletion for a 5
year frequency that was avoided with an annual assessment. This is not totally unexpected
because they fixed the TACs rather than projecting forward when setting harvest for rotation
years, so the weak year classes became fully selected during rotation years.
We know of no other published studies than ours that have evaluated what the influence
of a lag between when data are collected and when an assessment is completed and the results
used for management. Many management agencies make substantial efforts so that data from
the previous year are processed and used in an assessment completed early in the year for which
a harvest recommendation based on that assessment is applied. For example this approach has
been applied for walleye in Lake Erie and lake trout 1836 treaty waters (Thomas et al. 2005,
Caroffino et al.2009b). Our results suggest that such a rush to complete an assessment is
unnecessary, at least for fish that with similar or lower mortality rates and recruitment variability
as lake whitefish. In our study the influence of the lag was generally small and sometimes
undetectable.
When we compared three different rules of setting harvest limits for rotation years, the
Constant TAC (CT) rule performed the worst in terms of all performance metrics. Forward
projection based on Target F (TF) was the most conservative rule, with respect to greatest SSB
for each population and lowest risk of SSB falling below B20%. Calculating TACs during the
rotation years based on updating TACs to match observed yield from previous lag years (AY)
had the best fishery performance with highest yield across all areas and lowest annual variation.
While the effect is not large, it does seem like accounting for known yields can be useful when
setting TACs over multiple years when a full assessment is not done each year.

79

When comparing annual and multi-annual assessments, the performance of both
“separate” and “pooled” assessment was best for the annual assessment and worst for the longest
period between assessments, for all performance metrics except inter-annual variation of yield.
Higher assessment frequency always resulted in increasing IAV of yield. The magnitude of these
differences varied, and depended on the harvest limit setting rules for the rotation years. Across
all mixing scenarios, the difference in results between 3 and 5 year assessment frequency was
largest for the CT rule. For this rule SSB was larger and yield was higher across all populations
and areas for the 3 year frequency than for the 5 year frequency. For the AY rule, the 3 year
frequency had only slightly higher yield and no clear benefit in terms of higher SSB than the 5
year frequency. For the TF rule, increasing assessment frequency from 5 to 3 years provided no
benefit in terms of yield or SSB. This qualitative effect is not too surprising and is consistent
with ICES (2012), which used CT rules for setting TAC during rotation years and found that
changing from an annual assessment to a 5 year assessment could cause depletion of populations.
However, in contrast with ICES (2012), we found the effect of longer periods between
assessments to be quite modest, especially with the pooled assessment method.
In general, the differences in performance metrics due to assessment models (separate
versus pooled) were larger than the differences due to assessment frequency and approach to
setting TACs during rotational periods. This finding should be useful to fishery managers as they
consider where the right place is to put their time and resources. While our results are based on
lake whitefish, this species has is not dissimilar to many harvested fishes, and may in fact be
more prone to rapid changes in abundance than many. Consequently, we suspect that calls for
annual assessments (e.g., Mace et al, 2001) may often be misplaced, and that it may make more
sense to work on developing a correct assessment structure. Another concern based on our

80

result is that current 65% total mortality control rule may be not conservative enough for the low
productivity populations. We discuss this in detail in Chapter 1.
Like other simulation studies (Irwin et al. 2008, Deroba and Bence 2012), we made a
number of simplifying assumptions and choices, such as mixing pattern, different levels of
mixing rate and productivity of each population and which levels of productivity were most
representative. But we believe that our major qualitative conclusions are robust to those
assumption and simplifications. We emphasize here that our intent was not to make specific
tactical advice for a specific population, but rather to provide results that could provide general
guidance for managing the assessment process for populations somewhat similar to lake
whitefish. For example it might be reasonable to elect to move from annual to three year
assessments for a species with a similar life history, and use the resources freed up by this to
evaluate evidence for movement patterns (or other assumptions of the assessment) with a view
toward changing the assessment model based on the results. In our simulations the only
temporally varying process other than fishing was recruitment, and recruitment variation was
assumed to be distributed about a stationary stock recruitment relationship with uncorrelated
errors. When recruitment process are in flat or on other critical rates, such as natural mortality
are changing, these factors need to be considered when deciding on assessment frequency.
The basic premise of this study is that annual TACs would be set on the basis of a fitted
stock assessment model and that when the model was not fit every year TACs in rotational years
would be based on model projections since the last stock assessment. Alternatively, one could
view the periodic assessments as providing a calibration between some empiric quantity (such as
catch per effort) and an appropriate harvest level (Cox et al. 2008, Holland et al. 2010). One
version of this simply might treat periodic assessments as a way to update catchability estimates

81

to translate catch per effort to abundance. Alternatively, one could revise our view of
assessments to be primarily about gaining an understanding about how population dynamics
work, for use in evaluating alternative strategies (McDonald et al. 1997, Punt et al. 2008). In our
study the only use of data we considered for the period between assessments was in making
projections consistent with observed yield. Survey or fishery catch per effort might be more
informative and potentially could extend the period between assessments.

82

REFERENCES

83

REFERENCES

Caroffino, D.C., and S.J. Lenart. 2009a. Executive Summary in Caroffino, D.C., and S.J. Lenart
(eds.). Technical Fisheries Committee Administrative Report 2008: Status of Lake Trout and
Lake Whitefish Populations in the 1836 Treaty-Ceded Waters of Lakes Superior, Huron and
Michigan, with recommended yield and effort levels for 2008.

Caroffino, D.C., and S.J. Lenart. 2009b. Executive Summary in Caroffino, D.C., and S.J. Lenart
(eds.). Technical Fisheries Committee Administrative Report 2009: Status of Lake
Trout and Lake Whitefish Populations in the 1836 Treaty-Ceded Waters of Lakes
Superior, Huron and Michigan, with recommended yield and effort levels for 2009.
Caroffino, D.C. and Lenart, S.J. 2011a. Executive Summary in Caroffino, D.C., and Lenart, S.J.,
eds. Technical Fisheries Committee Administrative Report 2010: Status of Lake Trout
and Lake Whitefish Populations in the 1836 Treaty-Ceded Waters of Lakes Superior,
Huron and Michigan, with recommended yield and effort levels for 2010.
Caroffino, D.C. and Lenart, S.J. 2011b. Executive Summary in Caroffino, D.C., and Lenart, S.J.,
eds. Technical Fisheries Committee Administrative Report 2011: Status of Lake Trout
and Lake Whitefish Populations in the 1836 Treaty-Ceded Waters of Lakes Superior,
Huron and Michigan, with recommended yield and effort levels for 2011.
Caroffino, D.C. and Lenart, S.J. 2012. Executive Summary in Caroffino, D.C., and Lenart, S.J.,
eds. Technical Fisheries Committee Administrative Report 2012: Status of Lake Trout
and Lake Whitefish Populations in the 1836 Treaty-Ceded Waters of Lakes Superior,
Huron and Michigan, with recommended yield and effort levels for 2012.
Cox, S. P., and Kronlund, A. R. 2008. Practical stakeholder-driven harvest policies for
groundfish fisheries in British Columbia, Canada. Fisheries Research, 94: 224–237.
Deroba, J.J., Bence, J. R., 2012. Evaluationg harvestcontrol rules for lake whitefish in the Great
Lakes: accounting for variable loge-history traits. Fish. Res. 94:210-223.
Ebener, M. P., T. O Brenden, G. M. Wright, M. L. Jones, and M. Faisal. 2010. Spatial and
temporal distributions of lake whitefish spawning stocks in Northern lakes Michigan and
Huron, 2003-2008. Journal of Great Lakes Research 36:38-51.
Fournier, D.A., Skaug, H.J., Ancheta, J., Ianelli, J., Magnusson, A., Maunder, M.N., Nielsen, A.,
Sibert, J.,
2012. AD Model Builder: using automatic differentiation for statistical
inference of highly parameterized complex nonlinear models. Optim. Methods Softw.
27:233–249.
Healey, M.C. 1978. Fecundity changes in exploited populations of lake whitefish (Coregonus
clupeaformis) and lake trout (Salvelinus namaycush). Canadian Journal of Fisheries and
Aquatic Sciences 35:945-950.

84

Henderson, B.A., J.J. Collins, and J.A. Reckahn. 1983. Dynamics of an exploited population of
lake whitefish (Coregonus clupeaformis) in Lake Huron. Canadian Journal of Fisheries
and Aquatic Sciences 40:1556-1567.
Holland, D. S. (2010), “Management Strategy Evaluation and Management Procedures: Tools
for Rebuilding and Sustaining Fisheries”, OECD Food, Agriculture and Fisheries
Working Papers, No. 25, OECD Publishing. doi: 10.1787/5kmd77jhvkjf-en.
ICES, 2012. Report of the Workshop on Frequency of Assessments(WKFREQ), 6-8 March 2012,
By Correspondence. ICES CM 2012/ACOM:34. 29 pp.
Irwin, B.J., Wilberg, M.J., Bence, J.R., Jones, M.L., 2008. Evaluating Alternative Harvest
Policies for Yellow Perch in Lake Michigan. Fish. Res. 94:267–281.
Kell, L. T., Pilling, G. M., Kirkwood, G. P., Pastoors, M., Mesnil, B., Korsbrekke, K., Abaunza,
P. et al. 2005a. An evaluation of the implicit management procedure used for some ICES
roundfish stocks. ICES Journal of Marine ScICES. 2012ience, 62: 750–759.
Kratzer, J.F. 2006. Changes in growth, condition, fecundity, and egg lipid content of lake
whitefish in the upper Great Lakes between 1986-87 and 2003-05. Doctoral dissertation,
Michigan State University, East Lansing.
Mace P. M., N.W. Bartoo, A. B. Hollowed, P. Kleiber, R. D. Methot, S. A. Murawski, J. E.
Powers, and G. P., Scott. 2001. Marine Fisheries Stock Assessment Improvement Plan.
NOAA Technical Memorandum NMFS-F/SPO-56.
McDonald, A.D., Smith, A.D.M., Punt, A.E., Tuck, G.N. and A.J. Davidson. 1997. Empirical
evaluation of expected returns from research on stock structure for determination of total
allowable catch. Natural Resource Modelling. 10(1): 3-29.

Molton, K. J., Brenden, T.O., Bence, J.R., 2012. Control rule performance for intermixing lake
whitefish populations on the 1836 Treaty waters of the Great Lakes : A simulation-based
evaluation. Journal of Great Lakes Research, 38: 686-698.
NOAA Pacific Islands Fisheries Science Center. Quarterly Research Bulletin. 2011. Estimating
“steepness” of the stock-recruitment relationship, a key measure of fish stock
productivity. http://www.pifsc.noaa.gov/qrb/2011_06/article_08.php.
Punt, A. E. 2008. Refocusing Stock Assessment in support of policy evaluation. Pages 139-152
in K. Tsukamoto, T. Kawamura, T. Takeuchi, T. D. Beard, and M. J. Kaiser, editors.
Fisheries for Global Welfare and Environment, 5th World Fisheries Congress.
TERRAPUB, Tokyo.
Quinn, II, T. J., and Deriso. R. B., 1999. Quantitative Fish Dynamics. Oxford Univ. Press, New
York, NY, 542 p.

85

Thomas, M. V., and R. C. Haas. 2005. Status of yellow perch and walleye in Michigan waters of
Lake Erie, 1999–2003. Michigan Department of Natural Resources, Fisheries Research
Report 2082, Ann Arbor.
Woldt, A.P., Bence, J.R., and Ebener, M.P. 2006. Executive Summary in Woldt, A.P., Sitar, S.P.,
Bence, J.R., and Ebener, M.P. (eds.). Technical Fisheries Committee Administrative
Report 2005: Status of Lake Trout and Lake Whitefish Populations in the 1836 TreatyCeded Waters of Lakes Superior, Huron and Michigan in 2004, with recommended yield
and effort levels for 2005.
Woldt, A.P., Bence, J.R., and Ebener, M.P. 2007. Executive Summary in Woldt, A.P., and Sitar,
S.P. (eds.). Technical Fisheries Committee Administrative Report 2006: Status of Lake
Trout and Lake Whitefish Populations in the 1836 Treaty-Ceded Waters of Lakes
Superior, Huron and Michigan in 2005, with recommended yield and effort levels for
2006.
Woldt, A.P., Bence, J.R., and Ebener, M.P. 2008. Executive Summary in Woldt, A.P., and Caroffino,
D.C. (eds.). Technical Fisheries Committee Administrative Report 2007: Status of Lake
Trout and Lake Whitefish Populations in the 1836 Treaty-Ceded Waters of Lakes Superior,
Huron and Michigan in 2006, with recommended yield and effort levels for 2007.

86

Figure 2.1: Structure of a simulation framework for evaluating stock assessment models’ performance.
87

Figure 2.2: A conceptual diagram of stock intermixing for four hypothetical lake whitefish populations that are spatially segregated
during spawning, but subsequently intermix during the non-spawning period when exploitation takes place. For interpretation of the
references to color in this and all other figures, the reader is referred to the electronic version of this thesis.
88

Figure 2.3

89

Figure 2.3 (cont’d)

90

Figure 2.3 (cont’d)

91

Figure 2.3 (cont’d)

92

Figure 2.3 (cont’d): Influence of one year lag. Shown are mean annual spawning stock biomass
(SSB) for each population (Figure 2.3a), fishery yield for fishing areas surrounding each
spawning area over the last 25 years of simulations (Figure 2.3b), the percentage of years SSB
falling below B20% for each population (Figure 2.3c), and inter annual variation of yield(Figure
2.3d). The X-axis of each section indicates whether there was no lag (L0) or a one year lag (L1).
The horizontal section name represents the assessment model and population information (for
2.3a and 2.3c) from the low productivity (LP) population to the high productivity (HP)
population. The dashed line is the 20% of unfished SSB (B20%). In Figure 2.3b and 2.3d, the
horizontal section name identifies the assessment model names and the four fishing areas
surrounding the spawning areas of the LP to HP populations separately. The box tops and
bottoms cover the interquartile range; the horizontal middle line represents the median value of
all simulations for each scenario.

93

Figure 2.4
94

Figure 2.4 (cont’d): The influence of assessment frequency and harvest limit setting rule. Shown are mean annual spawning stock
biomass (SSB) for each population (Figure 2.4a), fishery yield for fishing areas surrounding each spawning area (Figure 2.4b). The Xaxis of each section represents six annual and multiannual quotas: “CT3”, “CT5”, “TF3”, “TF5”, “AY3”, and “AY5”. The horizontal
section name represents the assessment model and population information (for 2.4a) from the low productivity (LP) population to the
high productivity (HP) population. The dashed line is the 20% of unfished SSB (B20%). In Figure 2.4b, the horizontal section name
identifies the assessment models and the four fishing areas surrounding the spawning areas of the LP to HP populations separately.
The box tops and bottoms cover the interquartile range; the horizontal middle line represents the median value of all simulations for
each scenario.

95

Figure 2.5
96

Figure 2.5 (cont’d): The influence of assessment frequency and harvest limit setting rule. Shown are the proportion of years SSB
falling below B20% for each population (Figure 2.5a), and inter annual variation of yield (Figure 2.5b) under mixing scenario
“SR=0.5”. All results are for the last 25 years of simulations. The X-axis of each section represents six annual and multiannual quotas:
“CT3”, “CT5”, “TF3”, “TF5”, “AY3”, and “AY5”. The horizontal section name represents the assessment model and population
information (for 2.5a) from the low productivity (LP) population to the high productivity (HP) population. In Figure 2.5b, the
horizontal section name identifies the assessment models and the four fishing areas surrounding the spawning areas of the LP to HP
populations separately. The box tops and bottoms cover the interquartile range; the horizontal middle line represents the median value
of all simulations for each scenario.

97

Table 2.1: Four different levels of productivity for lake whitefish. Simulated populations have different levels of productivity and
steepness values. Their population indexes were defined based on their productivities, from low productivity (LP) to high productivity
(HP). Alpha and beta are the Ricker stock–recruitment coefficients that were adjusted by different steepness levels for lake whitefish
spawning populations.
Population index

Productivity level

Steepness

α

LP population

Low

0.7

5.23× 10

MLP population

Mid-low

1.1

9.19× 10

MHP population

Mid-high

1.5

1.35× 10

HP population

High

1.9

1.82× 10

98

β
-4
-4
-3
-3

-10

1.51× 10

-10

2.06× 10

-10

2.43× 10

-10

2.72× 10

Table 2.2: Equations used in stochastic simulation model

Equation

Description of

index

equation

(T.2.2.1)

Ricker stockrecruitment

Equation

Parameter

𝑅 𝑖,𝑦 = 𝛼 𝑖 𝑆𝑆𝐵 𝑖,𝑦−1 𝑒 −𝛽 𝑖 𝑆𝑆𝐵 𝑖,𝑦−1 𝑒 𝜀 𝑅,𝑖,𝑦

𝛼: see Table 1
𝛽: see Table 1

𝜀 𝑅,𝑖,𝑦 ~ N(0,

function by year

𝜎 𝑅 2)

(y) and
population (i)

𝜎 𝑅 = 0.6

99

Table 2.2 (cont’d)

(T.2.2.2)

age-specific SSB
by year (y)

(T.2.2.3)

(T.2.2.4)

Length at age

Weight at age

𝑆𝑆𝐵 𝑦 = � 𝐹𝑒𝑚 𝑁 𝑦,𝑎 𝑚 𝑎 𝑊𝑎
𝑎

𝐿 𝑎 =𝐿∞ (1 − exp(−𝜅(𝑎 − 𝑡0 )))

𝑊𝑎 = 𝛾𝐿 𝑎

𝐹𝑒𝑚 =0.5

𝐿∞ =60.9

𝜅=0.1686

𝑡0 =0.0

𝛾= 8.06 × 10−5

𝜓

𝜓=2.45

100

Table 2.2 (cont’d)

(T.2.2.5)

Maturity at age

(T.2.2.6)

Selectivity at
age

𝑚𝑎 =

𝑚∞
1 + exp(−𝜗(𝐿 𝑎 − 𝛿))

𝑎 𝜂 exp(−𝜏𝛼)
𝑠𝑎 =
10 𝜂 exp(−𝜏10)

101

𝜗=0.315

𝛿=37.9

𝜂= 13.074

𝜏= 1.26

Table 2.2 (cont’d)

(T.2.2.7)

Actual catch by
Baranov’s catch
equation by year
(y) and

𝐶 𝑖,𝑦

𝐹𝑖,𝑦,𝑎
=�
(1
𝑀 + 𝐹𝑖,𝑦,𝑎
𝑛

𝑎=1

− 𝑒 −𝑀−𝐹 𝑖,𝑦,𝑎 ) 𝑁 𝑖,𝑦,𝑎

population (i),
given fishing
mortality rates
and abundance

102

𝑀= 0.25

Table 2.2 (cont’d)

(T.2.2.8)

Actual catch by
year (y) and

𝐶

𝑗,𝑦

= 𝑇𝐴𝐶𝑗,𝑦 𝑒𝑥𝑝(𝜐 𝑖,𝑦 − 0.5𝜎 𝑐 2 )

population (i)
given the TAC.

(T.2.2.9)

likelihood
component for
total catch

𝑐̂ 𝑦
1
ℓ 𝑐 = 𝑛 𝑐 𝑙𝑜𝑔 𝑒 ( � 𝑐 ) + (
𝜎
) � 𝑙𝑜𝑔 𝑒 ( )2
̂𝑦
𝑐̃
2𝜎 𝑐 2 𝑦
�
𝑛 𝑐 = 𝑐̂ 𝑦 − ̂ 𝑦
𝑐̃

103

𝜐 𝑖,𝑦 ~ N(0, 𝜎 𝑐 2 )
𝜎 𝑐 = 0.1

�𝑐
𝜎

Table 2.2 (cont’d)

(T.2.2.10) Likelihood
component for

ℓ 𝜀𝐹 = 𝑛 𝜀𝐹 𝑙𝑜𝑔 𝑒 �
+(

fishing
mortality-effort
relationship

(T.2.2.11) Likelihood
component for
age composition

√0.25

0.25

�

)�
2𝜎 𝑐 2 𝑦
�

𝑙𝑜𝑔 𝑒 (𝜀𝐹)2

ℓ 𝑝 = − � 200 �(𝑝 𝑦,𝑎 𝑙𝑜𝑔 𝑒 � 𝑦,𝑎 )
�
𝑝
𝑦

𝑎

of the fishery
harvest

104

Table 2.3: Design of assessment process based on different timetable and frequency of assessment, and harvest limit setting rules for
rotation years.
Scenario names Assessment Frequency (Year) Lag (Year) Harvest limit setting between assessments
L0

1

0

/

L1 (status quo)

1

1

/

CT3

3

1

Constant TAC

CT5

5

1

Constant TAC

CF3

3

1

Target F

CF5

5

1

Target F

AY3

3

1

Add yield information

AY5

5

1

Add yield information

105

Table 2.4: Mixing scenarios. In all scenarios each of the four populations had different productivity, with one population taking each
of the four alternative productivity levels (Table 1).
Mixing

Description

Scenario
Scenario 1

All populations have same high stay rate (0.9)

Scenario 2

All populations have same medium-low stay rate (0.5)

Scenario 3

All populations have same low stay rate (0.25)

Scenario 4

Positive-correlated stay rates and productivity. Four stay rates (0.25, 0. 5, 0.75, 0.9) matched in rank order to
productivity of four populations

Scenario 5

Negative-correlated stay rates and productivity. Four stay rates (0.9, 0.75, 0. 5, 0.25) matched in rank order to
productivity of four populations

106

Table 2.5: The relative change of the median of LP SSB due to assessment frequency and assessment model under different mixing
scenarios
Change due to assessment frequency
Mixing Scenarios

Change due to assessment model

Model

Frequency

Relative change

Relative change

Separate

L1

0.349

Pool

-0.060

TF5

0.514

0.034

L1

-0.221

Pool

-0.062

TF5

-0.293

Separate

-0.007

L1

-0.229

Pool

-0.063

TF5

-0.273

Separate

-0.010

L1

0.139

Pool

-0.052

TF5

0.090

Separate

SR=0.9

-0.163

-0.082

L1

-0.278

Pool

-0.061

TF5

-0.262

Separate
SR=0.5

SR=0.25

po-cor

ne-cor

107

Table 2.6: The relative change of the median of total yield due to assessment frequency and assessment model under different mixing
scenarios
change due to assessment frequency

change due to assessment model

Mixing Scenarios

Model

Frequency

SR=0.9

Separate

-0.078

L1

0.013

SR=0.9

Pool

-0.018

TF5

0.079

SR=0.5

Separate

-0.028

L1

0.019

SR=0.5

Pool

-0.024

TF5

0.023

SR=0.25

Separate

-0.040

L1

0.019

SR=0.25

Pool

-0.025

TF5

0.035

po-cor

Separate

-0.041

L1

0.050

po-cor

Pool

-0.023

TF5

0.069

ne-cor

Separate

-0.031

L1

-0.002

ne-cor

Pool

-0.023

TF5

0.007

Relative change

108

Relative change

APPENDIX

109

APPENDIX

This appendix presents additional plots beyond those presented in the main text.
Displayed are all the results for four performance metrics, four populations with different levels
of productivity, three assessment models, five levels of intermixing rate, and eight assessment
frequency, lag, and TACs for rotation years setting rules.

110

Figure 3.1

111

Figure 3.1 (cont’d): Mean annual spawning stock biomass (SSB) for each population over the
last 25 years of simulations. The X-axis of each section indicates the assessment design scenarios.
The horizontal section name represents the five mixing scenarios. The horizontal section name
represents the five mixing scenarios. The labels in X-axis showed two assessment models. For
each assessment model, four boxes represent four populations from the low productivity (LP)
population to the high productivity (HP) population. The dashed line is the 20% of unfished SSB
(B20%). The box tops and bottoms cover the interquartile range; the horizontal middle line
represents the median value of all simulations for each scenario.

112

Figure 3.2: As for Figure 3.1, except y-axis is mean annual fishery yield for fishing areas
surrounding each spawning area.

113

Figure 3.3: As for Figure 3.1, except y-axis is probability of SSB for each population being less
than 20% of the unfished SSB level.

114

Figure 3.4: As for Figure 3.1, except y-axis is mean inter-annual percent variation in fishery
yield.

115