KEEPING UP WITH THE TIMES: ARE MORE CONSERVATIVE CONTROL RULES
NEEDED TO PROTECT INTERMIXING LAKE WHITEFISH POPULATIONS?

By
Kyle J. Molton

A THESIS
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
MASTER OF SCIENCE
Fisheries and Wildlife
2011

ABSTRACT
KEEPING UP WITH THE TIMES: ARE MORE CONSERVATIVE CONTROL RULES
NEEDED TO PROTECT INTERMIXING LAKE WHITEFISH POPULATIONS?
By
Kyle J. Molton
The goals of this research were to: 1) investigate how intermixing of populations affected
the performance of the 65% total mortality control rule that is currently used to manage lake
whitefish (Coregonus clupeaformis) fisheries in the 1836 Treaty waters (TW) of the Great
Lakes; and 2) explore the performance of alternative mortality rates for lake whitefish fisheries
in the 1836 TW under different intermixing and productivity scenarios. The simulation
framework that was developed modeled the dynamics of four intermixing, age-structured fish
populations with varying levels of productivity. The framework also included a full agestructured assessment of the mixed fisheries, with abundance, mortality and recruitment
estimates from these assessments used in combination with harvest control rules to set total
allowable catches for stocks. In chapter 1, the 65% total mortality control rule was found to
perform poorly in terms of protecting lower productivity populations. Yields from areas
occupied by low productivity populations were often similar in magnitude to areas occupied by
high productivity populations as a result of intermixing, which could result in managers thinking
low productivity populations could be fished more intensively. In chapter 2, 45% and 55% total
mortality control rules were found to perform better than the current control rule in ensuring
population sustainability, maximizing yields, and increasing yield stability under certain
productivity and intermixing levels. Alternative control rules resulted in mortality rates similar
to what has been estimated for lake whitefish stocks in the 1836 TW, reducing the potential
effects on commercial fishers if the control rule was indeed changed to this lower mortality rate.

ACKNOWLEDGEMENTS

I am extremely grateful to those who have influenced me and provided assistance to me
throughout my research program. My advisor, Dr. Travis Brenden provided guidance and helped
steer my academic wanderings to the appropriate bearing on numerous occasions, while fostering
my future aspirations. Weihai Liu provided invaluable assistance in model development that I
am certain prevented enormous frustration. My graduate committee, Dr. James Bence, Dr. Frank
Lupi, and Nicholas Popoff provided insight and perspective that benefited my project and
perspective considerably. The Modeling Subcommittee of the 1836 Treaty Waters helped to
inspire this project and my initial interest in population intermixing as it pertained to fisheries
management. Faculty and staff of the Fisheries and Wildlife Department provided assistance
that smoothed the pathway to completing my degree. Colleagues at the Quantitative Fisheries
Center always provided assistance and stimulating conversation. I also acknowledge support
from the Michigan Department of Natural Resources and the U.S.F.W.S Sportfish Restoration
Program (through Project F-80-R to the State of Michigan).
I would additionally like to thank all of my family and friends. My parents, Daryl and
Laurie Molton, have been supportive of me in so many ways and have encouraged my curiosity
for nature and the drive to challenge myself since I can remember. My sister, Jada Molton, helps
me to see the world from a different perspective and inspires the best in me. My grandparents,
with me both in person and in memory, provided the foundation upon which I cement my sense
of self. All of my friends, who always provide the much needed distraction and conversation
that sustains and inspires my excitement for the past, the present, and the future. To all of you I
am forever grateful. Thank you.

iii

PREFACE

The chapters of this thesis were drafted as standalone papers that will be submitted for
publication in peer-review journals. Chapter 1 is intended for submission to the Journal of Great
Lakes Research; Chapter 2 is intended for submission to Fisheries Research. The bibliographic
references in this thesis are therefore formatted according to the requisite reference style for
those publications. When submitted, both manuscripts will include Drs. Travis Brenden and
James Bence as co-authors. Consequently, both Chapters 1 and 2 are written with first person,
plural narratives, even though I am listed as the sole author of the thesis.

iv

TABLE OF CONTENTS
LIST OF TABLES ........................................................................................................................ vii
LIST OF FIGURES ..................................................................................................................... viii
INTRODUCTION .......................................................................................................................... 1
References ........................................................................................................................... 4
CHAPTER 1
CONTROL RULE PERFORMANCE FOR INTERMIXING LAKE WHITEFISH
POPULATIONS IN THE 1836 TREATY WATERS OF THE GREAT LAKES: A
SIMULATION-BASED EVALUATION ...................................................................................... 7
Abstract ............................................................................................................................... 7
Introduction ......................................................................................................................... 8
Methods............................................................................................................................. 12
Definitions of Terms ............................................................................................. 12
Model of Lake Whitefish Dynamics ..................................................................... 13
Observation Components ...................................................................................... 17
Assessment Model ................................................................................................ 19
Abundance Projections and TAC Calculations..................................................... 23
Experimental Design ............................................................................................. 23
Performance Metrics and Simulation Details ....................................................... 24
Results ............................................................................................................................... 25
All Shared Group .................................................................................................. 26
Shared Mixing Group ........................................................................................... 27
Shared Productivity Group ................................................................................... 28
Correlated Group .................................................................................................. 29
Discussion ......................................................................................................................... 30
Appendix ........................................................................................................................... 36
References ......................................................................................................................... 52
CHAPTER 2
HARVEST CONTROL RULES THAT CONSERVE SPAWNING BIOMASS MAY PROVIDE
HIGHER AND MORE STABLE YIELDS FOR INTERMIXED FISHERIES .......................... 59
Abstract ............................................................................................................................. 59
Introduction ....................................................................................................................... 60
Methods............................................................................................................................. 62
Operating Model ................................................................................................... 63
Observation components ....................................................................................... 65
Assessment Model and TAC Generation .............................................................. 66
Experimental Control Rules and Scenarios .......................................................... 69
Performance Metrics ............................................................................................. 72
Results ............................................................................................................................... 73
No Mixing Scenarios ............................................................................................ 73
Correlated Scenarios ............................................................................................. 75
v

State Shift Scenarios ............................................................................................. 77
Shared Intermixing, Varied Productivity Scenarios ............................................. 77
Discussion ......................................................................................................................... 79
Appendix ........................................................................................................................... 84
References ....................................................................................................................... 113
CONCLUSIONS......................................................................................................................... 119

vi

LIST OF TABLES
Table 1.1. Equations with descriptions and values for fixed variable inputs used in the simulation
of lake whitefish populations and fisheries in this analysis. ......................................................... 47
Table 1.2. Ricker stock-recruitment coefficients (Table 1.1) that were assumed for the different
productivity levels for lake whitefish spawning populations for assessing the effects of stock
intermixing on the current 65% total annual mortality control rule used to manage lake whitefish
fisheries in the 1836 Treaty waters of the Great Lakes. ............................................................... 48
Table 1.3. Assumed intermixing (M) and productivity (P) levels of individual spawning
populations for each of the scenarios investigated in this research. Intermixing values indicate
the percent of lake whitefish that move from the natal region during the harvest season.
Productivity levels refer to high (H), medium-high (MH), medium-low (ML), or low (L)
productivities as described in Table 1.2. ....................................................................................... 49
Table 1.4. Median of the mean relative error (MRE) and the mean absolute relative error
(MARE) for lake whitefish harvest and abundance estimates from the SCAA assessments across
stocks and simulations. The values in parentheses are the ranges of the MREs and MAREs
values. See Table 1.3 for a description of the Scenarios. ............................................................ 51
Table 2.1. Descriptions and values (if applicable) for index and state variables, structural
parameters, stochastic deviation and error terms, and likelihood components used in the
description of equations for models used in this analysis. Variables and parameters denoted with
diacritical marks (i.e. ^ or ¯) are identical to those describe in Table 2.1, but are used to denote
either an estimated quantity (^) or the mean (¯) of a variable. ................................................... 106
Table 2.2. Operating and assessment model equations. Variables and parameters denoted with
diacritical marks (i.e. ^ or ¯) are identical to those describe in Table 2.1, but are used to denote
either an estimated quantity (^) or the mean (¯) of a variable. ................................................... 108
Table 2.3. Productivity levels, intermixing rates, and control rules used in each of the scenarios
evaluated in this research. Varied productivity refers to cases where the 4 different spawning
population were assigned unique stock recruitment relationship. .............................................. 110
Table 2.4. Recruitment parameters for the four productivity levels assigned to spawning
populations in this analysis. ........................................................................................................ 112

vii

LIST OF FIGURES
Figure 1.1. Ricker-stock recruitment relationships for the four levels of productivity used to
investigate the effects of population intermixing on the 65% total annual mortality control rule
used to manage lake whitefish fisheries in the 1836 Treaty waters of the Great Lakes. .............. 37
Figure 1.3. Mean annual cumulative fishery yield summed for each investigated scenario. Boxes
th

th

indicate the 25 and 75 percentiles over the simulations, while whiskers indicate 1.5 times the
interquartile range over simulations. Horizontal lines indicate the median of the yields for the
simulations. On the x-axis, vertically oriented labels correspond to specific scenarios. See Table
1.3 for a description of the scenarios (A=all shared; B=shared mixing; C=shared productivity;
D=correlated). ............................................................................................................................... 40
Figure 1.4. As for Fig. 1.3, except y-axis is mean inter-annual percent variation in fishery yield.
....................................................................................................................................................... 42
Figure 1.5. As in Fig. 1.3, except y-axis is the mean percentage of years in each simulation that
the spawning stock biomass declined to less than 20 percent of the unfished spawning stock
biomass (SSBF=0). ........................................................................................................................ 44
Figure 1.6. As in Fig 1.3, except y-axis is mean annual percentage of unfished spawning stock
biomass (SSBF=0) for the spawning populations ......................................................................... 46
Figure 2.1. The four productivity levels used in this simulation analysis. The higher steepness at
low SSB indicates higher capacity for the population to rebound from depletion and therefor
higher productivity. Recruitment is defined as age-1 fish in the population the year following
spawning. ...................................................................................................................................... 85
Figure 2.2. Performance metrics for scenarios without intermixing between stocks. Labels along
the y-axis represent the different performance metrics used to compare harvest policies in this
analysis. Mean annual yield is represented in tonnes. Inter-annual variation in yield, the
percentage of years spawning stock biomass fell below 20% of unfished spawning stock biomass
(SSBF=0), and mean percentage of SSBF=0 are all expressed in a percentage. The labels along
the x-axis describe the productivity and intermixing level of the spawning population in each
stock, while the numbers at the tick marks correspond to the allowable annual mortality rates
investigated in this analysis. ......................................................................................................... 87
Figure 2.3. As in Figure 2.2, except for scenarios when productivity and intermixing are
positively correlated. ..................................................................................................................... 89
viii

Figure 2.4. As in Figure 2.2, except for scenarios when productivity and intermixing are
negatively correlated ..................................................................................................................... 91
Figure 2.5. Mean annual cumulative fishery yield summed for each investigated scenario.
Cumulative yields for the No Mixing group of scenarios are not presented as for these scenarios
stocks differed in the harvest control rules so comparisons of yields with other scenarios would
th

th

not be informative. Boxes indicate the 25 and 75 percentiles over the simulations, while
whiskers indicate 1.5 times the interquartile range over simulations. Horizontal lines indicate the
median of the yields for the simulations. On the x-axis, numbered labels correspond to specific
scenarios within each category. See Table 2.3 for a description of the scenarios. ...................... 92
Figure 2.6. As in Figure 2.2, except for the state shift scenarios with relatively high productivity
and relatively low intermixing. ..................................................................................................... 94
Figure 2.7. As in Figure 2.2, except for the state shift scenarios with relatively low productivity
and relatively high intermixing. .................................................................................................... 96
Figure 2.8. As in Figure 2.2, except for the shared mixing scenarios with varied productivity and
low intermixing. ............................................................................................................................ 98
Figure 2.9. As in Figure 2.2, except for the shared mixing scenarios with varied productivity and
medium-low intermixing. ........................................................................................................... 100
Figure 2.10. As in Figure 2.2, except for the shared mixing scenarios with varied productivity
and medium-high intermixing..................................................................................................... 102
Figure 2.11. As in Figure 2.2, except for the shared mixing scenarios with varied productivity
and high intermixing. .................................................................................................................. 104
Figure 2.12. Total mortality estimates for the highest selected age class for selected lake
whitefish stocks in northern Lakes Huron and Michigan according to the 2010 stock assessments
(Carrofino and Lenart, 2011). These values are compared to the total annual mortality targets
under the control rules investigated in this research study. ........................................................ 105

ix

INTRODUCTION
Management of lake whitefish (Coregonus clupeaformis) fisheries in the 1836 Treaty
waters (TW) of the Great Lakes uses a stock-based management approach, with assessments
conducted on and total allowable catches set for individual stocks (Ebener et al., 2005; Woldt et
al., 2007). A common assumption with stock-based management is that exploited fisheries are
comprised of fish from a single spawning population. Recent evidence, however, suggests that
lake whitefish populations in the 1836 TW intermix considerably during non-spawning periods
and that many of the fish stocks exploited by commercial fishers consist of individuals from
multiple spawning populations (Ebener et al., 2010). This intermixing is not accounted for in
current assessment and management of lake whitefish fisheries, but nevertheless is a source of
concern. Intermixing of populations can have implications on fishery yields and sustainability of
individual populations depending on the degree of mixing, the underlying dynamics of the
populations, and the harvest policies that are used to manage the fisheries (Heifetz et al., 1997;
Quinn and Deriso, 1999; Punt et al., 2005; Dichmont et al., 2006; Punt, 2008; Kell et al,. 2009;
Kerr et al., 2010). Despite a general consensus that intermixing of fish populations is important,
a lack of understanding as to its effects makes it difficult to know if existing harvest policies for
lake whitefish fisheries in the 1836 TW are appropriate. Alternate strategies have been proposed
to account for population intermixing in some lake whitefish management units in the 1836 TW
(Ebener et al., 2010), but, to date, no formal assessment has been conducted to compare
performance of these different strategies.
Management of commercial and recreational fisheries often depends on harvest policies
set by managers seeking specific ecological, economic, and social outcomes. Balance between
conservation and economic objectives can be difficult to achieve due to conflicts between the

1

objectives (Hall and Donovan, 2002). It has been recommended that harvest policies be chosen
using computer-based simulations that consider uncertainties intrinsic to the system being
managed, weighing the ability of different approaches to meet desired outcomes (Cooke, 1999;
Smith et al., 1999; Punt et al., 2002; Kell et al., 2006; Deroba and Bence, 2008). Simulationbased evaluations have been used to investigate performance of different harvest policies for lake
whitefish fisheries in the Great Lakes while accounting for factors such as stochasticity in life
history attributes (Deroba, 2009). To date, simulation-based evaluations of the performance of
different harvest policies that also account for intermixing among lake whitefish populations
have not been conducted. Simulation modeling has shown considerable promise as a method to
better understand the management implications of spatial structure of stocks (Kerr et al., 2010),
but spatial structure has seldom been incorporated into actual evaluations. Notable exceptions
include the evaluations conducted by Heifetz et al. (1997), Punt et al. (2005), Dichmont et al.
(2006), Wilberg et al. (2008), and Kell et al. (2009). Two reasons why spatial structure or
intermixing of fish populations is not commonly included in formal harvest policy evaluations
are that there are limited methods for modeling intermixing of fish populations and also many
systems lack reliable estimates of intermixing rates required for such an analysis (Quinn and
Deriso, 1999).
The goal of this research was to determine the effectiveness of the current control rule
and alternative variants of that rule for management of lake whitefish in the 1836 TW of the
Great Lakes, taking into consideration recent evidence that some populations intermix
considerably during the harvest season. In Chapter 1, I investigate how intermixing of
populations affects the performance of the 65% total mortality control rule that is currently used
to manage lake whitefish fisheries in the 1836 TW. In Chapter 2, I explore the performance of

2

alternative control rules for lake whitefish populations under different scenarios of population
intermixing and productivity levels. Each chapter was intended to provide valuable information
regarding the management of lake whitefish fisheries in the Great Lakes, but also to be
informative to broader audiences due to the commonness of population intermixing.

3

REFERENCES

4

References
Cooke, J. G., 1999 Improvement of fishery-management advice through simulation testing of
harvest algorithms. ICES J. Mar. Sci. 56, 797-810.
Deroba, J. J., 2009. How many fish are there and how many can we kill? Improving catch per
effort indices of abundance and evaluating harvest control rules for lake whitefish in the
Great Lakes. Doctoral dissertation. Michigan State University, East Lansing.
Deroba, J. J., Bence, J. R., 2008. A review of harvest policies: Understanding relative
performance of control rules. Fish. Res. 94, 210-223.
Dichmont, C. M., Deng, A. R., Punt, A. E., Venables, W., Haddon, M., 2006. Management
strategies for short-lived species: the case of Australia's Northern Prawn Fishery: 1.
accounting for multiple species, spatial structure and implementation uncertainty when
evaluating risk. Fish. Res. 82, 204-220.
Ebener, M. P., Bence, J. R., Newman, K., Schneeberger, P. J., 2005. Application of statistical
catch-at-age models to assess lake whitefish stocks in the 1836 Treaty-Ceded Waters of
the upper Great Lakes, In: Mohr, L. C., Nalepa, T. F., (Eds.), 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, pp. 271-309.
Ebener, M. P., Brenden, T. O., Wright, G. M., Jones, M. L., Faisal, M., 2010. Spatial and
temporal distributions of lake whitefish spawning stocks in Northern lakes Michigan and
Huron, 2003-2008. J. Great Lakes Res. 36 (Supplement 1), 38-51.
Hall, M. A., Donovan, G. P., 2002. Environmentalists, fishermen, cetaceans and fish: is there a
balance and can science find it? In: Evans, P. G., Raga, J. A., (Eds.), Marine mammals:
biology and conservation. Kluwer Academic/Plenum Publishers. New York, pp. 491-521.
Heifetz, J., Fujioka, J. T., Quinn, T. J. II., 1997. Geographic apportionment of sablefish,
Anoplopoma fimbria, harvest in the northeastern Pacific Ocean. NOAA Tech Rep,
National Marine Fisheries Service 130, 229-237.
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., De Oliveira, J. A. A., Punt, A. E., McAllister, M. K., Kuikka, S., 2006. Operational
management procedures: an introduction to the use of evaluation frameworks, In: Motos,
L., Wilson, D., (Eds.), The Knowledge Base for Fisheries Management. Elsevier. Oxford,
United Kingdom, pp. 379-407.

5

Kerr, L. A., Cadrin, S. A., Secor, D. H., 2010. Simulation modeling as a tool for examining the
consequences of spatial structure and connectivity on local and regional population
dynamics. ICES J. Mar. Sci. 67, 1631-1639.
Punt, A. E., 2008. Refocusing stock assessment in support of policy evaluation, In: Tsukamoto,
K., Kawamura, T., Takeuchi, T., Beard, T. D., Kaiser, M. J., (Eds.), Fisheries for Global
Welfare and Environment, 5th World Fisheries Congress. TERRAPUB, Tokyo, pp. 139152.
Punt, A. E., Pribac, F., Taylor, B. L., Walker, T. I., 2005. Harvest strategy evaluation for school
and gummy shark. J. Northwest Atl. Fish. Sci. 35, 387-406.
Punt, A. E., Smith, A. D. M., Cui, G., 2002. Evaluation of management tools for Australia's
South East Fishery 1. Modeling the South East Fishery taking account of technical
interactions. Mar. Freshw. Res. 53, 615-630.
Quinn, T. J. II., Deriso, R. B., 1999. Quantitative fish dynamics. Oxford University Press, New
York.
Smith, A. D. M., Sainsbury, K. J., Stevens, R. A., 1999. Implementing effective fisheriesmanagement systems-management strategy evaluation and the Australian partnership
approach. ICES J. Mar. Sci. 56, 967.
Wilberg, M. J., Irwin, B. J., Jones, M. L., Bence, J. R., 2008. Effects of source-sink dynamics on
harvest policy performance for yellow perch in southern Lake Michigan. Fish. Res. 94,
282-289.
Woldt, A.P., Bence, J. R., Ebener, M. P., 2007. Recommendations and future directions to
improve assessments, In: Woldt, A. P., and Sitar, S. P., (Eds.) 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. Technical
Fisheries Committee Administrative Report 2006, pp. 17-22.

6

CHAPTER 1
CONTROL RULE PERFORMANCE FOR INTERMIXING LAKE WHITEFISH
POPULATIONS IN THE 1836 TREATY WATERS OF THE GREAT LAKES: A
SIMULATION-BASED EVALUATION

Abstract
We conducted a simulation-based evaluation exploring the effects of population
intermixing on the current 65% total annual mortality control rule used to manage lake whitefish
(Coregonus clupeaformis) fisheries in the 1836 Treaty waters of the Laurentian Great Lakes.
The simulations incorporated intermixing among four populations with characteristics similar to
that of populations in northern lakes Huron and Michigan. Dynamics of each population were
simulated for 100 years with each stock exploited by a single fishery. An age-structured
assessment of each stock was conducted every third year, with the abundance, mortality, and
recruitment estimates used with the current control rule to set future harvest limits. Mean annual
yield, inter-annual variation in yield, mean percentage of unfished spawning biomass (SSBF=0),
and percentage of years that spawning biomass declined to less than 20% SSBF=0 were used to
evaluate the performance of the 65% total annual mortality control rule to different population
intermixing and productivity scenarios. Mean annual yield was the most sensitive metric to
assumptions about intermixing and population productivity. Yields from areas occupied by low
productivity populations were often similar to those occupied by high productivity populations
when intermixing occurred, which could result in managers thinking low productivity
populations could be fished more intensively. Large yields occurred despite spawning biomass
7

levels of low productivity populations generally being less than 20% of SSBF=0, suggesting that
the current control rule may not offer adequate protection to low productivity populations and
that more conservative rules may be needed to ensure sustainability of intermixed populations.

Introduction
The 1836 Treaty waters (TW) of lakes Huron, Michigan and Superior is a region of the
Laurentian Great Lakes comprising approximately 5.8 million ha that was ceded to the U.S.
federal government by the Chippewa and Ottawa Nations of Native Americans as part of the
Treaty of Washington. Although lands and waters within the treaty boundaries were ceded to the
federal government, tribal members retained the right to subsistence hunt and fish free of state
regulations. The right to subsistence fish in the 1836 TW was upheld in both a 1979 U.S.
District Court ruling (United States v. Michigan, 1979) and a 1981 U.S. Court of Appeals ruling
(United States v. Michigan, 1981). In addition to having the recognized right to fish free of state
regulations, Native American tribes also are expected to participate in the management of 1836
TW fisheries to ensure protection and future sustainability of the resources (Brenden et al., in
press). Two federal-ordered Consent Decrees that govern the management, allocation, and
regulation of fishery resources within the 1836 TW have been enacted that have evolved through
negotiations between representatives of the State of Michigan, the U.S. Department of Interior,
and several Chippewa-Ottawa tribal governments (Ebener et al., 2008). The first Consent
Decree was enacted in 1985; the second was enacted in 2000 and will expire in 2020.
Management of lake whitefish (Coregonus clupeaformis) and lake trout (Salvelinus namaycush)
stocks within the 1836 TW is the primary focus of the 1985 and 2000 Consent Decrees, although
management of several other species is also addressed.

8

As part of the 2000 Consent Decree, a set of guidelines for managing lake whitefish
fisheries in each of the 18 lake whitefish management units that lie within the 1836 TW was
enacted. The guidelines define a maximum allowable annual mortality rate of 65%, which has
been further refined to a harvest control rule of 65% total allowable annual mortality on the age
class with the greatest fishing mortality. Additionally, it has been stipulated that spawning stock
biomass per recruit (SSBR) in each of the management areas should not fall below 20% of what
each stock would achieve without fishing (Mohr and Ebener, 2005). If a 65% mortality rate
results in SSBR falling below this level, then the mortality rate is reduced until a 20% SSBR
level is obtained. The 2000 Consent Decree specifies that harvest limits within each
management unit will be calculated using appropriate statistical and mathematical modeling
techniques. Presently for most management units, statistical catch-at-age (SCAA) models are
used to annually estimate mortality rates and project lake whitefish abundances at age (Caroffino
and Lenart, 2011). These projected abundances along with the 65% total annual mortality
control rule are then used to generate total allowable catches (TAC) for each unit (Ebener et al.,
2005; Mohr and Ebener, 2005). Apportionment of the TAC to state and tribal fishers differs by
management unit with the exact apportionments specified in the 2000 Consent Decree.
Lake whitefish management units were originally delineated to represent the spatial
distributions of reproductively isolated spawning populations and the dynamics of the fisheries
that exploited the populations (Rybicki and Schneeberger, 1990; Ebener et al., 2005, 2008). This
stock-based approach to management was proposed in the 1970s to protect spawning populations
and thereby maintain genetic diversity of lake whitefish populations (Patriarche, 1977; Spangler
et al., 1981; MacLean and Evans, 1981). The intensive management actions implemented in the
1836 TW and elsewhere in the Great Lakes, along with reductions in sea lamprey (Petromyzon

9

marinus) densities, habitat restoration, and water quality improvements, have been credited with
the phenomenal rebound of lake whitefish from the low abundance levels of the 1950s and 1960s
(Ebener, 1997; Ebener et al., 2008). Recently, concerns have arisen that sustainability of lake
whitefish populations may be at risk due to major changes in the Great Lakes benthic
communities, including the collapse of the preferred prey of lake whitefish, Diporeia spp., and
increased abundance of non-native dreissenid mussels (Nalepa et al., 1998, 2007, 2009a). One
purported consequence of dreissenid mussel invasion has been a decrease in pelagic productivity
in invaded lakes (Vanderploeg et al., 2002; Higgins et al., 2011). This decline in productivity
coupled with increased lake whitefish abundance in the Great Lakes may be resulting in altered
lake whitefish foraging behavior (Pothoven and Madenjian, 2008; Nalepa et al., 2009b) as well
as reduced growth and body condition (Pothoven et al., 2001, Rennie et al., 2009), reduced egg
production and egg quality (Kratzer et al., 2007), and shifts in depth distribution (Mohr and
Ebener, 2005). Recent tagging and genetic studies conducted in northern lakes Huron and
Michigan suggest that movement of lake whitefish has also increased considerably over the last
15 to 30 years with fish from various spawning populations now intermixing substantially during
non-spawning periods (VanDeHey, 2009; Ebener et al., 2010; Stott et al., 2010). Although it is
not known definitively what has led to increased movement of lake whitefish, one obvious
hypothesis is that it is a consequence of reduced densities of Diporeia, which has resulted in fish
expanding foraging areas to meet energetic needs (Ebener et al., 2010).
Stock-based management, such as that implemented for lake whitefish in the 1836 TW,
has been a relatively common management approach both within the Great Lakes and more
broadly (Stephenson, 1999). A common underlying assumption of stock-based management is
that exploited stocks consist of fish from a single spawning population rather than consisting of

10

fish from multiple spawning populations. When exploited stocks consist of intermixed fish
populations, past research has found that stock-based management approaches can perform
poorly (Heifetz et al., 1997; Quinn and Deriso, 1999; Punt et al., 2005; Dichmont et al., 2006;
Punt, 2008). The sustainability of harvest and spawning populations under marine protected
areas (MPA), a quasi-form of stock-based management with certain stocks closed to fishing, can
be reduced when there is movement between populations, particularly when there are both
source and sink populations (Crowder et al., 2000; Sanchirico et al., 2006; Armstrong, 2007).
Wilberg et al. (2008) found that source-sink dynamics could affect harvest policy performance
for yellow perch (Perca flavescens) in Lake Michigan beyond a protected area context. Fu and
Fanning (2004) and Kell et al. (2009) each found that metapopulations of fish could be extirpated
if intermixing of populations was not accounted for in a manner consistent with actual
conditions. Perhaps the most well-known case of admixed fisheries negatively affecting
individual spawning populations have occurred in the Pacific Northwest of North America,
where entire spawning populations of Chinook (Oncorhynchus tshawytscha), coho (O. kisutch),
pink (O. gorbuscha), chum (O. keta), sockeye (O. nerka), and steelhead salmon have been
extirpated due in part to overfishing of low productivity populations in admixed stocks
(Morishima and Henry, 1999).
Despite wide recognition that population intermixing can be important, spatially-explicit
assessment models are rarely implemented, although recently this has begun to change (Cadrin
and Secor, 2009; Goethel et al., 2011). Ultimately, the effect that intermixing has on fish
populations depends on the mixing rates, the productivities of the populations, and the particular
policies that are used to manage the stocks. Within the 1836 TW, lake whitefish fisheries
continue to be managed primarily through a stock-based approach. It is not currently known

11

how populations may be affected by intermixing under the current 65% total annual mortality
control rule. Originally, this control rule was adopted based on research that indicated that this
level of mortality was sustainable, and substantially higher mortality rates were not (Ebener et
al., 2008). Deroba (2009), found the 65% control rule to perform reasonably even with changes
in life history characteristics of lake whitefish in recent years, however the considerable
ecosystem-level changes that have occurred in the Great Lakes, including greater rates of
intermixing among populations with differing levels of productivity, still raise concern as to
whether the current limit on mortality is sufficient to protect genetic diversity of populations in
the 1836 TW.
The purpose of this research was to evaluate the performance of the 65% total annual
mortality control rule that is currently in effect in the 1836 TW under different scenarios of
population productivity and intermixing. The intent was to provide guidance to managers as to
what effect different intermixing and productivity scenarios could have on commercial fishery
harvest and sustainability of lake whitefish populations if they continued to be managed under
the existing control rule.

Methods
Definitions of Terms
Herein, “population” and “spawning population” are used interchangeably and refer to a
group of fish that spawn in the same geographical area and exhibit natal philopatry. Similarly,
“stock” and “mixed stock” are also used interchangeably and refer to fish that reside in a
particular geographic area during the period of fishery harvest, and may contain fish from several
different spawning populations if mixing occurs. This means that all aspects of the fishery (i.e.

12

harvest and assessment) occur in relation to stocks, while measures such as spawning biomass
and recruitment are characteristics of populations.

Model of Lake Whitefish Dynamics
We simulated the dynamics of four fish populations that were assumed to intermix to
varying degrees during large portions of the year but which maintained strong spawning site
fidelity and thus did not intermix during spawning. Conceptually, this matched the overlap”
assumption with reproductive isolation described by Porch (2003) and Cadrin and Secor (2009).
The simulated populations had characteristics similar to those of lake whitefish populations in
northern lakes Huron and Michigan, but were not meant to exactly replicate particular
populations. The composition of each population was represented by fish ages 1 (age of
recruitment) through 11, and an aggregated group of all fish ages 12 and older. Fish were
assumed to intermix immediately after spawning, with certain fractions of each population either
staying within their natal areas or moving to areas where the other populations spawned. After
movement occurred, each mixed stock was assumed to be commercially exploited during the
remainder of the year. Surviving fish redistributed among the stocks each year, with mature fish
spawning in their natal stocks after returning at the end of each year.
Four different levels of intermixing were assigned to spawning populations in this
analysis. No mixing where all fish stayed in their natal area during the harvest season, low
mixing where 10% of the fish moved from their natal area to the other areas, intermediate mixing
where 40% of the fish moved from their natal area to the other areas, and high mixing where
80% of the fish moved from their natal area to the other areas. The levels of high, intermediate
and low intermixing were based in part on the results of tagging studies conducted by Ebener et

13

al. (2010), who found comparable levels of intermixing for lake whitefish populations in
northern Lakes Huron and Michigan. We assumed that the proportion of the fish emigrating
from an area would be equally divided among the other areas of the mixed stock system.
Abundances at age of each of the populations were simulated using an exponential
population model, with total mortality partitioned into natural and fishing mortality components.
Instantaneous natural mortality for all ages for each of the populations was set equal to 0.25,
which is within the range of natural mortality rates reported for the 1836 TW (Caroffino and
Lenart, 2011). Recruitment of the populations was modeled with a Ricker recruitment model
using egg production of the spawning population as stock size (SSE) and with recruits defined as
numbers of age-1 fish produced in the year following spawning (Table 1.1). Stochasticity was
incorporated via a multiplicative lognormal process error. We chose the Ricker formulation for
modeling recruitment because of strong evidence for over-compensation in lake whitefish
populations at high abundances (Healey, 1978; Henderson et al., 1983; Kratzer et al., 2007) and
because it is the assumed recruitment relationship for lake whitefish assessment models in the
1836 TW (Caroffino and Lenart, 2011).
Differences in productivity among the four spawning populations were incorporated via
adjustments to the coefficients of the recruitment functions. Specifically, the coefficients were
adjusted so that each population in the absence of intermixing had equal maximum sustainable
yields (MSY) but at differing levels of exploitation. For our evaluations, we considered four
productivity levels for the spawning populations: high, medium-high, medium-low, and low
productivities (Figure 1.1). High productivity populations were defined such that they had
spawning potential ratios (the ratio of spawning stock biomass per recruit at MSY exploitation to
unfished spawning stock biomass) of 20% (Table 1.2). Medium-high, medium-low, and low

14

productivity populations were defined such that they had spawning potential ratios of 30, 40 and
50%, respectively (Table 1.2). Based on deterministic models sharing the same stock
recruitment parameters and fishery characteristics used in this analysis, the estimated MSY
instantaneous fishing mortality rate on the most selected age class for each productivity level was
0.258 (low productivity), 0.393 (medium-low productivity), 0.631 (medium-high productivity),
and 1.15 (high productivity). The range of the recruitment parameter coefficients used to
characterize the different productivity levels was similar to what has been estimated for lake
whitefish fisheries in the 1836 TW (Deroba, 2009).
Egg production of the spawning populations was calculated as the product of abundance
at age, proportion mature at age, weight at age, proportion of females in the population, and the
number of eggs per kilogram of fish (Table 1.1). Lengths at age were predicted with a von
Bertalanffy growth model, weight at age was predicted using an allometric growth model, and
maturity was modeled as a logistic function (Table 1.1). The ratio of males to females at all ages
was assumed to be equal and the number of eggs produced per kg of fish was constant (Table
1.1). Total SSE was calculated by summing age-specific SSE.
For simplicity, it was assumed that each stock was exploited independently by a single
commercial fishery, and that the age-specific vulnerability (i.e., selectivity) patterns were the
same for each stock, although the level of exploitation for the stocks varied according to the
allotted TAC. Age-specific fishing mortalities were modeled as the product of a fully-selected
fishing rate and the age-specific selectivities
Fi, y, a  sa Fi, y ,

where sa indicates selectivity at age (a), and Fi,y represents the fully-selected fishing mortality
rate in year y for a given area (i) regardless of which area fish originated in. Fishery selectivity
15

was modeled as a gamma function of age (Table 1.1), which permitted a dome-shaped
relationship between selectivity and age. Selectivity was set equal to 0 for age-2 and younger
fish as these ages of fish are rarely harvested in the 1836 TW. Selectivities were scaled such that
the fully selected age class had a selectivity value of 1.0.
The fully-selected fishing mortality rates that fish experienced in the simulations were
determined from how much harvest occurred in each year and area and the abundance at age of
all fish in the particular area at the time of exploitation. Implementation error associated with the
TAC was incorporated via an independent lognormal error









2
2
Ci, y  TACi, y exp i, y  0.5 C ; i, y ~ N 0,  C ,

where C is the actual amount of commercial harvest for an area, TAC is the assessed TAC
i, y
i, y
for an area, and 

i, y

is a normally distributed random variable with expectation 0 and variance of

 2 , which was set equal to 0.01. A correction factor was included so that the expectation of
C
actual harvest was equal to the target TAC. The intent of the implementation error was to mimic
management actions that alter exploitation levels but do so imperfectly as a consequence of
managers not having complete control over a fishery. Because the fishery was assumed to occur
throughout the year with age-specific vulnerabilities, the fishing mortality rate that produced the
correct amount of harvest in each area and year was solved for numerically using a NewtonRaphson algorithm as described in Deroba (2009).
Given the intermixing and population dynamics framework described above, abundance
at age of a particular population depended on what fraction of the population moved to other
areas and the amount of fishing mortality that each of these fractions experienced in the areas to
which they moved. Using an exponential population model, abundances at age of a particular
16

spawning population could be represented as









Ni, y  1, a  1  Ni, y, ai  i exp M  Fi, y, a   Ni, y, ai  j exp M  F j , y, a ,
j

where Ni,y,a is the abundance of fish from spawning population i of age a in year y,  is the
fraction of each spawning population either located within their natal area (ii) or located in
other areas after movement (ij), M is the natural mortality rate that is assumed for this
research to be constant across populations, years, and ages, and Fi,y,a is the year- and agespecific instantaneous fishing mortality rate of fish occurring in the natal area of spawning
population i. This specification of abundances at age for the spawning populations matched the
discrete-time format of the Beverton and Holt (1957) box-transfer model for describing changes
in abundance as a result of movement across a region boundary (Goethel et al., 2011). The total
abundance of fish in a particular area once intermixing occurred ( N i, y, a ) could be represented
as

Ni, y, a  Ni, y, ai  i   N j, y, a j  i .
j

Observation Components
The data available for use in stock assessment models was assumed to consist of fishery
harvest-at-age for each stock and year and a reported measure of the amount of fishing effort
occurring in each area and year, which matches the data used in many of the lake whitefish
assessments in the Great Lakes. Observed harvest for a given fished area differed from actual

17

harvest as a result of observation error (Francis and Shotton, 1997; Butterworth and Punt, 1999),
which like implementation error was modeled as an independent lognormal error









Ci, y  Ci, y exp  i, y  0.5 2 ;  i, y ~ N 0,  2 ,
C
C
~
where C is observed commercial harvest and 
is a normally distributed random variable
i, y
i, y

with expectation 0 and variance of  2 , which was assumed to equal 0.01. We modeled
~
C
observed proportions at age in the harvest as though they arose from a multinomial distribution
with probabilities equal to the actual age composition of harvest and an assumed sample size of
200 fish. Again, this was intended to mimic the real-world situation where harvest estimates
arise from a harvest reporting system and the age composition of the harvest arise from a
biological sampling program; consequently, there is some level of error associated with both
observations.
The amount of fishing effort that occurred in each area and year was calculated by
dividing the fully-selected fishing mortality rate for that area and year by a catchability of
-6

1.50×10e . Observation error in the effort measurements was again modeled as an independent
lognormal error
Ei, y 

Fi, y
1.50 10e-6









exp  i, y  0.5 2 ;  i, y ~ N 0,  2 ,
E
E

~
where E is observed effort, F is the fully selected fishing mortality rate, and  is a
i, y
i, y
i, y

normally distributed random variable with expectation of 0 and variance of  2 , which was
~
E
assumed to equal 0.04.

18

Assessment Model
The assessment model that was used to estimate abundances and mortality rates for the
purpose of determining the TACs for each simulated stock in each year consisted of a SCAA
model similar to those currently used to assess lake whitefish stocks in the 1836 TW (Ebener et
al., 2005; Caroffino and Lenart, 2011). The estimates from the assessment model used to
implement the harvest control rule each year were based on the highest posterior density
estimates (sometimes referred to as maximum penalized likelihood estimates). The data used in
fitting the SCAA models included observed harvest, observed age composition of the harvest,
and observed fishing effort for each area. The objective function for the SCAA model consisted
of the sum of three components being either negative log-likelihood components or negative logprior (penalty) components. Lognormal distributions were assumed for the total annual harvest
from the fishery and for the log-prior (penalty) component associated with the fishing mortalityeffort relationships as explained below. The proportions at age of the harvest in each year were
assumed to have arisen from a multinomial sample. When fitting the SCAA model, the
dispersion parameter for the negative log-likelihood for the fishery harvest data component was
included as one of the estimated parameters. The dispersion parameter for the negative log-prior
(penalty) component for the fishing mortality-effort relationship deviation was set equal to fourtimes the value of the estimated fishery harvest dispersion parameter. The negative loglikelihood component for the fishery harvest age composition was weighted by the assumed
effective sample size of 200.
In the 2000 Consent Decree, it is specified that lake whitefish harvest limits are to be set
in the year preceding that in which the limits will take effect using data collected two years prior
to the effective harvest year (Ebener et al., 2008); thus TACs set for 2011 are based on

19

assessments conducted in 2010 using data collected through 2009. We incorporated a similar
time lag in our simulations. When fitting the assessment models, only the 20 years of data prior
to the year for which current abundances and mortality rates were assessed were included.
Because assessments were only conducted when 20 years or more of data were available, no
assessments were conducted during the first 20 years of the simulation period. During this
“burn-in” period, the TAC for each area and year was set based on actual abundances rather than
the unavailable assessed abundances. This “burn-in” period was simply a method to obtain an
initial abundance at age for year 21, at which point a full fishery harvest policy analysis,
including actual assessment of the stocks, could be implemented.
The structure of the SCAA model that was used to assess the stocks was similar to that
used to simulate the population dynamics (e.g., abundances were computed using the exponential
population with fishing and natural mortality components). Abundance at age in the SCAA
model were estimated for ages 3 to 12, with the last age class consisting of an aggregate group
that included age-12 and older fish. For the SCAA model, it was assumed that biologists were
unaware of or ignored population intermixing and thus did not attempt to incorporate fish
movement in the assessment models. Natural mortality rates were not estimated in the SCAA
models; rather, the natural mortality rates in the SCAA models were set equal to the values used
to simulate dynamics of the populations (0.25). Fishing mortality for the fishery component
included in the SCAA model was assumed to be separable into age and year effects (Doubleday,
1976; Quinn and Deriso, 1999). Specifically, instantaneous fishing mortality for each stock was
estimated as
ˆ
ˆ ˆ
Fi, y, a  si, a qi Ei, yi, y

20

ˆ
ˆ
where Fi, y,a was the estimated fishing mortality rate by stock, year, and age, si,a was the
~
ˆ
estimated selectivity at age for each stock, qi was the estimated catchability for each stock, E
i, y

was the measured fishing effort in each stock and year, and i,y were stock and year
multiplicative deviations from the direct proportionality between observed fishing effort and
fishing mortality. The annual deviations in the fishing mortality-effort relationships were
constrained to sum to zero and as suggested earlier were assumed to be distributed lognormally
in terms of their contribution to the objective function used in fitting the model. As when
simulating the stock dynamics, selectivities in the SCAA model were calculated as gamma
functions of age with the parameters of the functions estimated as part of the model fitting
process. Estimated selectivities at age were scaled relative to age-10 selectivities.
Initial abundances at age for age-4 to age-12 fish in the SCAA models were estimated as
the product of a mean abundance value multiplied by an annual multiplicative deviation. Annual
recruitment in the SCAA models (age-3 abundance) was also estimated as the product of a mean
recruitment value multiplied by an annual multiplicative deviation. The deviations for both
initial abundances and recruitments were constrained to sum to 0, but no distributions were
assumed for the deviations so large differences in annual values from the means were not
penalized. Age-specific harvest from each stock in the SCAA models was predicted using the
Baranov catch equation. Total harvest was calculated by summing age-specific values, and age
composition of the harvest for the stocks was calculated by dividing age-specific harvest by the
total harvest. Both totals and composition contributed to the objective function via comparison
with actual (simulated) values based on their assumed distributions.

21

Because of the considerable processing time needed to conduct the simulations for this
research, the SCAA model assessments were conducted on the stocks every third year rather than
annually. In the intervening years, TACs for the stocks remained at the levels set from when the
SCAA model assessments were last conducted. Although this diverges from how the
assessments have been conducted for lake whitefish stocks in the 1836 TW, there are some
within the group responsible for conducting the assessments on the lake whitefish stocks
suggesting a move from conducting annual assessments in favor of every other or every third
year assessments (M. P. Ebener, Chippewa-Ottawa Resource Authority, personal
communication). Based on this, we did not believe that designing our simulations such that
assessments were conducted every three years was farfetched; rather, we thought it would
provide useful guidance to those who conduct the actual lake whitefish assessments as to the
positive and negative aspects of switching when the assessments were conducted.
The search for the HPD SCAA model parameter estimates used the quasi-Newton
optimization algorithm implemented in AD Model Builder (Fournier et al., in press). The SCAA
models were considered to have converged on a solution when the maximum gradient of
parameters with respect to the objective function was less than 0.001. Upper and lower bounds
were specified for all parameters to help keep the optimization algorithm from flat parts of the
likelihood surface. These bounds were chosen to represent values above or below which would
be considered implausible. In rare cases where the assessment model failed to converge properly
as defined above, the previous TAC generated for the stock was implemented until the next
assessment was performed so faulty assessment outputs would not bias the analysis.
The performance of the SCAA model was assessed by calculating the mean relative error
(MRE) and mean absolute relative error (MARE) between the estimated and true harvest for the

22

20 years of harvest data included each time an assessment was performed. We also calculated
the MRE and MARE between the estimated and true abundances of the stocks (after mixing but
prior to fishery harvest) in the last year of each assessment.

Abundance Projections and TAC Calculations
The SCAA model estimates of abundances at age, age-specific mortality rates, and
recruitment levels were used to project future abundances at age and calculate TACs for each
stock area. The projections used the abundance-at-age estimates from the beginning of the last
year of the stock assessment model, along with the mean recruitment levels and mortality rates
from the previous five years to project abundances. The target age-specific fishing mortality
rates were then calculated by subtracting the natural mortality rates from a 65% total annual
mortality rate control rule (converted to an instantaneous scale) and multiplying this difference
by the age-specific selectivities that were estimated in the last year of the SCAA model. These
target age-specific fishing mortality rates were then included in the Baranov catch equation along
with the projected abundance at age estimates to determine what the allowable TAC would be
for each stock.

Experimental Design
A total of 21 scenarios consisting of different combinations of population intermixing
rates and productivity levels were examined to assess the performance of the 65% total annual
mortality control rule. It is not presently known what factors contribute to intermixing of lake
whitefish populations or why some populations in northern lakes Huron and Michigan appear to
move little while others disperse widely. Thus, we examined a broad range of scenarios so as to

23

provide managers with the most information possible in the event that intermixing-productivity
relationships within lake whitefish populations are better clarified. The examined scenarios were
categorized into four groups (All Shared, Shared Mixing, Shared Productivity and Correlated).
The exact intermixing rates and productivity levels that were assumed for the populations under
each investigated scenario are listed in Table 1.3. In the All Shared grouping, productivity and
intermixing levels were set at the same values for all populations. The intent of these scenarios
was to test the performance of the control rule when all populations experienced the same
intermixing and productivity levels. The Shared Mixing group consisted of three scenarios in
which all populations intermixed at the same rate but had varied levels of productivity. For this
grouping of scenarios, it was assumed each lake whitefish population had one of the four
productivity levels developed for the analysis. The Shared Productivity grouping of scenarios
was in the same vein as the Shared Mixing group except that productivity levels of the
populations were the same and the mixing rates were assumed to be different. The Correlated
group consisted of just two scenarios in which movement of fish from spawning areas was either
positively or negatively (inversely) correlated with population productivity levels. In the
negatively correlated scenario, the population with the lowest rate of intermixing had the highest
productivity level. In the positively correlated scenario, the population with the lowest rate of
intermixing had the lowest productivity level.

Performance Metrics and Simulation Details
The performance of the 65% total annual mortality control rule to each examined
scenario was evaluated based on the assumption that the management objectives for the fisheries
were to have high and stable yields and for populations to be sustainable over long time periods.

24

Based on these objectives, metrics that were used to evaluate performance included mean fishery
yield for each area, the mean aggregate fishery yield (sum of the yields across the areas), interannual variability in fishery yields, mean percentage of unfished SSB (SSBF=0), and the
percentage of years the SSB declined to less than 20% of SSBF=0. The 20% SSBF=0 is a
frequently used measure of risk of depletion (Beddington and Cooke, 1983; Francis, 1992; Punt,
1995, 1997), although as pointed out by Hilborn (1997) the 20% level is arbitrary.
Simulations were conducted in AD Model Builder (Fournier et al., in press). Each
simulation involved the projection of stock dynamics under the assumed intermixing and
productivity levels over a 100 year time span. Performance metrics were only calculated based
on the data from the last 80 years of the simulations (i.e., the burn-in period was not included in
the calculations). One thousand simulations were conducted for each investigated scenario, with
comparisons among scenarios based on both the central tendency (median) and dispersion
(range) of the simulation results.

Results
The SCAA assessments that were conducted on the stocks performed well. Nonconvergence of the SCAA models was a rare occurrence with at most only two assessments
failing to converge during any 100 year model run, which was unlikely to have any bearing on
the overall results of this research. The harvest MRE and MARE were generally quite small
with the median harvest MRE and MARE for all scenarios being less than 3.0% (Table 1.4). The
abundance MRE and MARE were greater than those for harvest, with median abundance MRE
as large as 19% in some scenarios, with median abundance MARE as large as 29% (Table 1.4).

25

All Shared Group
The highest mean annual yields were for the medium-high productivity scenarios,
followed by the high and medium-low productivity scenarios (Figure 1.2). Not surprisingly,
mean annual yield was the lowest for the scenarios with low productivity populations. The range
of yields across the simulations was greater for the medium-low and low productivity scenarios
than for the high and medium-high productivity scenarios (Figure 1.2). Overall, intermixing had
little effect on fishery yields, which was to be expected for this scenario as all populations had
the same productivities and thus intermixing led to nearly equal levels of movement to and from
stocks areas. Cumulative mean annual yield results were similar to the mean annual yield
results; that is, the greatest yields were found for the medium-high productivity scenarios with
intermixing having very little effect on cumulative yields and the range of yields across the
simulations being greatest for medium low and low productivity scenarios (Figure 1.3). As for
inter-annual variability in yield, there was an inverse relationship between variability and
intermixing for the different productivity scenarios, with inter-annual variability decreasing with
higher rates of intermixing (Figure 1.4).
Both the mean percent of years that SSB declined to less than 20% of SSBF=0 (Figure
1.5) and the mean percent of SSBF=0 (Figure 1.6) were highly dependent on the productivity of
the spawning population. The percentage of years that spawning stock biomass declined to less
than 20% of SSBF=0 was low (<10%) for high productivity populations, and high (>80%) for
low productivity populations (Figure 1.5). Medium-high productivity populations performed
similar to that of high productivity populations, having very low percentages of years below the
threshold, while the medium-low productivity populations had a median value of around 50% of

26

years below the threshold with at range covering near 0 to 100% (Figure 1.5). In terms of the
mean percent of SSBF=0, for high productivity populations median SSBs were approximately
50% of SSBF=0. For medium-high, medium-low, and low productivity populations, mean
percent of SSBF=0 was on the order of 40%, 20%, and 5% respectively. As with the other
performance metrics, intermixing appeared to have little overall effect on the mean percent of
years that SSB declined to less than 20% of SSBF=0 and mean percent of SSBF=0 with perhaps a
slight decrease in the mean percent of years that SSB declined to less than 20% of SSBF=0 and a
slight increases in mean percent of SSBF=0 with higher rates of intermixing (Figures 1.5 and
1.6).

Shared Mixing Group
For the shared mixing group of scenarios, intermediate and high rates of intermixing led
to decreases in mean annual yield for high and medium-high productivity areas. For mediumlow productivity areas there was little change in yield with intermixing rate but the range about
the yield decreased slightly with increased mixing (Figure 1.2). Conversely, for low productivity
areas, mean annual yield increased considerably under intermediate rates of stock intermixing
compared to low rates of intermixing, and increased even more profoundly under high rates of
intermixing (Figure 1.2). The magnitude of increase in mean annual yield for the stock with low
productivity levels under high rates of intermixing was such that yields were nearly comparable
to those of areas with higher productivity levels under the All Shared group of scenarios. The
cumulative mean annual yield was approximately 550 tonnes for all three scenarios, suggesting

27

that overall yield from the mixture system was relatively unaffected by intermixing and it
primarily resulted in reallocating harvest to different areas (Figure 1.3). Across all productivity
levels, inter-annual variability in yield declined as intermixing rates increased, although the
decline observed for the low and medium low productivity areas was slightly less than that
observed for the high and medium high productivity areas (Figure 1.4).
The results for percentage of years that SSB declined to less than 20% SSBF=0 and mean
percentage of SSBF=0 were similar to that observed for the All Shared grouping. That is, the
percentage of years that SSB declined to less than 20% SSBF=0 was less than 20% for high and
medium high productivity populations, near 50% for medium-low productivity populations, and
generally greater than 80% for low productivity populations (Figure 1.5). Additionally, for high
productivity populations, mean percentage of SSBF=0was generally around 50%, while lower
productivity populations mean percentages were around 35, 20 and 5%, respectively (Figure
1.6).

Shared Productivity Group
The mean annual yield for simulations in the Shared Productivity group varied
considerably with both rate of intermixing and productivity. When all populations had high
productivity levels, the medians of the mean annual yields varied from over 200 tonnes in the
area with no intermixing to nearly 75 tonnes in the area with high intermixing (Figure 1.2). Most
notably, a high productivity population with high intermixing could have yields similar to that of
low productivity populations in the all shared scenarios. Similar results were obtained when all
populations had medium-high and medium-low productivity levels, although the range in values

28

obtained from the simulations was somewhat greater for the medium-low productivity level than
it was for the high productivity levels. When all populations had low productivity levels, mean
annual yields for areas with no or low intermixing were near100 tonnes. Areas with high
intermixing rates had mean annual yields ranging from 25 to 50 tonnes (Figure 1.2). Much like
what was observed for the All Shared scenarios, the cumulative mean annual yield depended on
the productivity of the populations in the scenario, with the cumulative yields obtained for the
various productivity levels nearly equal to the corresponding All Shared scenarios (Figure 1.3),
again suggesting that overall yield from the mixture system was relatively unaffected by
intermixing. Inter-annual variability in yield was fairly similar across the areas regardless of the
productivity levels assumed for the populations, although it did appear to decline with both lower
productivity levels and higher intermixing rates (Figure 1.4).
The results for percentage of years that SSB was less than 20% SSBF=0 (Figure 1.5) and
mean percent of SSBF=0 (Figure 1.6) were similar to the previous scenarios. The percentage of
years that SSB was less than 20% SSBF=0 level was generally less than 20% when populations
had high or medium-high productivity levels, between 20 and 60 % when populations had
medium-low productivity and greater than 80% when populations had low productivity levels
(Figure 1.5). The mean percentage of SSBF=0 when populations had high productivity levels
was approximately 50%; and for low productivity levels the mean percentage of SSBF=0 was
around10%, with the medium-high and medium-low populations in between (Figure 1.6).

Correlated Group

29

When population productivity and intermixing levels were inversely correlated (i.e.,
lower productivity populations had higher intermixing rates), mean annual yields in high
productivity populations increased to levels greater than those of medium-high productivity
populations in the all shared scenarios. For medium-high and medium-low productivity
populations, yields remained relatively stable, whereas yields for low productivity populations
decreased considerably from those of low productivity populations in the all shared scenarios.
When population productivity and intermixing levels were positively correlated (i.e., more
productive populations had higher intermixing rates), mean annual yields of areas with high
productivity populations declined to levels comparable to that of areas with low productivity
populations in the all shared scenarios (Figure 1.2). Similarly, mean annual yields of stocks with
less productive populations increased to levels comparable to that of stocks with high
productivity populations in the all shared scenarios. For medium-high productivity populations,
yields decreased to levels similar to medium-low productivity populations in the all shared
scenarios, whereas yields for medium-low productivity populations increased to levels similar to
medium-high productivity populations in the all shared scenarios. In terms of cumulative mean
annual yield, yields were nearly equal to those in the shared mixing scenarios with the positively
correlated mixing scenario slightly greater to that of the negatively correlated scenario (Figure
1.3). The inter-annual variability in yield (Figure 1.4), percentage of years that SSB was less
than 20% SSBF=0 (Figure 1.5), and mean percentage of SSBF=0 (Figure 1.6) result were similar
to those from other examined scenarios.

Discussion

30

The performance of harvest control rules for managing lake whitefish fisheries in the
Laurentian Great Lakes has previously been evaluated by Jacobson and Taylor (1985) and
Deroba (2009). In both cases, constant mortality control rules were found to perform adequately
with respect to maximizing fishery yield (Jacobson and Taylor, 1985; Deroba, 2009), although
Deroba (2009) found that biomass-based control rules were better at minimizing risk of depletion
if stock-specific levels of unfished biomass were known. Neither of these previous research
studies accounted for population intermixing in the harvest evaluations that were performed,
although Deroba (2009) did account for substantial complexity and uncertainty in various lifehistory characteristics of fish populations (e.g., growth and recruitment rates). Overall, we found
intermixing to have little influence on inter-annual variability in fishery yields, at least at the
population productivity levels considered in this research. Risk of depletion to fish populations
as measured by the percentage of years that SSB declined to less than 20% SSBF=0 also was not
affected by stock intermixing, but was strongly linked to assumed productivity levels.
Conversely, fishery yields in each stock area were clearly influenced by population intermixing
and productivity levels, and our research demonstrated that under particular combinations a
population can have a high risk of depletion even though the amount of harvest from the area
near where the population spawns was high as a result of fish from other populations moving
into the area. In essence, the productivities of the populations determined the yield from the
system as a whole, as demonstrated by the relatively stable cumulative fishery yields in the
shared mixing group of scenarios, but intermixing influenced the realizable yield from each area
by redistributing harvest. In particular, when higher productivity populations mixed
substantially into areas occupied by low productivity populations, the yield from the area
approached that of areas associated with high productivity populations. Similarly, it was

31

possible for areas where highly productive populations spawned to have yields similar in
magnitude to that of areas where low productivity populations spawned.
Perhaps the most concerning result was that the 65% total annual mortality control rule
may not be sufficiently conservative for low productivity populations, but it would be difficult
for managers to determine this without knowledge as to the actual productivity levels of the
populations. This is in contrast to Deroba (2009), who found that the 65% mortality control rule
performed relatively well for lake whitefish stocks, even accounting for changes in life history
characteristics that concern managers (minus intermixing). One potential reason for the
mismatch in conclusions was that Deroba (2009) looked at the probability of outcomes for
harvest policies, with stock recruitment (productivity) values drawn from a set of estimated
values in each simulation. This meant the effects on low productivity populations were not
investigated directly, but included in a distribution of outcomes with higher productivity
populations. Another explanation for the mismatch is that the stock recruitment relationships in
Deroba (2009) were estimated from stock assessments conducted on lake whitefish stocks in the
TW, so intermixing may have led to overestimates of productivity in low productivity
populations. Our analysis, in contrast, investigated a plausible range of productivity levels,
without linking the productivities in our analysis to assessments performed on intermixing
stocks.
Because allowable catches were based on assessments that only made use of fishery
harvest and effort data, TACs were entirely based on the number of fish in a stock area during
the harvest season rather than the size of the spawning population. This discrepancy between the
spatial management approach and the data used in the assessment led to estimates of biomass
that were not reflective of the resident populations spawning stock biomass (Belcher and

32

Jennings, 2009). This issue is often combated by including fishery independent data that targets
the spawning population spatially or seasonally and is thus less biased into assessments (Mesnil
et al., 2009; Harms et al., 2010). Consistent with the findings of Kell et al. (2009) who showed
that when catches from two simulated fish metapopulations were mixed in a virtual population
analysis assessment, it was possible for the collapse of one population to go entirely undetected,
raising concern that assessment mismatch may put some populations at risk.
The modeling subcommittee, which is responsible for assessment modeling of lake trout
and lake whitefish fisheries in the 1836 TW, has begun taking steps to account for the
intermixing of some lake whitefish populations. In northern Lake Huron, four lake whitefish
management units (WFH-01 to WFH-04) that were previously assessed and managed separately
are now being assessed with a single SCAA model that includes biological and commercial
fishery data from each management unit (Caroffino and Lenart, 2011). The impetus for this
change was the extensive intermixing of lake whitefish populations from these management units
based on the results of a tagging study conducted by Ebener et al. (2010). Although combining
intermixing stocks into a single assessment and management system is one reasonable approach
for dealing with stock intermixing, lumping the assessment can, depending on details, lead to
biased estimates of abundance and mortality rates (Kell et al., 2009). Furthermore, how the
combined TAC for a mixed stock is allocated spatially or to different fishery components can
influence sustainability (Heifetz et al., 1997), making knowledge about productivity of individual
populations important.
An alternative to pooling the assessment for management units with significant levels of
intermixing would be to construct a tag-integrated assessment model, which would incorporate a
tag-recapture component within an SCAA assessment model (Goethel el. al., 2011). Such an

33

approach would certainly complicate the existing management system and require a long-term
commitment to tagging lake whitefish throughout the 1836 TW, but ultimately may prove useful
for lake whitefish management in the 1836 TW. Regardless, there still would remain the issue of
whether the 65% total annual mortality control rule is appropriate given current productivity
levels of lake whitefish stocks in the Great Lakes. Short of reducing allowable mortality, spatial
closures, seasonal closures, and regional or temporal allocation of TAC may also be useful to
account for intermixing. Another alternative to pooled or tag-integrated assessment models
would be to incorporate in existing SCAA models a fishery independent assessment of the lake
whitefish stocks during the spawning season in order to index spawning population size.
A simulation-based framework such as that used in this research is a relatively common
approach for providing advice to fishery managers about performance of fishery harvest control
rules and to explore how aspects of fish behavior and ecology or fishery dynamics can influence
management (Cooke, 1999; Deroba and Bence, 2008; Ralston and O’Farrel, 2008; Kerr et al.,
2010). Ebener et al. (2010) estimated that proportions of lake whitefish tagged at spawning sites
in northern lakes Huron and Michigan and recaptured in other management areas ranged from 19
to 90%, although it is not presently known with certainty what factors govern lake whitefish
movement. As previously indicated, one hypothesis is that movement rates are linked to food
availability and that stocks with locally depleted food resources move more widely in search of
areas with more abundant resources. Additional research to better understand intermixing in lake
whitefish stocks and what factors lead to high rates of intermixing would be beneficial for
providing more directed advice to fishery managers. Developing a better understanding of the
productivity of the lake whitefish spawning populations in the Great Lakes would allow us to
better determine how actual populations compare to the productivity levels we used in our

34

analysis. Investigations that focus on the productivity of genetically and geographically distinct
spawning aggregations may lead to a better understanding of the true productivity of lake
whitefish populations in the upper Great Lakes than the current stock focused analyses.
Managers should keep in mind that the productivity levels of spawning populations have
important effects on the sustainability of the control rule used in the 1836 TW. If several
populations with different productivity levels intermix considerably, the assessments used do not
allow biologists and managers to develop a good understanding of the population responses to
fishing, limiting the capacity to improve management of lake whitefish populations.
Understanding the effects of productivity and intermixing on the performance of this control rule
will help to better manage lake whitefish into the future. Caution is required for managing
mixed stocks of lake whitefish as the lower productivity populations in the mixed stock may be
put at considerable risk if the stock is managed to harvest at a rate more appropriate for higher
productivity populations (Stephenson 1999).

35

APPENDIX

36

Figure 1.1. Ricker-stock recruitment relationships for the four levels of productivity used to
investigate the effects of population intermixing on the 65% total annual mortality control rule
used to manage lake whitefish fisheries in the 1836 Treaty waters of the Great Lakes.

37

Figure 1.2

38

Figure 1.2 (cont’d)
Mean annual fishery yield for each unit stock for the investigated scenarios. Boxes indicate the
th

th

25 and 75 percentiles over the simulations, while whiskers indicate 1.5 times the interquartile
range over simulations. Horizontal lines indicate the median of the yields for the simulations.
The symbols appearing above the boxplots indicate the level of intermixing and productivities
for the populations spawning in each stock region (square=no mixing, upside down triangle=low
mixing, diamond=intermediate mixing, triangle= high mixing; black=high productivity, dark
grey=medium high productivity, light grey=medium low productivity, white=low productivity).
On the x-axis, vertically oriented labels correspond to specific scenarios. See Table 1.3 for a
description of the investigated scenarios (A=all shared; B=shared mixing; C=shared
productivity; D=correlated).

39

Figure 1.3. Mean annual cumulative fishery yield summed for each investigated scenario. Boxes
th
th
indicate the 25 and 75 percentiles over the simulations, while whiskers indicate 1.5 times the
interquartile range over simulations. Horizontal lines indicate the median of the yields for the
simulations. On the x-axis, vertically oriented labels correspond to specific scenarios. See Table
1.3 for a description of the scenarios (A=all shared; B=shared mixing; C=shared productivity;
D=correlated).

40

Figure 1.4

41

Figure 1.4 (cont’d)
As for Fig. 1.3, except y-axis is mean inter-annual percent variation in fishery yield.

42

Figure 1.5

43

Figure 1.5 (cont’d)
As in Fig. 1.3, except y-axis is the mean percentage of years in each simulation that the spawning
stock biomass declined to less than 20 percent of the unfished spawning stock biomass
(SSBF=0).

44

Figure 1.6

45

Figure 1.6 (cont’d)
As in Fig 1.3, except y-axis is mean annual percentage of unfished spawning stock biomass
(SSBF=0) for the spawning populations

46

Table 1.1. Equations with descriptions and values for fixed variable inputs used in the simulation
of lake whitefish populations and fisheries in this analysis.
Description of Equation

Equation

Abundance (N) at age of
recruitment (age 1) by
year (y)

2
N y,1   SSE y  1 exp   SSE y  1 exp  R





Spawning Stock Biomass
(SSB) by year (y)
Length (L) at age (a)

SSE y   N y, a ma wa Fem  Eggs
a

Weight (w) at age (a)

wa   La



La  L 1  exp    a  t0  

Maturity (m) at age (a)

ma 
Selectivity (s) at age (a)

sa 

m
1  exp    La    

a exp   a 

10 exp   10 

47



 

Parameter
Coefficients
 = see Table 1.2
 = see Table 1.2
2
 R = 0.36
Fem = 0.5
Eggs = 19937/kg
L = 60.9 cm
 = 0.1686
t0 = 0.0 years

 = 8.06x10
 = 2.45
m  1.0

  0.315
  37.9 cm
 = 13.074

 = 1.26

-5

Table 1.2. Ricker stock-recruitment coefficients (Table 1.1) that were assumed for the different
productivity levels for lake whitefish spawning populations for assessing the effects of stock
intermixing on the current 65% total annual mortality control rule used to manage lake whitefish
fisheries in the 1836 Treaty waters of the Great Lakes.
Productivity Level

Alpha (  )

Low

0.000369

7.1708x10

Medium-Low

0.000516

1.2780x10

Medium-High

0.0007687

2.2758x10

High

0.001281

4.2988x10

Beta (  )

48

-11
-10
-10
-10

Table 1.3. Assumed intermixing (M) and productivity (P) levels of individual spawning
populations for each of the scenarios investigated in this research. Intermixing values indicate
the percent of lake whitefish that move from the natal region during the harvest season.
Productivity levels refer to high (H), medium-high (MH), medium-low (ML), or low (L)
productivities as described in Table 1.2.
Group

Scenario

All Shared

HP LM (High Prod.,
Low Mix.)
HP IM (High Prod.,
Int. Mix.)
HP HM (High Prod.,
High Mix.)
MHP LM (Med-High Prod.,
Low Mix.)
MHP IM (Med-High Prod.,
Int. Mix.)
MHP HM (Med-High Prod.,
High Mix.)
MLP LM (Med-Low Prod.,
Low Mix.)
MLP IM (Med-Low Prod.,
Int. Mix.)
MLP HM (Med-Low Prod.,
High Mix.)
LP LM (Low Prod.,
Low Mix.)
LP IM (Low Prod.,
Int. Mix.)
LP HM (Low Prod.,
High Mix.)
VP LM (Varied Prod.,
Low Mix.)
VP IM (Varied Prod.,
Int. Mix.)
VP HM (Varied Prod.,
High Mix.)
HP VM (High Prod.,
Varied Mix.)
MHP VM (Med-High Prod.,
Varied Mix.)
MLP VM (Med-Low Prod.,
Varied Mix.)
LP VM (Low Prod.,
Varied Mix.)

Shared
Mix.

Shared
Prod.

Pop. 1
M
P
10
H

Pop. 2
M
P
10
H

Pop. 3
M
P
10
H

Pop. 4
M
P
10
H

40

H

40

H

40

H

40

H

80

H

80

H

80

H

80

H

10

MH

10

MH

10

MH

10

MH

40

MH

40

MH

40

MH

40

MH

80

MH

80

MH

80

MH

80

MH

10

ML

10

ML

10

ML

10

ML

40

ML

40

ML

40

ML

40

ML

80

ML

80

ML

80

ML

80

ML

10

L

10

L

10

L

10

L

40

L

40

L

40

L

40

L

80

L

80

L

80

L

80

L

10

H

10

MH

10

ML

10

L

40

H

40

MH

40

ML

40

L

80

H

80

MH

80

ML

80

L

0

H

10

H

40

H

80

H

0

MH

10

MH

40

MH

80

MH

0

ML

10

ML

40

ML

80

ML

0

L

10

L

40

L

80

L

49

Table 1.3 (cont’d)
Correlated

NEGC (Varied Prod.,
Negatively Correlated Mix.)
POSC (Varied Prod., Positively
Correlated Mix.)

0

10

MH

40

ML

80

L

0

50

H
L

10

ML

40

MH

80

H

Table 1.4. Median of the mean relative error (MRE) and the mean absolute relative error (MARE) for lake whitefish harvest and
abundance estimates from the SCAA assessments across stocks and simulations. The values in parentheses are the ranges of the
MREs and MAREs values. See Table 1.3 for a description of the Scenarios.
Group.

Scenario

Harvest MRE

Harvest MARE

Abundance MRE

Abundance MARE

All
Shared

HP LM
HP IM
HP HM
MHP LM
MHP IM
MHP HM
MLP LM
MLP IM
MLP HM
LP LM
LP IM
LP HM
VP LM
VP IM
VP HM
HP VM
MHP VM
MLP VM
LP VM
VP NC
VP PC

0.0001 (-0.03600.0063)
-0.0004 (-0.00710.0067)
-0.0005 (-0.00790.0068)
-0.0005 (-0.03600.0051)
-0.0012 (-0.01000.0053)
-0.0013 (-0.00890.0062)
-0.0002 (-0.00690.0059)
-0.0004 (-0.00760.0065)
-0.0005 (-0.00680.0123)
0.0000 (-0.00630.0062)
-0.0001 (-0.00780.0063)
-0.0001 (-0.00700.0063)
-0.0002 (-0.00740.0058)
-0.0002 (-0.00650.0060)
-0.0002 (-0.00690.0067)
-0.0009 (-0.03420.0536)
-0.0011 (-0.00810.0073)
-0.0008 (-0.00710.0952)
-0.0001 (-0.03690.0068)
-0.0007 (-0.03670.0146)
-0.0006 (-0.00740.0563)

0.0279 (0.02090.0636)
0.0286 (0.02100.0385)
0.0286 (0.02120.0390)
0.0278 (0.02030.0657)
0.0286 (0.01940.0392)
0.0286 (0.02150.0398)
0.0278 (0.02000.0379)
0.0286 (0.02140.0571)
0.0287 (0.02100.0459)
0.0279 (0.02050.0380)
0.0289 (0.02120.0387)
0.0290 (0.02120.0421)
0.0280 (0.02010.0367)
0.0287 (0.02140.0401)
0.0289 (0.02100.0382)
0.0286 (0.02130.0819)
0.0286 (0.02010.0443)
0.0285 (0.02050.1271)
0.0285 (0.02140.0670)
0.0285 (0.02080.0663)
0.0286 (0.02090.0879)

-0.0005 (-0.13470.1273)
-0.0340 (-0.20160.1018)
-0.0550 (-0.18740.0743)
-0.0791 (-0.30500.1344)
-0.1537 (-0.35080.0919)
-0.1902 (-0.32240.0153)
-0.0106 (-0.31900.1893)
-0.0296 (-0.34580.2370)
-0.0467 (-0.33110.2857)
0.0151 (-0.17690.4471)
0.0217 (-0.17890.3273)
0.0232 (-0.23760.3684)
-0.0034 (-0.29580.2736)
-0.0076 (-0.27550.3230)
-0.0143 (-0.25210.2459)
-0.1190 (-0.38970.7883)
-0.1768 (-0.41170.7651)
-0.0625 (-0.41490.6202)
0.0056 (-0.33670.5842)
-0.0689 (-0.39140.9644)
-0.0294 (-0.41950.7538)

0.1353 (0.07480.2071)
0.1297 (0.06520.2239)
0.1287 (0.07250.2152)
0.1611 (0.07190.3101)
0.1883 (0.08840.3543)
0.2084 (0.09070.3224)
0.1473 (0.07780.3190)
0.1491 (0.07680.3458)
0.1494 (0.07020.3350)
0.1397 (0.07450.5197)
0.1434 (0.07580.3808)
0.1470 (0.07740.4187)
0.1440 (0.07670.3062)
0.1419 (0.07650.3598)
0.1437 (0.07540.2783)
0.2482 (0.07590.7883)
0.2901 (0.07900.7651)
0.2163 (0.08450.6506)
0.1480 (0.07570.5888)
0.2041 (0.08270.9644)
0.1792 (0.07780.7719)

Shared
Mix.
Shared
Prod.

Corr.

51

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52

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population of lake whitefish. N. Am. J. Fish. Manag. 5, 537-546.
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Mesnil, B., Cotter, J., Fryer, R. J., Needle, C. L., Trenkel. V. M., 2009. A review of fisheryindependent assessment models, and initial evaluation based on simulated data. Aquat.
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Huron, In: Mohr, L. C., Nalepa, T. F., (Eds.) Proceedings of a workshop on the dynamics
of lake whitefish (Coregonus clupeaformis) and the amphipod Diporeia spp. in the Great
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macroinvertebrate populations in southern Lake Michigan, 1980–1993. Can. J. Fish.
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trends in benthic macroinvertebrate populations in Lake Huron over the past four
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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 lake whitefish
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community in Lake Michigan: recent shift from the native amphipod Diporeia spp. to the
invasive mussel Dreissenia rostriformus bugensis. Fresh. Biol. 54, 466–479.
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waters of northern Lake Michigan. Trans. Am. Fish. Soc.106, 295-308.
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whitefish after dreissenid mussel invasions in lakes Michigan and Huron. N. Am. J. Fish.
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Punt, A. E., 1995. The performance of a production-model management procedure. Fish. Res.
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and gummy shark. J. Northwest Atl. Fish. Sci. 35, 387-406.
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VanDeHey, J. A., Sloss, B. L., Peeters, P. J., Sutton, T. M., 2009. Genetic structure of lake
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282-289.

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CHAPTER 2
HARVEST CONTROL RULES THAT CONSERVE SPAWNING BIOMASS MAY PROVIDE
HIGHER AND MORE STABLE YIELDS FOR INTERMIXED FISHERIES

Abstract
We conducted a simulation-based evaluation of harvest control rule performance for four
intermixing fish populations that were loosely patterned after lake whitefish (Coregonus
clupeaformis) fisheries in northern lakes Michigan and Huron. The developed framework
included an operating model that simulated the dynamics of each population, the harvests from
fisheries exploiting the intermixed populations, and a full age-structured assessment of each
exploited stock. The four harvest control rules that were evaluated included a 65% total
mortality control rule that presently is used to manage lake whitefish fisheries in northern lakes
Michigan and Huron and three more conservative control rules (35, 45, and 55% total mortality
control rules). Mean annual yields varied considerably with control rule and rate of intermixing,
while sustainability metrics depended primarily on productivity characteristics of the spawning
populations. Under many scenarios, the current 65% total mortality control rule was found to
have high risk of overexploitation of lower productivity spawning populations, which reduced
overall harvest across stocks. More conservative control rules generally resulted in more
sustainable fisheries and in some instances increased overall yield from the stocks. Our analysis
suggests that control rules that conserve spawning biomass through lower mortality rates may
provide multiple benefits including greater yields from mixture fisheries, reduced inter-annual
variability in yields, and reduced risk of depleting low productivity spawning populations. We
encourage the implementation of precautionary harvest control rules for fisheries that exploit
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stocks consisting of intermixed spawning populations with differing productivity levels to help
ensure sustainability of less productive stocks.

Introduction
Stock-based management of exploited fish populations has long been an important tool of
fisheries managers. This management approach typically involves assigning spatial management
units and assessing the dynamics of fish populations occurring within the boundaries of each
management unit to set harvest levels. One of the perceived benefits of stock-based management
is that it protects spawning populations by managing at spatial scales best suited for ensuring
sustainability of individual populations thus promoting overall intra-species diversity (Patriarche,
1977; Spangler et al., 1981; MacLean and Evans, 1981; Stephenson, 1999). Although stockbased management is widely used, it is not infallible. For one, it is generally assumed that
managed fisheries consist of fish from a single spawning population (Quinn and Deriso, 1999).
However, management unit boundaries are often based on jurisdictional or management
convenience and may not accurately reflect the dynamics of individual populations (Goethel et
al., 2011). Recent research using tag-recovery and genetics data have in some fisheries found
considerable discrepancy between management units and spawning population distributions
(Reiss et al., 2009; Ebener et al., 2010). Further, movement and therefore intermixing may be a
dynamic feature with changes in the environment or abundance leading to changes in the spatial
distribution of populations (Perry et al., 2005; Ebener et al., 2010). As a result, appropriateness
of management unit boundaries may wane over time.
Population intermixing during periods of fishery harvest is common in both freshwater
and marine environments (Policansky and Magnuson, 1998; Stephenson, 1999). Despite its

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ubiquity, there is a general lack of understanding as to what effects intermixing may have on
exploited populations because most harvest policy evaluations have ignored intermixing and
spatial structure of fish populations (Deroba and Bence, 2008). The research that has been
conducted has shown that effects can vary depending on the magnitude of mixing (Tuck and
Possingham, 2000; Sanchirico et al., 2006) and the underlying dynamics of the populations
(Heifetz et al., 1997; Kerr et al., 2010).
Lake whitefish (Coregonus clupeaformis) fisheries in the Laurentian Great Lakes of
North America are examples of commercially exploited freshwater fisheries managed using a
stock-based approach in which management unit boundaries do not align with the complex
spatial structure exhibited by spawning components. Throughout large areas of lakes Michigan,
Huron, and Superior, lake whitefish fisheries are managed with 65% total annual mortality
controls, the basis of which is empirical observations that stocks with mortality exceeding this
level perform poorly (Ebener et al., 2005). Over the last 15 to 30 years, intermixing of lake
whitefish spawning populations has increased considerably (VanDeHey et al., 2009; Ebener et
al., 2010). As well, the intrinsic productivity of lake whitefish spawning populations is believed
to have declined as a result of massive ecosystem level changes that have occurred in the Great
Lakes subsequent to the invasion of dreissenid mussels (Pothoven et al., 2001; Kratzer et al.,
2007; Rennie et al., 2009). The combination of increased mixing rates and declining
productivity calls into question whether some lake whitefish populations may be at risk of
overexploitation under the existing 65% allowable annual mortality control rule.
The potential for mixture fisheries to negatively influence individual spawning
populations, even to the point of extirpation, has been well documented. Frank and Brickman
(2000) and Kell et al. (2009) each found that subpopulations could be extirpated in mixed stock

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fisheries even though conventional assessments suggested stocks were healthy. Ying et al.
(2011) found that managing a metapopulation as several independent populations may lead to
overexploitation, while managing metapopulations as single units may lead to depletion of
components. Erosion of spawning components was documented in Atlantic cod (Gadus morhua)
and Atlantic herring (Clupea harengus) stocks that subsequently collapsed (Sinclair et al., 1996;
Cury et al., 2000), and has been implicated in the slow recovery of cod and herring stocks even
after considerable reductions in fishing mortality (Smedbol and Stephenson, 2001; Ames, 2004;
Lilly et al., 2008). From a biological standpoint, extirpation of spawning population is
problematic as it can lead to a loss of genetic diversity, reducing the evolutionary potential of a
species and possibly suppressing characteristics adapted for local environments (Stephenson and
Kenchington, 2000).
The goal of this research was to conduct conducted a simulation-based evaluation of
harvest control rule performance of four intermixing fish populations with characteristics similar
to those of lake whitefish populations in northern lakes Huron and Michigan. Our intent was to
provide fishery managers guidance as to whether the current management approach is adequate
for ensuring the goals of maximizing harvest, increasing fishery yield stability, and ensuring long
term protection of spawning populations.

Methods
For clarity, we define some of the common terms used herein. Population and spawning
population are used interchangeably to refer to a group of fish that spawn in the same region and
exhibit natal philopatry. Mixed stock and stock are also used interchangeably to refer to fish
from multiple spawning populations residing in a particular region during periods of
exploitation. This means that all aspects of the fishery, such as harvest and assessment, occur in
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relation to stocks, while measures such as spawning biomass and recruitment are characteristics
of populations.

Operating Model
Abundances at age of the four fish populations were represented through an operating
model in which the true dynamics of each population were specified. In the operating model, the
four fish populations were assumed to intermix to varying degrees during the non-spawning
season but maintained strict spawning site fidelity and were therefore unmixed during the
spawning season. This matches the overlap with reproductive isolation assumption described in
Porch (2003) and Cadrin and Secor (2009). Although the simulated populations had
characteristics similar to lake whitefish populations in the upper Great Lakes, our simulations
were not meant to replicate particular populations. Each population included fish ranging from
age 1 (age of recruitment) to age 12, with the last age class an aggregate group including age-12
and older fish. Fish from each spawning population were assumed to intermix with other
populations immediately after spawning, with a population specific proportion staying within
their natal area and the remainder moving into the spawning areas of the other populations. The
proportion that moved to areas occupied by other populations was assumed to equally distribute
themselves among the other three areas. Each stock was assumed to be exploited commercially
throughout the time fish were intermixed. All fish surviving the year were assumed to return to
their natal regions at the end of the year, with only the sexually mature fraction spawning.
Parameter definitions and equations used in the description of the operating model and
elsewhere in the text are presented in Tables 2.1 and 2.2. An exponential population model (Eq.
T.2.2.1) was used to project abundances at age, with instantaneous total mortality partitioned into

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natural and fishing mortality components (Eq. T.2.2.2). Instantaneous natural mortality rates for
all ages and populations were assumed to be constant (Table 2.1). Recruitment to each
population was modeled using a Ricker recruitment function with stock size equal to the egg
production potential of mature females (SSE) and recruits defined as the abundance of age-1 fish
produced the year after spawning (Eq. T.2.2.3). Stochasticity was included in the stock
recruitment relationship via a multiplicative lognormal error.
Total SSE was calculated as the sum of the product of abundance at age, proportion
mature at age, weight at age, proportion of females in the population, and the eggs produced per
kilogram of mature female (Eq. T.2.2.4). Length at age was modeled with a von Bertalanffy
growth model (Eq. T.2.2.5) with weight at age predicted as a function of length through an
allometric growth model (Eq. T.2.2.6). Maturity was modeled as a logistic function of length
(Eq. T.2.2.7). The von Bertalanffy growth, allometric weight, and logistic maturity models were
parameterized such that the simulated populations had characteristics similar to lake whitefish
stocks in northern lakes Huron and Michigan (Table 2.1). The sex ratio in all populations was
assumed to be 50:50, with the number of eggs produced per kg of mature female a constant
across all scenarios (Table 2.1).
Each stock was assumed to be exploited by a single commercial fishery. Age-specific
fishing mortality rates were modeled as the product of a fully-selected fishing mortality and agespecific selectivities (Eq. T.2.2.8). The fisheries operating in each stock were assumed to have
common selectivity patterns. Fishery selectivity at age was modeled with a gamma function
scaled such that the maximum selectivity at age had a value of one (Eq. T.2.2.9). Selectivities
for age-2 and younger fish were set equal to 0 as these ages are rarely captured or retained in the

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lake whitefish fishery. The parameters of the selectivity function were chosen such that
selectivity was dome-shaped with peak selectivity at age 10 (Table 2.1).
The fishing mortality rate that each stock experienced was dependent on the total
allowable catch (TAC) that was set in each year and the abundance of fish that moved into a
stock area during harvest. The actual amount of harvest that a stock experienced included an
implementation error component to account for the fact that perfect control over a fishery can
rarely be exerted. Implementation error was incorporated via an independent lognormal error
(Eq. T.2.2.10). Fully-selected fishing mortality rates capable of producing the actual level of
harvest were solved for numerically using a Newton-Raphson algorithm as described in Deroba
(2009). Given this intermixing framework, abundance at age of each population depended on
what fraction of the population moved to other stock areas and the level of exploitation that each
of these fractions experienced in the other stock areas. Under an exponential population model,
abundance at age of each spawning population could be represented with Eq. T.2.2.11, while the
total abundance of fish found in any stock after intermixing occurred could be represented with
Eq. T.2.2.12.

Observation components
The information available for use in the stock assessment models was assumed to consist
of fishery harvest-at-age for the stocks and a reported measure of the amount of fishing effort
occurring in each stock area. This matches the data currently used in most Great Lakes lake
whitefish assessment models (Caroffino and Lenart, 2011). Observed harvest in the stock areas
was assumed to differ from actual harvest as a result of observation error (Francis and Shotton,
1997; Butterworth and Punt, 1999), which like implementation error was modeled as an

65

independent lognormal error (Eq. T.2.2.13). Observed age composition of the harvest was
generated from a multinomial distribution with probabilities equal to the actual age composition
of harvest and an assumed sample size of 200 fish (Eq. T.2.2.14). The amount of fishing effort
that each stock experienced was calculated by dividing the fully-selected instantaneous fishing
mortality rate in each stock and year by an assumed catchability value (Eq. T.2.2.15; Table 2.1).
As with fishery harvest, observation error was incorporated in the fishery effort measurements.

Assessment Model and TAC Generation
A statistical catch-at-age (SCAA) model that was similar to the assessment models used
to assess lake whitefish stocks in the upper Great Lakes was used to estimate abundance,
mortality, and recruitment levels for the purpose of setting the TACs for the stocks based on the
evaluated harvest control rules (Ebener et al., 2005; Caroffino and Lenart, 2011). The estimates
from the assessment models used to set the TACs were the highest posterior density (HPD)
estimates, which also are referred to as maximum penalized likelihood estimates (Schnute,
1994). The objective function of the assessment model consisted of the sum of three negative
log-likelihood or negative log-prior components. Lognormal distributions were assumed for the
log-likelihood component for the total fishery harvest (Eq. T.2.2.16) and for the log-prior
component associated with the fishing mortality-effort relationship (Eq.T.2.2.17). The
dispersion parameter for the negative log-likelihood component for total fishery harvest was
estimated as part of the model fitting process, with the dispersion parameter for the negative logprior component for the fishing mortality-effort relationship deviation set equal to four times the
value of the estimated fishery harvest dispersion parameter. The age composition of the fishery

66

harvest was assumed to have a multinomial distribution, and was weighted by an assumed
effective sample size of 200 fish (Eq. T.2.2.18).
The current guidelines for setting lake whitefish harvest limits across much of lakes
Huron, Michigan, and Superior is for them to be set in the year preceding that in which they will
take effect using data collected two years prior to the effective harvest year (Ebener et al., 2008).
We incorporated a similar time lag into our assessments. When fitting the assessment models
only the 20 years of data prior to the year for which abundances, mortality rates, and recruitment
levels were to be assessed were included. Although the operating model assumed selectivity,
catchability, and natural mortality rates were constant, in a natural system factors like these are
highly dynamic. Consequently, the use of a continually growing time series with assumed
constant conditions would provide an unrealistic perception of certainty in the system. Because
assessments were only conducted when 20 years or more of data were available, assessments
were not conducted during the first 20 years of each simulation. During this “burn-in” period the
TAC for each stock was calculated using the true abundance rather than estimated assessmentbased abundance. The “burn-in” period was used to obtain an initial abundance at age at year
21, so that a model-based assessment of the stock could be conducted.
The SCAA model estimated abundance at age 3 to age 12, with the last age group an
aggregate group similar to what was assumed in the operating model. Also like the operating
model, abundances at age in the SCAA model calculated under an exponential population model
with fishing and natural mortality components. We assumed that biologists did not realize
intermixing was occurring and therefor it was not incorporated into the assessment models. We
did not attempt to estimate natural mortality in the SCAA model, rather these rates were set
equal to those assumed in the operating model. Fishing mortality was separated into both age

67

and year effects (Eq. T.2.2.19) (Doubleday, 1976; Quinn and Deriso, 1999). Annual
multiplicative deviations were included to relax the direct proportionality assumption for the
fishing mortality-effort relationship (Eq. T.2.2.19). As in the operating model, selectivities were
modeled as gamma functions of age, with parameters of the gamma model estimated as part of
the SCAA model fitting process (Eq. T.2.2.20). Catchability was estimated as part of the SCAA
model fitting process as well.
The SCAA model estimated initial abundances for ages 4 to 12 as the product of a mean
abundance and an annual multiplicative deviation term (Eq. T.2.2.21). Recruitment in the
assessment (annual age-3 abundance) was estimated similarly using the product of a mean
recruitment value and a multiplicative annual deviation term (Eq. T.2.2.22). The deviations for
initializing abundance and age-3 recruitment summed to 0, but no other distributional
assumptions were made with regards to the deviations so large fluctuations in recruitment and
initial abundances were not penalized. The Baranov catch equation was used to predict harvest
at age (Eq. T.2.2.23). Age composition of the harvest was calculated by dividing age-specific
harvest by total harvest (Eq. T.2.2.24). Total harvest was calculated by summing age-specific
values, and age composition of the harvest for the stocks was calculated by dividing age-specific
harvest by the total harvest.
In our simulations, assessments were conducted every third year with TACs in
intervening years set to the level based on the most recent SCAA model assessment. The main
reason for conducting assessments every third year was to reduce processing time of the
simulations, although in reality avoiding annual assessments may be of interest to managers and
stakeholders as complicated statistical assessment results are often controversial and can add to
conflict or distrust in some management systems (Roel and De Oliveira, 2007; Cox and

68

Krunlund, 2008). Preliminary comparisons did not reveal major changes in performance metrics
in annual versus triennial assessments in a limited group of explored scenarios.
The search for the HPD SCAA model parameter estimates used the quasi-Newton
optimization algorithm implemented in AD Model Builder (Forunier et al., in press). Models
were considered to have converged on a solution when the maximum gradient for the SCAA
parameters was less than 0.001. To avoid implausible values and keep the optimization
algorithm from flat regions of the likelihood surface, parameters were assigned upper and lower
boundary values.
The SCAA model estimates of abundances at age, age-specific mortality rates, and
recruitment levels were used to project future abundances at age and calculate TACs for each
stock area. The projections used the abundance-at-age estimates from the beginning of the last
year of the stock assessment model, along with the mean recruitment levels and mortality rates
from the previous five years to project abundances. The target fishing mortality at age was then
calculated by subtracting the natural mortality rate from the instantaneous target mortality rate
for the different control rules and multiplying the difference by the age-specific selectivity
estimated in the last year of the SCAA model. The TAC for each stock was generated by
inputting the target fishing mortality at age and the projected abundance at age into the Baranov
catch equation.

Experimental Control Rules and Scenarios
The control rules explored in this research were total allowable annual mortality control
rules, which, based on our assumption of constant natural mortality, were equivalent to constant
fishing mortality control rules (Deroba, 2009). Each control rule was defined by the target total

69

mortality rate on the fully selected age class. Target total annual mortality rates considered
ranged from 35% to 65% in 10% increments. The range of mortality rates considered was based
on consultation with Great Lakes fishery managers and biologists, with the upper limit
corresponding to the existing target annual mortality for lake whitefish stocks in the upper Great
Lakes.
Thirty-six scenarios grouped into four major categories were examined (Table 2.3).
Scenarios consisted of different combinations of population intermixing and productivity levels
combined with a particular control rule. Five levels of intermixing between populations were
considered in this research; no mixing in which 0% of the spawning populations mixed with
other populations, low in which 10% of the spawning populations mixed with other populations,
medium-low in which 30% of the spawning population mixed with other populations, mediumhigh in which 60% of the spawning population mixed with other populations, and high in which
80% of the spawning population mixing with other populations. The rates of intermixing
considered in this research roughly overlap the range of intermixing rates observed in tagging
studies of lake whitefish in lakes Huron and Michigan (Ebener et al., 2010). Four productivity
levels were considered: high, medium-high, medium-low, and low productivities (Figure 2.1).
Differences in productivity levels between spawning populations were accounted for through
adjustments to the coefficients of the Ricker recruitment functions. Specifically, coefficients
were adjusted so that each population would sustain an identical maximum sustainable yield at a
constant fishing mortality rate in the absence of intermixing, but at different levels of
exploitation (Table 2.4). The stock-recruitment function coefficients used to represent the
different productivity levels were similar to values estimated in past analyses concerning lake
whitefish recruitment in the upper Great Lakes (Deroba, 2009).

70

The first category of scenarios, the “No Mixing” category, included four scenarios (Table
2.3). In each scenario, all populations shared the same level of productivity and no intermixing
of the populations was assumed to occur. Each of the four stocks was assigned a different total
allowable mortality control rule. The intent of these scenarios was to establish a baseline
performance of each control rule for each of the productivity level to which results from
scenarios with intermixing could be compared. Because the four populations had similar
characteristics and no mixing occurred, their performance under the different harvest policies
would be similar apart from random errors at a particular productivity level, which is why we felt
it was sufficient to simply evaluate the response of a single population with a particular
productivity level to each control rule.
The second category of scenarios, the “Correlated” category, included eight scenarios
(Table 2.3). These scenarios were intended to investigate the performance of the different
control roles in circumstances where there is a strong positive or negative relationship between
the rate of intermixing and the productivity characteristics of a spawning population. In the case
of the positively correlated scenarios, a population with a high rate of productivity was assigned
a high rate of intermixing, while in the negatively correlated scenarios a population with a high
rate of productivity was assigned a low rate of intermixing. In all scenarios, the intermixing and
productivity levels varied among populations so that each was assigned a particular combination
of levels.
The third category of scenarios, the “State Shift” category, included eight scenarios
(Table 2.3). In the first four scenarios for this category, populations were assigned either
medium-high or high productivity levels, and either medium-low or low intermixing rates. Each
scenario was then assigned a different control rule for all stocks. The next four scenarios were

71

set up identically, except that populations were assigned either medium-low or low productivity
levels, and either medium-high or high intermixing rates. These scenarios were intended to
compare the performance of each control rule between two alternative system states, one with
strong productivity and low mixing and another with poor productivity and higher intermixing.
Our reason for examining these two scenarios is that it is believed that such a shift has occurred
in the Great Lakes subsequent to invasion of dreissenid mussels and we were interested in
exploring how this might affect control rule performance. We also believed that this would be
broadly informative for evaluating the effect of regime shifts and changes in migratory behavior
of fish populations on control rule performance.
The final category of scenarios, the “Shared Mixing” category, included 16 scenarios
(Table 2.3). Under each of these scenarios spawning populations were assigned a different
productivity level so that all four levels of productivity were represented in each scenario. Each
scenario was then assigned a level of intermixing that was shared between all populations in the
scenario so that four scenarios shared each level of intermixing. Each scenario in each of these
groups was then assigned a different harvest control rule that was applied to all stocks in the
scenario. These scenarios were intended to investigate relative performance of the different
harvest policies under circumstances where populations with different productivity
characteristics intermixed at similar rates.

Performance Metrics
Metrics used to evaluate performance of the different control rules included those that
measured attributes of the fisheries exploiting the stocks (fishery metrics) as well as those of the
spawning populations (sustainability metrics). Fishery metrics included mean annual yield (both

72

cumulative and for individual stocks) and the mean inter-annual variability in yield, while the
sustainability metrics were related to spawning stock biomass (SSB) and included mean annual
percentage of unfished SSB (SSBF=0) and the percentage of years the SSB declined to less than
20% of SSBF=0. These performance metrics were chosen because in combination they measure
the desirable properties of maximizing harvest, minimizing risk to the resource, and minimizing
industry volatility (Butterworth and Punt, 1999).
Simulations were conducted in AD Model Builder (Fournier et al., in press). Each
simulation involved the projected dynamics under the assumed intermixing rates, productivity
levels, and harvest control rule over a 100 year timespan. Performance metrics were not
calculated for the burn-in period. One thousand simulations were investigated for each of the
scenarios described in Table 2.4. The distributions of results for the different performance
metrics for each of the investigated scenarios were summarized using box plots.

Results
No Mixing Scenarios
Mean annual yield varied with both productivity level and control rule in the absence of
intermixing (Figure 2.2). Hereafter, stocks will be referred to by the productivity of the
population that spawns in that stock area so an area with a high productivity spawning
population will be referred to as a high productivity stock keeping in mind the high productivity
is really a characteristic of the spawning population. In the high productivity stocks, the greatest
mean annual yield (median near 165 tonnes) occurred with a 65% total mortality control rule and
decreased at lower allowable mortality rules, with the lowest mean annual yield (median near 75
tonnes) at the 35% control rule. In stocks with medium-high productivity, yields at the 65 and
73

55% control rules were similar (median near 180 tonnes), with slightly lower yields under the
55% control rule. For medium-low productivity stocks, both the 55 and 45% control rule had
high mean annual yields (median near 190 tonnes), while the 35 and 65 % control rules had
slightly lower annual yields (medians near 150 tonnes). In stocks with low productivity, the
highest yield occurred under the 45% control rule (median near 190 tonnes) with the lowest yield
under the 65% control rule (median near 75 tonnes).
Inter-annual variability in yield also varied with both control rule and productivity level
(Figure 2.2). In all scenarios, the median inter-annual variation in yield was between 17 and 23
percent, with higher productivity stocks near the upper end of the range and lower productivity
stocks near the lower end. Inter-annual variation in yield also decreased with more conservative
harvest policies across the productivity levels although the differences were slight and there
remained substantial overlap in the range of results across the scenarios.
Productivity level and control rule also influenced the percentage of years that the
spawning population declined to less than 20% SSBF=0 and the mean percentage of SSBF=0
(Figure 2.2). For high productivity populations, the percentage of years that SSB declined to less
than 20% SSBF=0 was generally less than 10% with a mean percentage of SSBF=0 in excess of
50% for all control rules. For medium-high productivity populations the percentage of years that
SSB declined to less than 20% of SSBF=0 was slightly higher than for the high productivity
populations but still was generally less than 15% for each of the different target mortality rates.
As well, the mean percentage of SSBF=0 was generally in excess of 40% for medium-high
productivity populations for each of the control rules. For medium-low productivity stocks, the
percentage of years that SSB declined to less than 20% SSBF=0 increased considerably (median
74

near 50%) under the 65% total mortality rule relative to the other productivity levels, although it
was generally comparable to the higher productivity levels for the 35% to 55% total mortality
rules (<15%). Mean percentage of SSBF=0 ranged from approximately 20% to 75% for the 35%
to 65% target mortality control rules. For the low productivity populations, the 65% total
mortality control rule resulted in a large percentage (median 100%) of years with SSB below
20% SSBF=0 and a low mean percentage of SSBF=0 (median 5%). The 55% total mortality rule
also resulted in a large percentage (median 55%) of years with SSB less than 20% SSBF=0, with
a mean percentage of SSBF=0 near 20%. Conversely, in less than 10% of years the SSB
declined to less than 20% SSBF=0 for low productivity populations under the 45% and 35% total
mortality control rules. Mean percentage of SSBF=0 exceeded 40% for these lower mortality
control rules as well.

Correlated Scenarios
The mean annual yield for the stocks by productivity level was considerably different in
cases where mixing and productivity were positively (Figure 2.3) and negatively correlated
(Figure 2.4). In the case of positive correlations between mixing and productivity levels, high
productivity stocks with high mixing had low yield (less than expected under baseline
conditions) under each of the control rules, while low productivity stocks with low mixing had
greater yields (Figure 2.3). The greatest yields in the case of a positive correlation occurred
under the 45% total mortality control in the low productivity and low intermixing stock, which
resulted from fish mixing into that stock from other populations. For inverse correlations

75

between productivity and rate of intermixing, high productivity stocks with low mixing had the
greatest yields under all control rules, while low productivity stocks with high mixing rates had
the lowest yields under all rules (Figure 2.4). The greatest yields for the negative correlation
scenarios occurred under the 55% total mortality control rule in the high productivity, low
mixing stock, although the yields for the 65% and 45% control rule in the high productivity, low
mixing stock were also quite large.
Mean annual cumulative yields exhibited a similar pattern in results to the individual
stock yields. For both positively and negative correlated scenarios, the greatest cumulative
yields occurred under 45 and 55% control rules (Figure 2.5). The yield under the 65% total
mortality control rule was the next greatest, followed by yields under a 35% control rule (Figure
2.5). Overall yield levels were similar between positively and negative correlated scenarios
under a particular control rule, with slightly larger yields obtained for the positively correlated
scenarios.
The inter-annual variation in yield for the different control rules for the correlated
scenarios was similar to those observed for the no mixing scenarios. That is inter-annual
variation generally declined with more conservative control rules. Compared to the no mixing
scenarios, inter-annual variation in yield declined slightly for the negative and positive
correlation scenarios across all the control rules, however, the differences were generally less
than 5%. The percentage of years the SSB declined to less than 20% SSBF=0 and the mean
percent of SSBF=0 also had very similar responses to the no mixing group of scenarios without
intermixing with risk of depletion depending both on the productivity of the populations and the
evaluated control rule.

76

State Shift Scenarios
The mean annual yield in all stocks in the first state shift case (high productivity levels
and low rates of intermixing) was greatest for all stocks under the 65% control rule (Figure 2.6).
As control rules became more conservative, mean annual yield decreased with the greatest
difference between the 45 and 35% control rules. In the second state shift case (low productivity
and high rates of intermixing) mean annual yield was the greatest for all stocks under the 45%
control rule and lowest under the 65% control rule (Figure 2.7). The mean cumulative yield of
the scenarios reflected the findings for the yield from the individual stocks. Under the first state
shift case, the greatest cumulative yield was obtained with the 65% control rule, while in the
second case it was obtained with the 45% control rule (Figure 2.5).
As in earlier scenario categories, the inter-annual variation in yield decreased slightly
with more conservative control rules although there was overlap in the distributions for the
control rules (Figures 2.6 and 2.7). This was true for the scenario with higher productivity and
lower intermixing and the scenario with lower productivity and higher intermixing. The
variation in yield was slightly higher (3 to 5%) for the case with higher productivity and lower
intermixing characteristics. The percentage of years that SSB declined to less than 20% SSBF=0
and the mean percentage of SSBF=0 had very similar responses to different control rules for the
various levels of productivity when compared to the scenarios without intermixing.

Shared Intermixing, Varied Productivity Scenarios
The mean annual yields for stocks with low intermixing rates were largely indiscernible
from those when stocks did not intermix (Figure 2.8). For high productivity stocks, the 65%
mortality control rule resulted in the largest mean annual yields, while for the medium-low and
77

low productivity stocks the 45% total mortality control rule resulted in the largest mean annual
yield. When stocks intermixed at a medium-low rate, there were noticeable changes in mean
annual yields from the baseline condition (Figure 2.9). Perhaps most notably, the 65% total
mortality control rule no longer resulted in the largest yields from the most productive stock,
rather the 55% mortality control rule resulted in the largest yields. Under medium-high rates of
intermixing, the improved performance at the 55% mortality control rule compared to the 65%
mortality control rule in terms of fishery yield became more apparent (Figure 2.10). However,
the 45% mortality control rule began resulting in mean annual yields comparable to those under
the 55% mortality control rule at higher productivities. Under high intermixing rates, the 45%
total mortality control rule produced mean annual yields that were very similar to those produced
by the 55% mortality control rule (Figure 2.11). Unlike the yield for the individual stocks, the
mean annual cumulative yield showed an almost identical pattern across harvest policies
regardless of the rate of intermixing, with the greatest cumulative yields at the 55% and 45%
control rule. Considerably lower cumulative yields were observed under the 65% and 35%
control rules (Figure 2.5).
As in earlier scenario categories, the inter-annual variation in yield decreased slightly
with more conservative harvest policies, although there remained substantial overlap in the
distributions under the examined control rules at each level of productivity. There were slight
changes in variation in yield as intermixing rates increased. Inter-annual variation in yield under
an assumption of high intermixing was approximately 5% lower than that observed under low
intermixing rates. The percentage of years that SSB declined to less than 20% SSBF=0 and the
mean percentage of SSBF=0 had very similar responses to different harvest policies for the
various scenarios when compared to the scenarios without intermixing.
78

Discussion
Our research indicated that across a wide range of intermixing and productivity scenarios
control rules for mixture fisheries that preserve spawning biomass of the lowest productivity
spawning components can produce more desirable outcomes than those that seek simply to
maximize harvest. Not only did more conservative control rules lower the risk of populations
being overexploited, but in some cases they also produced greater yields than control rules that
allowed greater exploitation of mixed stocks. In other words, more conservative control rules
could produce outcomes that were desirable from both economic and biological standpoints.
Thus, although “resource-oriented” and “user-oriented” management objectives are often seen as
conflicting (Hall and Donovan, 2002), under the scenarios and policies investigated in our
research these objectives were found to be in agreement regarding the best options for managing
mixture fisheries.
In addition to producing greater yields and lowering risk of depletion, this research also
demonstrated that inter-annual variation in yield could be lessened, albeit only somewhat, with
more conservative harvest policies. This likely was a consequence of lower exploitation rates
resulting in populations with an SSB closer to that of SSBF=0, which resulted in more stable
populations as a result of less variability in annual recruitment levels. Nevertheless, fishery
managers will undoubtedly find this a beneficial result given that stable harvest levels are
generally of interest to commercial fishers because it helps ensure a somewhat consistent
livelihood from year to year. Our finding that inter-annual variation in yield was reduced with
more conservative harvest policies supports the findings of Ricker (1958) and Anderson et al.
(2008) who found that exploitation can lead to instability in the dynamics of fish populations.

79

In previous evaluations of constant fishing mortality control rules, it has been well
established that control rule performance depends heavily on the productivities of the exploited
populations, in particular the ability of populations to rebound from low stock sizes (Walters and
Parma, 1996; Brodziak, 2002). The importance of population productivity levels on the results
of all the performance metrics that we evaluated in this research confirms these earlier findings.
However, our results also indicate that when intermixing of populations occurs, determining the
appropriateness of a constant mortality control rule no longer simply is a function of the
productivity of a single population. Rather, it depends on the productivity of all the components
populations of that fishery as well as the mixing rates of the populations. This in turn can lead to
considerable confusion regarding what level of exploitation a stock can support with high yields
coming from areas where low productivity populations spawn (as demonstrated in Chapter 1 of
this thesis), which could lead to managers thinking the population could support even greater
exploitation rates. Recently, preservation of low productivity populations has focused on
reducing harvest in regions where populations spawn, even when the rate of intermixing between
populations may be significant (Stephenson, 1999). Our results suggest that rather than
developing individualized harvest policies for each stock, a management approach of fishing at
mortality rates that account for the underlying productivity over larger geographic regions can
provide surprisingly desirable fishery outcomes. Similarly, Walters and Parma (1996) and
DiNardo and Wetherall (1999) found that constant fishing mortality rules performed well in
cases without intermixing when regime shifts or climate variation occurred if the rates chosen
were conservative enough to not put populations at risk during low productivity periods. This is
especially encouraging for systems with limited data or in situations where managers must take

80

action before adequate studies can be completed on intermixing and productivity of population
components.
In this research, we limited our evaluations to total mortality control rules because for
Great Lakes lake whitefish stocks this is considered the most viable type of policy for making
management decisions. Although prior simulation-based evaluations have found biomass-based
control rules to perform well for lake whitefish fisheries (Deroba, 2009), such rules have not
been adopted in the Great Lakes because of the perceived difficulty in identifying appropriate
biomass reference points. Other researchers as well have pointed out the difficulty in specifying
reference points for managing fisheries using biomass-based control rules (Cadrin and Pastoors,
2008; Dowling et al., 2008; Haltuch et al., 2008; Prince et al., 2008; Smith et al., 2008). Despite
our not considering a wide array of control rules, we still believe our results to be broadly
informative given the widespread use of constant fishing mortality control rules.
In terms of lake whitefish management, our research suggests that the 65% total
allowable mortality control used to manage fisheries across much of the upper Great Lakes has
the potentially to negatively influence sustainability of lower productivity populations and that
fisheries could benefit from more conservative control rules. Our analysis suggests that if a
single control rule is used to manage intermixing lake whitefish stocks, it should be sufficiently
conservative to account for the sustainability of the lowest productivity component. Given the
productivity levels used in the research, the 45% mortality control rule produced the best
performance, with low risk of depletion, high yields, and low inter-annual variation in yield. The
55% mortality control rule, although not ranked as highly as the 45% rule, was found to have
more desirable performance that the 65% rule for many metrics, especially sustainability metrics.

81

These findings are somewhat conflictive with those of Deroba (2009) who found that the 65%
total mortality control rule performed well for lake whitefish fisheries in a simulation-based
control rule evaluation for the upper Great Lakes. This discrepancy in results is likely related to
differences in the approach and assumptions of these two analyses. Deroba (2009) accounted for
uncertainty in future growth and recruitment as influenced by ecosystem level changes by
assessing the probability of outcomes for lake whitefish stocks under control rules with
recruitment drawn from assessment-based estimates of recruitment relationships in TW stocks.
This approach included the lower and higher productivity groups in the outcome distribution, so
the effect on low productivity populations was not directly measured. Additionally, since
estimates of recruitment were based on assessments, and assessments can be biased by
intermixing, the estimates of productivity may not have adequately captured the dynamics of
lower productivity components. Our analysis focused instead on the control rule performance on
individual populations, and included plausible productivity levels instead of assessment based
recruitment. Given that our range of productivity levels was somewhat arbitrary, we cannot be
certain to have more appropriately described the distribution of productivity of Great Lakes
whitefish populations than did Deroba. However, we believe our choices were reasonable given
the available information, and the lack of a comprehensive analysis reconsidering population
productivity accounting for the effect of intermixing on stock assessment estimates of
recruitment and spawning biomass.
Annual mortality rates for lake whitefish stocks in northern lakes Huron and Michigan
are generally lower than the 65% currently allowed (Caroffino and Lenart, 2011; Figure 2.12),
meaning that cutting TACs in many units to the 55% or even 45% control rule may not result in
major reductions in harvest compared to that in recent years, strengthening the argument for

82

reducing mortality. In some cases, the lower-than-allowed mortality rates in lake whitefish
stocks may be allowing lower productivity spawning aggregations to persist under the existing
policy even while filling TAC’s may put them at considerable risk of depletion. It is important
to keep in mind that the productivity levels used in this analysis were used to examine a plausible
range of productivity levels for lake whitefish in the upper Great Lakes, not to reflect the
productivity of any particular lake whitefish populations.
By comparing results between the state shift scenarios, we found that changes in the
productivity and intermixing of spawning populations, as is believed to be the case for Great
Lakes lake whitefish, could lead to changes in the performance of control rules. Despite the
lower productivity and higher intermixing rates, it was still possible for overall yields to
approach or even surpass those of the earlier state by matching control rules to the correct
productivity levels. For the Great Lakes, this has important consequences given the current state
of the system and it continuing to be threatened by invasion of additional exotic species. The
threat of additional invasions, along with the threats of global climate change and other
environmental changes, suggest that Great Lakes fishery managers need to continue to evaluate
whether harvest control rules are appropriate for the stocks they manage (Roessig et al., 2004;
Ficke et al., 2007).

83

APPENDIX

84

Figure 2.1. The four productivity levels used in this simulation analysis. The higher steepness at
low SSB indicates higher capacity for the population to rebound from depletion and therefor
higher productivity. Recruitment is defined as age-1 fish in the population the year following
spawning.

85

Figure 2.2

86

Figure 2.2 (cont’d)
Performance metrics for scenarios without intermixing between stocks. Labels along the y-axis
represent the different performance metrics used to compare harvest policies in this analysis.
Mean annual yield is represented in tonnes. Inter-annual variation in yield, the percentage of
years spawning stock biomass fell below 20% of unfished spawning stock biomass (SSBF=0),
and mean percentage of SSBF=0 are all expressed in a percentage. The labels along the x-axis
describe the productivity and intermixing level of the spawning population in each stock, while
the numbers at the tick marks correspond to the allowable annual mortality rates investigated in
this analysis.

87

Figure 2.3

88

Figure 2.3 (cont’d)
As in Figure 2.2, except for scenarios when productivity and intermixing are positively
correlated.

89

Figure 2.4

90

Figure 2.4 (cont’d)
As in Figure 2.2, except for scenarios when productivity and intermixing are negatively
correlated

91

Figure 2.5. Mean annual cumulative fishery yield summed for each investigated scenario.
Cumulative yields for the No Mixing group of scenarios are not presented as for these scenarios
stocks differed in the harvest control rules so comparisons of yields with other scenarios would
th
th
not be informative. Boxes indicate the 25 and 75 percentiles over the simulations, while
whiskers indicate 1.5 times the interquartile range over simulations. Horizontal lines indicate the
median of the yields for the simulations. On the x-axis, numbered labels correspond to specific
scenarios within each category. See Table 2.3 for a description of the scenarios.

92

Figure 2.6

93

Figure 2.6 (cont’d)
As in Figure 2.2, except for the state shift scenarios with relatively high productivity and
relatively low intermixing.

94

Figure 2.7

95

Figure 2.7 (cont’d)
As in Figure 2.2, except for the state shift scenarios with relatively low productivity and
relatively high intermixing.

96

Figure 2.8

97

Figure 2.8 (cont’d)
As in Figure 2.2, except for the shared mixing scenarios with varied productivity and low
intermixing.

98

Figure 2.9

99

Figure 2.9 (cont’d)
As in Figure 2.2, except for the shared mixing scenarios with varied productivity and mediumlow intermixing.

100

Figure 2.10

101

Figure 2.10 (cont’d)
As in Figure 2.2, except for the shared mixing scenarios with varied productivity and mediumhigh intermixing.

102

Figure 2.11

103

Figure 2.11 (cont’d)
As in Figure 2.2, except for the shared mixing scenarios with varied productivity and high
intermixing.

104

Figure 2.12. Total mortality estimates for the highest selected age class for selected lake
whitefish stocks in northern Lakes Huron and Michigan according to the 2010 stock assessments
(Carrofino and Lenart, 2011). These values are compared to the total annual mortality targets
under the control rules investigated in this research study.

105

Table 2.1. Descriptions and values (if applicable) for index and state variables, structural
parameters, stochastic deviation and error terms, and likelihood components used in the
description of equations for models used in this analysis. Variables and parameters denoted with
diacritical marks (i.e. ^ or ¯) are identical to those describe in Table 2.1, but are used to denote
either an estimated quantity (^) or the mean (¯) of a variable.
Variable
Description
Index Variables
i
Current population or stock
j
Population or stock other than the current
y
Year
a
Age
State Variables
N
Abundance
Z
Instantaneous total mortality
Recruitment function stock size (in number of eggs
SSE
produced)
F
Instantaneous fishing mortality
m
Maturity
w
Weight
L
Length
s
Selectivity
TAC
Total allowable harvest in a management unit
Stock abundance after intermixing
N
Observed stock harvest
C
Actual stock harvest
C
Observed age composition of harvest
P
Actual age composition of harvest
P
Observed effort
E
Structural Parameters
Instantaneous natural mortality

Recruitment function productivity coefficient

Recruitment function density dependence coefficient
2
Recruitment function variance
R

Proportion of population female
Eggs
Eggs per kilogram mature female
L
Growth model theoretical maximum length
Growth model growth coefficient

t0
Growth model time coefficient (age at length = 0)



m

Allometric model condition factor
Allometric model curvature parameter
Asymptotic maturity for logistic maturity model

106

Value

0.25
See Table 2.4
See Table 2.4
0.36
0.5
19937
60.9
0.1686
0.0
8.06x10
2.45
1.0

-5

Table 2.1 (cont’d)







2
C


2
C
q

2
E
2
F

Slope parameter for logistic maturity model
Inflection point length for logistic maturity model
Parameter 1 of gamma selectivity function
Parameter 2 of gamma selectivity function
Implementation error variance

0.01

Proportion of population mixing into another
management unit
Harvest observation error variance
Catchability







0.04

Assessment fishing mortality deviation variance

0.01

TAC implementation error

C

Harvest observation error

E

Effort observation error

F

Assessment fishing mortality deviations

N 412

Assessment initial abundance deviations



Assessment recruitment deviations
N3
Likelihood components (assessment model)
Harvest likelihood component
C

P

0.01

Effort deviation variance

C

F

Varied with scenario
and stock

1.5x10

Stochastic deviation and error terms
R
Recruitment stochastic error



0.315
37.9
13.074
1.26

Fishing mortality deviation likelihood component
Proportion at age likelihood component

107

-6

Table 2.2. Operating and assessment model equations. Variables and parameters denoted with
diacritical marks (i.e. ^ or ¯) are identical to those describe in Table 2.1, but are used to denote
either an estimated quantity (^) or the mean (¯) of a variable.
Equation

Equation
Number

Operating Model



N y 1,a 1  N y,a exp Z y,a
Z y,a  M  Fy,a



T.2.2.1







N y,1    SSE y 1 exp   SSE y 1 exp  R  ;  R

SSE y   N y,a ma wa  Eggs
a
La  L 1  exp    a  t0  



2
N 0,  R

T.2.2.2



T.2.2.3
T.2.2.4



T.2.2.5

wa   La

ma 

T.2.2.6

m
1  exp    La    

T.2.2.7

Fy,a  sa Fy

sa 

T.2.2.8

a exp   a 

T.2.2.9

10 exp   10 







C  TAC exp   0.5 2 ;  ~ N 0,  2
y
y
C
C
C
C







T.2.2.10



Ni, y 1,a 1  Ni, y,ai i exp M  Fi, y.a   Ni, y,ai  j exp M  F j , y.a
j

Ni, y,a  Ni, y,ai i   N j, y,a j i
j
Observed Data
C  C exp   0.5 2 ;  ~ N 0,  2
y
y
C
C
C
C



Py,a









T.2.2.13





T.2.2.11
T.2.2.12

MN 200, Py,a
F
y
E 
exp   0.5 2 ;  ~ N 0,  2
y 1.50 10e-6
E
E
E
E







108

T.2.2.14



T.2.2.15

Table 2.2 (cont’d)
Assessment Model


 1
ˆ
C  nC loge  C    2
ˆ
2
 C

F

 n


C
 log  y
ˆ
 e  C
 y
 y






2
T.2.2.16



ˆ
0.25 
 

loge  C   
log   2
F
 2 2   e F
 0.25 
ˆ
 C y





ˆ
P   200 Py,a loge Py,a
y
a

ˆ
ˆˆ
Fy,a  qsa E y exp  F  ;  F

T.2.2.18



2
N 0,  F



T.2.2.19

ˆ
a exp  ˆa 
ˆ
sa 
ˆ
10 exp  ˆ10 

T.2.2.20



ˆ
N412  N412 exp  
;
N412 



ˆ
N y,3  N3 exp  
;
N3 



ˆ
C y, a 

T.2.2.17

  N412  0

  N3  0

ˆ
Fy,a
ˆ
ˆ
N y,a exp  Fy,a  M
ˆ
Fy,a  M



T.2.2.21
T.2.2.22



T.2.2.23

ˆ
C y, a
ˆ
Py,a 
ˆ
 C y,a
a

T.2.2.24

109

Table 2.3. Productivity levels, intermixing rates, and control rules used in each of the scenarios
evaluated in this research. Varied productivity refers to cases where the 4 different spawning
population were assigned unique stock recruitment relationship.
Category

Scenario

Mixing

Productivity

No Mixing

1
2
3
4

Corr

1

8

None
None
None
None
Low, Med. Low,
Med. High, High
Low, Med. Low,
Med. High, High
Low, Med. Low,
Med. High, High
Low, Med. Low,
Med. High, High
Low, Med. Low,
Med. High, High
Low, Med. Low,
Med. High, High
Low, Med. Low,
Med. High, High
Low, Med. Low,
Med. High, High

(All Stocks) Low
Med. Low
Med. High
High
Low, Med. Low, Med.
High, High
Low, Med. Low, Med.
High, High
Low, Med. Low, Med.
High, High
Low, Med. Low, Med.
High, High
High, Med. High, Med.
Low, Low
High, Med. High, Med.
Low, Low
High, Med. High, Med.
Low, Low
High, Med. High, Med.
Low, Low

State Shift

1
2
3
4
5
6
7
8

2 Low, 2 Med. Low
2 Low, 2 Med. Low
2 Low, 2 Med. Low
2 Low, 2 Med. Low
2 Med. High, 2 High
2 Med. High, 2 High
2 Med. High, 2 High
2 Med. High, 2 High

Shared

1

(All Stocks) Low

Mixing

2

Low

3

Low

4

Low

2 Med. High, 2 High
2 Med. High, 2 High
2 Med. High, 2 High
2 Med. High, 2 High
2 Low, 2 Med. Low
2 Low, 2 Med. Low
2 Low, 2 Med. Low
2 Low, 2 Med. Low
Low, Med. Low, Med.
High, High
Low, Med. Low, Med.
High, High
Low, Med. Low, Med.
High, High
Low, Med. Low, Med.
High, High

2
3
4
5
6
7

110

Control Rule
65,55,45,35 (1
stock with each)
65,55,45,35
65,55,45,35
65,55,45,35
65 (all stocks)
55
45
35
65
55
45
35
65 (all stocks)
55
45
35
65
55
45
35
65 (all stocks)
55
45
35

Table 2.3 (cont’d)
5
6

Med. Low

7

Med. Low

8

Med. Low

9

Med. High

10

Med. High

11

Med. High

12

Med. High

13

High

14

High

15

High

16

Low, Med. Low, Med.
High, High
Low, Med. Low, Med.
High, High
Low, Med. Low, Med.
High, High
Low, Med. Low, Med.
High, High
Low, Med. Low, Med.
High, High
Low, Med. Low, Med.
High, High
Low, Med. Low, Med.
High, High
Low, Med. Low, Med.
High, High
Low, Med. Low, Med.
High, High
Low, Med. Low, Med.
High, High
Low, Med. Low, Med.
High, High
Low, Med. Low, Med.
High, High

Med. Low

High

111

65
55
45
35
65
55
45
35
65
55
45
35

Table 2.4. Recruitment parameters for the four productivity levels assigned to spawning
populations in this analysis.
Productivity Level



Low

0.000369

7.1708x10

Medium Low

0.000516

1.2780x10

Medium High

0.000769

2.2758x10

High

0.001281

4.2988x10

b

112

-11
-10
-10
-10

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113

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118

CONCLUSIONS
The results of the analyses included in this thesis have important implications for lake
whitefish management in the upper Great Lakes, as well as being generally informative for
fisheries management when stock intermixing occurs. In Chapter 1, the performance of the
existing control rule for lake whitefish stocks in the 1836 Treaty waters was found to vary with
the intermixing and productivity of the populations that made up mixed stocks. Harvest in a
management unit was a poor indicator of the health of the underlying spawning population when
there was considerable intermixing. Yield varied considerably between stocks under different
scenarios. The sustainability and risk of depletion of spawning populations was dependent on
their productivity level, with low productivity populations having a very high risk of depletion
and maintaining a very small proportion of their unfished biomass. I conclude that intermixing
of populations with varying levels of productivity can seriously affect management of lake
whitefish fisheries in the 1836 Treaty waters and could foreseeably result in overharvest of some
low productivity populations.
In Chapter 2, the performance of several control rules were compared across a wide
spectrum of scenarios for intermixing and productivity of spawning populations. Control rules
more conservative than the current 65% mortality policy were found to perform better at
preserving spawning biomass and reducing the risk of depletion. The inter-annual variability in
yield was also found to decrease slightly at more conservative control rules. Yield varied
between stocks under each scenario, but in general control rules more conservative than the
existing rule, but less conservative than the 35% mortality control rule, had the highest annual
yields. I concluded that the 45% allowable mortality control rule provided very high
sustainability regardless of productivity and high overall yield across the majority of scenarios,
119

making it an excellent candidate for lake whitefish management. Additional research into the
stock recruitment (productivity) relationships for spawning populations would better inform the
selection of an appropriate harvest level for lake whitefish stocks in the 1836 Treaty waters.

120