ESTIMATION OF SIZE-SPECIFIC SEA LAMPREY WOUNDING RATES ON LAKE
TROUT: SPATIAL AND TEMPORAL PATTERNS IN THE UPPER GREAT LAKES
By
Carson G. Prichard

A THESIS
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
MASTER OF SCIENCE
Fisheries and Wildlife
2012

 
 

ABSTRACT
ESTIMATION OF SIZE-SPECIFIC SEA LAMPREY WOUNDING RATES ON LAKE
TROUT: SPATIAL AND TEMPORAL PATTERNS IN THE UPPER GREAT LAKES
By
Carson G. Prichard
The purpose of this research was first, to develop sea lamprey (Petromyzon marinus)
wounding rate models for lake trout (Salvelinus namaycush) from each of the lakes within 1836
Treaty-ceded waters, and second, to explain how and why the length distributions of lake trout
attacked by sea lamprey have differed spatially and over time. Despite substantial control
efforts, the negative impacts of parasitic sea lamprey predation on native lake trout remain an
important fisheries concern in the Great Lakes. In Chapter 1, I estimate wounding rates as a
logistic function of lake trout length. A model comparison framework was used to develop
unique wounding rate models for each of Lakes Huron, Michigan, and Superior. Models that
assumed a negative binomial wound distribution and allowed for spatial and temporal effects in
the shaping parameters were selected for each lake. Large spatial differences and temporal
trends in sea lamprey size-selectivity were found. Chapter 2 attempts to explain spatial and
temporal patterns in sea lamprey size-selectivity in a foraging theory context. Foraging theory
predicts that in the scarcity of larger, more desirable prey, a predator will shift its feeding
behavior by incorporating smaller, less desirable prey types. Wounding rate model parameter
estimates were related to large lake trout abundance estimates to look for patterns consistent with
foraging theory. Large lake trout abundance was a poor predictor of sea lamprey size-selectivity,
but future research suggestions to examine the influence of alternative hosts and lake trout strain
are described.

 
 

ACKNOWLEDGEMENTS

I would like to thank foremost my advisor, Jim Bence, whose guidance helped me
complete the work herein. I would also like to thank my committee members Brian Irwin and
Juan Pedro Steibel who provided useful instruction throughout the completion of this project. I
thank the Modeling Subcommittee of the Technical Fisheries Committee, and especially Ted
Treska and Jory Jonas, for providing data. I would like to acknowledge the support of the
Michigan State University High Performance Computing Center through which my models were
run, as well as Travis Brenden and Darren Thornbrugh who helped generate map figures.
Finally, I am grateful to my friends and colleagues within the MSU Department of Fisheries and
Wildlife.
Funding for this research was provided by the Great Lakes Fishery Commission, by the
Michigan Department of Natural Resources, and through them by the U.S.F.W.S. Sportfish
Restoration Act program.

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PREFACE

The work contained in Chapter 1 was written as a standalone document and has been
submitted for publication to the Journal of Great Lakes Research as a co-authored paper by
Carson G. Prichard and James R. Bence. It is presented here in essentially the same form as the
submitted manuscript. For this reason, Chapter 1 is written in the first person plural narrative,
although the thesis is singularly authored. All references are formatted in a style consistent with
that journal.

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TABLE OF CONTENTS

LIST OF TABLES ......................................................................................................................... vi
LIST OF FIGURES ...................................................................................................................... vii
INTRODUCTION ...........................................................................................................................1
History of Lake Trout and Sea Lamprey in the Upper Great Lakes ........................1
Current Status of Lake Trout Populations ...............................................................3
Research Goals.........................................................................................................4
References ............................................................................................................................8
CHAPTER 1
ACCOUNTING FOR CHANGING PATTERNS OF SIZE-SPECIFIC WOUNDING OF
LAKE TROUT BY SEA LAMPREY IN THE UPPER GREAT LAKES ....................................12
Introduction ........................................................................................................................13
Methods..............................................................................................................................18
Wound Data ...........................................................................................................18
Model Development...............................................................................................19
Results ................................................................................................................................25
Model Selection .....................................................................................................25
Patterns in Estimated Wounding Rates ..................................................................27
Trends in Parameter Estimates...............................................................................29
Discussion ..........................................................................................................................32
Improved Wounding Rate Estimates .....................................................................36
Concluding Remarks..............................................................................................37
References ..........................................................................................................................39
CHAPTER 2
SEA LAMPREY SIZE SELECTION OF LAKE TROUT IN A FORAGING THEORY
CONTEXT .....................................................................................................................................43
Introduction ........................................................................................................................44
Methods..............................................................................................................................46
Large Lake Trout Abundance Data........................................................................46
Approaches to Examining Selectivity ....................................................................49
Results ................................................................................................................................51
Dynamics in Large Lake Trout Abundance ...........................................................51
Time-varying βs .....................................................................................................56
Abundance-varying βs ...........................................................................................58
Discussion ..........................................................................................................................59
References ..........................................................................................................................67

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LIST OF TABLES

Table 1.1: Description of the α and β parameters for the candidate set of models
used in estimating sea lamprey wounding rates on lake trout. Random walk is
abbreviated as “r. w.” ...............................................................................................................21
Table 1.2: Akaike’s Information Criterion (AIC) comparison for wounding
models using the negative binomial distribution for wounding rate on lake
trout of a given length. Δ AIC values are relative to the best fitting model for
each lake, respectively. Model Y produced the best fit to the Lake Huron data
and model X produced the best fit to both the Lake Michigan and Lake
Superior data. Models A-M for each lake had much greater Δ AIC values and
their results are not shown. Convergence was not achieved for models N, S
and T for Lake Michigan .........................................................................................................26

vi
 

LIST OF FIGURES

Figure 1.1: An example of the logistic model fit to lake trout wound data from
southern Lake Huron (MH3456) in 1985 overlaid with observed data on
wounds per fish. Observed wounds per fish were averaged for 20mm length
bins for visual clarity, although the model was fit to observed values from
individual fish. From eq. 1.1, θ represents the asymptotic wounding rate, β
corresponds to lake trout length at the inflection point, and αθ/4 is the slope of
the function at the inflection point. The increased variability in the plotted
data for larger fish likely resulted from smaller sample sizes for those size
classes ......................................................................................................................................15
Figure 1.2: Lakes Huron, Michigan and Superior with the regions used in this
study specified. Region names and boundaries correspond to combinations of
lake trout management units defined for Lake Superior (Hansen 1996) or
statistical districts (Smith et al. 1961) for the other lakes. For example,
MM123 is the combined areas of the statistical districts MM1, MM2, and
MM3. The shaded region is the state of Michigan .................................................................19
Figure 1.3: Wounding rate estimates for 500mm (solid circles) and 650mm (open
circles) lake trout from each region analyzed in this study. Estimates
correspond to model Y for Lake Huron and model X for Lakes Michigan and
Superior (Table 1.1). Region abbreviations correspond to those described in
Figure 1.2. Wounding rates were estimated on a loge scale and values shown
represent back-transformed estimates with error bars corresponding to
estimates plus or minus one asymptotic standard error ...........................................................28
Figure 1.4: Lake trout length at which 50% of the asymptotic wounding rate was
reached (β, eq. 1.1) for models selected for each lake in this analysis. β
estimates correspond to model Y for Lake Huron and model X for Lakes
Michigan and Superior (Table 1.1) ..........................................................................................30
Figure 1.5: Asymptotic wounding rate (θ, eq. 1.1) parameter estimates of models
selected for each lake in this analysis. θ estimates correspond to model Y for
Lake Huron and model X for Lakes Michigan and Superior (Table 1.1).
Asymptotic wounding rate parameters were not estimated for some unit-year
combinations for Lake Michigan due to low sample size........................................................31
Figure 1.6: A visual example of how a change in the selectivity of sea lamprey
for smaller lake trout could result in a shift of the logistic function describing
wounding rates versus lake trout length. The shift from the solid curve to the
dashed curves is the type of shift hypothesized to occur in response to a
decrease in the abundance of larger lake trout .........................................................................33

vii
 

Figure 1.7: Wounding rate estimates for 500mm and 650mm fit to Lake Huron
wound data. Region abbreviations correspond to those described in Figure
1.2. Estimates corresponding to the model selected by Rutter and Bence
(2003) are given by the solid line and estimates corresponding to model Y
(Table 1.1) are given by the dashed line ..................................................................................36
Figure 2.1: Lakes Huron, Michigan and Superior with the regions used in this
study specified. Region names and boundaries correspond to lake trout
management units defined for Lake Superior (Hansen 1996) or statistical
districts (Smith et al. 1961) for the other lakes. MM123 is the combined areas
of the statistical districts MM1, MM2, and MM3. The shaded region is the
state of Michigan......................................................................................................................47
Figure 2.2: Estimates of large (>600mm) lake trout (LAT) abundance and timevarying β estimates for regions MH1 (1984-2010) and MH2 (1984-2008) in
Lake Huron. .............................................................................................................................52
Figure 2.3: Estimates of large (>600mm) lake trout (LAT) abundance and timevarying β estimates for regions Lake Michigan regions MM123, MM4, and
MM5 for years 1984-2010. The left y-axis corresponds to abundances and
time-varying βs for MM123, and the right y-axis corresponds to estimates for
MM4 and MM5........................................................................................................................53
Figure 2.4: Estimates of large (>600mm) lake trout (LAT) abundance and timevarying β estimates for Lake Superior. For large LAT abundances, the left yaxis corresponds to MI5 and the right y-axis corresponds to MI6 and MI7.
For time-varying β estimates, the left y-axis corresponds to the combined
region MI4/MI5 and the right y-axis corresponds to the combined region
MI6/MI7. ..................................................................................................................................54
Figure 2.5: β estimates versus abundance of large lake trout for each management
unit. Region abbreviations correspond to those described in Figure 1.2.
Wounding rates were fit to the logistic wounding rate model (eq. 1.1), with β
varying as a quadratic function of large lake trout abundance (eq. 2.1). Error
bars represent one standard error. ............................................................................................59
Figure 2.6: The proportion stocked lake trout that are Seneca strain from years
1985-2010. Prior to 1985, Seneca strain lake trout were not stocked in Lakes
Huron and Michigan. Data correspond to combined totals of lake trout
stocked in regions MH1 and MH2 for Lake Huron, and MM123, MM4, and
MM5 for Lake Michigan. Data from the Great Lakes Fishing Stocking
Database (http://www.glfc.org/fishstocking/). .........................................................................63

viii
 

INTRODUCTION

History of Lake Trout and Sea Lamprey in the Upper Great Lakes
Prior to European colonization in the eighteenth and nineteenth centuries, lake trout
(Salvelinus namaycush) were the dominant pelagic predator in the Great Lakes. Early in the
twentieth century, large commercial fisheries supported by the diverse stocks of lake trout had
developed on Lakes Huron, Michigan, and Superior. Each lake supported a massive commercial
fishing industry with annual harvests exceeding 2 million kilograms dating back to the late 1800s
(Hansen 1999). However, beginning in the late 1930s, lake trout populations in each lake
collapsed – first in Lake Huron, second in Lake Michigan, and last in Lake Superior. This is
evidenced by declines in annual commercial harvest – decreasing from 2.7 million to 0.18
million kilograms in Lake Huron (1935-1947), from 3.1 million to 0.16 million kilograms in
Lake Michigan (1943-1949), and from 2.1 million to 0.23 million kilograms in Lake Superior
(1950-1960) (Baldwin et al. 2009, Hansen 1999). With each successive collapse, fishing effort
shifted to areas where lake trout were still in abundance so that by the 1950s, after collapses in
Lakes Huron and Michigan, the only commercial fisheries left for lake trout existed in Lake
Superior (Hansen 1999). Lake trout populations in Lake Superior were so severely reduced that
in 1962 both United States and Canadian governments imposed a general closure on lake trout
fishing (Smith and Tibbles 1980). Lake trout commercial fisheries that had supported an annual
combined average catch of 7 million kilograms in the 1940s had been reduced to nothing.
Sea lampreys (Petromyzon marinus), a parasitic fish native to the Atlantic Ocean, were
first recorded in Lake Huron in 1937, Lake Michigan in 1936, and Lake Superior in 1946 (their
observance in Lake Michigan prior to Lake Huron suggests they were present in Lake Huron

1
 

before 1937; Smith and Tibbles 1980). Assessing the extent to which sea lamprey mortality
contributed to the collapse of lake trout in each lake is difficult due to the timing of their arrivals,
and evidence of declining lake trout stocks in each lake is apparent several years before the
establishment of significant abundances of sea lamprey. Total lake trout harvests remained at
consistently high levels despite sharp increases in fishing effort and gear efficiency after World
War II, prior to sea lamprey population explosions, implicating commercial fishing in early lake
trout declines (Krueger and Ebener 2003). However, it is known that in the Great Lakes, lake
trout serve as the principal host species (Bence et al. 2003, Harvey et al. 2008), and sea lamprey
were abundant in all the Great Lakes by the 1950s. Although the extent to which commercial
overfishing and sea lamprey predation contributed to these collapses is a source of much debate,
it is generally accepted that each played a major role in the demise of lake trout (Hansen 1999).
Responding to the collapse of Great Lakes fisheries populations and the rapid expansion
of sea lamprey populations, the U.S. and Canadian governments established the international
Great Lakes Fishery Commission (GLFC) in 1955 with the following mandates:

(1)

to develop coordinated programs of research on the Great Lakes, and, on the
basis of the findings to recommend measures which will permit the maximum
sustained productivity of stocks of fish of common concern; and,

(2)

to formulate and implement a program to eradicate or minimize sea lamprey
populations in the Great Lakes.

2
 

Initial control efforts to reduce spawning runs of sea lamprey were physical and electrical
barriers installed in streams in order to restrict access of adult sea lamprey to spawning grounds.
By 1960, 162 such barriers had been installed on tributaries to Lake Michigan and Lake Superior
(Christie and Goddard 2003); however, the number of adults returning had not declined.
Lamprey-specific toxicants discovered in the 1960s targeting the larval, stream-dwelling life
stage proved most effective and their application reduced the return of spawning sea lampreys to
8% of peak abundances in Lake Superior tributaries by 1978 and showed similar success in
Lakes Michigan and Huron (Smith and Tibbles 1980). More recently, releasing sterile males
during the spawning period was implemented as an additional control technique (Twohey et al.
2003), although the use of sterile males as a control method have recently been scaled back.

Current Status of Lake Trout Populations
The status of lake trout rehabilitation differs greatly across the lakes. My analyses focus
on 1836 Treaty-ceded waters and as such I do not address the statuses of Lakes Erie and Ontario
here. Lake Superior lake trout populations are generally considered recovered. Wild, naturally
reproducing populations of lake trout have been established lakewide (Hansen et al. 1995) such
that stocking efforts have been largely reduced. Across Michigan waters of Lake Superior,
modern lake trout abundances are at least as high as historic abundances (Wilberg et al. 2003).
The restoration program of Lake Superior now focuses on limiting fishing mortality through total
allowable catches to manage the predominantly wild fish stocks, as well as reducing the effects
of sea lamprey induced mortality. Aside from natural mortality, sea lamprey mortality is the
greatest mortality source affecting adult lake trout.

3
 

Only two small, naturally reproducing lake trout populations avoided collapse in Lake
Huron – those of Iroquois Bay and Parry Sound (Berst and Spangler 1973). Stocking efforts
were focused on offshore reefs in the mid-1980s where by the mid-1990s wild fry were observed
(Desorcie and Bowen 2003). More recently, lakewide population collapses of alewife (Alosa
pseudoharengus) in 2003-2004, as well as lake trout age-class expansion following reductions in
sea lamprey abundances, have led to increased observances of basinwide wild recruitment of
lake trout (Fitzsimons et al. 2010, He et al. 2012). Current management for lake trout in Lake
Huron has focused on stocking strains that experience less sea lamprey predation (i.e., Seneca
strain) and thus are better able to survive to reproductive age, as it appears that reproducing lake
trout produce viable wild offspring.
Despite reductions in sea lamprey abundances and massive stocking efforts, lake trout
rehabilitation efforts have been met with limited success in Lake Michigan. Natural recruitment
has not been observed, and populations are reliant almost solely on stocked fish.

Research Goals
The impetus for sea lamprey control is improving the survival of fish populations
targeted by management efforts through the reduction of sea lamprey populations (Christie and
Goddard 2003). Although current control techniques have been effective in drastically reducing
sea lamprey abundances, eradication is unfeasible (Christie et al. 2003). With this realization,
the GLFC adopted an integrated pest management policy called the Integrated Management of
Sea Lamprey (IMSL) (Davis et al. 1982). The goals defined by the IMSL are in terms of
tolerable levels of sea lamprey abundance and reducing associated damages to levels

4
 

commensurate with fish community objectives established for Lakes Huron, Michigan and
Superior (Desjardine et al. 1995, Eshenroder et al. 1995, Horns et al. 2003).
Accurate measure of the performance of sea lamprey control thus relies on an
understanding of the damages caused by sea lamprey (Jones 2007). However, direct
measurement of the numbers of fish killed by sea lampreys is difficult as victims tend to sink, are
rarely observed, and are difficult to sample (Bergstedt and Schneider 1988). Early assessments
of sea lamprey control focused only on estimates of adult lamprey abundances during spawning
runs. More recently, methods have been developed to infer sea lamprey mortality rates based
upon wounding rates observed on fish surviving sea lamprey attacks. Wound classification keys
allow wounds observed on sampled fish to be assigned to a given sea lamprey feeding season,
based on their stage of healing, with relatively high certainty (King and Edsall 1979, Ebener et
al. 2006). In conjunction with lab estimates of the survivability of hosts to sea lamprey attacks
(Swink 1990, Swink 2003, Madenjian et al. 2008), approaches to estimate sea lamprey mortality
were developed (Sitar et al. 1999, Rutter and Bence 2003). Rutter and Bence (2003) successfully
modeled sea lamprey wounding rates as a logistic function of lake trout length for wound data
from Lake Huron, and fishery managers currently use variants of their model in statistical catchat-age models to estimate lake trout population abundances and calculate acceptable harvest
levels (Caroffino and Lenart 2011).
Given the importance of wounding rates for Great Lakes fishery management, I sought to
improve these estimates and explain trends in the wounding rate versus host length relationship.
In Chapter 1, several alternative parameterizations of the logistic shaped wounding model
developed by Rutter and Bence (2003) were explored that allowed for varying degrees of spatial
and temporal variability in the parameters that govern the shape of the function. I successfully

5
 

constructed unique wounding rate models for wound data from each of Lakes Huron, Michigan
and Superior using an Akaike’s Information Criterion model selection framework.
In my second chapter, I attempt to explain the trends in sea lamprey size-selection
observed in Chapter 1. Foraging theory describes that in the scarceness of desirable prey a
predator will shift its feeding behavior to include alternative less desirable prey (Pulliam 1976),
yet the influence of host community composition on the distribution of sea lamprey attacks is
largely unknown (Jones 2007). In this context, I hypothesized that sea lamprey would shift their
feeding behavior to include smaller lake trout when large lake trout were lower in abundance. I
used two approaches to examine the relationship between sea lamprey size selectivity and large
lake trout abundance. First, I related inflection point estimates of the logistic wounding rate
models selected in chapter one to large lake trout abundance estimates. A positive correlation
would provide support for my hypothesis. Second, I modeled the position of the inflection point
as a function of the abundance of large lake trout. An increasing function over the observed
range of large lake trout abundances would also support my hypothesis. My analyses suggest
that large lake trout abundance by itself is not a strong predictor of the trends observed in the
size-selectivity of sea lamprey.
Despite the continued large investments in sea lamprey control, they remain a concern
and the effects of the parasitic life stage on host fish need to be monitored into the future. As
wounding rates are the key indicator of such effects, and the relationship between wounding
rates and lake trout size has changed over time, continued refinement of our interpretation and
assessment of wound data remains important (Krueger and Marsden 2007). Accordingly, the
work herein makes substantial advances in the methodology for summarizing sea lamprey
wounding data by applying recent advances in estimation software and computing efficiency. It

6
 

also explains how the wounding rate versus lake trout size relationship has changed over time
and serves as the baseline for addressing reasons for such changes. Although my initial
hypothesis of why this relationship has changed over time was not confirmed, understanding the
factors that influence sea lamprey host selection remains an important component of mitigating
damages associated with sea lamprey attacks. Subsequent research should explore the extent to
which length distributions and abundances of host species other than lake trout may affect sea
lamprey size-selectivity. Further research in Lakes Huron and Michigan, where strains stocked
have shown differential susceptibility to sea lamprey predation, should examine how strainspecific lake trout abundances and length distributions relate to sea lamprey size-selectivity, both
for specific strains and across all lake trout.

7
 

REFERENCES

8
 

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Commercial Fish Production in the Great Lakes 1867-2006 [online]. Available from
http://www.glfc.org/databases/commercial/commerc.php.
Bence, J.R., Bergstedt, R.A., Christie, G.C., Cochran, P.A., Ebener, M.P., Koonce, J.F., Rutter,
M.A., Swink, W.D., 2003. Sea Lamprey (Petromyzon marinus) parasite-host interactions
in the Great Lakes. J. Great Lakes Res. 29, 253-282.
Bergstedt, R.A., Schneider, C.P., 1988. Assessment of sea lamprey (Petromyzon marinus)
predation by recovery of dead lake trout (Salvelinus namaycush) from Lake Ontario,
1982-85. Can. J. Fish. Aquat. Sci. 45, 1406-1410.
Berst, A.H., Spangler, G.R., 1973. Lake Huron, the ecology of the fish community and man’s
effects on it. Great Lakes Fish. Comm., Tech. Rep. 21.
Caroffino, D.C., Lenart, S.J., 2011. Exectutive Summary in Caroffino, D.C. and Lenart, S.J., eds.
Technical Fisheries Committee Administrative Report 2010: Status of Lake Trout and
Lake Whitefish Populations in the 1836 Treaty-Ceded waters of Lakes Superior, Huron
and Michigan, with recommended yield and effort levels for 2010.
Christie, G.C., Adams, J.V., Steeves, T.B., Slade, J.W., Cuddy, D.W., Fodale, M.F., Young, R.J.,
Kuc, M., Jones, M.L., 2003. Selecting Great Lakes streams for lampricide treatment
based on larval sea lamprey surveys. J. Great Lakes Res. 29, 152-160.
Christie, G.C., Goddard, C.I., 2003. Sea lamprey international symposium (SLIS II): Advances
in the integrated management of sea lamprey in the Great Lakes. J. Great Lakes Res. 29,
1-14.
Davis, J., Manion, P., Hanson, L., Johnson, B.G.H., Lamsa, A.K., McCallum, W., Moore, H.,
Pearce, W., 1982. A strategic plan for integrated management of sea lamprey in the Great
Lakes. Great Lakes Fish. Comm., Ann Arbor, Michigan.
Desjardine, R.L., Gorenflo, T.K., Payne, R.N., Schrouder, J.D., 1995. Fish-community
objectives for Lake Huron. Great Lakes Fish. Comm. Spec. Pub. 95-1, 38p.
Desorcie, T.J., Bowen, C.A., 2003. Evidence of offshore lake trout reproduction in Lake Huron.
N. Am. J. Fish Manage. 23, 1253-1256.
Ebener, M.P., King, E.L., Edsall, T.A., 2006. Application of a dichotomous key to the
classification of sea lamprey marks on Great Lakes fish. Great Lakes Fish. Comm. Misc.
Pub. 2006-02.
Eshenroder, R.L., Holey, M.E., Gorenflo, T.K., Clark Jr., R.D., 1995. Fish-community objectives
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Fitzsimons, J.D., Brown, S., Brown, L., Honeyfield, D., He, J., Johnson, J.E., 2010. Increase in
lake trout reproduction in Lake Huron following the collapse of alewife: relief from
thiamine deficiency or larval predation? Aquat. Ecosyst. Health 13, 73-84.
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restoration. Pages 417-453 in W.W. Taylor and C.P. Ferreri, editors. Great Lakes fishery
policy and management: A binational perspective. Michigan State University Press, East
Lansing, Michigan.
Hansen, M.J., Peck, J.W., Schorfhaar, R.G., Selegeby, J.H., Schriener, D.R., Schram, S.T.,
Swanson, B.L., MacCallum, W.R., Burnham-Curtis, M.K., Curtis, G.L., Heinrich, J.W.,
Young, R.J., 1995. Lake trout (Salvelinus namaycush) populations in Lake Superior and
their restoration in 1959–1993. J. Great Lakes Res. 21, 152–175.
Harvey, C.J., Ebener, M.P., White, C.K., 2008. Spatial and ontogenetic variability of sea lamprey
diets in Lake Superior. J. Great Lakes Res. 34, 434-449.
He, J.X., Ebener, M.P., Riley, S.C., Cottrill, A., Kowalski, A., Koproski, S., Mohr, L., Johnson,
J.E., 2012. Lake trout status in the main basin of Lake Huron, 1973-2010. N. Am. J. Fish
Manage. 32, 402-412.
Horns, W.H., Bronte, C.R., Busiahn, T.R., Ebener, M.P., Eshenroder, R.L., Gorenflo, T.,
Kmiecik, N., Mattes, W., Peck, J.W., Petzold, M., Schreiner, D.R., 2003. Fishcommunity objectives for Lake Superior. Great Lakes Fish. Comm. Spec. Pub. 03-01.
78p.
Jones, M.L., 2007. Toward improved assessment of sea lamprey population dynamics in support
of cost-effective sea lamprey management. J. Great Lakes Res. 33, 35-47.
King, E. L., Edsall, T. A., 1979. Illustrated field guide for the classification of sea lamprey attack
marks on Great Lakes lake trout. Great Lakes Fish. Comm. Spec. Pub. 79-1.
Krueger, C.C., Marsden, J.E., 2007. Sea lamprey research: balancing basic and applied research,
and using themes to define priorities. J. Great Lakes Res. 33, 1-6.
Krueger, C.C., Ebener, M.P., 2004. Rehabilitation of lake trout in the Great Lakes: past lessons
and future challenges. Pages 37-56 in J.M. Gunn, R.J. Steedman, and R.A. Ryder, editors.
Boreal shield watersheds: lake trout ecosystems in a changing environment. Lewis
Publishers, Boca Raton, Florida.
Madenjian, C.P., Chipman, B.D., Marsden, J.E., 2008. New estimates of lethality of sea lamprey
(Petromyzon marinus) attacks on lake trout (Salvelinus namaycush): implications for
fisheries management. Can. J. Fish. Aquat. Sci. 65, 535-542.
Pulliam, H.R., 1974. On the theory of optimal diets. Amer. Nat. 100, 65–74.
Rutter, M.A., Bence, J.R., 2003. An improved method to estimate sea lamprey wounding rate on
hosts with application to lake trout in Lake Huron. J. Great Lakes Res. 29, 320-331.
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Sitar, S.P., Bence, J.R., Johnson, J.E., Ebener, M.P., Taylor, W.W., 1999. Lake trout mortality
and abundance in southern Lake Huron. N. Am. J. Fish. Manage. 19, 881-900.
Smith, B.R., Tibbles, J.J., 1980. Sea lamprey (Petromyzon marinus) in Lakes Huron, Michigan,
and Superior: history of invasion and control, 1936–1978. Can. J. Fish. Aquat. Sci. 27,
1780–1801.
Swink, W.D., 2003. Host selection and lethality of attacks by sea lampreys (Petromyzon
marinus) in laboratory studies. J. Great Lakes Res. 29, 307-319.
Swink, W.D., 1990. Effect of lake trout size on survival after a single sea lamprey attack. T. Am.
Fish. Soc. 119, 996-1002.
Twohey, M.B., Heinrich, J.W., Seelye, J.G., Fredricks, K.T., Bergstedt, R.A, Kaye, C.A.,
Scholefield, R.J., McDonald, R.B., Christie, G.C., 2003. The sterile-male release
technique in Great Lakes sea lamprey management. J. Great Lakes Res. 29, 410-423.
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lake trout in Michigan waters of Lake Superior: implications for restoration goals. N.
Am. J. Fish Manage. 23, 100-108.

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CHAPTER 1
ACCOUNTING FOR CHANGING PATTERNS OF SIZE-SPECIFIC WOUNDING OF LAKE
TROUT BY SEA LAMPREY IN THE UPPER GREAT LAKES

Abstract: A primary fishery concern in the Laurentian Great Lakes is mitigating the persistent
negative impact of parasitic sea lamprey (Petromyzon marinus) on native lake trout (Salvelinus
namaycush). Wounds observed on surviving lake trout are commonly used by managers to
assess damages associated with sea lamprey predation. We estimated the relationship between
wounding rates and lake trout size, and how this varied spatially and temporally. We built upon
previously published work by fitting wound rates as a logistic function of lake trout size. By
using longer time series and data from three Great Lakes, our analysis harnessed substantially
more contrast in host populations than previous work, and we also employed software advances
for nonlinear mixed-effect models. Candidate models allowed logistic function parameters to be
constant or to vary spatially, temporally, or both. Temporal effects were modeled as random
walk processes. We also considered models that assumed either Poisson or negative binomial
distributions for the number of wounds per fish at a given length. Models that allowed for both
spatial and temporal effects in the shaping parameters and assumed a negative binomial wound
distribution resulted in the best fit as indicated by Akaike’s Information Criterion. This research
provides managers with a tool to obtain more reliable estimates of sea lamprey marking.

12
 

INTRODUCTION
A primary Great Lakes fishery concern is the continued adverse effects of sea lamprey
(Petromyzon marinus) on native lake trout (Salvelinus namaycush), and how to mitigate these
effects (Stewart et al. 2003, Irwin et al. accepted). In the mid-twentieth century, each of the
upper Great Lakes experienced rapid collapses in their lake trout populations. This is evidenced
by sharp declines in annual commercial harvest of lake trout – dropping from 2.7 million to 0.18
million kilograms in Lake Huron (1935-1947), from 3.1 million to 0.16 million kilograms in
Lake Michigan (1943-1949), and from 2.1 million to 0.23 million kilograms in Lake Superior
(1950-1960) (Baldwin et al. 2009). Such sharp declines in lake trout populations are most often
attributed to commercial fishing exploitation, predation by the invasive sea lamprey, and habitat
degradation (Hansen 1999). Although the magnitude of the contribution of each of these causes
is often debated, the evidence for adverse effects of sea lamprey on lake trout is compelling
(Bence et al. 2003). For example, lake trout total mortality has been shown to be positively
related to wounding rates (Pycha 1980), and Bergstedt and Schneider (1988) showed a positive
correlation between the number of lake trout carcasses observed with fresh sea lamprey marks
and the number of fresh wounds observed on live lake trout sampled in the same year in Lake
Ontario. Since the implementation of the sea lamprey control program, sea lamprey abundances
have been greatly reduced (Smith and Tibbles 1980). During this time, observed marking rates
on sampled lake trout have decreased (Rutter and Bence 2003), lake trout abundances have
increased with the help of stocking (Hansen et al. 1995, Holey et al. 1995), and the age
composition of lake trout populations has expanded to include older individuals (Hansen et al.
1995).
Prior to their spawning runs as adults in the spring, sea lampreys parasitize teleost fish for

13
 

a single growing season (Bergstedt and Swink 1995). The majority of sea lamprey growth
occurs in the late summer and fall preceding the adult spawning migrations in the spring, and this
is the period when most potentially lethal attacks on lake trout occur. Host fish that survive such
attacks are left with easily observed marks called wounds. Wounds can be classified based upon
their stage of healing (King and Edsall 1979, King 1980, Ebener et al. 2006). During spring,
observed wounds that are in the earliest stages of healing are attributed to the most recent sea
lamprey feeding season (Eshenroder and Koonce 1984).
Owing to the difficulty in observing parasitic phase sea lamprey, wounds are essentially
the only non-laboratory source of information about sea lamprey-host interactions (i.e., sea
lamprey-induced mortality). Trends in wounding rates have been used by fishery managers to
assess the success of the sea lamprey control program (Adams et al. 2003), and to help estimate
lake trout mortality rates for use in catch-at-age models and for other purposes (Bence et al.
2003, Bence et al. 2011). One approach to analyze wound data involves reporting average
wounding rates for each of several size classes of lake trout (Eshenroder and Koonce 1984).
This method, however, does not take advantage of the predictability of the increasing incidence
of wounds with lake trout length, nor does it account for the biases associated with year-to-year
variability in the size distributions of fish sampled within each length bin. Rutter and Bence
(2003) addressed these concerns by modeling mean sea lamprey wounding rate as a continuous
function of lake trout length using a logistic function (Figure 1.1).

14
 

Figure 1. An exam of the lo
.1:
mple
ogistic mode fit to lake t
el
trout wound data from s
d
southern Lak
ke
Huron (MH3456) in 1985 ov
)
verlaid with observed dat on wound per fish. O
o
ta
ds
Observed
nds
w
ed
m
s
clarity, altho
ough the mod
del
woun per fish were average for 20mm length bins for visual c
was fit to observe values fro individua fish. From eq. 1.1, θ r
f
ed
om
al
m
represents th asymptoti
he
ic
woun
nding rate, β corresponds to lake trou length at t inflection point, and αθ/4 is the s
s
ut
the
n
slope
of the function at the inflectio point. Th increased variability i the plotted data for lar
e
t
on
he
in
d
rger
fish likely resulte from smal sample sizes for thos size class
ed
ller
s
se
ses.

With no chan
W
nges in host survival or size-selection of hosts by sea lamprey, the mean
s
n
y
wounding rate would be expected to change proportional across all sizes of lak trout in
d
d
lly
l
ke
response to changes in sea lampr and lake trout abunda
i
rey
ance. With other param
meters fixed, such
a change can be captu
ured in the asymptotic wounding rat parameter of the logis function
a
w
te
r
stic
ual
y
mprey contro program, n
ol
natural
(Bence et al. 2003). Due to annu actions by the sea lam
interannu variation in survival of sea lampr larvae in streams, an the single parasitic fee
ual
rey
n
nd
eding
season of each cohor interannua and spatia variation in the abunda
f
rt,
al
al
n
ance of parasitic-phase s
sea
lamprey is large. The asymptote parameter would be exp
e
w
pected to sho similar la
ow
arger interan
nnual

15
 

and spatial variation (Bence et al. 2003, Rutter and Bence 2003). Bence et al. (2003) argued that
selection for large lake trout over small ones was the primary reason why wounding rates
increased with lake trout size before reaching an asymptote, although they acknowledged that
differential survival did play some role. Furthermore, foraging theory predicts that when
desirable prey is scarce a predator will shift its feeding behavior to incorporate less desirable
prey types (Pulliam 1974). Following Bence et al. (2003) and Rutter and Bence (2003), we
hypothesize that parasitic sea lamprey may be responding in this way by increasing their relative
selection for smaller lake trout when more desirable large lake trout are less abundant. In terms
of the logistic relationship relating wounding rate and lake trout size, these changes in selectivity
would be reflected in the parameters governing the inflection point (the shaping parameters,
Figure 1.1). Such changes might be expected to be gradual, as they would be tracking changes in
the size distribution and abundance of the long-lived lake trout host.
Rutter and Bence (2003) fit the logistic wounding model to data from Lake Huron for
1984 to 2000. They considered a range of models that differed in how parameters varied
spatially and temporally. Based upon Akaike’s Information Criterion (AIC), they selected a
model with a different inflection point for each region of Lake Huron that was constant over
time, a slope at the inflection point that was the same for each region and also constant across all
years, and with asymptotes estimated freely for each year-region combination. They attributed
the spatial differences in the inflection point to adaptive changes in host selection. Their failure
to find gradual temporal changes was viewed as somewhat puzzling, but possibly due to a lack of
contrast in the data.
Given the importance of wounding rates for fishery management, we sought to improve
these estimates. More specifically, the purpose of this research was to expand upon the methods

16
 

of Rutter and Bence for the following reasons. First, the published application was limited to
Lake Huron wounding data. Management agencies, however, have been using variants of the
model selected by Rutter and Bence for Lake Huron to estimate sea lamprey mortality within
stock-assessment models for other lakes. To our knowledge, a thorough evaluation of alternative
models allowing for spatial and temporal variation on these other lakes has not been conducted.
We used model comparison to select – from a suite of candidate models – the model that best
described sea lamprey wounding data on lake trout separately for each of Lakes Huron,
Michigan and Superior. Second, advances in estimation software have made it possible to use
random effects models that were not available to Rutter and Bence. Thus our approach is truly a
maximum likelihood estimation approach for all models we consider. As a result, our model
comparison using AIC is more appropriate than that done by Rutter and Bence. They used a
method technically known as “highest posterior density” estimation, which has important
drawbacks in comparison to true maximum likelihood estimation. These included the inability to
freely and uniquely estimate variance parameters for process errors in the models allowing for
temporal variation in the shaping parameters, and inappropriate AIC values that may have acted
against selection of such models. These technical issues are further discussed in the Methods
section. Third, Rutter and Bence assumed a Poisson distribution for the number of wounds per
fish of a given length, but discussed some evidence of overdispersion. We explored the negative
binomial distribution in addition to the Poisson distribution to see which distribution provided
the best model fit. Lastly, many more data, with much more contrast in lake trout and sea
lamprey abundance, were available for our analysis than were analyzed by Rutter and Bence.

17
 

METHODS
Wound Data
We included wounding observations for individual lake trout within 1836 Treaty-ceded
waters, which span much of the Michigan waters of Lakes Huron, Michigan and Superior. Data
were for years 1984 to 2010 for Lakes Huron and Michigan, and 1971 to 2010 for Lake Superior,
for fish sampled during April-June primarily from agency surveys using gill nets. The sum of
marks observed on individual fish classified as AI, AII and AIII were used as the number of
wounds on each fish (King and Edsall 1979). This is also consistent with the current practice of
using spring and early summer wounding rates to estimate sea lamprey-induced mortality that
occurred in the previous year in lake trout catch-at-age models (Bence et al. 2003). We restricted
attention to treaty waters of these lakes because (a) data were readily available due to their
ongoing use in lake trout assessments, and (b) sampling focused on lake trout is done during
spring and early summer in all these lakes, allowing for a more consistent interpretation of marks
left by sea lamprey on lake trout.
Recent methods of estimating sea lamprey-induced mortality in the upper Great Lakes
have pooled data into larger spatial regions, and this practice was used in our analysis. These
pooled areas represent combinations of either lake trout management units for Lake Superior
(Hansen 1996) or statistical districts for Lakes Michigan and Huron (Smith et al. 1961). Lake
Huron data were pooled into three regions (MH1, MH2, and MH3456), Lake Michigan data into
four regions (MM123, MM4, MM5, MM678), and Lake Superior data into two regions (MI45
and MI67) (Figure 1.2). Where these areas overlap with 1836 Treaty-ceded waters (all but
MH3456), they correspond to the same areas used to summarize sea lamprey marking for treaty

18
 

water lak trout asses
ke
ssments. Th MH3456 region match the area used to sum
he
r
hes
mmarize mark
king
for an on
ngoing lake trout assessm in the so
t
ment
outhern part of Lake Hu
t
uron (e.g., Si et al. 199
itar
99).

Figure 1. Lakes Hu
.2:
uron, Michig and Sup
gan
perior with th regions us in this st
he
sed
tudy specifie
ed.
Regio names an boundarie correspond to combina
on
nd
es
d
ations of lak trout mana
ke
agement uni
its
defin for Lake Superior (H
ned
Hansen 1996) or statistica districts (S
)
al
Smith et al. 1
1961) for the
e
other lakes. For example, MM
r
e
M123 is the combined a
areas of the s
statistical dis
stricts MM1,
MM2 and MM3. The shaded region is the state of M
2,
Michigan.

Model Development
D
In general, se lamprey wounding rat increase g
n
ea
w
tes
gradually as a function o lake trout
of
length, ev
ventually ap
pproaching an asymptote Taking ad
n
e.
dvantage of t observat
this
tion, we follo
owed

19
 

Rutter and Bence (2003) and used the logistic function to describe how expected number of
wounds ( w ) increased with lake trout length (l):
w l  


1  exp  1   

(1.1)

where θ	describes the asymptotic wounding rate, β corresponds to the length of lake trout at the
inflection point, and αθ/4 is the slope at the inflection point (Figure 1.1). In all cases, models
were fit separately for each of the Great Lakes, with regional differences within lakes accounted
for by model parameters. The asymptote parameter, θ, varied over years and regions with a
fixed-effect parameter estimated freely for each year and region combination for all models. We
considered a range of models that varied in the extent to which the shaping parameters (α and β)
of the logistic function varied spatially and temporally (Table 1.1). When the shaping
parameters varied over time, the year effects were modeled as random walks. Details regarding
random walks are described in the subsection “Models for spatial and temporal effects for
shaping parameters”, but in short, a random walk allows for gradual change over time by
modeling interannual changes as process errors. When the shaping parameters varied spatially
and over years, we considered models where the process errors either had different variances in
different regions, or used a common (“lakewide") variance. The different approaches used for
the asymptote and shaping parameters reflect the different ways for which these parameters are
expected to vary, as described in the Introduction.
Lastly, we fit all candidate models (Table 1.1) assuming either the Poisson distribution,
as used by Rutter and Bence (2003), or a negative binomial distribution for the expected number
of wounds per fish of a given length. The negative binomial distribution allows the variance to

20
 

Table 1.1: Description of the α	and β parameters for the candidate set of models used in estimating sea lamprey wounding rates on
lake trout. Random walk is abbreviated as “r. w.”
Model
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y

α	
Constant across regions and years
Constant across regions and years
Constant across regions and years
Constant across regions and years
Constant across regions and years
Region-effects, constant across years
Region-effects, constant across years
Region-effects, constant across years
Region-effects, constant across years
Region-effects, constant across years
One r. w. across years for all regions
One r. w. across years for all regions
One r. w. across years for all regions
One r. w. across years for all regions
One r. w. across years for all regions
Region-specific r. w.’s across years
Region-specific r. w.’s across years
Region-specific r. w.’s across years
Region-specific r. w.’s across years
Region-specific r. w.’s across years
Region-specific r. w.’s across years (lakewide σ)
Region-specific r. w.’s across years (lakewide σ)
Region-specific r. w.’s across years (lakewide σ)
Region-specific r. w.’s across years (lakewide σ)
Region-specific r. w.’s across years (lakewide σ)

21
 

β	
Constant across regions and years
Region-effects, constant across years
One r. w. across years for all regions
Region-specific r. w.’s across years
Region-specific r. w.’s across years (lakewide σ)
Constant across regions and years
Region-effects, constant across years
One r. w. across years for all regions
Region-specific r. w.’s across years
Region-specific r. w.’s across years (lakewide σ)
Constant across regions and years
Region-effects, constant across years
One r. w. across years for all regions
Region-specific r. w.’s across years
Region-specific r. w.’s across years (lakewide σ)
Constant across regions and years
Region-effects, constant across years
One r. w. across years for all regions
Region-specific r. w.’s across years
Region-specific r. w.’s across years (lakewide σ)
Constant across regions and years
Region-effects, constant across years
One r. w. across years for all regions
Region-specific r. w.’s across years
Region-specific r. w.’s across years (lakewide σ)

increase as a function of the mean expected wounding rate by incorporating an additional scaling
2

parameter according to variance=m+m /s, where m is the mean of the distribution and s is the
parameter that scales the variance-mean relationship. Large values of s resemble a case where
the mean is equal to the variance, and in such situations the Poisson distribution will be favored
because it has one less parameter.
Models for spatial and temporal effects for shaping parameters
As indicated above, we used random walks to model interannual changes in the shaping
parameters. A random walk allows for sharing of information over time and has a tendency
toward gradual changes, without specifying an underlying mechanism. We used the Gaussian
form of a random walk:

 

 t ~ N 0,  2

 t   t 1   t ;

(1.2)

For our applications,  t represents either log e ( ) or log e (  ) , which was either the value for
the entire lake (“one random walk across years for all regions”) or for a single region (“regionspecific random walks across years”). Eq. 1.2 can be rewritten as:
i t

 t     i 1 i ;

 

 t ~ N 0,  2

(1.3)

which allows us to consider models with random walks as extensions of models without them.
Thus the models we considered for log e ( ) and log e (  ) were:
 r,t  g

(1.4)

 r,t  g r

(1.5)
i t

 r , t  g   i 1 i ;
i t

 r , t  g r   i 1 r , i ;

 

 i ~ N 0,  2





 

 i ~ N 0,  r 2 or  i ~ N 0,  2
22

 

(1.6)
(1.7)

where r and t describe region and year of estimation, respectively. In the context of the text
descriptions of Table 1.1, eq. 1.4 corresponds to “constant across regions and years,” eq. 1.5 to
“region-effects, constant across years”, eq. 1.6 to “one random walk across years for all regions”
and eq. 1.7 to “region-specific random walks across years”. When both spatial and temporal
variation were allowed (eq. 1.7), the variances for the process errors either varied uniquely
among regions, (i.e.,  r 2 ), or were the same for all regions (“lakewide σ”).
Approach to estimation
We used the random effects module of AD Model Builder (ADMB) to estimate
parameters by maximum likelihood (Fournier et al. 2012). We then used Akaike’s Information
Criterion (AIC) for model comparison to choose the best model for each lake. It is important to
discern fixed effects from random effects, as fixed effects are treated as parameters in AIC
calculations. From the frequentist perspective we used for estimation, the fixed-effect
parameters were the θs, the gs of eqs. 1.4-1.7, and the σs for any process errors influencing the
αs and βs. In contrast, the εs should be viewed as random effects and not parameters. The
general form of the log‐likelihood that is maximized is:
LogL =

 f X  ,  p d

(1.8)

where X represents the data, f() is the probability density (or mass) function for the data given
the vector of parameters (φ), and the vector of random effects (δ), and p() is the assumed
probability density (or mass) function for the vector of random effects. The form of f() depended
on whether a Poisson or negative binomial distribution was assumed. As shown in eq. 1.8,
during estimation the random effects were integrated out of the likelihood. In essence, the
overall likelihood that was maximized was a weighted sum (or more accurately, integral) of the
likelihood conditional on values for the random effects over all possible values of the random
23
 

effects, with weights being the probability density for a given vector of random effects. ADMB
integrates out random effects using the Laplace approximation. Predictions of random effects
(loosely termed estimates) were those that maximized the term inside the integral of eq. 1.8, with
parameters fixed at their maximum likelihood estimates.
For purely technical reasons, we specify the γs rather than the process error term as the
effect that is integrated out (i.e., in eq. 1.8, δ would be the vector of γs). We did this because the
conditional likelihood of data (i.e., f  X  ,   ), considered a year at a time, depends only on the
γ for that year. The full likelihood (eq. 1.8) also involves the probability density for δ. Although
we have not directly expressed a density for the vector of γs, this can be determined from the
assumed normal distribution for ε (eq. 1.2), and the fact that each ε can be expressed as a
function of just two of the γs:

 t   t   t 1

(1.9)

This approach is computationally much less expensive and numerically more robust than directly
integrating out the εs (Fournier et al. 2012).
The likelihood function (eq. 1.8) was said to be maximized when absolute values for
gradients of less than 1.0E-4 for all parameters were achieved and the variance-covariance
matrix was calculable. The model was thus said to have converged upon the best parameter
estimates. Convergence was not achieved if during the model fitting process either of these
conditions were not satisfied.
The approach used by Rutter and Bence (2003) differed from the true maximum
likelihood approach described above. They found the combination of what we call parameters
and random effects that maximized the term inside the integral of eq. 1.8. From a Bayesian
perspective, that term is proportional to the posterior density for the vector {φ,δ}, hence these
24
 

estimates are sometimes called highest posterior density estimates (HPD, Schnute 1994) – they
are also referred to as maximum penalized likelihood estimates. Rutter and Bence were not able
to uniquely estimate the process error variances with HPD, a weakness that our analysis was able
to overcome. Rutter and Bence obtained estimates for the σs, but only by carefully choosing
starting values so that the estimates did not move toward zero or infinity. A second issue is that
in comparing models that have a different number of random effects with AIC, using HPD as
though it is likelihood may not be valid, and it is unclear what the number of parameters should
be. Rutter and Bence treated each process error (i.e., the εs from our analysis) as a parameter.
This overstated model complexity because these were not freely estimated parameters, and thus
their analysis may have been biased against selecting for time-varying models. In contrast, we
treated only process error variances and starting values of each random walk as parameters, and
integrated out the εs.

RESULTS
Model Selection
Results from AIC comparison showed that all negative binomial distribution models fit
much better (typically hundreds of AIC units lower) than their respective Poisson distribution
models for all 25 models differing in fixed effects parameters (Table 1.1). All further results will
be presented from models fit using a negative binomial distribution.
AIC comparison shows that models that allowed for temporal and spatial variation in the
shaping parameters resulted in the best fit (Table 1.2). All models that did not allow for such
variation were greater than 40 AIC units worse than the best fitting model for each lake. The
choice among models that either did or did not use a lakewide variance for the shaping

25
 

Table 1.2: Akaike’s Information Criterion (AIC) comparison for wounding models using the
negative binomial distribution for wounding rate on lake trout of a given length. Δ AIC
values are relative to the best fitting model for each lake, respectively. Model Y produced
the best fit to the Lake Huron data and model X produced the best fit to both the Lake
Michigan and Lake Superior data. Models A-M for each lake had much greater Δ AIC
values and their results are not shown. Convergence was not achieved for models N, S and T
for Lake Michigan.
Model
N
O
P
Q
R
S
T
U
V
W
X
Y

Lake Huron
-127.6
-127.0
-94.6
-72.8
-44.4
-4.6
-3.2
-93.4
-71.2
-40.4
-2.4
0.0

Δ AIC
Lake Michigan
NA
-202.2
-76.9
-56.5
-47.2
NA
NA
-73.1
-52.2
-44.3
0.0
-6.1

Lake Superior
-161.0
-160.2
-187.5
-183.7
-98.0
-1.6
-3.2
-185.7
-181.7
-96.2
0.0
-1.0

parameters across regions varied between lakes. Near-zero Δ AIC values suggest that more than
one model is plausible for Lakes Huron and Superior. Convergence was not achieved for models
N, S, and T for Lake Michigan wound data. However, for both Lakes Huron and Superior,
models N, S, and T finished no better than third overall. Thus, we suspect that neither models N,
S, nor T would not have been the best model for Lake Michigan data, and that convergence was
achieved for the best fitting model for Lake Michigan. We present estimated wounding rates and
parameter estimates for only the models with the lowest AIC values for each respective lake,
except when making explicit comparison with the status quo model of Rutter and Bence (2003).
Even though several alternative models were plausible, we present only a single set of wounding
rate estimates, rather than adopting a model averaging approach, because plausible alternative
models made very similar predictions of these estimated quantities.
26
 

Patterns in Estimated Wounding Rates
Differences in sea lamprey wounding between lakes and regions were examined by
comparing estimated wounding rates from selected models for 500mm and 650mm lake trout
across all years. Both of these sizes were generally well-represented in the data, with the major
exception of MH1 prior to 1991 when lake trout rarely exceeded 650mm. Temporal trends in
wounding rates varied greatly, with differences between lakes being much greater than
differences between regions within the same lake. In addition, wounding rates on 650mm lake
trout were generally much higher than on 500mm lake trout (Figure 1.3).
Wounding rates were high and variable in Lake Huron from 1984-1998 with wounding
rates approaching 0.80 wounds per 650mm fish estimated for MH2 in 1985 and 1995.
Wounding rates in all regions of Lake Huron began to decline in the mid to late 1990s and have
reached generally low and much less variable levels.
Wounding rates on 500 and 650mm lake trout in Lake Michigan were generally low for
much of the entire time series in all regions, with the exception of northern Lake Michigan
(MM123), where sea lamprey wounding began increasing for both sizes beginning in 2001.
Wounding rates on 650mm lake trout in northern Lake Michigan have since leveled off at around
0.35 for the past eight years, and are much higher than recent wounding rates in any of the other
regions of Lake Michigan or Lake Huron. Estimates for Lake Superior have been much more
temporally variable, especially at 650mm. Yearly wounding rates were generally between 0.05
and 0.35 in MI45 and MI67 for much of the time series for 650mm lake trout, but show a slightly
increasing trend in both regions since 1994. Wounding rates on 500mm lake trout have been
very low since the mid-1990s in both MI45 and MI67.

27
 

Figure 1. Woundin rate estim
.3:
ng
mates for 500
0mm (solid c
circles) and 6
650mm (ope circles) la
en
ake
trout from each re
egion analyz in this st
zed
tudy. Estima correspo to mode Y for Lake
ates
ond
el
e
Huron and model X for Lake Michigan and Superio (Table 1.1). Region ab
l
es
or
bbreviations
s
correspond to tho described in Figure 1.2. Woundi rates wer estimated on a loge sc
ose
d
1
ing
re
d
cale
and values shown represent back-transfor
v
n
b
rmed estima with erro bars corre
ates
or
esponding to
o
estim
mates plus or minus one asymptotic standard erro
a
s
or.

28
 

Trends in Parameter Estimates
Overall, temporal variation in β generally had more influence on the shape of the logistic
function than did temporal variations in α over the observed range of estimated values for these
parameters. Changes in β are also more interpretable in the context of our hypothesis in that the
position of the inflection point is predicted to shift toward smaller lake trout lengths when
preferred large lake trout become scarce. Nonetheless, allowing for temporal variation in α led
to substantial decreases in AIC (Table 1.2). Such large improvements in AIC associated with
temporal variation in α are likely in part due to small improvements in model fit added up across
very large amounts of data: 36,018 observations for Lake Huron, 37,123 for Lake Michigan, and
148,833 for Lake Superior. For these reasons we do not provide a figure with estimates of α.
Estimates of the length of lake trout at the inflection point, β, showed great variation
between lakes, and also between regions within the same lake (Figure 1.4). Estimates of β were
greatest in regions MM4, MM5 and MM678 of Lake Michigan, with values generally greater
than 650mm until the late 1990s. In Lake Huron, distinct decreases in β of nearly 100mm
occurred in both MH2 and MH3456 over the time series. Decreasing trends were also seen in
MM123, MM4 and MM678 in Lake Michigan, with β decreasing nearly 150mm from 1992 to
2010 in MM4. Smaller decreases of about 50mm were seen in MM123 and MM678. Temporal
trends in Lake Superior were less distinct, as β remained constant near 640mm in MI45 and
gradually increased from 580mm to 640mm from 1971 to 2010 in MI67. Interestingly, although
models allowing temporal variation in β were selected, variance estimates for the random walks
for MM5 and MI45 were near-zero.
The asymptotic wounding rate parameter, θ, also varied greatly between the lakes (Figure
1.5). For Lakes Huron and Superior, trends in θ mimic those seen in estimated wounding rates

29
 

on 650mm lake trout (Figure 1.3). In Lake Michigan, wh
t
M
here β estim
mates tended to be much
higher th the other lakes for mu of the time series, th relationsh between 650mm
han
r
uch
he
hip

.4:
ut
w
o
ptotic wound
ding rate wa reached (β eq.
as
β,
Figure 1. Lake trou length at which 50% of the asymp
1.1) for models selected for each lake in this analysis β	estimate correspon to model Y for
f
e
t
s.
es
nd
Lake Huron and model X for Lakes Mich
m
r
higan and Su
uperior (Tab 1.1).
ble
30
 

Figure 1. Asympto woundin rate (θ, eq 1.1) param
.5:
otic
ng
q.
meter estimat of model selected fo
tes
ls
or
each lake in this analysis. θ	e
a
estimates correspond to model Y for Lake Huron and model X
r
l
for Lakes Michig and Supe
gan
erior (Table 1.1). Asymp
ptotic wound
ding rate par
rameters wer not
re
estim
mated for som unit-year combination for Lake M
me
ns
Michigan du to low sam size.
ue
mple

31
 

wounding rates and asymptotic wounding rates is not as tight. Due to high estimates for β in
Lake Michigan, especially earlier in the time series for MM4, asymptotic wounding rates were
unlikely to be realized. An extreme example is seen in 1993 where the asymptotic wounding
rate in MM4 spiked to 0.97 wounds per fish, while the wounding rate on 780mm lake trout
(corresponding to the ninety-fifth percentile of lake trout lengths for fish sampled in MM4 in
1993) was only 0.65 wounds per fish. Thus, in Lake Michigan, the asymptote is often
extrapolated beyond the range of the data (i.e., represents wounding rates on lake trout larger
than those actually sampled).

DISCUSSION
Generally, wounding rates are governed by two things, the first of which is the ratio of
sea lamprey abundance to host abundance. Assuming an asymptotic functional response
relating sea lamprey attack rates to host density, increases in host abundance in the asymptotic
range would produce an overall decrease in wounding rates because the same number of attacks
would be distributed among more hosts. Additionally, with host abundance held constant,
overall marking rates would be expected to scale in direct proportion to the abundance of sea
lamprey. In Lakes Michigan and Superior, general directional trends in wounding rates on lake
trout (Figure 1.3) appear to be closely linked to trends in lakewide estimates of spawning phase
sea lamprey abundance (Sullivan and Adair 2010). In Lake Huron, drastic decreases in
wounding rates in the regions examined herein coincide with a gradual decrease in spawning
phase sea lamprey abundance estimates, however, McLeod et al. (2011) found that overall
wound probability increased 12.1% in Canadian waters of Lake Huron from 2000 to 2009. This
suggests that wounding rates may be more influenced by the observed increases in lake trout

32
 

abundanc and age-c
ce
class expansi observed in Michiga waters of Lake Huron (Caroffino and
ion
d
an
n
Lenart 20
011).

Figure 1. A visual example of how a chang in the sel ectivity of se lamprey f smaller lake
.6:
ge
ea
for
trout could result in a shift of the logistic function de scribing wou
t
f
unding rates versus lake
s
e
trout length. The shift from the solid cur to the das
e
t
rve
shed curves is the type o shift
of
thesized to occur in resp
o
ponse to a de
ecrease in the abundance of larger la trout.
e
e
ake
hypot

nding rates are affected by the size-s
a
b
selectivity of sea lampre We
f
ey.
Second, woun
sized that sea lamprey se
a
elect for sma
aller lake trou when larg more des
ut
ger,
sirable, lake trout
hypothes
are scarcer. Changes in size-sele
s
ection at vary
ying prey ab
bundances ha been sho for othe
ave
own
er
erner and Ha 1974) but to our know
all
t
wledge such relationship have not b
ps
been
fish species (e.g., We
shown fo parasitic fish such as sea lamprey. A possible indicator of changes in size-selectio of
or
fi
s
e
f
on
sea lamprey could be major shift in the posi
e
ts
ition of the in
nflection point of the log
gistic functio
on
relating sea lamprey wounding ra to lake tr
s
ate
rout size (Fig
gure 1.6). If estimates o β and
f
of
33
 

abundance of large lake trout were positively correlated over the same time span, this would be
consistent with optimal foraging theory.
Our results do not seem to support our initial hypothesis. The three largest shifts in β
occurred in central and southern Lake Huron (MH2 and MH3456) and in Grand Traverse Bay
(MM4). In all three regions β decreased, suggesting the possibility of a shift in selectivity
toward smaller lake trout. However, there is much evidence suggesting the increase in
abundance of large lake trout hosts in Lake Huron. For example, in the case of MH2, estimates
of spawning stock biomass increased from near-zero levels in the early 1990’s to levels more
recently exceeding 200,000 pounds annually (2000-2008). Nevertheless, the size-selectivity of
sea lamprey shifted to include smaller lake trout even though the abundance of large lake trout
increased.
Further complicating the relationship between sea lamprey size-selectivity and large lake
trout abundance are the dynamic abundances of alternative hosts. Although evidence does
suggest that lake trout are the preferred host species of sea lamprey in the Great Lakes, as
evidenced by higher proportions of attacks on lake trout relative to their proportion in survey
catches compared other species (Harvey et al. 2008), population dynamics of alternative hosts
likely have an impact on overall wounding rates across all species, thus impacting lake trout
wounding rates.
In general, further research relating the temporal trends in the abundance of certain size
classes of lake trout to sea lamprey size selection is needed. No analyses have been published
that have documented changes in abundance of certain sizes of lake trout, per se. However,
catch-per-effort (CPE) and biological data exist for these regions in support of lake trout
assessments conducted regularly for 1836 Treaty-ceded waters. In a future manuscript we will

34
 

explore the nature of changes in size selection by sea lamprey and the connection between size
selection and abundance of lake trout of certain sizes.
A possible explanation for the observance of overdispersion in each lake, as implied by
the negative binomial models producing the best fits, is a difference in habitat use by lake trout
and sea lamprey across lake trout sampling sites. If sea lamprey habitat and lake trout habitat
differentially overlap among sampling sites then it is conceivable that lake trout sampled where
they more frequently overlap with sea lamprey may exhibit a greater number of wounds than
would be expected across all sampling sites. Another possible explanation for overdispersion
may arise from differences in wounding between strains of stocked lake trout. It has long been
observed that Seneca Lake origin strain lake trout generally have lower incidence of wounding
than both wild and Great Lakes origin strains stocked in the Great Lakes (Schneider et al. 1996),
and for this reason they have been stocked in increasing numbers in Lakes Huron and Michigan
(Ebener 1998). However, the spatial distribution of parasitic phase sea lamprey in the Great
Lakes remains unknown. Relating wounding rates to sampling sites and lake trout strain was
beyond the scope of this study, but warrants further investigation.
On another technical note, one might envision that a constant shape would correspond to
models with constant shape parameters. This is not the case with our parameterization in which
the slope at the inflection point depends upon both α and β. The asymptote varied, thus to
maintain a constant shape α would also have to vary. Attempts to implement an alternative
parameterization such that the slope itself was modeled as a parameter, rather than as a function
of α and β, were met with failures to achieve convergence for models L and more complex.
However, for the less complex models (i.e., A through M), AIC values were improved with slope
modeled as an explicit parameter.

35
 

Improved Wounding Rate Estim
d
g
mates
A main objec
ctive of this research was to improve sea lamprey wounding rate estimat
r
s
e
y
tes.
One use of these is in lake trout population assessments. Thus, it is o interest to examine th
n
p
a
of
o
he
differenc in sea lam
ces
mprey wound
ding rates be
etween woun
nding rate m
models curren used to
ntly
provide estimates for lake trout assessment with those se
e
r
a
w
elected in the analysis. C
e
Currently, fis
shery
managers use variant of the mod selected by Rutter an Bence (20
s
ts
del
nd
003), to estim sizemate

.7:
ng
mates for 500
0mm and 650
0mm fit to L
Lake Huron w
wound data.
Figure 1. Woundin rate estim
Regio abbreviat
on
tions corresp
pond to those described i Figure 1.2 Estimates correspond
e
in
2.
s
ding
to the model selected by Rutt and Benc (2003) are given by th solid line and estimate
e
ter
ce
e
he
es
corresponding to model Y (T
Table 1.1) are given by th dashed lin
e
he
ne.

36
 

specific sea lamprey wounding rates for each of the lakes. Their selection did not allow for
temporal variation in either of the shaping parameters, and only allowed spatial variation in the
position of the inflection point. This corresponds to model B (Table 1.1) of this analysis with a
Poisson distribution assumed for the number of wounds per fish of a given length, and is further
referred to as the Rutter model. To examine how the improvement in model fit affected model
predictions, wounding rate estimates were compared between the Rutter model and model Y
(Table 1.1), the model selected for Lake Huron in this analysis. We limited the examination of
differences to Lake Huron because it was wounding data from this lake to which the Rutter
model was originally fit.
Wounding rate estimates for 500mm and 650mm lake trout follow similar trends between
the Rutter model and model Y, but some key differences are apparent (Figure 1.7). Generally,
differences in estimated wounding rates between the two models on large (represented by
650mm) lake trout were minimal. However, in years 1992 to 1997, estimates for wounding rates
on 650mm lake trout were noticeably higher for the Rutter model. Although wounding rate
estimates for 500mm lake trout were generally low, they sometimes showed substantial percent
differences between the two models (MH2 and MH3456, 2006-2010).

Concluding Remarks
As the time series of wound data for each lake continue to grow, models that account for
temporal variation should become increasingly favored over models that do not. Factors that
affect the relationship between sea lamprey wounding rates and lake trout length have been
shown to change dramatically over time. Thus, allowing parameters to vary over time as random
walks permits sharing of information over time, with data from the years nearest the year of

37
 

estimation to have the most influence on estimated wounding for that year, reducing the
influence of historic trends on the estimates for a specific year. However, a drawback to this
approach is increasing difficulty in achieving model convergence with the addition of successive
years of data. We suggest further research be conducted to determine a model that incorporates
flexibility in parameter estimates over time, while simplifying the models such that convergence
is more easily achieved.

38
 

REFERENCES

39
 

References

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M.L., McDonald, R.B., Mullett, K.M., Young, R.J., 2003. Assessing assessment: can the
expected effects of the St. Marys River sea lamprey control strategy be detected? J. Great
Lakes Res. 29, 717-727.
Baldwin, N.A., Saalfeld, R.W., Dochoda, M.R., Buettner, H.J., Eshenroder, R.L., 2009.
Commercial Fish Production in the Great Lakes 1867-2006 [online]. Available from
http://www.glfc.org/databases/commercial/commerc.php.
Bence, J., Sitar, S., Ebener, M., 2011. Stock Assessment Models. Pages 5-16 in: D.C. Caroffino
and S.J. Lenart (eds), Statistical catch-at-age models used to describe the status of lean
lake trout populations, a report prepared by the 1836 Treaty Waters Modeling
Subcommittee for Technical Fisheries Committee, Parties to the 2000 Consent Decree,
and the Amici Curiae. Available at: www.michigan.gov/greatlakesconsentdecree
described as "Lake trout long report" as of December 15, 2011.
Bence, J.R., Bergstedt, R.A., Christie, G.C., Cochran, P.A., Ebener, M.P., Koonce, J.F., Rutter,
M.A., Swink, W.D., 2003. Sea Lamprey (Petromyzon marinus) parasite-host interactions
in the Great Lakes. J. Great Lakes Res. 29, 253-282.
Bergstedt, R.A., Schneider, C.P., 1988. Assessment of sea lamprey (Petromyzon marinus)
predation by recovery of dead lake trout (Salvelinus namaycush) from Lake Ontario,
1982-85. Can. J. Fish. Aquat. Sci. 45, 1406-1410.
Bergstedt, R.A., Swink, W.D., 1995. Seasonal growth and duration of the parasitic life stage of
the landlocked sea lamprey (Petromyzon marinus). Can. J. Fish. Aquat. Sci. 52, 12571264.
Caroffino, D.C., Lenart, S.J., 2011. Exectutive Summary in Caroffino, D.C. and Lenart, S.J., eds.
Technical Fisheries Committee Administrative Report 2010: Status of Lake Trout and
Lake Whitefish Populations in the 1836 Treaty-Ceded waters of Lakes Superior, Huron
and Michigan, with recommended yield and effort levels for 2010.
Caroffino, D.C., Lenart, S.J., 2010. Exectutive Summary in Caroffino, D.C. and S.J. Lenart
(eds.). Technical Fisheries Committee Administrative Report 2009: Status of Lake Trout
and Lake Whitefish Populations in the 1836 Treaty-Ceded waters of Lakes Superior,
Huron and Michigan, with recommended yield and effort levels for 2010.
Ebener, M.P., King, E.L., Edsall, T.A., 2006. Application of a dichotomous key to the
classification of sea lamprey marks on Great Lakes fish. Great Lakes Fish. Comm. Misc.
Pub. 2006-02.
Ebener, M.P., Bence, J.R., Bergstedt, R.A., Mullett., K.M., 2003. Classifying sea lamprey marks
on Great Lakes lake trout: observer agreement, evidence on healing times between
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classes, and recommendations for reporting of marking statistics. J. Great Lakes Res. 29,
283-296.
Ebener, M.P., 1998. A lake trout rehabilitation guide for Lake Huron. Great Lakes Fish. Comm.
48p.
Eshenroder, R.L., Koonce, J.F., 1984. Recommendations for standardizing the reporting of sea
lamprey marking data. Great Lakes Fish. Comm. Spec. Pub. No. 84-1.
Fournier, D.A., Skaug, H.J., Ancheta, J., Ianelli, J., Magnussen, A., Maunder, M.N., Nielsen, A.,
Sibert, J., 2012. AD Model Builder: using automatic differentiation for statistical
inference of highly parameterized complex nonlinear models. Optim. Methods Softw. 27,
233-249.
Hansen, M.J., 1999. Lake trout in the Great Lakes: basin-wide stock collapse and binational
restoration. Pages 417-453 in W.W. Taylor and C.P. Ferreri, editors. Great Lakes fishery
policy and management: A binational perspective. Michigan State University Press, East
Lansing, Michigan.
Hansen, M.J. [ED.]., 1996. A lake trout restoration plan for Lake Superior. Great Lakes Fishery.
Commission. 34 p. Available at: www.glfc.org/pubs/SpecialPubs/LakeTroutRepSup.pdf
as of December 16, 2011.
Hansen, M.J., Peck, J.W., Schorfhaar, R.G., Selegeby, J.H., Schriener, D.R., Schram, S.T.,
Swanson, B.L., MacCallum, W.R., Burnham-Curtis, M.K., Curtis, G.L., Heinrich, J.W.,
Young, R.J., 1995. Lake trout (Salvelinus namaycush) populations in Lake Superior and
their restoration in 1959–1993. J. Great Lakes Res. 21, 152–175.
Harvey, C.J., Ebener, M.P., White, C.K., 2008. Spatial and ontogenetic variability of sea lamprey
diets in Lake Superior. J. Great Lakes Res. 34, 434-449.
He, J.X., Bence, J.R., Johnson, J.E., Clapp, D.F., Ebener, M.P., 2008. Modeling variation in
mass-length relations and condition indices of lake trout and Chinook salmon in Lake
Huron: a hierarchical Bayesian approach. T. Am. Fish. Soc. 137, 801-817.
Holey, M.E., Rybicki, R.W., Eck, G.W., Brown Jr., E.H., Marsden, J.E., Lavis, D.S., Toneys,
M.L., Trudeau, T.N., Horrall, R.M., 1995. Progress toward lake trout rehabilitation in
Lake Michigan. J. Great Lakes Res. 21, 128-151.
Irwin, B. J., Liu, W., Bence, J. R., Jones, M. L., (in press). Defining economic injury levels for
sea lamprey control in the Great Lakes Basin. N. Am. J. Fish. Manage.
King, E.L., 1980. Classification of sea lamprey Petromyzon marinus attack marks on Great
Lakes lake trout. Can. J. Fish. Aquat. Sci. 37, 1989-2000.
King, E.L., Edsall, T.A., 1979. Illustrated field guide for the classification of sea lamprey attack
marks on Great Lakes lake trout. Great Lakes Fish. Comm. Spec. Pub. 79-1.

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McLeod, D.V., Cottrill, R.A., Morbey, Y.E., 2011. Sea lamprey wounding in Canadian waters of
Lake Huron from 2000 to 2009: Temporal changes differ among regions. J. Great Lakes
Res. 37, 601-608.
Pulliam, H.R., 1974. On the theory of optimal diets. Amer. Nat. 100, 65–74.
Pycha, R.L., 1980. Changes in mortality of lake trout (Salvelinus namaycush) in Michigan waters
of Lake Superior in relation to sea lamprey (Petromyzon marinus) predation, 1968-78.
Can. J. Fish. Aquat. Sci. 37, 2063-2073.
Rutter, M.A., 2004. A model of sea lamprey feeding with implications for lake trout dynamics
in Lake Huron. Ph.D. dissertation. Michigan State University, East Lansing, Michigan.
157 pages.
Rutter, M.A., Bence, J.R., 2003. An improved method to estimate sea lamprey wounding rate on
hosts with application to lake trout in Lake Huron. J. Great Lakes Res. 29, 320-331.
Schneider, C.P., Owens, R.W., Bergstedt, R.A., O’Gorman, R., 1996. Predation by sea lamprey
(Petromyzon marinus) on lake trout (Salvelinus namaycush) in southern Lake Ontario,
1982-1992. Can. J. Fish. Aquat. Sci. 53, 1921-1932.
Schnute, J.T., 1994. A general framework for developing sequential fisheries models. Can. J.
Fish. Aquat. Sci. 51, 1676-1688.
Sitar, S.P., Bence, J.R., Johnson, J.E., Ebener, M.P., Taylor, W.W., 1999. Lake trout mortality
and abundance in southern Lake Huron. N. Am. J. Fish. Manage. 19, 881-900.
Smith, B.R., Tibbles, J.J., 1980. Sea lamprey (Petromyzon marinus) in Lakes Huron, Michigan,
and Superior: history of invasion and control, 1936–1978. Can. J. Fish. Aquat. Sci. 27,
1780–1801.
Stewart, T.J., Bence, J.R., Bergstedt, R.A., Ebener, M.P., Lupi, F.L., Rutter, M.A., 2003.
Recommendations for assessing sea lamprey damages: toward optimizing the control
program in the Great Lakes. J. Great Lakes Res. 29, 783-793.
Sullivan, P., Adair, R., 2010. Integrated management of sea lampreys in the Great Lakes 2009,
Annual Report to the Great Lakes Fishery Commission. Ann Arbor, MI.
Werner, E.E., Hall, D.J., 1974. Optimal foraging and the size selection of prey by the bluegill
sunfish (Lepomis machrochirus). Ecol. 55, 1042-1052.

42
 

CHAPTER 2
SEA LAMPREY SIZE SELECTION OF LAKE TROUT IN A FORAGING THEORY
CONTEXT

Abstract: The observed number of marks per fish (wounding rate) on host fish that survive sea
lamprey (Petromyzon marinus) attacks has generally been higher on larger hosts in the Great
Lakes. A widely held belief is that this pattern largely reflects that sea lampreys are sizeselective and prefer to attack larger hosts. However, it remains unclear how a sea lamprey
discerns host size and makes subsequent choices to either attack or not attack a host. It has been
suggested, according to foraging theory, that sea lamprey may shift their feeding behavior to
include smaller, less desirable prey when larger, more desirable prey are less available. The
analyses of Chapter 1 revealed large differences in sea lamprey size-selectivity across lake trout
(Salvelinus namaycush) management units, as well as shifts in size-selectivity over time. The
purpose of this chapter is to examine how length distributions of sea lamprey wounding on lake
trout relate to annual abundance estimates of large lake trout. This was done by (1) relating the
shaping parameter estimates from Chapter 1 to large lake trout abundance estimates, and (2) by
refitting the wounding rate models from Chapter 1 to obtain new shaping parameter estimates,
where certain parameters of the logistic function relating sea lamprey predation to lake trout
length were assumed to be a function of the annual large lake trout abundance estimates. My
analyses suggest that large lake trout abundance, by itself, is not a strong predictor of spatial
differences and temporal trends of sea lamprey size-selectivity.

43
 

INTRODUCTION
Sea lamprey (Petromyzon marinus) attacks on host fish leave easily observable wounds
on surviving fish, providing fishery managers with an important source of information useful in
assessing the sea lamprey control program (Adams et al. 2003), and for estimating host mortality
rates for use in population assessment models (Bence et al. 2003). In the Great Lakes, wounding
rates on host fish that survive attacks have generally been higher on larger hosts (Berst and
Wainio 1967, Pycha and King 1975). A series of lab studies of single sea lamprey attacks on
hosts of alternative sizes have supported observations of sea lamprey size selection for larger
hosts, as summarized by Swink (2003). That sea lamprey are size-selective is now a widely held
belief, supported more recently by studies using field samples of marked lake trout from the
Great Lakes.
Schneider et al. (1996) collected dead lake trout (Salvelinus namaycush) using bottom
trawls in Lake Ontario and found that the vast majority of lake trout recovered bore sea lamprey
wounds, and that 81% of AI marks (those in the most recent stage of healing and indicative of
sea lamprey-induced mortality; King and Edsall 1979) observed on dead lake trout were on fish
>600mm total length. In concurrent gillnet samples they found that length distributions of live,
sea lamprey-marked lake trout did not differ significantly from length distributions of collected
dead lake trout. Their results indicate plainly that sea lamprey preferentially attack larger lake
trout hosts, and that previous observations of higher wounding rates on larger fish that survived
attacks were not just the result of differential survivability between lake trout of different sizes.
Sitar (1996) used wounds observed on lake trout from spring gillnet surveys from 19841994 to estimate annual wounding rates for four large size bins for the Michigan waters of Lake
Huron. He used the sum of AI, AII and AIII wounds as these are assumed to have come from

44
 

potentially lethal attacks from the previous fall lamprey feeding season. He found that in central
and southern Lake Huron, wounding rates increased significantly with length class of lake trout.
This works was expanded upon by Rutter and Bence (2003) who modeled mean Lake Huron sea
lamprey wounding rates as a continuous, logistic-shaped function of lake trout length (see Figure
1.1), taking advantage of the predictable way in which sea lamprey marking rates tend to
increase with host size. Based upon the model chosen in their model selection analysis, they
observed large interannual variability in the wounding rates observed on large lake trout between
northern, central and southern Lake Huron. They also found an increase in the length at which
50% of the asymptotic wounding rate (the wounding rate on large lake trout) was reached
moving from northern to southern Lake Huron (529mm in northern, 576mm in central, 596mm
in southern). They hypothesized that in northern Lake Huron, where large lake trout were at low
abundance during their years of analysis, sea lampreys may have been directing more attacks
towards smaller fish as a behavioral response. Such a hypothesis is consistent with foraging
theory (Pulliam 1976) which describes that a predator will shift its feeding behavior to include
smaller prey when larger prey become scarce.
In Chapter 1, the methods of Rutter and Bence (2003) were expanded upon to create
unique wounding rates models for Lakes Huron, Michigan and Superior, respectively. Models
that allowed for spatial and temporal variability in the shaping parameters – those governing the
position and slope of the inflection point of the logistic wounding rate function – were selected
as the best models for each lake based on model comparison. The position of the inflection point
showed great variation between lakes, and also between regions within the same lake. This
parameter is related to the size-selectivity of sea lamprey as it determines the size range over
which sea lamprey predation on lake trout occurs. If estimates of this parameter were positively

45
 

correlated with estimates of large lake trout abundances over time this would support the
hypothesis that sea lamprey shift their feeding behavior according to foraging theory (Rutter and
Bence 2003, Bence et al. 2003).
Although in Chapter 1 I discussed the density of large lake trout as one potential
explanation for spatial and temporal variation in sea lamprey size-selectivity, no analyses were
done that explicitly documented changes size-specific abundance or density of lake trout in the
region and time-period wounding patterns were examined. Here, I use long time series of lake
trout abundance estimates to examine the extent to which the annual abundances of large,
desirable lake trout have changed, and how such changes may be related to the observed spatial
and temporal differences in sea lamprey size-selectivity of lake trout. First, I compare trends in
large lake trout abundance over time with the time-varying β parameter estimates from Chapter 1
to look for patterns consistent with foraging theory. Second, I develop wounding rate models for
each region that allow β to vary as a function of large lake trout abundance and examine if this
parameterization supports a foraging theory-type explanation of the observed temporal changes
sea lamprey size-selectivity.

METHODS
Large Lake Trout Abundance Data
Lake trout assessments are regularly conducted for 1836 Treaty-ceded waters (Caroffino
and Lenart 2011). The assessments produce yearly age-specific estimates of lake trout
abundance. I used the most recent abundance estimates from stock assessment model runs for
each of the following regions: MH1 and MH2 in Lake Huron, MM123, MM4, and MM5 in Lake
Michigan, and MI5, MI6, and MI7 in Lake Superior (Figure 2.1). These provided estimates of

46
 

abundanc for 1984-2010 for Lak Michigan For Lake Superior, es
ce
ke
n.
stimates start in 1975 (
ted
(MI5
and MI7) or 1978 (M and end in 2008 (MI7) or 201 (MI5 and MI6). In La Huron,
)
MI6)
ded
(
10
ake
assessme estimates started in different year depending on area, bu were avail
ent
s
d
rs
g
ut
lable for both
h
areas star
rting in 1984 and ending in 2008 (M
4
g
MH2) or 2010 (MH1). Th
0
hese were us in
sed
conjuncti with esti
ion
imates of me lake trou length-at-a to derive annual abu
ean
ut
age
e
undances of l
large
lake trout.

.1:
uron, Michig and Sup
gan
perior with th regions us in this st
he
sed
tudy specifie
ed.
Figure 2. Lakes Hu
Regio names an boundarie correspond to lake trou managem units def
on
nd
es
d
ut
ment
fined for Lak
ke
Super (Hansen 1996) or st
rior
n
tatistical dist
tricts (Smith et al. 1961) for the othe lakes. MM
h
)
er
M123
is the combined areas of the statistical dis
e
a
s
stricts MM1 , MM2, and MM3. The shaded regi is
d
e
ion
the st of Michi
tate
igan.
47
 

The methods used to obtain abundance estimates for large lake trout differed between the
three lake basins based upon availability of size-at-age data. For Lakes Huron and Superior,
mean length-at-age matrices from lake trout stock assessments (i.e., Caroffino and Lenart 2011)
were used to determine which age classes for a given year constituted large hosts. For the Lake
Huron estimates, length-at-age data from regions MH1 and MH2 for years 1975 to 2010 were fit
to a von Bertalanffy growth model that accounted for time-varying growth according to He and
Bence (2007), producing a matrix of mean length-at-age estimates for years 1976 to 2010.
Growth model convergence was not achieved when the individual regions of Lake Huron were
treated separately, so the data from regions MH1 and MH2 were combined resulting in a single
matrix of mean lengths-at-age over time representative of the Michigan waters of Lake Huron.
For the Lake Superior length-at-age estimates, the traditional von Bertalanffy growth model was
fit to time blocks of data for each region corresponding to observed growth stanzas among years
to decrease the chance of large annual variability in mean length-at-age estimates (S. Sitar,
personal communication). We defined “large” for our analysis of Lakes Huron and Superior as
fish within a cut-off age-class or older age-classes. The cut-off age was the age-class whose
mean length-at-age was closest to 600mm. The length of 600mm was chosen based upon Swink
(1991) who observed that sea lamprey avoid lake trout <600mm when larger fish are available.
This length has also been previously used as the division comparing wounding rates between
small and large hosts (e.g., Sitar et al. 2008). We chose to use a cut-off age to avoid situations
where a poorly sampled older age might not be included in the large category because of chance
variations. With such cut-off ages defined for each year for Lakes Huron and Superior, annual
estimates of large lake trout abundance were calculated as the sum of age-specific abundance
estimates starting at the cut-off age.

48
 

For Lake Michigan, von Bertalanffy estimates of mean length-at-age data were not
readily available. Mean values of length for survey estimates of lake trout ages 4-7 from
MM123 and MM5 (J. Jonas, unpublished data) show no obvious trends in lake trout growth
among ages closest to 600mm. Age 5 lake trout were closest to 600mm across the time period
examined, thus we assumed that age 5 and older lake trout were large for all years in MM123
and MM5. The findings of Madenjian and Desorcie (2010), who analyzed lake trout growth in
the Northern Refuge of Lake Michigan between years 1991-1999 and 2000-2008, confirm that
this is a reasonable assumption for MM123 (within which the refuge lies) and MM5 (which
borders a portion of the refuge). They conducted a two-way analysis of variance, and found that
time period had no significant effect on lake trout total length or weight. The interaction
between lake trout age and time period also was not significant for total length or weight.
Declines in mean length values for survey estimates of lake trout from MM4 (J. Jonas,
unpublished data), however, suggest decreases in lake trout length-at-age in this region. Annual
mean lengths were closest to 600mm for age-5 lake trout for much of the time series, but
declined such that in years 1998 to 2010 age 6 was closest to 600mm. Accordingly, for MM4 we
assumed age 5 and older fish were large for years 1984-1997, after which age 6 became the
cutoff age.

Approaches to Examining Selectivity
We took two approaches to examining the relationship between large lake trout
abundance estimates and sea lamprey size-selectivity. Both approaches rely on understanding
the general relationship between sea lamprey wounding rates and host size. The logistic function
is a three parameter model first used to describe the general relationship between sea lamprey

49
 

wounding rates versus lake trout length by Rutter and Bence (2003). This model allows
wounding rates to increase gradually with host length and eventually approaches an asymptote.
The parameterization used by Rutter and Bence (2003), as well as Chapter 1 herein, is given by
equation 1.1, rewritten below:
w l  


1  exp  1   

where w is the average wounding rate of a fish of given length, l. Parameterized this way, θ
describes the wounding rate experienced by very large fish (the asymptotic wounding rate), αθ/4
is the slope at the inflection point, and β is the lake trout length at 50% of the asymptotic
wounding rate (Figure 1.1).
With the first approach, we used estimates of β from Chapter 1 in which β was allowed to
follow a random walk process over time to account for potential temporal changes in sea
lamprey size selection of lake trout. These estimates, hereafter referred to as “time-varying βs,”
were plotted against large lake trout abundance estimates to observe any general patterns in the
relationship that might suggest evidence of size-selectivity. It should be noted that in Chapter 1,
unique vectors of time-varying βs were generated for each respective region analyzed with the
exception of Lake Superior. Due to the pooling of wound data in wounding rate models, in
chapter 1 time-varying β vectors were estimated for the combined regions of MI4 and MI5
(called MI45), and MI6 and MI7 (called MI67), rather than for the individual management units.
Thus, time-varying βs derived for the larger region MI45 were plotted against large lake trout
abundance estimates for MI5, and time-varying βs derived for the larger region MI67 were
plotted against large lake trout abundance estimates for MI6 and MI7, respectively.

50
 

In the second approach, wounding rate models were refit separately for each management
unit following the general approach used in Chapter 1 (see the section titled Model

Development). However, β was allowed to vary as a three-parameter quadratic function:
∗
where the

∗

(2.1)

s are the year-specific large lake trout abundance estimates. In these respective

models the asymptote parameter, θ, varied freely over time with a fixed-effect parameter
estimated for each year, and only a single α was estimated for each model, which was held
constant over time. A negative binomial distribution was assumed for the number of wounds per
fish of a given length according to methods used in Chapter 1 (see Model Development). The
scaling parameter, s, was fixed at estimated values obtained in Chapter 1 to aid in model
convergence. The β estimates from this approach are henceforth referred to as “abundancevarying βs.”

RESULTS
Dynamics in Large Lake Trout Abundance
Large lake trout abundances varied greatly across the years examined for each
management unit. Patterns in large lake trout abundance appeared uncorrelated between lakes,
but appeared related within regions of the same lakes. General temporal trends in abundance
were very similar between the regions analyzed in Lake Huron (Figure 2.2). Age classes
representative of large lake trout were almost nonexistent in MH1 until the early 1990s, and were
at similarly low levels in MH2. Beginning in the early 1990s, large lake trout abundance
increased sharply in both regions, peaking in 2008 and 2004 in MH1 and MH2, respectively.
From years 1984-1989 to 2003-2008, average annual abundances of large lake trout increased

51
 

Figure 2. Estimate of large (>
.2:
es
>600mm) lak trout (LA abundanc and timeke
AT)
ce
-varying β
estim
mates for regi
ions MH1 (1
1984-2010) and MH2 (1984-2008) in Lake Huro
a
n
on.

52
 

Figure 2. Estimate of large (>
.3:
es
>600mm) lak trout (LA abundanc and timeke
AT)
ce
-varying β
estim
mates for regi
ions Lake Michigan regi
M
ions MM123 MM4, and MM5 for y
3,
d
years 1984-2
2010.
The left y-axis co
l
orresponds to abundance and time-v
o
es
varying βs fo MM123, a the right yor
and
t
axis corresponds to estimates for MM4 and MM5.
c
s

53
 

.4:
es
>600mm) lak trout (LA abundanc and timeke
AT)
ce
-varying β
Figure 2. Estimate of large (>
estim
mates for Lak Superior. For large LA abundan
ke
AT
nces, the left y-axis corre
t
esponds to M
MI5
and th right y-ax correspon to MI6 and MI7. Fo time-varyi β estima
he
xis
nds
a
or
ing
ates, the left y
yaxis corresponds to the comb
c
bined region MI4/MI5 an the right y
nd
y-axis corres
sponds to the
e
comb
bined region MI6/MI7.
54
 

33-fold and 4.9-fold in MH1 and MH2, respectively. This is consistent with age-class
expansions shown by He et al. (2012) who found that prior to 1997, age-5 and younger fish
comprised at least 75% of annual spring gill-net survey catches in the main basin of Lake Huron,
but by 2005 the proportion of age-5 and younger fish was only 13%.
In Lake Michigan, abundance estimates of large lake trout (Figure 2.3) showed roughly
similar patterns among MM123, MM4, and MM5, especially after 1989. Among all regions,
abundances decreased from 1990 to 1994, increased to peak (MM123 and MM4) or near-peak
(MM5) abundances by the mid-1990s, decreased to time series-low abundances by the early
2000s, and have since generally increased through 2010. The most remarkable change in large
lake trout abundance occurred in MM123 within which large lake trout abundance decreased
from a peak of 298,000 in 1996 to 60,000 by 2002.
Trends in large lake trout abundances in Lake Superior (Figure 2.4) were similar between
MI5 and MI6, but much different in MI7. Abundances generally increased in MI5 and MI6
beginning in 1978 to peak abundances in each region in 1996 and subsequently decreased 19962010. Abundances in MI7 peaked in 1982, sharply decreased 1982-1991, and have generally
increased through 2008.
Coefficients of variation (CV) for total lake trout abundance estimates (i.e., the
asymptotic standard error of the estimate divided by the estimate) from 2010 population
assessment models (Figures 2.2-2.4) ranged from 1.5% to 6.1% for Lake Huron, 1.3% to 6.5%
for Lake Michigan, and 7.4% to 24.8% for Lake Superior. These were reported with the
statistical catch-at-age assessments used to assess lake trout abundance. Given the complexity of
how “large lake trout” was defined it was not possible to quantitatively estimate uncertainty in
these estimates. However, given the CVs of annual total large lake trout abundance, and that

55
 

typically hundreds of fish were measured and aged forming the basis for what proportion we
deemed large, I believe the apparent trends seen in large lake trout abundances are largely real
and not primarily estimation error. Furthermore, treating these estimates as known in subsequent
analyses was reasonable because the uncertainty in the estimates was much less than the actual
variability in large lake trout abundance.

Time-varying βs
The time-varying βs, as estimated in Chapter 1, were plotted against large lake trout
abundances for each region analyzed (Figures 2.2-2.4). The largest shift was seen in MM4,
where β remained relatively stable from 1984 to 1992, then decreased nearly 190mm from 1993
to 2010. Other large shifts were seen in MM123 (decreased 100mm, 1991-2008), MH2
(decreased 70mm, 1992-2010), and MI67 (increased 50mm, 1975-2010). Intermediate
variability was seen in MH1, where β decreased slightly from 1984 to 1997 and then increased
roughly 30mm by 2010. β estimates remained essentially constant across the time series for
MI45 and MM5.
Because β determines the position of the logistic wounding curve with respect to lake
trout total length, I expected the value of this parameter to increase or decrease with large lake
trout levels. In general, however, temporal trends observed in time-varying β estimates did not
track those of large lake trout abundances. Comparing the trends of large lake trout abundances
and time-varying βs in figures 2-4, there is little evidence that the size-selectivity of sea lamprey
varies with large lake trout abundances.
My hypothesis appears inconsistent with these observations in two ways. First, in
adjacent regions with similar patterns in large lake trout abundances, sea lamprey size-selectivity

56
 

behaved differently. This is seen in Lake Huron where large lake trout abundances showed
generally similar trends across the entire time series among MH1 and MH2, while the timevarying βs in each region exhibited dissimilar temporal patterns. Likewise, in Lake Superior,
time-varying βs increased in the combined MI6/MI7 region across the entire time series, while
they remained constant in the combined MI4/MI5 region; this is in contrast with the similarly
trending large lake trout abundances among adjacent units MI5 and MI6. However, an exception
was seen in Lake Michigan with MM123 and MM4 where similar temporal trends were observed
in both time-varying βs and large lake trout abundance.
The second inconsistency with my foraging theory-type hypothesis is that in no region is
the expected positive correlation between time-varying βs and large lake trout sustained across
the entire series. Although there were some years during which changes in abundance were
positively correlated with shifts in β, these instances appear coincidental, in no region is such a
correlation sustained across the entire time series. In MH1, time-varying βs show no strong
evidence of a positive correlation with large lake trout abundances. Contrary to my hypothesis,
in MH2 where large lake trout abundances increased for most of the duration of the time series,
time-varying β estimates decreased more than 60mm, suggesting that sea lamprey actually
selected for smaller lake trout when larger, more desirable prey were becoming increasingly
prevalent. In Lake Michigan, time-varying βs in MM5 were constant despite large fluctuations
in large lake trout abundances, and although decreasing βs in both MM123 and MM4 were
coincident with large declines in large lake trout abundances in the late 1990s and early 2000s,
the correlation was not sustained throughout the rest of the time series. In Lake Superior,
constant time-varying β estimates in MI4/MI5 and increasing estimates in MI6/MI7 do not

57
 

reflect the dynamically fluctuating large lake trout abundances seen in seen in MI5, MI6 and MI7
in a manner consistent with foraging theory.

Abundance-varying βs
Models that allowed β to vary as a quadratic function (eq. 2.1) of large lake trout
abundance were successfully fit for each of the management units examined. The resulting
abundance-varying β estimates are shown in Figure 2.5. In general, there does not appear to be a
consistent relationship among regions relating the size-selectivity of sea lamprey to large lake
trout abundance.
In Lake Huron, where adjacent units MH1 and MH2 had similarly trending patterns in
large lake trout abundance (Figure 2.2), sea lamprey in MH1 selected larger hosts when large
lake trout were more abundant, but in MH2 selected smaller hosts as large lake trout became
more abundant. Results were similar among MM123 and MM4, with sea lamprey selecting for
larger hosts at higher large lake trout abundances in MM123, while selecting for the largest hosts
at intermediate abundances in MM4. Much the same as with the time-varying βs, sea lamprey
size selectivity in MM5 changed little across the time series, despite dynamic large lake trout
abundances. Sea lamprey size selection in regions MI5 and MI6 in Lake Superior appears
consistent with foraging theory – increasing with respect to large lake trout abundance.
However, in MI7, abundance-varying βs were negatively correlated with large lake trout
abundance.

58
 

Figure 2. β estimates versus ab
.5:
bundance of large lake tro for each managemen unit. Region
l
out
nt
abbre
eviations cor
rrespond to those describ in Figure 1.2. Woun
t
bed
e
nding rates w fit to th
were
he
logist wounding rate model (eq. 1.1), with β varyin as a quadr
tic
g
l
w
ng
ratic function of large lak
n
ke
trout abundance (eq. 2.1). Er bars repr
(
rror
resent one st
tandard erro
or.

SSION
DISCUS
Temporal cha
T
anges in larg lake trout abundances appear largely unrelated to the chan
ge
d
nges

59
 

in the size ranges of lake trout attacked by sea lamprey. Thus, the hypothesis proposed that sea
lamprey will select for smaller, less optimal prey when large, more preferable prey are less
abundant is not supported. The results are not likely due to the time series being too short in
duration, as the shortest time series was 25 years (1984-2008, MH2). Additionally, these results
are not an artifact of a narrow range of large lake trout abundances, as each region had a
substantial contrast between maximum and minimum abundances.
A major assumption made for this analysis was that the size-selectivity of sea lamprey for
lake trout would be independent of the length distributions and abundances of other host species.
In this analysis, I expected spatial and temporal trends in large lake trout abundances alone to
drive sea lamprey size selection. The failure find such a relationship indicates that sea lamprey
may not conform to the expectations of foraging theory, but it could also be the case that the sea
lamprey’s desired prey type was not accurately defined.
Several studies have shown sea lamprey select for lake trout (Christie and Kolenosky
1980, Johnson and Anderson 1980, Morse et al. 2003, Harvey et al. 2008), but sea lamprey
damages to other host species are often substantial. In Lake Huron, lake whitefish (Coregonus

clupeaformis) are a major host species for parasitic sea lamprey. Mortality of lake whitefish is
great enough that population assessments for 1836 Treaty-ceded waters of Lake Huron account
for sea lamprey mortality when forecasting lake whitefish annual abundances (Caroffino and
Lenart 2011). Similar to patterns observed on lake trout, sea lamprey wounding is generally
greater on large lake whitefish (Ebener et al. 2010). Total biomass of lake whitefish in Lake
Huron has followed generally similar trends among management units corresponding roughly to
regions MH1 and MH2, and it is likely that length distributions of lake whitefish among these
regions also followed similar trends. Consequently, lake whitefish dynamics do not explain the

60
 

differences seen between MH1 and MH2 in the size-selectivity of sea lamprey for lake trout
(Figure 2.2).
Unlike Lakes Huron and Michigan, a deepwater form of lake trout called siscowet lake
trout inhabit Lake Superior. Siscowets are generally found in water greater than 80m (Bronte et
al. 2003), deeper than water typically included in spring gillnet surveys for lake trout population
assessments, and data on siscowets are not included in the wound data used in population models
as fisheries tend to target lean lake trout (the morphotype also present in Lakes Huron and
Michigan). Much less information exists on the population dynamics and ecology of siscowet
than lean lake trout, although siscowets are now known to be the most abundant pelagic predator
in Lake Superior (Bronte et al. 2003).
Sitar et al. (2008) compared differences in sea lamprey wounding rates between small
(<600mm) and large (≥600mm) siscowets among three depth zones at sites within regions MI5
and MI6. They found that, similar to lean lake trout, wounding rates were significantly higher on
large siscowets than on small siscowets. For large siscowets, they reported type A wounding
rates of 0.831 in the shallow (<200m) zone, 1.385 in the deep (200-394m) zone, and 1.000 in the
deepest (395-399m) zone. Comparing these to the 2006 asymptotic wounding rates (average
wounding rates for large lake trout) for regions MI45 (θ = 0.296) and MI67 (θ = 0.267) as
calculated for lean lake trout in Chapter 1 (Figure 1.5), siscowet wounding rates were much
15

13

higher. Additionally, results of stable isotope (δ N and δ C) analyses by Harvey et al. (2008)
imply that sea lamprey actively select both the lean and siscowet forms of lake trout over other
more abundant species in Lake Superior.
Given that sea lamprey prey heavily upon siscowets, and that siscowets are more much
more abundant than lean lake trout in Lake Superior, if sea lamprey size-selection of hosts is
61
 

consistent with foraging theory it is likely to be influenced strongly by the population dynamics
and length distributions of siscowets. Abundance of siscowets has risen steadily as indicated by
-1

increases in U.S. and Canadian commercial gillnet catch and effort data – from >20kg·km in
-1

the early 1950s to near 250 kg·km by the late 1990s (Bronte et al. 2003). Mata (2009) reported
that siscowet abundance increases in the Michigan waters of Lake Superior likely leveled off
between 2000 and 2006. Interestingly, time-varying β estimates for MI67 increased across the
time series and appeared to level off in a pattern similar to that of siscowet lake trout abundances
(Figure 2.4). This does not necessarily support my proposed hypothesis, but it may at least be
consistent with foraging theory if siscowet hosts influence sea lamprey selectivity more than lean
lake trout, although it does not explain the constant size-selectivity seen in MI45 (Figure 2.4).
Evidence also strongly suggests that sea lamprey attack rates differ even among strains of
lake trout stocked in the Great Lakes. The Seneca strain of lake trout has been stocked in
varying amounts since 1985 in Lake Huron and 1995 in Lake Michigan. In Seneca Lake, New
York, from where this strain is derived, lake trout utilize deeper habitats than other strains
stocked in the Great Lakes, so the original motivation behind stocking this strain was in hopes
that these traits would increase the population diversity and promote lake trout rehabilitation
(Ebener 1998). Several studies have since shown that this strain of lake trout is less susceptible
to sea lamprey predation than other strains, and as a result Seneca strain lake trout are now the
predominant strain stocked in Lake Huron and a large component of lake trout stocked in Lake
Michigan (Figure 2.6).
The difference in sea lamprey attack rates between lake trout strains was first published
by Schneider et al. (1996) who conducted bottom trawls of Lake Ontario to recover dead lake
trout that had sank. They found that less than 1% of dead Seneca strain lake trout recovered
62
 

Proportion Seneca

1.0
0.8

Michigan
Huron

0.6
0.4
0.2
0.0
1985

1990

1995

2000

2005

2010

Year
Figure 2.6: The proportion stocked lake trout that are Seneca strain from years 1985-2010. Prior
to 1985, Seneca strain lake trout were not stocked in Lakes Huron and Michigan. Data
correspond to combined totals of lake trout stocked in regions MH1 and MH2 for Lake
Huron, and MM123, MM4, and MM5 for Lake Michigan. Data from the Great Lakes
Fishing Stocking Database (http://www.glfc.org/fishstocking/).

could be attributed to sea lamprey, compared to 60% and 5% for Superior and Clearwater Lake
strains, respectively. Lower wounding rates of Seneca strain lake trout have since been reported
in Lake Huron (Eshenroder et al. 1995) and Lake Michigan (Bronte et al. 2007). However,
McKee et al. (2004) found that Marquette strain lake trout survived better than Seneca strain in
observations at Sheboygan Reef in Lake Michigan, but the higher survival occurred prior to age
3 before sea lamprey predation was a factor.
That Seneca strain lake trout are less vulnerable to sea lamprey predation presents a
dilemma when relating size-selectivity of sea lamprey to abundances and length distributions of
potential prey. Seneca strain lake trout are included in the spring gillnet lake trout surveys from
which my wound data were obtained, and for my analyses, lake trout strain was not considered.
63
 

Specifically, if Seneca strain lake trout comprise a substantial portion of what I classified as
“large” lake trout, my analysis may be inaccurately qualifying what a sea lamprey perceives as
an available and desirable prey type.
Interestingly, the mechanism by which Seneca strain lake trout avoid sea lamprey attack
more than other strains has not been established. Schneider et al. (1996) suggest two potential
aspects of Seneca strain behavior that may contribute to different attack rates: (1) differential
bathythermal distributions between strains, and (2) avoidance. They found that in gillnet surveys
concurrent with their bottom trawls, Seneca strain lake trout were caught in deeper, colder water
than both the Superior and Clearwater Lake strains. They reasoned that lower wounding rates on
Seneca strain lake trout are potentially attributable to less habitat overlap with sea lamprey than
other strains.
Bergstedt et al. (2003) used archival temperature tags to examine the extent to which
differences in lake trout thermal habitat use could be attributed to lake trout strain in Lake
Huron. Seneca strain lake trout generally occupied colder temperatures than other strains, with
Seneca strain occupying significantly cooler temperatures from mid June to mid August during
thermal stratification of the lake. A subsequent study in which Lake Huron lake trout were
implanted with archival tags that recorded temperatures as well as depths was able to discern that
the once again observed differences in thermal habitat use between Seneca and other strains of
lake trout was attributable to deeper habitat use, and not simply differences in geographic
distribution (Bergstedt et al. 2012). These two studies confirm that Seneca strain lake trout
occupy colder, deeper water.
Evidence is lacking, however, that Seneca strain lake trout occupying deeper and colder
habitat as the reason for lower wounding rates. Siscowet lake trout in Lake Superior occupy

64
 

much colder, deeper water than lean lake trout. Sitar et al. (2008) rarely found lean lake trout at
depths >50m, however, siscowets were caught only in waters >40m, including depths nearing
400m. Siscowets were no less subjected to sea lamprey predation, suggesting that sea lamprey
do occupy cold, deep habitats. Additionally, it is suspected that sea lamprey are endemic to the
Seneca Lake, thus lake trout of this strain may have evolved an ability to avoid predation
(Christie 1973, Ebener 1998).
Large lake trout abundance estimates for this analysis were derived from lake trout
population assessments that rely on the sea lamprey wounding rate models currently used by
fisheries biologists. As described in Chapter 1, such models do not allow for temporal variation
in the shaping parameters of the logistic wounding rate function, and there is evidence of
discrepancies in wounding rate estimates between these models and those selected for in Chapter
1 (Figure 1.7). Lake trout abundance estimates, however, were similar between lake trout
population assessment model runs that incorporated sea lamprey mortalities estimated using
either the currently used sea lamprey wounding rate models or those selected for in Chapter 1.
For this reason I feel confident that the time-varying βs analysis is valid.
This work provides a baseline for understanding spatial differences and temporal trends
seen in sea lamprey size selectivity. Although my analyses suggest that foraging theory does not
explain the spatial differences and temporal changes observed in sea lamprey size-selectivity,
large lake trout abundance alone, as defined in this analysis, may not accurately describe sea
lamprey’s preferred prey type. Further research is needed to understand the influence of
alternative hosts. In Lake Superior, siscowet lake trout are clearly important, as are lake
whitefish in Lake Huron, although there is strong evidence of other important hosts particularly
in Lake Huron where substantial marking has been seen on a diversity of species (I. Tsehaye and

65
 

J. Bence, unpublished analyses). Other large salmonine hosts have also been important at certain
times and locations (Bence et al. 2003, Morse et al. 2003). Additionally, a better understanding
of the differences in sea lamprey selection between Seneca strain lake trout and other strains
stocked in Lakes Huron and Michigan is needed. Archival tag studies of parasitic phase sea
lamprey, such as those conducted for Lake Huron lake trout, would help determine the extent to
which sea lamprey and Seneca strain lake trout habitat use overlaps. Furthermore, independent
analysis of abundance of and sea lamprey wounding on Seneca and non-Seneca lake trout could
help elucidate sea lamprey size selection dynamics. Such work is a challenge given that current
lake trout assessment models and wound data do not distinguish lake trout strains, but moving in
this direction could potentially improve assessments above and beyond providing better
understanding of sea lamprey size-selection.

66
 

REFERENCES

67
 

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