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This is to certify that the
dissertation entitled

Recruitment dynamics in Great Lakes sea lamprey
(Petromyzon man'nus) populations and implications for
integrated pest management

presented by

Heather A. Dawson

has been accepted towards fulﬁllment
of the requirements for the

Doctoral degree in Fisheries and Wildlife

 

 

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RECRUITMENT DYNAMICS OF GREAT LAKES SEA LAMPREY (PE TROM YZON
MARIN US) POPULATIONS AND IMPLICATIONS FOR INTEGRATED PEST
MANAGEMENT

BY

HEATHER A. DAWSON

A DISSERTATION

Submitted to
Michigan State University
in partial fulﬁllment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Fisheries and Wildlife

2007

ABSTRACT
RECRUITMENT DYNAMICS OF GREAT LAKES SEA LAMPREY (PE TROMYZON
MARIN US) POPULATIONS AND IMPLICATIONS FOR INTEGRATED PEST
MANAGEMENT
BY
Heather A. Dawson

To determine whether the rate of sea lamprey (Petromyzon marinus) control in the
Great Lakes is sufﬁcient to achieve lasting beneﬁts, we must understand sea lamprey
recruitment and growth dynamics as the population is driven to low levels. The Great
Lakes Fishery Commission (GLFC) wishes to reduce reliance on lampricides, and use
alternative (adult) sea lamprey control methods that seek to reduce the number of
spawners in order to decrease subsequent recruitment. However, management actions that
aim to reduce reproductive success might not result in concomitant reductions in
recruitment, for two reasons. First, populations may compensate for reduced spawning
numbers through increased larval survival or growth. Second, density-independent
factors that affect recruitment may vary among streams and years.

Sea lamprey stock-recruitment observed in streams across the Great Lakes basin
indicated both compensation (density-dependent survival) and a large amount of density-
independent recruitment variation. Lakes Superior and Michigan tributaries, streams with
larger numbers of lamprey competitors, and streams regularly requiring lampricide
treatment showed signiﬁcantly higher recruitment, but year did not affect the observed
recruitment pattern. Therefore, management models should account for differences in

recruitment dynamics among sea lamprey-producing streams, but not common year

effects.

Measuring recruitment in sea lamprey populations requires accurate assessments
of larval sea lamprey age, so a standard protocol was developed for estimating the
population age composition of larval sea lamprey using both length-frequency data and
statolith data, which have both been used for age determination in sea lampreys. By
establishing known-age populations in two contrasting streams and comparing the age
determined by statolith interpretation to the known age, I was able to assess bias in this
method of aging. When statolith data were bias-corrected and combined with length-
frequency data in a statistical model to determine proportion-at-age in a sampled sea
lamprey population, the precision of this estimate was substantially increased than when
using only length-frequency data.

To evaluate control strategies, the GLFC has used models of sea lamprey
population dynamics, but models can misinform managers if they fail to account properly
for process error, measurement error, and model uncertainty. Since the effectiveness of
adult control methods depends on the ability to overcome recruitment variation and the
effectiveness of lampricide control depends on good stream selection, a sea lamprey
population model that accounts for recruitment variation and larval assessment
uncertainty was developed. This model simulates the existing control program for Lake
Michigan and estimated the cost and effort at which adult control becomes a viable
complement, or alternative to lampricide control. Assuming our current best estimates of
adult control costs and efﬁcacy, results suggest that increasing adult control efforts at the
expense of lampricide use will result in an increased abundance of sea lamprey. Adult
control measures must become less costly and more effective before using a combination

of both control methods will compare favorably to using only lampricide control.

DEDICATION
I dedicate this dissertation to my family, who by reading this can ﬁnally

understand what I have been doing all these years.

iv

ACKNOWLEDGEMENTS

I thank my advisor, Dr. Michael Jones, for his support and guidance throughout
my graduate program. His ideas and excitement for this project helped inspire me, and
his high standards challenged me to produce work far greater than I thought myself
capable. I thank my advisory committee, Dr. Daniel Hayes, Dr. James Miller, and Dr.
Weiming Li, for their guidance and encouragement. This project was funded through
grants from the Great Lakes Fishery Commission, and I thank Gavin Christie for data
support and encouragement. I thank all those that participated in data collection for this
study, including ﬁeld staff for the US. Fish and Wildlife Service and the Canadian
Department of Fisheries and Oceans, as well as Randy Seymour, Aaron Shultz, Kristy
Bartlett, Scott Marvin, Jenny Nelson, Annie Dyczko, and Ryan Howe. I thank Mike
Steeves and Lisa O’Connor for never turning me away when I needed
logistical/technical/mechanical/physical help at many points along the way, and for their
great hospitality. I thank Rod McDonald, Mike Fodale, and Mike Twohey for sea
lampreys, time, equipment, and cooperation. I am grateful to the numerous landowners
who allowed those involved with this project access to their property. I thank Bill Swink
and Jean Adams for providing valuable comments on earlier drafts of chapter 1. I thank
Anna (Hollett) Cuthbertson for training in statolith extraction and age assessment using
statoliths. Dr. Mike Wilberg and Brian Linton helped answer my questions concerning
AD Model Builder, and suggested code for estimating sea lamprey age composition.
They also provided statistical/modeling support, along with Dr. Tyler Wagner. The sea

lamprey simulation model was made possible through the ideas of my advisor and Dr.

Jim Bence and by the programming skills of Wenjing Dai and Weihai Liu. Dr. Emily
Szalai helped to work out some of the “bugs” in this simulation model. Andy Treble
incorporated current estimates of larval assessment uncertainty based on the results of
Mike Steeves Masters thesis. Dr. Brian Irwin helped in reﬁning the simulation model
description. Kendra Porath helped signiﬁcantly on all aspects of this project by
collecting data in the ﬁeld, patiently wrestling with statoliths and assigning ages, entering
data, running model simulations, and being a good friend.

I thank my friends, family, and colleagues for being there along the way. I thank
my friends and colleagues in the J ones-Bence lab who provided support and a great
environment, whether it was serious or amusing. I thank my long-time friends who were
there when I needed them. I thank my family for understanding that all of this school
will result in a real job some day. Finally, I thank Arica for her consideration, sense of

humor, and endless encouragement.

vi

TABLE OF CONTENTS

LIST OF TABLES ........................................................................................................... viii
LIST OF FIGURES ............................................................................................................ x
INTRODUCTION .............................................................................................................. 1
Chapter 1.
FACTORS AFFECTING RECRUITMENT DYNAMICS OF GREAT LAKES SEA
LAMPREY POPULATIONS ............................................................................................. 9
Abstract ........................................................................................................................... 9
Introduction ................................................................................................................... l 0
Methods ........................................................................................................................ 12
Results ........................................................................................................................... 18
Discussion ..................................................................................................................... 19
Chapter 2.
DEVELOPMENT OF A STANDARD PROTOCOL TO IMPROVE ASSIGNMENT OF
AGES TO LARVAL SEA LAMPREY POPULATIONS ................................................ 34
Abstract ......................................................................................................................... 34
Introduction ................................................................................................................... 35
Methods ........................................................................................................................ 39
Bias and precision in “known-age” samples ......................................................... 39
Comparing two methods of statolith evaluation ................................................... 41
Applying a statistical model to estimate age distribution ..................................... 43
Results ........................................................................................................................... 46
Discussion ..................................................................................................................... 49
Chapter 3.

COMPARING SEA LAMPREY CONTROL STRATEGIES USING STOCHASTIC
RECRUITMENT DYNAMICS AND ASSESSMENT UNCERTATNTY IN A SEA

LAMPREY DECISION MODEL .................................................................................... 67
Abstract ......................................................................................................................... 67
Introduction ................................................................................................................... 68
Methods ........................................................................................................................ 71

Description of the model ....................................................................................... 71

Model calibration and simulations ........................................................................ 78
Results ........................................................................................................................... 8]
Discussion ..................................................................................................................... 83
MANAGEMENT RECOMMENDATIONS .................................................................... 96
REFERENCES ................................................................................................................. 99

vii

LIST OF TABLES

CHAPTER 2

Table 1. Descriptive statistics of the sea lamprey in the entire sampled population of the
“known-age” streams, N=number of sea lamprey. ........................................................... 55

Table 2. Descriptive statistics of the sea lamprey from the “known-age” streams whose
statoliths were examined in 2006, N=number of statoliths ............................................... 55

Table 3. Bias and precision of age estimates by two readers using statoliths from sea
lampreys sampled from the “known-age” streams in 2006, N=number of statoliths. ...... 56

Table 4. Descriptive statistics of the sea lamprey whose statoliths were examined in three
rivers in 2005, N=number of statoliths. ............................................................................ 56

Table 5. Bias and precision of the Crystal Bond and the Immersion Oil methods
evaluated in 2005, N=number of statoliths. ...................................................................... 57

Table 6. Aging error matrix used to remove bias from the observed proportion-at-age
determined by statolith aging when three age-classes are present. ................................... 57

Table 7. Aging error matrix used to remove bias from the observed proportion-at-age
determined by statolith aging when four age-classes are present. .................................... 57

Table 8. The true proportion-at-age and proportions-at-age estimated by the model for the
two “known-age” streams from information only on length, and when using both bias-
corrected age and length. .................................................................................................. 58

Table 9. Grafton Creek proportions-at-age determined by information only on length,
only on bias-corrected age, and using both bias- corrected age and length (N =19 sea
lamprey aged) .................................................................................................................... 58

CHAPTER 3

 

Table 1. Parameters, their assumed values, and state variables used in the sea lamprey
population model. ............................................................................................................. 87

Table 2. Parameters, their assumed values, and state variables used in applying sea
lamprey control. ................................................................................................................ 89

Table 3. Comparison of the number of times the ten largest streams were treated with

lampricide under only lampricide control and when using different levels of adult control.
........................................................................................................................................... 89

viii

Table 4. Detailed data on the comparison of treating four similar sets of regular sea
lamprey-producing streams and irregular sea lamprey-producing streams with adult
control. .............................................................................................................................. 90

ix

LIST OF FIGURES

CHAPTER 1

Figure 1. Location of streams from which we obtained sea lamprey stock-recruitment
data. The four long-term study streams are highlighted with names. The numbers
indicate the number of years of stock-recruitment data we have for each stream. ........... 27

Figure 2. Females and yearling sea lamprey numbers are expressed as densities- 100 m'2
of larval habitat (a) observed stock and recruitment for 90 stream-years and (b) includes
only data when spawner densities were less than 5-100 111'2 ............................................. 28

Figure 3. Observed sea lamprey stock and recruitment for the four long—term study
streams (24 stream-years) when spawner densities were less than 0.5- 100 m'z. .............. 29

Figure 4. The linearized sea lamprey stock-recruitment relationship (ln(R/S) versus S) for
the data plotted in Figure 2. Ln(R/S) is an index of sea lamprey survival to age 1. The
regression line estimates are shown in the graph panel. ................................................... 30

Figure 5. Least squares mean plot of ln(R/S) for age-l sea lampreys versus lake from the

general linear model on all available data (error bars represent 95% conﬁdence intervals).
........................................................................................................................................... 31

Figure 6. Least squares mean plot of ln(R/S) for age-1 sea lampreys versus
competitors 100 m"2 of habitat from the general linear model on all available data (error
bars represent 95% conﬁdence intervals). ........................................................................ 32

Figure 7. Least squares mean plot of ln(R/S) for age-1 sea lampreys versus stream from
the mixed-effects model on the four long-term study streams (error bars represent 95%
conﬁdence intervals). ........................................................................................................ 33

CHAPTER 2

 

Figure 1. Location of streams in which I established “known-age” sea lamprey
populations. ....................................................................................................................... 59

Figure 2. Length-frequency distributions for all ages combined and for ages 1, 2, 3 and 4
are shown for the Big Garlic River “known-age” sea lamprey population after four years
of sampling. Sea lamprey lengths range from about 20 to 110 mm and N indicates the
total number of sea lamprey sampled. .............................................................................. 60

Figure 3. Length-frequency distributions for all ages combined and for ages 1, 2, and 3
are shown for the Ogemaw Creek “known-age” sea lamprey population after three years
of sampling. Sea lamprey lengths range from about 30 to 160 mm and N indicates the
total number of sea lamprey sampled. .............................................................................. 61

Figure 4. Age bias plots constructed from statoliths evaluated in 2007 from the two
“known-age” streams that were aged by two readers. Panels a and b show the average
age coded by each reader compared to the true age when evaluating the Big Garlic River
population. Panels c and (I show the average age coded by each reader compared to the
true age when evaluating the Ogemaw Creek population. Error bars indicate 95%
conﬁdence intervals surrounding the mean age assigned by each reader to the true age. 62

Figure 5. Age bias plots constructed from statoliths evaluated in 2005 from the Big Garlic
River sea lamprey population that were aged by two readers. Panels a and b show the
average age coded by each reader compared to the true age when using the Crystal Bond
method. Panels c and (1 show the average age coded by each reader compared to the true
age when using the Immersion Oil method. Error bars indicate 95% conﬁdence intervals
surrounding the mean age assigned by each reader to the true age. ................................. 63

Figure 6. Age bias plots constructed from statoliths evaluated in 2005 from the Ogemaw
Creek sea lamprey population that were aged by two readers. Panels a and b show the
average age coded by each reader compared to the true age when using the Crystal Bond
method. Panels c and d show the average age coded by each reader compared to the true
age when using the Immersion Oil method. Error bars indicate 95% conﬁdence intervals
surrounding the mean age assigned by each reader to the true age. ................................. 64

Figure 7. The actual length-frequency data for the Grafton Creek sea lamprey population
is shown in gray with the approximate age-class distributions outputted by the model
indicated as age 1, age 2, and age 3. Panel (a) shows the age-class distributions
approximated by the model using only length information, and panel (b) shows
approximations of the model using both length and bias-corrected age information.
Proportions-at-age estimations are shown in the right-hand corner of each panel. .......... 65

Figure 8. Likelihood proﬁles for the model estimates of proportion-at-age-l for the
Grafton Creek sea lamprey population when using a) only length information and b)
when using both length and bias-corrected age information. 95% conﬁdence limits for
the estimates are shown in the lower right-hand comer of each panel. ............................ 66

CHAPTER 3

Figure l. The regression of lampricide cost data for all streams in the model against the
total stream reach area. The resulting line equations provide the cost structure inputted
into the model of Total cost=ﬁxed cost + unit cost ' stream reach area. The ﬁxed cost
used in the model was adjusted to be slightly below the lowest lampricide control cost.
Small stream reaches (<400,000m2), illustrated by closed circles and the solid line, were
found to follow a different linear relationship than large stream reaches (>400,000m2),
illustrated by open circles and the dashed line. The resulting line equations were 8000 +
0.52 - stream reach area and 60000 + 0.12 ' stream reach area for small and large streams,
respectively. ...................................................................................................................... 91

xi

Figure 2. The regression of adult cost data for a subsample of streams in the model
against the total larval habitat area. The resulting line equation provides the cost structure
inputted into the model of total cost=ﬁxed cost + unit cost ° larval habitat area. The
resulting line equation, illustrated by the solid line, was 39500 + 0.06 - larval habitat area.
........................................................................................................................................... 92

Figure 3. The median number of spawners produced versus the cumulative cost of adult
control when using adult control costs and spawner reductions achieved by adult control
of a) $39500 + $0.06 ° larval habitat area and 88%; and b) $39500 + $0.01 - larval habitat
area and 88%. The horizontal line in each graph represents the median number of
spawners resulting from the application of only lampricide control. The number next to
each point represents the number of streams treated by adult control; one to ten of the
largest streams received adult control, added in order of decreasing size. ....................... 93

Figure 4. The median number of spawners produced versus the cumulative cost of adult
control when using adult control costs and spawner reductions achieved by adult control
of a) $39500 + $0.06 - larval habitat area and 88%; and b) $39500 + $0.06 - larval habitat
area and 100%. The horizontal line represents the median number of spawners resulting
from the application of only lampricide control. The number next to each point
represents the number of streams treated by adult control; one to ten of the largest
streams received adult control, added in order of decreasing size .................................... 94

Figure 5. The median number of spawners produced versus the cumulative cost of adult
control when using adult control costs and spawner reductions achieved by adult control
of a) $39500 + $0.03 ° larval habitat area and 94%; and b) $39500 + $0.04 - larval habitat
area and 96%. The horizontal line in each graph represents the median number of
spawners resulting from the application of only lampricide control. The number next to
each point represents the number of streams treated by adult control; one to ten of the
largest streams received adult control, added in order of decreasing size. ....................... 95

xii

INTRODUCTION

Sea lampreys (Petromyzon marinus) are parasitic pests that were a
contributing factor in the collapse of lake trout (Salvelinus namaycush), Whiteﬁsh
(Coregonus clupeaformis), deepwater cisco (Leucichthysjohannae) and blackﬁn cisco
(Coregonus nigripinnis) populations in the Great Lakes during the 19405 and 19505. Sea
lamprey entered the Great Lakes from the Atlantic Ocean through a series of shipping
canals that were built to connect the Upper Great Lakes with the Atlantic Ocean
(Morman et al. 1980). Sea lampreys had invaded all of the Great Lakes by 193 8, and by
the early 19603 lake trout ﬁshery harvests had declined to 2% of pre-invasion levels
(Schneider et al. 1996). Management efforts began in the 19505, and continue today to
control sea lamprey populations throughout the Great Lakes.

The life cycle of the sea lamprey in the Great Lakes begins in lake tributaries
where fertilized eggs hatch into small, wormlike larvae called ammocoetes which burrow
into soft stream bottoms to feed on detritus for 3 to 6 years. After ammocoetes reach a
certain size (~120 mm) they metamorphose into parasitic juveniles and migrate into the
Great Lakes where they feed for 12 to 20 months. Maturing adults then migrate into
streams to spawn, after which they die. The complete life cycle, from egg to adult, can
take an average of 5 to 8 years to complete.

Juvenile sea lamprey do their damage by attaching to large ﬁsh with their suction-
cup mouth and rasping a hole through the ﬁsh’s scales and skin with their teeth so they
can feed on its blood and body ﬂuids. During its parasitic lifetime a single sea lamprey
has been estimated to destroy 6.6 to 18.9 kg of hosts from May through September

(Swink 2003). Bence et al. (2003) calculated values of 1.36, 1.32, and 0.75 for lake trout

deaths per sea lamprey in lakes Superior, Huron, and Michigan, respectively. In the
Great Lakes sea lampreys have no commercial value and other ﬁsh do not normally feed
on them, so there are no natural population controls for sea lamprey. Due to destruction
of valuable ﬁsh stocks and the adverse effect of sea lampreys on the ecological balance of
ﬁsh species in the Great Lakes, the Great Lakes Fishery Commission (GLFC) was
established in 1955 by a treaty between Canada and the United States. Their mission is
to coordinate efforts to formulate and implement a program to eradicate or minimize sea
lamprey populations in the Great Lakes (Pearce et al. 1980).

The sea lamprey control program uses several techniques to reduce abundance of
sea lampreys during different stages of their life cycle. The primary technique involves
applying a lampricide, 3-triﬂuoromethy1-4-nitrophenol, called TFM, to streams to kill
ammocoetes while they are burrowed in the stream bottom. TFM is effective at killing
ammocoetes, and its impact on other ﬁsh species, aquatic plants, invertebrates, and
wildlife is minimal or of very short duration (Dahl et al. 1980). Lampricide treatments
are believed, when effective, to remove between 95 and 99% of the ammocoetes from
treated streams. Currently, about 250 Great Lakes tributaries are treated at regular
intervals with lampricide, although the cost of TFM prohibits treating all streams that will
produce parasitic sea lampreys each year (Steeves 2002). Through biological
assessments and careful TFM use, the GLFC and its agents have successfully reduced sea
lamprey populations in the Great Lakes by 90% from peak population levels. In 1995,
the GLF C adopted an Integrated Pest Management Strategy, which included deﬁning

targets for control that optimize beneﬁts, use of quantitative methods and systems

approaches, and application of alternative methods of control (Christie and Goddard
2003).

Alternative methods of control have been used to target adult sea lampreys and
include; 1) using barriers to prevent upstream migration during spawning; 2) sterilizing
and releasing adult male lampreys; 3) and trapping adult lampreys during their spawning
run. Newer barrier designs include velocity barriers that take advantage of the lampreys'
poor swimming ability; electrical barriers that repel sea lampreys during the spawning
run without risk to other ﬁsh or animals; and adjustable-crest barriers, which can be
inﬂated during the spawning run and then deﬂated to allow other ﬁsh to pass during the
rest of the year (Lavis et al. 2003). The sterile-ma]e-release-technique has shown
promise in larger streams such as the St. Marys River, where lampricide treatments and
barriers are impractical (Schleen et al. 2003). Sea lamprey traps are also employed to
catch adult lampreys during their upstream migration, and the use of pheromones to lure
sea lampreys into traps is a relatively new alternative control method being investigated
(Twohey et al. 2003b). Each of these alternative control techniques operates by reducing
the effective size of the spawning population of sea lamprey in order to decrease
subsequent recruitment, and thus are referred to here collectively as adult control
methods.

These strategies are being considered as alternatives to the use of lampricides
despite the obvious success of lampricides because of public concern about pesticide use
and rising costs of TFM. Speciﬁcally, the GLFC wants to achieve 50% of control
through adult control methods (GLFC 2001). However, the degree to which these adult

control methods are effective will depend on the degree to which reductions in

reproductive success consistently result in reduced recruitment. There are two reasons
why reducing reproductive success might not result in concomitant reduction in
recruitment. First, reducing the spawning population may result in lamprey populations
compensating for this reduction with an increase in larval survival or growth rates.
Second, density-independent factors affecting recruitment, such as winter severity may
vary widely among streams and years leading to inconsistent patterns of recruitment
relative to spawner numbers. Density-independent variation in lamprey recruitment
poses a threat when using adult controls, because even at low spawner densities high
recruitment events can result in larval densities that exceed acceptable levels.

Sea lamprey program managers using adult controls wish to reduce the spawning
population to low levels and get a concomitant decrease in the level of recruitment.
However, a stock-recruitment meta-analysis involving data from 49 stream-years, found
evidence for signiﬁcant compensation in Great Lakes sea lamprey populations and the
existence of large recruitment events that occurred even when the number of spawning
females was quite low (< 2 females per 100 m2) (Jones et al. 2003). Priority should be
given to establishing long term stock-recruitment data sets for a number of Great Lakes
streams that provide good contrast in environmental conditions under conditions that
mimicked adult control methods that reduce spawners to a low level, as differences
among streams may give us insight into how density-independent factors affect
recruitment (Jones et al. 2003). The stock-recruitment data we currently have on Great
Lakes sea lamprey consists of a few years of data on many streams, which makes it
difﬁcult to distinguish “stream” effects from “year” effects. Two factors that vary

considerably among lamprey-producing streams and that are likely to inﬂuence

recruitment are stream productivity and growing season length, and investigating factors
such as these that may affect recruitment might help to determine when and where to
apply adult controls. Analysis of a large sea lamprey stock-recruitment dataset can also
be used to suggest to management a level of control on adult sea lamprey reproduction
required to reasonably ensure success of adult control strategies.

Quantifying recruitment can be limiting due to error in larval age determination,
because evaluating the recruitment of sea lamprey involves assessing the larval
population in streams and separating the population into age classes. Identiﬁcation of age
classes through the inspection of length-frequency distributions is subjective, especially
because there is often overlap in lengths between age classes. The error associated with
this approach introduces uncertainty that is difﬁcult to quantify into abundance at age 1
(i.e., recruitment) estimates and other analyses requiring estimation of the age
composition of sea lamprey populations. Otoliths have been used to estimate age in
teleosts, but lampreys do not have otoliths, having instead an analogous structure called a
statolith. Statoliths are the only calciﬁed structure found in lampreys, and when oriented
properly and viewed under transmitted light, two types of bands appear as layers within
the statoliths; the combination of the two corresponding bands has been shown to
represent annual growth (Hollett 1998). However, of the techniques that have been used
to prepare and evaluate age in sea lamprey statoliths, age determination of sea lamprey
using statoliths has never been validated for more than one year, and the most accurate
method has yet to be determined.

To develop a standard protocol for ammocoete age-assessment using both length-

frequency and statolith data, requires the validation and improvement of both methods of

age interpretation. Currently, age interpretation using length-frequency data is
subjective; however Schnute and Foumier (1980) describe a statistical method for
objectively estimating age composition from length-frequency data that assumes (1) a
von Bertalanffy growth function and (2) that variance of length increases with age for
larval sea lampreys. Foumier (1983) amended the approach to include partial age
composition information, presumably obtained from a sample of ﬁsh from which a
calciﬁed structure was removed. To use statoliths as a method of aging larval sea
lampreys it must be validated that the banding pattern can be repeatably visualized and
represents the true age of the ammocoete over multiple years. Only by using mark-
recapture studies or known-age ﬁsh can all age classes in a population be validated
(Beamish and McFarlane 1983). This can most easily be accomplished by collecting
statoliths over time from a single cohort of known age sea lamprey to determine which
method of statolith evaluation more accurately estimates ammocoete age. Using a
statistical method that combines length-frequency and statolith data to estimate age
composition of sea lamprey populations would lead to more accurate estimates of
recruitment, ammocoete growth rate, survival, and age at metamorphosis, which is very
important life history information to the pursuance of sea lamprey control.

Models that have been used in the past to guide integrated management of sea
lamprey and evaluate adult control strategies have not accounted for density-independent
recruitment variation. Management models that did not explicitly incorporate density-
independent recruitment variation substantially overestimated the beneﬁts of adult
lamprey control options that rely on reducing adult reproductive success (Jones et al.

2003). Current models also fail to include larval assessment uncertainty in short-term

projections of juvenile sea lamprey populations to prioritize streams for lampricide
control. Consequently, the estimates of abundance produced often do not accurately
reﬂect actual lamprey abundance for a majority of streams (Steeves 2002). Models that
guide the integrated management of sea lamprey are based partly on a synthesis of
knowledge of sea lamprey demographics conducted during the 19803. Components of
management models, such as the recruitment, growth, survival, assessment, and
abundance components need to be revised through data synthesized as part of the second
Sea Lamprey International Symposium (SLIS) in 2000.

Accounting for density-independent recruitment variation, and uncertainty in
larval growth and assessment in management models is important to facilitate a realistic
comparison of the effectiveness of lampricide and adult control strategies. The use of
models to explore the potential for hybrid strategies, where sea lampreys are controlled
through a combination of lampricide and adult control, has been emphasized as a possible
option, but has yet to be investigated. The use of adult control methods on larger streams
is unlikely to eliminate the need for lampricide control; it is possible that simply reducing
the frequency at which these streams need to be treated would be sufﬁcient to justify the
costs of adult control. Considerable savings may be achieved by directing adult control
efforts at these rivers, but there are still many unanswered questions about the costs and
efﬁcacy of adult control. A more realistic sea lamprey population model that accounts for
recruitment variation and assessment uncertainty, and allows for the evaluation of a range
of sea lamprey control strategies is what is needed to estimate the cost and effort at which

adult control becomes a viable complement or alternative to lampricide control.

Accurate estimation of the beneﬁts of adult control strategies is essential for
effective integrated management of sea lampreys. To address this issue this dissertation;
in chapter 1 i) measures recruitment variation in lampreys at low spawning stock size in
contrasting streams and investigates factors that may affect recruitment; in chapter 2 ii)
creates “known-age” populations of larval sea lamprey to be used to validate age
determination using statoliths and develops a standard protocol for ammocoete age
assessment using length-frequency data and partial age composition data; and in chapter
3 iii) develops a realistic sea lamprey simulation model including current recruitment and
assessment uncertainty and demographic information to assess the relative performance

of sea lamprey management strategies.

Chapter 1

FACTORS AFFECTING RECRUITMENT DYNAMICS OF GREAT
LAKES SEA LAMPREY POPULATIONS
Abstract
Knowledge of stock-recruitment dynamics is as important for control of pest

species such as the sea lamprey (Petromyzon marinus) as it is for sustainable harvest
management of exploited ﬁsh species. Sea lamprey stock-recruitment data combined
from streams across the Great Lakes basin indicated both compensation (density-
dependent survival) and a large amount of density-independent recruitment variation. A
mixed-effects model tested factors that might affect recruitment variation, using a Great
Lakes dataset comprising 90 stream-years. Lakes Superior and Michigan tributaries,
streams with larger numbers of lamprey competitors, and streams regularly requiring
lampricide treatment showed signiﬁcantly higher recruitment. Year (as a random effect),
alkalinity, and thermal stability did not affect the observed recruitment pattern. In four
long-term study streams we observed signiﬁcant differences among streams but not
among years. Differences in recruitment were consistent with anecdotal evidence of
quality of spawning and larval habitat among streams. Our ﬁndings indicate that
management models need to account for differences in recruitment dynamics among sea

lamprey-producing streams but not common year effects.

Introduction

Stock-recruitment relationships are widely used in ﬁshery management to
determine sustainable harvest rates for exploited ﬁsh populations (of. Hilbom and
Walters 1992, Ricker 1975). In contrast to this goal of sustaining economically valuable
stocks to provide future beneﬁts, the objective for pest species is to remove individuals
from the population at a greater rate than they can be replaced. Although the
management objective is quite different, understanding the stock-recruitment relationship
is equally valuable, because it is the recruitment of the pest species as the population is
driven to low levels that will determine whether the rate of control is sufﬁcient to achieve
lasting beneﬁts. In this paper we present an analysis of stock and recruitment in an
important pest ﬁsh species, the Great Lakes sea lamprey (Petromyzon marinus) and
discuss the implications of our ﬁndings for management of this species.

The sea lamprey is a parasitic ﬁsh that was a major factor in the collapse of lake
trout, Whiteﬁsh, and chub populations in the Great Lakes during the 19403 and 19503
(Smith and Tibbles 1980). Since the late 19503, sea lamprey control has been achieved
through the use of both chemical and non-chemical (adult) control methods. Chemical
methods have been the primary means of control, and involve the application of a
lampricide, 4-nitro-3-(triﬂuoromethyl) phenol (TFM), to remove larvae from a stream
before they become parasites (Smith and Tibbles 1980, Brege et al. 2003). When
effective these methods are believed to remove between 95 and 99% of the ammocoetes
from treated streams (William Swink, US. Geological Survey, Hammond Bay Biological
Station, unpublished data). Adult methods of control use adult trapping (Mullett et a1.

2003), barriers (Hunn and Youngs 1980, Lavis et al. 2003), and the release of sterile

10

males (Twohey et al. 2003a). Pheromones (Li et al. 2003, Sorensen and Vrieze 2003)
also are being explored as a future alternative to lampricides. The Great Lakes Fishery
Commission (GLF C) is seeking to increase their reliance on methods other than
lampricides to achieve ﬁshery goals in the Great Lakes (GLFC 2001). The available adult
control methods all seek to reduce the number of spawners in order to decrease
subsequent recruitment, but are unlikely to achieve suppression levels near 100%.
Accordingly, the degree to which adult control is effective will depend on the recruitment
dynamics of sea lamprey when spawner abundance is reduced to low levels.
Management actions that aim to reduce reproductive success might not result in
concomitant reductions in recruitment, for two reasons. First, sea lamprey populations
may compensate for reduced spawning numbers through increased larval survival or
growth; in a stock-recruitment meta-analysis involving data from 49 stream-years, Jones
et al. (2003) found evidence for signiﬁcant compensation in Great Lakes sea lamprey
populations. Second, density-independent factors that affect recruitment, such as winter
severity, may vary among streams and years, and cause variations in recruitment that are
unrelated to spawner numbers. Peterman et al. (1998) found that important
environmental processes affecting variation in sockeye salmon survival rate from
spawners to recruits operate at regional scales, rather than at the larger, ocean-basin scale.
Sockeye salmon productivity within a region may therefore be driven by persistent
changes in the environment rather than management actions such as enhancement or
harvesting (Peterman et al. 1998). In their meta-analysis, Jones et al. (2003) found that
density-independent recruitment variation was large and concluded that further research

was needed to discriminate between “stream” effects and “year” effects. Density—

ll

independent variation in sea lamprey recruitment can limit the effectiveness of adult
controls that reduce spawner abundance, because even at low spawner densities high
recruitment events can produce larval densities that exceed acceptable levels.
Deterministic sea lamprey management models that do not explicitly incorporate density-
independent recruitment variation (e. g. Koonce et al. 1993) will substantially
overestimate the beneﬁts of adult sea lamprey control options that rely on reducing adult
reproductive success (Jones et al. 2003).

This research differs from our earlier investigation of sea lamprey recruitment
dynamics Jones et al. (2003) in ﬁve ways: (i) the number of stream-years of stock-
recruitrnent data analyzed (90); (ii) the use of an objective, likelihood-based model, as
opposed to subjective interpretation of length-frequency data, to separate age-1 recruits
from other age-classes of sea lamprey; (iii) the assembly of data on stream characteristics
analyzed to attempt to explain variation in recruitment patterns among streams; (iv) the
establishment of four long-term study streams where we introduced spawners at a low
level to mimic adult control reductions in spawner abundance, and measured the
subsequent recruitment at age 1 over several years; and (v) an analysis of data from these
four long-term study streams that aims to separate stream and year effects on sea lamprey

recruitment dynamics.

Methods
We assembled data on spawning population size and on larval recruitment at age
1 in the following year from Jones et al. (2003), and from similar data collected

subsequently, resulting in a database of 90 stream-years of sea lamprey stock-recruitment

12

data (Figure 1). Spawner abundances were controlled by deliberately releasing adult sea
lampreys above barriers in 55 cases, or spawning population abundance was estimated in
35 cases using a mark-recapture method applied to sea lampreys captured in adult
assessment traps (Mullett et al. 2003). We estimated age-1 larval abundance using the
same electroﬁshing survey technique in all streams, as described in Jones et al. (2003).
Habitat was classiﬁed at randomly-spaced transects along the stream as Type 1 (ﬁne sand
and silt which is preferred by sea lampreys), Type II (coarser sand which is acceptable for
sea lampreys), or Type III/IV (gravel, cobble, bedrock, exposed islands, all of which are
unsuitable for sea lampreys. Using a backpack electroﬁsher we surveyed Type I plots at
approximately half of the transects, and Type II plots were surveyed at about every eighth

transect. Stock and recruitment were calculated from
R"
9 R 2 ii: (1 )9

respectively, where S is the total number of spawning females, R is the total abundance

of yearling larvae, and H w is the total amount of larval habitat in each stream, weighted

by the relative suitability of Type I and Type II habitat

D
HW:AI+TD—ﬂ“AII (2)

I
where A is the area of habitat (m2) and D is the density of yearlings. Type II habitat is
weighted less heavily than Type I habitats based on sea lamprey density differences in the

two habitats (Slade et al. 2003). Density of yearlings in Type II and Type I were

13

.—

. . D . . .
determined for all streams and the ratio —_’—’ used in habitat calculations was the average
1

ratio across all streams in the data set.

To determine the proportion of ammocoetes in our surveys that were age 1 we
used a statistical method, similar to that described by Schnute and F ournier (1980) for
objectively estimating age composition from length-frequency data (see chapter 2). This
method was used because there is not consensus on the accuracy of statoliths for
determining age composition of larval sea lampreys, and because we felt that the
statistical methods would be preferable to a subjective determination of age composition
from length-frequency data. The statistical method relies on an assumption about the
growth dynamics of the ﬁsh stock of interest; we assumed larvae grew according to a
von—Bertalanffy growth function and that individual variation in length increased linearly
with age. We estimated age composition using maximum likelihood methods
implemented in AD Model Builder (Otter Research 2000). We were able to determine
proportion at age 1 using this model for nearly all stream-years that contained more than
one age class of ammocoetes. In ten stream-years either only the age-1 class was present
(ﬁve cases), or proportion at age 1 was determined subjectively by visual inspection of
length-frequency plots, because the model did not converge to a solution (ﬁve cases).
The estimated proportion at age 1 was multiplied by the total sea lamprey catch to
estimate age-1 sea lamprey catch in each stream-year.

To learn how differences among streams might affect recruitment, we also
collected data from four study streams (Figure 1) over a period of several years. We
selected four streams that had previous years of sea lamprey stock-recruitment data: two

warm, high-alkalinity streams in the Lake Ontario drainage (Port Britain and Grafton

14

creeks -- 27 km apart) and two cold, low-alkalinity streams along the north shore of Lake
Superior (Carp and Big Carp river3-- 48 km apart). Three years of data from Port Britain
and Grafton creeks (1999-2001) and four years from Carp (1997-2000) and Big Carp
rivers (1998-2001) were available prior to this study. We wished to assess recruitment
under conditions that mimicked adult control methods that reduce spawners to a low
level, and further investigate how recruitment varies at very low spawner densities. Jones
et al. (2003) stock-recruitment data indicated that no high recruitment events were
observed at stock sizes of less than 0.5 spawning females- 100 m'z. In our study streams,
by adding 10 pairs of spawners each year to each stream we kept stock size below 0.5
females- 100 m'z. We added only 10 adult male and 10 adult female sea lampreys above
barriers in these streams for three years starting in 2002 (Carp and Big Carp rivers) or
2003 (Port Britain and Grafton creeks).

The mean age-l density in each habitat type, the area of each habitat type and
resulting abundance of age-1 larvae (i.e., recruitment) were computed for each stream-

year. We ﬁt the data to a Ricker stock-recruitment model of the form

R=a°S-e_ﬂ'5+g (3)

which can be rewritten as a linear model
R
ln[§] = ln(a) — ,8 - S + a (4)

where ln(R/S) is an index of survival to age 1 (effectively recruitment, in this study), S is
the number of female spawners-100 rn'2 of larval habitat, (1 describes average survival
across stream-years when S is close to zero, [3 describes the degree to which survival falls

. . . . . . 2
as S increases, and a 13 a normally distributed error term With mean zero and variance 0 .

15

Jones et al. (2003) concluded that measurement error was a negligible component of the
observed, overall error in ln(R/S), given the survey methods we used. To calculate an
overall sea lamprey stock-recruitment relationship and to combine data from multiple
streams in the stock-recruitment analysis, we assumed that all streams shared a common
a term and that B depended on the availability of larval habitat in each stream, such that if
S is expressed in adults per unit of larval habitat, B will also have a common value for all
streams, determined by intra-speciﬁc larval competition for rearing habitat.

The linear form of the Ricker stock-recruitment function allowed us to use a
general linear mixed-effects model (Littell et al. 1996) to assess other factors that might
signiﬁcantly affect recruitment. We tested each factor’s main effect on recruitment, but

did not test higher-order effects due to sample size limitations. The model we ﬁt was
R
ln(§)=1n(a)+v+x+5+2+p+b—ﬂo5+e (5)

where b and s are normally distributed with mean zero and variance 02.

a = Average survival across all streams when number of spawners is zero
v = Lake effect
I = Thermal stability effect

6 = Alkalinity effect
I1 = Consistency of sea lamprey production effect
p = Competitor effect

b= Year effect (random)
,8 = Density dependence term

a = Error term

Lake (Superior, Huron, Michigan, Ontario) was used as a surrogate for the effect
of a stream’s location. Thermal stability was included as a categorical variable, as stream
temperatures were determined by sea lamprey control agents to either parallel air

temperature (warm) or be more regulated by groundwater input (cold). In general, warm

16

streams were those where summer water temperatures frequently exceeded 20°C. The
thermal niche of larval sea lamprey is considered to be between 17.8 and 21.8 °C, and lab
studies found maximal survival of exogenous feeding sea lamprey larvae reared at 21°C,
and no survival at 23°C after a three-month period (Holmes and Lin 1994; Rodriguez-
Muﬁoz et al. 2001). Alkalinity was used as a surrogate for stream productivity, and
streams were classiﬁed as high if reported alkalinities were greater than 100 mg-L'l
CaCO3 and low if they were below 100 mg-L'l CaCO3. The factor “consistency of sea
lamprey production” refers to an a priori categorization of streams by sea lamprey
control agents into regular or irregular sea lamprey producers. Regular producers are
streams subjected to a reliable cycle of lampricide treatments (i.e., they have been treated
every 3, 4, or 5 years, depending on the stream). Irregular producers are subjected to a
less consistent cycle of treatment. The competitor effect was a categorical variable and
was based on estimated numbers of native lampreys of all ages (Ichthyomyzon spp. or
Lampetra appendix) and sea lampreys that were not age 1; i.e., all lampreys that were
potential competitors to age-1 sea lamprey recruits. Categories were <100- 100 m'2 (few),
between 100 and 299- 100 m'2 (some), and >= 300 lamprey competitors- 100 m'2 of larval
habitat (many). The year of recruitment was included as a random factor, to account for
year to year variability (Littell et al. 1996). The variance in the index of survival that can
be attributed to the random effect was estimated using the Minimum Variance Quadratic
Unbiased Estimators (MIVQUE) for estimating variance components and tested for
signiﬁcance using Restricted Maximum Likelihood (REML) in Statistica 7.0 (StatSoft,
Inc. 2004), to see if year as a random effect should be included in the ﬁnal model. All

effects other than year were modeled as ﬁxed effects.

17

We ran a separate analysis on the four long-term study streams established in this
study (a total of 24 stream-years worth of observations) to test for the effect of stream and
year on recruitment variation, using a mixed-effects model with stream as a ﬁxed effect

and year as a random effect, normally distributed with mean zero and variance 02.

Results

Doubling the size of the sea lamprey stock-recruitment database did not
substantially alter the overall pattern described in an earlier study (Jones et al. 2003).
Recruitment of sea lampreys was highly variable among streams, even after accounting
for the effect of stock size (Figure 2a). The index of survival (ln(R/S) was lower at
higher stock size, indicating the occurrence of compensation. As well, large recruitment
events occurred even at stock sizes below 1-100 m'z, although they were not observed at
very low stock sizes (< 0.2 females- 100 m'z; Figure 2b). In our four long-term study
streams we introduced spawners at low levels since 2002 (< 0.5 females- 100 m'z) to
mimic adult control methods that reduce spawner abundance; recruitment was low (<50
age 1 larvae- 100 m'z) in all but one case (Figure 3).

The regression of ln(R/S) on S revealed a statistically signiﬁcant, negative slope
(B = -0.1584, SE = 0.0225, p([3 = 0) < 0.0001, df=88; Figure 4), which provides
statistical evidence of compensation. The amount of variance in the index of survival
attributable to the random effect of year was close to zero (oyear = 0.0532, Geno, =2.103),
and the variance component was not signiﬁcantly different from zero (REML= 0.2030,
p=0.48). Therefore, year was removed from the model and we tested the remaining ﬁxed

effects on survival. The resulting general linear model revealed signiﬁcant effects of

18

stock size, lake, consistency of sea lamprey production, and competitor abundance. Lake
signiﬁcantly affected survival (p=0.002, F 3.30:5.367), and Tukey HSD pair-wise
comparisons indicated that streams tributary to Lakes Superior and Michigan experienced
signiﬁcantly higher survival than streams tributary to Lakes Huron and Ontario (Figure
5). Survival in streams with regular sea lamprey production was signiﬁcantly higher than
in those with irregular production (p=0.001, F1,30=11.18, Regular producer LS
mean=4.00, Irregular producer LS mean=2.86). The number of competitors signiﬁcantly
affected survival (p=0.002, F 2,30=6.602), but contrary to expectations, Tukey HSD pair-
wise comparisons indicated signiﬁcantly lower survival in streams with the fewest
competitors (Figure 6).

The mixed model testing the effect of stream and accounting for year to year
variability on the four long-term study streams revealed a signiﬁcant effect of stream
(p=0.0002, F3,12=15.68) on survival. Tukey HSD pair—wise comparisons indicated Carp
River had signiﬁcantly higher and Port Britain Creek had signiﬁcantly lower survival
than the other streams (Figire 7). As with the larger dataset, the amount of variance in
the index of survival attributable to the random effect of year was close to zero (oyear =
0.0162, Germ, =1.005), and the variance component was not signiﬁcantly different from

zero (REML= 0.0705, p=0.89).

Discussion
When pest management includes tactics that aim to reduce the size of the
reproducing population, it is valuable to know something about the relationship between

stock and recruitment, just as it is for the management of exploited species.

19

Understanding the stock-recruitment relationship of a population will reduce
uncertainties and risks related to management decisions not only about how to
sustainably harvest a population, but how to effectively reduce the population of a
harmful pest species. Density-independent variation in the survival of offspring can
cause high or low recruitment from the same initial number of fertile, mature adults,
which suggests that a better understanding of the factors causing this variation would be
of use to managers, especially if those factors can be controlled or manipulated. Density-
dependent, compensatory variation in survival can thwart efforts to control pests by
targeting the adult stock, so an understanding of the power of a pest population to
compensate is important to specifying the level of control necessary to overcome this
compensatory power and reduce pest abundance over the long run.

In this study we provided further evidence of signiﬁcant density-dependent
compensation for sea lamprey populations in 37 streams in the Great Lakes basin. We
also conﬁrmed the presence of a large amount of density-independent recruitment
variation (overall observed variance was 3.28), and showed that this variation can be
partially explained by differences among streams, but not by coherent variation among
years. Management models that are used to assess strategies for sea lamprey control
aimed at adult sea lamprey should explicitly account for these stock-recruitment
dynamics. Failure to do so will lead to optimistic assessments of the overall promise of
such strategies (Jones et al. 2003) and potentially to sub-optimal decisions about where to
target efforts to reduce adult numbers, as we discuss further below.

Many pest control techniques, such as the sterile male technique, were ﬁrst

developed to manage agricultural pests and achieved some success (Knipling 195 5).

2O

Early models of sterile insect release dynamics were simple algebraic models that
assumed density-independent population regulation, 30 they predicted if the same
numbers of sterile insects were released in each generation the percent decline in the pest
population per generation would increase with time (Knipling 195 5). However, many
populations exhibit compensation at low population density, which can result in numbers
rebounding after a release (Gould and Schliekelman 2004). Thus, the “increasing effect
over time” predicted by the early models did not always occur, leading to failure of many
pest eradication programs (Gould and Schliekelman 2004). Considerable ﬁnancial
resources have been invested in novel (mostly molecular) techniques designed to control
pests, unfortunately the investment in population dynamics and population genetics
research that is needed to assess, and potentially improve, the utility of the techniques has
not been paralleled (Gould and Schliekelman 2004). Scott et al. (2002) found that
different mechanisms of population regulation in mosquitoes that transmit malaria and
dengue virus could lead to an unpredicted advantage for populations we are attempting to
control through novel means, which could lead to disastrous results; only by gaining
knowledge of their population regulation can we accurately begin to predict outcomes of
proposed interventions.

The importance of density-dependent mechanisms for other vertebrate pest
control strategies has also received recent attention. European rabbit (Oryctolagus
cuniculus) populations were observed to exhibit strong compensatory increases in
survival and recruitment when up to 80% of adult females were sterilized (Twigg and
Williams 1999). Frederiksen et al. (2001) developed a population model for great

cormorants (Phalacrocorax carbo sinensis) in northern Europe that demonstrated the

21

limited effectiveness of culling operations due to observed density-dependent adult
survival and maturation rates. They proposed that culling rates should be density-
dependent themselves in order to stabilize future cormorant populations — that is, culling
rates should decrease as cormorant densities decline. Brown and Walker (2004)
developed a population model for carp (C yprinus carpio) in Australia that included an
empirical stock-recruitment relationship and used it to evaluate alternative strategies for
carp control. Not surprisingly, they showed that the performance of “ﬁshing down”
strategies was sensitive to moderate variations in stock-recruitment parameters, and
emphasized the importance of developing a larger empirical data set of stock and
recruitment for carp, just as we have attempted to do for sea lampreys. Finally, Davis et
al. (1999) emphasized the importance of recruitment variation by using a simple
population model to demonstrate that the rate of introgression of inducible fatality or
sterility transgenes into a population was underestimated if recruitment variation was not
included in the model.

Our results can be used to specify a level of control on adult sea lamprey
reproduction required to reasonably ensure success of adult control strategies. We did
not observe large recruitment events (>200 age 1 larvae-100m'2) when spawner
abundance were below 0.2 females-100m"2 in either the full data set or the long-term
study streams (Figs. 2, 3). When planning future adult control initiatives, such as
trapping and/or sterile male release, sea lamprey managers should aim to reduce spawner
abundance to this value or below to try and ensure low recruitment of sea lamprey

populations.

22

Of the 35 cases in this study where natural spawning populations were estimated
rather than intentionally introduced, over 80% had spawner abundances greater than 0.2
females- 100 m'2 of larval habitat and over 50% had spawner abundances greater than 1
female- 100 m'z. To the extent that these streams are typical of sea lamprey producing
streams in the Great Lakes, this implies that achieving the target abundance of 0.2
females- 100 in2 in approximately half of the streams will require trapping efﬁciencies (or
reductions due to both trapping and sterile male releases) of 80% or greater. Currently in
Great Lakes streams, sea lamprey trapping efﬁciencies range from 5% to 91% with a
mean trapping efﬁciency of 39% (Gavin Christie, Great Lakes Fishery Commission, Ann
Arbor, Michigan, personal communication). However, recent research has demonstrated
that sea lamprey pheromones hold considerable promise as a tool to enhance trapping
efﬁciency (Wagner et al. 2006, Johnson et al. 2006), which suggests that the targets
implied by our recruitment research are achievable.

Our proposed target of 0.2 females- 100 in2 is a general reference point that could
be applied to all streams, but an objective of this study was to determine whether we
could explain density-independent variation in recruitment among our study streams,
such that different streams might require different targets. We found that streams
described by sea lamprey program staff as having a regular and predictable cycle of
lampricide treatment experienced signiﬁcantly higher survival than less predictable
(irregular) streams. This result suggests that not only are these streams consistent sea
lamprey producers, but they also tend to produce more recruits at a given stock size. We
also found that streams in Lakes Superior and Michigan produced higher survival than

streams from Lakes Huron or Ontario. Consistent with this ﬁnding, survival in our two

23

Lake Superior long-term study streams was higher than in the two Lake Ontario streams.
This ﬁnding was in contrast to what we might have expected, because in general Lake
Ontario sea lamprey streams tend to be warmer and more productive and require
treatment with lampricide more frequently than streams on the upper Great Lakes.
Finally, we found that survival was higher in streams where the number of competitors
was greater, which again contradicted our predictions.

We hypothesize that these results are the consequence of differences among
streams in habitat quality. Our meta-analysis included streams from throughout the Great
Lakes, but they were not selected at random. Stream habitat quality for sea lampreys
may, in general, be better in Lakes Superior and Michigan than in Lakes Huron and
Ontario, or the streams included in this study may simply have had better habitat quality
in the ﬁrst two lakes. It seems plausible that streams classiﬁed as regular producers have
better habitat, and similarly that streams with better habitat have larger populations of
native lampreys (i.e., competitors).

We did not attempt to quantify habitat supply in the streams included in this
study. It is likely that not only the quality and quantity, but also the distribution of both
spawning and larval habitat in a stream contributes to recruitment differences among
streams. Spawning sea lampreys require gravel 1 to 5 centimeters in diameter for nest
construction, with small amounts of sand available to which the eggs will adhere in the
nest, while larval sea lamprey require soﬂ bottom types to make their burrows (Applegate
1950). Because larvae are typically carried downstream in the current after hatching,
suitable larval habitat must occur somewhere downstream of suitable spawning areas.

One long-term study stream, the Carp River, had abundant amounts of clean gravel at the

24

 

top of the reach with numerous patches of silt/sand bottom downstream. Another study
stream, Port Britain Creek, has very limited areas of clean gravel with large closely-
spaced cobble armored by sand for most of the stream length. We observed relatively
high survival in the Carp River and low survival in Port Britain Creek (Figure 7),
consistent with our hypothesis that habitat differences may explain recruitment variation.

An important next step in process-level research of sea lamprey recruitment
variation will be to develop measures of habitat differences among streams that appear to
explain recruitment variation. Baxter (1954) found that the stream gradient for sea
lamprey streams in England was between 5 to 14.5 m-km", which allowed for good
spawning habitat in the upper reaches and depositional areas for larval habitats
downstream. Young et al. (1990) found that the presence/absence of sea lamprey
ammocoetes within the Great Lakes was controlled, to a large degree, by substrate
particle size. Alternative quantitative descriptions of habitat supply, that account for the
juxtaposition of spawning and larval habitats on an ecologically meaningful scale
(Derosier et al. 2007), should be included in future investigations of recruitment
variation. If a measure of habitat supply can be shown to explain signiﬁcant among-
stream variation in recruitment after accounting for density-dependent (stock) effects,
then this factor should be used to inform management. Streams with an abundance of
good habitat would require greater reductions in spawner numbers to achieve target
recruitment levels, on average, and thus would not be preferred candidates for adult
control.

Both the full meta-analysis model (90 stream-years) and our four stream model

revealed that the year of recruitment, speciﬁed as a random effect, was not a signiﬁcant

25

component of the overall variance in survival among observations (the estimate was
essentially zero). Myers et al. (1997) looked at recruitment variation among populations
of 19 species of ﬁsh from marine, marine-freshwater (anadromous) and freshwater
habitat, and noted that recruitment patterns were correlated over time among nearby
(<500 km apart) populations of marine ﬁshes but only weakly and at short distances for
freshwater species. Similar patterns of temporal covariation have been demonstrated for
north Paciﬁc stocks of sockeye (Oncorynchus nerka) and pink (0. gorbuscha) salmon
within but not among broad regions such as the Fraser River and Bristol Bay (Peterman
et al. 1998; Pyper et al. 2001). These studies suggest that moderate to large-scale,
temporally variable environmental factors inﬂuence ﬁsh recruitment in marine systems,
but are less important in freshwater systems. Our analysis of sea lamprey recruitment is
consistent with this View — we found differences in temporal patterns of recruitment
between streams as little as 27 and 48 km apart. In sea lampreys, where recruitment (as
we have deﬁned it here) takes place in individual streams, recruitment variation appears
to be more strongly inﬂuenced by stream-speciﬁc factors, or by interactions between
stream-speciﬁc factors and temporally varying environmental factors. From a
management perspective this implies that simulation models of stream-level recruitment
dynamics should treat interannual recruitment variation among streams as independent

stochastic processes.

26

  
   
 
 
    

arm
4 Big Carp7

Port

Britin5 rafton5
2 A

  
 

Figure 1. Location of streams from which we obtained sea lamprey stock-recruitment
data. The four long-term study streams are highlighted with names. The numbers
indicate the number of years of stock-recruitment data we have for each stream.

27

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96 400 -
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ﬂ
‘- 2oo -
d»
O)
< o

 

 

 

 

a
.
.
}.

.
. C.
o

D
k... -....Q.g. .-. .. an
O 10 20 3O 40 50 60

Females-100 m”2
b
.
.
C
.
. C

g
0 O . Q 0
me..- ~-., on!“ .
O 1 2 3 4 5

Females-100 rn'2

Figure 2. Females and yearling sea lamprey numbers are expressed as densities- 100 m'2
of larval habitat (a) observed stock and recruitment for 90 stream-years and (b) includes
only data when spawner densities were less than 5' 100 m'z.

28

1050

 

 

‘7‘
E
o O
2 1000*
‘E
(D
g
"é
o
2
(D
g -.
L“ 50" .
‘1' 40 .
:ce’; 30 '
20 . ' '
10 ' O .
0 o o . 9
0.0 0.1 0.2 0.3 0.4

Females-100 m'2

Figure 3. Observed sea lamprey stock and recruitment for the four long-term study
streams (24 stream-years) when spawner densities were less than 0.5- 100 m'z.

29

1

10

ln(R/S) = 4.3925 - 0.1584 - s (o=1.81)
p(B=O) < 0.0001

0.“ 0".

Ln(R/S)

 

 

_4 a . L . - .\‘ .
O 10 20 30 4O 50 60

Females-100 m'2

Figure 4. The linearized sea lamprey stock-recruitment relationship (ln(R/S) versus S) for

the data plotted in Figure 2. Ln(R/S) is an index of sea lamprey survival to age 1. The
regression line estimates are shown in the graph panel.

30

5.5 r

5.0

4.5 ~

4.0 -

Ln(R/S)

2.5 -

2.0 ~

1.5 -

1.0

3.5 -

3.0 -

 

 

 

 

 

 

Superior Michigan Huron Ontario
Lake

Figure 5. Least squares mean plot of ln(R/S) for age-1 sea lampreys versus lake from the
general linear model on all available data (error bars represent 95% conﬁdence intervals).

31

5.0 r

4.5 ~

4.0 r

3.5 *

Ln(R/S)

3.0 ~

2.5 ~

2.0 -

1.5

 

 

 

 

 

Few Some Many

Competitors-100 m'2

Figure 6. Least squares mean plot of ln(R/S) for age-1 sea lampreys versus
competitors- 100 rn'2 of habitat from the general linear model on all available data (error
bars represent 95% conﬁdence intervals).

32

 

 

 

Ln(R/S)

 

 

 

 

Big Carp Carp Port Britain Grafton
Stream

Figure 7. Least squares mean plot of ln(R/S) for age-1 sea lampreys versus stream from
the mixed-effects model on the four long-term study streams (error bars represent 95%
conﬁdence intervals).

33

Chapter 2

DEVELOPMENT OF A STANDARD PROTOCOL TO IMPROVE

ASSIGNMENT OF AGES TO LARVAL SEA LAMPREY POPULATION S

Abstract
A standard protocol for more accurately determining larval sea lamprey

(Petromyzon marinus) population age composition, provided it is not too costly, would be
very valuable for sea lamprey control. Developing a standard method of age-assessment
using both statolith and length-frequency data requires the validation and improvement of
both methods of age interpretation. Identiﬁcation of age classes through the inspection of
length-frequency distributions is subjective, especially because there is often overlap in
lengths between age classes. In this study, 1 evaluated a likelihood-based statistical
model that estimated age composition from a large sample of length-frequency data and
smaller sample of age composition information obtained from statoliths. Age
determination of sea lampreys using statoliths has never been validated for more than one
year, so I also established “known-age” populations in two contrasting streams by
introducing a single cohort of sea lampreys and then compared the age determined by
statolith interpretation to the known age using two different methods for statolith
preparation and evaluation. Multiple independent age readings of sea lamprey statoliths
indicated that the overall average percent error measuring bias was 33.0% for the Crystal
Bond method and 27.3% for the Immersion Oil method. The statolith data were bias-
corrected and combined with length-frequency data in the statistical model to determine

proportion-at-age in a sampled sea lamprey population using all available information,

34

which resulted in a substantial increase in the precision of this estimate compared with

using only information on length.

Introduction

Age, grth rate, and mortality rate are three of the most inﬂuential life history
characteristics controlling the productivity of ﬁsh populations (Campana and Thorrold
2001). Measuring productivity and recruitment in sea lamprey (Petromyzon marinus)
populations across the Great Lakes requires accurate assessments of larval sea lamprey
age. Historically, aging of larval sea lamprey has relied on the use of length-frequency
distributions. Jones et al. (2003) measured recruitment to age 1 by identifying age-1
individuals through inspection of length-frequency distributions. However, this method
is subjective and there is often overlap in lengths between the age-1 group and older age
classes, which introduces uncertainty into the estimation of the abundance of the age
class (Potter 1980). The error associated with this approach introduces uncertainty that is
difﬁcult to quantify into estimates of abundance at age 1 (i.e., recruitment) and other
analyses requiring estimation of the age composition of sea lamprey populations.

Statoliths, the analogous structure in lampreys to otoliths in teleosts, have been
used for age determination in sea lampreys (Beamish and Medland 1988, Hollett 1998).
Statoliths are the only calciﬁed structure found in lampreys, and when oriented properly
and viewed under transmitted light, two types of bands appear as layers within the
statoliths; the combination of the two corresponding bands has been shown to represent
annual growth (V olk 1986). However, this age determination method has never been

validated for more than one year using a “known-age” population of ammocoetes. Also,

35

 

statoliths from sea lamprey experiencing different ambient calcium ion concentrations
display diversity in their reliability for estimating age when compared with length-
frequency distributions (Barker et al. 1997). I wished to develop a protocol for more
objectively determining age composition using length-frequency and statolith age
information, which requires the validation and improvement of both methods of age
interpretation.

Different methods have been employed for statolith preparation and evaluation to
determine ages of larval lampreys (e. g., Volk 1986; Beamish and Medland 1988; Hollett
1998). Volk (1986) evaluated statolith banding patterns by balancing statoliths on their
edges in immersion oil to view them from a posterior or lateral aspect (Immersion Oil
method). Hollett (1998) evaluated statolith annuli by ﬁrst storing statoliths in glycerin
for a period of two weeks and then inserting them into a clear adhesive, which could be
heated to reposition the statolith in the proper orientation (Crystal Bond method). Single-
year validation of both methods has been completed using oxytetracycline marking of
larvae (Beamish and Medland 1988 using Volk’s (1986) Immersion Oil method), and
animals undergoing metamorphosis (Hollett 1998 using the Crystal Bond method).
These year-long studies concluded that a narrow dark band appeared beyond the region
marked with oxytetracycline in larvae and animals undergoing metamorphosis. In
accordance with criteria applied to the aging of teleost ﬁshes, the narrow dark band on
the statolith that formed during slow growth was taken as the annulus (Beamish and
McFarlane 1983). However, Beamish and Medland (1988) and Hollett (1998) measured
the precision, not the accuracy of the age they assigned to individual animals. Validation

means proving a technique is accurate (Beamish and McFarlane 1983). We need to

36

validate that the banding pattern can be repeatably visualized and represents the true age
of the ammocoete over multiple years in contrasting environments, and also determine
which method of statolith evaluation more accurately estimates ammocoete age. Only by
using mark-recapture studies or known-age ﬁsh can all age classes in a population be
validated (Beamish and McFarlane 1983).

The validation of statolith evaluation as an aging technique requires the
examination of known-age sea lampreys from varying environments. Statolith growth
and banding pattern have been found to be intimately associated with temperature, with
annuli formation corresponding to sharp seasonal changes in grth (Medland and
Beamish 1991). Barker et al. (1997) found that larval lamprey statoliths exhibited
irregularities in size or presence from stream with alkalinities below 30 mg/L CaCO3,
which is most likely due to resorption of calcium from the statolith in animals from low-
alkalinity environments. Beamish and Medland (1988) marked sea lamprey larvae from
only one Great Lakes stream, a cold, low-alkalinity Lake Superior stream (Big Garlic
River) and placed them in holding cages in their natal stream for one year. Hollett (1998)
marked premetamorphic and metamorphic sea lamprey from four Great Lakes streams
and placed them in laboratory tanks where all populations were reared in dechlorinated
tap water, under temperatures that mimicked a warm Lake Ontario stream (Dufﬁns
Creek). To validate the use of statoliths as an aging method over multiple years in
varying environments, statoliths could be collected over time from single cohorts of
known-age sea lamprey in streams that contrast in temperature and alkalinity, but which
both experience seasonal changes and have calcium ion levels that support statolith

growth.

37

 

Using an objective, likelihood-based method in the development of a standard
protocol for ammocoete age-assessment would be an important advance in sea lamprey
management. Schnute and Foumier (1980) describe a statistical method for objectively
estimating age composition from length-frequency data that relies on an assumption
about the growth dynamics of the ﬁsh stock of interest. Foumier (1983) amended the
approach to include partial age composition information, presumably obtained from a
sample of ﬁsh from which a calciﬁed structure was removed. When discerning age-
classes of ammocoetes, obtaining age information from a subsample of the ﬁsh helps
determine the number of age-classes present in the sample and avoid gross errors such as
misaging all the ﬁsh by 1 year (Foumier 1983). Obtaining direct age information can
also help adjust for errors, observed when using only length-frequency information, in
parameter estimation of the von Bertalanffy growth equation, due to intrapopulation
variability in growth parameters (Smith et al. 1997). Also, if bias in aging data can be
quantiﬁed this error can be statistically removed from a set of age frequencies by using
an aging error matrix (Richards et al. 1992). Combining length-frequency and age
information to determine ammocoete ages makes the best use of the information
contained in all the available data.

The objectives of this study were to create “known-age” populations of larval sea
lamprey to be used to validate age determination using statoliths, and develop a standard
protocol for larval sea lamprey (ammocoete) age assessment using length-frequency data
and partial age composition data. To address these objectives, I ﬁrst created a single year
class of sea lamprey above barriers in two Michigan streams that contrast greatly in

growing season length and alkalinity, as a tool to validate aging techniques. A sample of

38

larval sea lampreys from the streams was collected each year and the reliability of current
methods that use statoliths to accurately assess larval age was compared. Statolith data,
which provided information on the growth dynamics of the ﬁsh stock, was bias-corrected
and combined with length-frequency data to estimate age composition of the “known-
age” streams and a stream with three age-classes of sea lamprey using an objective,
likelihood-based statistical model. By using all available information to determine

proportion-at-age we can try to increase the precision of ammocoete age assessments.

Methods
Bias and precision in “known-age ” samples

I established “known-age” populations of sea lampreys in two streams by
introducing 25 pairs of spawners above barriers. Big Garlic River, a cold, low-alkalinity
(mean alkalinity = 52 mg/L CaCO3) Lake Superior stream, received spawners in spring
2002, while Ogemaw Creek, a warmer, high-alkalinity (mean alkalinity = 175 mg/L
CaCO3) Lake Huron stream, received spawners in the spring of 2003 (Figure 1).
Spawners were introduced in one year, and since populations were established above
low-head barriers no other age classes of sea lamprey were present. Each stream was
sampled by an AbP-2 backpack electroshocker, with the Big Garlic River sampled in the
summer of 2003, 2004, 2005, and 2006 and Ogemaw Creek in 2004, 2005, and 2006.
Soon after sampling, larvae that were identiﬁed as Petromyzon marinus were frozen and
then weighed to the nearest milligram and measured to the nearest millimeter. Samples
were kept frozen until 2006 when subsamples of larvae from each stream-year were

randomly chosen for statolith evaluation.

39

Animals were prepared for statolith extraction by ﬁrst cutting off the body
posterior to the gills. Then under a dissecting microscope (10X) the head region was
placed dorsal side up and sliced along the notochord from the anterior to the posterior of
the animal. The otic capsules were located on either side of the notochord and were
pierced with ﬁne-tip forceps. The forceps were then used to grab material in which the
statolith could be found, which was transferred to a Petri dish. An attempt was made to
remove both right and left statoliths from each animal. The statoliths were cleaned using
distilled water and allowed to dry. The statoliths were then prepared and evaluated based
on either the Crystal Bond or the Immersion Oil method, to be described later.

Annuli were viewed most clearly when the statolith was oriented laterally by
using both a dissecting microscope (75X) and transmitted light and a compound
microscope (400X), however annuli could be seen more clearly at lower magniﬁcation.
This is most likely due to the difﬁculty of using a compound microscope with a single
plane of focus to evaluate the three-dimensional structure of a statolith (Hollett 1998).
Annuli were counted by two readers; a light and a dark band were interpreted as
comprising an annulus. Each reader aged each statolith twice. The bias of this statolith
aging technique for Great Lakes sea lampreys was examined visually by age bias plots
(Campana et al. 1995) and by comparing estimates of average percent error (APE). Age
bias plots were constructed to compare the ages assigned by each reader to the true age.

APE was calculated from:

1 N 1 R ‘Xij_Xj
looxﬁz EZT (1).

j=l i=1 ij

40

where N is the number of statoliths aged, R is the number of times each statolith was
aged, Xij is the ith age determination of the jth statolith, and Xj is the reference age
(Beamish and Foumier 1981).

Most aging studies use the mean age observed by all readers for each structure as
the reference age in APE calculations; in this study the true age is used as the reference
age. However, I compared the APE using the mean age calculated by readers to get an
estimate of precision, to that obtained when using the true age, which is an estimate of
bias. This gives an indication of the inﬂuence of not knowing the true age on this
measure of accuracy. I also plotted the length-frequency distributions for all sea
lampreys sampled in each stream (across years) and compared this to the length versus

true age distributions.

Comparing two methods ofstatolith evaluation

To compare two methods of statolith preparation and evaluation samples were
kept frozen until 2005 when subsamples of larvae were randomly chosen from each
stream-year (except 2006) for statolith evaluation by each method. “Known-age” ﬁsh
only included ages 1-3 and I wished to avoid readers being able to limit their age
interpretations to 3 or less. To that end, I added a sample of animals (N =3 1 , mean length
86 mm) of unknown age, obtained from Bowmanville Creek, a Lake Ontario tributary, to
the collection of statoliths to be interpreted. The Crystal Bond and Immersion Oil
methods were evaluated by comparing the estimates of bias and precision in aging using
the average percent error. The method observed to be the less biased and more precise

was subsequently used to evaluate statoliths from the “known-age” streams in 2006 (Bias

41

and precision in “known-age ” samples) and when estimating the age distribution of sea
lampreys in Grafton Creek in 2006 (Applying a statistical model to estimate age
distribution).

The Crystal Bond method required that statoliths be transferred using a dissection
pin to individual wells within a multiwell plate ﬁlled with glycerin, where they were
stored for at least 9 days at room temperature. Hollett (1998) found that statoliths tended
to disintegrate in glycerin after a period of 15 days. Because I was extracting statoliths
from smaller animals than Hollett (1998), whose animals had a mean length of 115 mm, 1
was conservative by not allowing the statoliths to exceed 13 storage days in glycerin.
After the storage period statoliths were removed from the wells by a pipette and placed
on a microscope slide in a small amount of clear Crystal Bond TM(Aremco). Crystal
Bond could be heated to allow for proper positioning of statoliths for clear visualization
of annuli. Each statolith was assigned a random number that was written on the slide,
and linked back to an animal after “blind” age-assessments were conducted by readers.

The Immersion Oil method required that statoliths be transferred using a
dissection pin to random individual wells within a multiwell plate ﬁlled with immersion
oil, where they were stored for at least 9 days, and no longer than 18 days at room
temperature. Each well in which a statolith was immersed was assigned a random
number, to link back to an animal after “blind” age-assessments were conducted by
readers. After the storage period statoliths were removed from the wells by a pipette and
placed on a depression microscope slide in a small amount of immersion oil. As found in
Volk (1986), viscous immersion oil facilitated maneuvering of the statolith so that an

optimum orientation could be achieved.

42

Applying a statistical model to estimate age distribution

To create a statistical model to estimate proportion of ages in a randomly sampled
sea lamprey population I used a method similar to that described by Schnute and F oumier
(1980) and Foumier (1983). The method requires structural assumptions about how the
ﬁsh in the population grow and how individual ﬁsh vary in their growth rates. These two
assumptions allow a prediction of the length composition of a mixed-age population,
which can be compared to actual data. Using maximum likelihood methods, a set of
growth and variation parameters that best ﬁts the observed data can be obtained, and used
to infer the age composition of the population. If we let u; be the mean length of ﬁsh at

age a, then if these means lie on a curve of the type proposed by von Bertalanffy, u; is

described by

u. 2 L00 (1 — e‘K(“i"0)) (2).

I

In this equation, L 00 is the theoretical maximum length which ﬁsh approach as they grow
older, K relates to the fraction by which the gap between current length and maximum
length is reduced each year, and t0 is the age at which ﬁsh length extrapolates back to
zero along the curve. Schnute and Foumier (1980) deﬁned new parameters for von
Bertalanffy growth that have greater biological meaning and numerical stability than the
conventional parameters They used the parameter set (L, LM_ k), which is much more
appropriate to length-frequency analysis than (L 00 , K, to), with Li being the mean length
of the youngest age class, LM being the mean length of the oldest age class, and k being

the distance between two successive mean lengths. Using these parameters ui is

described by

43

l—kH

ul. = Ll +(LM —L1)W,

i: I,...,M. (3),

with t being the age class and M being the maximum number of age classes (Schnute and
Foumier 1980). I assumed for each age-class the lengths were normally distributed
around their mean length and the standard deviations increased as a linear function of
age-class. I estimated the most likely proportions at age using a multinomial log-
likelihood function implemented in Ad Model Builder (Otter Research 2000). In chapter
1 I used this model to separate out the age-1 age-class from length-frequency data for the
stock-recruitment streams.

I amended the statistical model (following F ournier 1983) to include partial age
composition information. The observed proportion-at-age for a stream was determined
through aging statoliths from a subsample of animals, and the bias observed in aging
statoliths from “known-age” streams was corrected by using an aging error matrix to

obtain the corrected proportion-at-age described by

A
pa : zCa.a' . p'a' (4),
a'=l

where p, p’ are the corrected and observed proportions-at-age, respectively, C is an aging
error matrix, with rows a — true ages, and columns a ’ - observed ages, and A is the total
number of ages. I added a second multinomial likelihood term to the objective function
to use the corrected proportion-at-age in the model, which combined with length-
frequency data, estimated the predicted proportion—at—age.

I tested the accuracy of the statistical model by estimating proportion-at-age for
the two “known-age” populations when cohorts sampled from multiple years were

combined into a single length-frequency plot. Sea lamprey sampled in 2003, 2004, 2005,

44

and 2006 for the Big Garlic River, and 2004, 2005, and 2006 for Ogemaw Creek were
combined into one length-frequency distribution for each stream. Using the statistical
model I then estimated the proportion-at—age using only length-frequency information
and compared the estimate with the “known” proportion-at age.

I also used these data to evaluate the statistical model when partial age-
composition data were included. The aging error matrix I developed to adjust the bias in
statolith aging was based on statoliths from both “known-age” streams evaluated in 2006
using the Immersion Oil method (my results showed this method to be the less biased and
more precise on average). Results suggest that the direction of the aging bias was similar
for both “known-age” streams, so data from both streams was used to develop the aging
error matrix to correct the bias for both Ogemaw Creek and Big Garlic River. The
statistical model estimated the most likely proportion-at—age given both length and age
information, and I then compared the estimates with the “known” proportion-at-age.

I applied a similar method to estimate proportion-at-age using length-frequency
and statolith data from one of our long-term study streams (see chapter 1). I used sea
lampreys sampled from Grafton Creek in 2006 to compare proportion-at-age estimated
by the statistical model when using just length information to that obtained using both
length and age (statolith) information. Age information was obtained by taking a random
sample of sea lampreys from the populations, removing their statoliths and aging them
using the Immersion Oil method. Animals 25 mm or less were determined to be young-
of-the-year, and since statoliths could not be evaluated for this population they were
removed from this analysis. The Grafton Creek population only included ages 1-3 and I

wished to avoid readers being able to limit their age interpretations to 3 or less. To that

45

end, I added a sample of animals (N=5, mean length 110 mm) of unknown age, obtained
from Ceville Creek, a Lake Michigan tributary, to the collection of Grafton Creek
statoliths to be interpreted. Two readers aged each statolith two times and the average
age of all readings was rounded to result in an age of 1, 2, or 3 for each statolith. Aging
error was corrected using the aging error matrix based on statoliths from both “known-
age” streams evaluated in 2006 using the Immersion Oil method. To evaluate the
precision of the estimate, I derived approximate conﬁdence limits from likelihood
proﬁles. Using AD Model Builder the likelihood proﬁles are determined by calculating
the conditional maximum of the likelihood function and then normalizing it so that it
integrates to 1 (Otter Research 2000). I chose the 2.5th and 97.5Lh percentiles of the

likelihood proﬁle to represent 95% conﬁdence limits.

Results
Bias and precision in “known-age ” samples

Because I collected animals from each “known-age” stream in each year
following spawner introduction I have lengths of the animals in each age class. The
length-frequency distribution of animals from the Big Garlic River and Ogemaw Creek
for all years combined indicated effectively no modal separation among age classes 2, 3,
and 4 (Figure 2) and age classes 2 and 3 (Figure 3), respectively.

By 2006, we had sampled the cohort in the Big Garlic River at age-1, age-2, age-
3, and age-4, and had sampled the cohort in Ogemaw Creek at age-1, age-2 and age-3. In
2006, I chose 98 statoliths at random from the entire collection to interpret using the

Immersion Oil method (the less biased method). Animals whose statoliths were

46

examined were a good representation of the sampled population for each stream-year
(Tables 1 and 2). Overall APE was much larger for both readers when calculating APE
based on the true age than when using the mean age, which indicates bias as well as
imprecision in the interpretations (Table 3). Big Garlic animals that were age-1 were
over-aged, with age-2 animals being slightly under-aged and animals older than age-2
being under-aged (Figure 4). Ogemaw Creek animals aged 1 and 2 were over-aged, with
age-3 animals aged close to the true age by reader 1 and under-aged by reader 2 (Figure
4). Statolith interpretations differed from the true age between streams in a similar
pattern as animals older than age 2 tended to be under-aged while animals aged 1 and 2

tended to be over-aged (Figure 4).

Comparing two methods of statolith evaluation

By 2005, we had sampled the cohort in the Big Garlic River at age-1, age-2, and
age-3, and had sampled the cohort in Ogemaw Creek at age-1 and age-2. When
removing statoliths from sea lamprey from our “known-age” populations, they were
sometimes lost or broken in the extraction or mounting process. However, of the
statoliths successfully extracted and mounted using the Crystal Bond method I chose 100
statoliths at random to interpret. I chose 52 statoliths at random to interpret using the
Immersion Oil method. With a random sample some stream-years were over-
represented, but animals whose statoliths were examined were a good representation of
the sampled population for each stream-year present in 2005 (Tables 1 and 4).

Ages assigned by both readers using both evaluation methods differed from the

true age in both streams. Overall APE was much larger for both readers when calculating

47

APE based on the true age than when using the mean age, which indicates larger bias
than imprecision in the interpretations (Table 5). The bias in aging was higher using the
Crystal Bond method, but when interpreting statoliths from Ogemaw Creek animals the
Crystal Bond method was more precise. Both methods of statolith evaluation produced a
similar pattern of how statolith interpretations differed from the true age between
streams. Interpretations of statoliths from age-1 and age-2 animals from the Big Garlic
River were less biased than those of the same age ﬁ'om Ogemaw Creek, while age-3
animals from the Big Garlic tended to be under-aged (Figure 5). Ogemaw Creek age 1

and 2 statoliths were over-aged by both readers (Figure 6).

Applying a statistical model to estimate age distribution

Because of the similarity observed in the direction of bias between the two
streams the aging error matrix used data from both “known-age” streams to adjust bias in
aging in the model for both “known-age” streams and Grafton Creek (Tables 6 and 7).
The statistical model’s estimate of proportion-at-age for the two “known-age” streams
when age composition data were included was very similar to the true proportions-at-age.
The model’s ability to accurately estimate proportion-at-age was improved by adding
bias-corrected age data to the Big Garlic River estimate (Table 8). However, the
estimates of the proportion-at-age for Ogemaw Creek were actually closer to the true
values when only the length—frequency data were included (Table 8).

Using only length information from the 2006 Grafton Creek population, our
statistical model estimated over one-half of the population to be one-year-olds, and about

one-fourth of the population to be two-year-olds, and the rest three-year-olds (Table 9,

48

Figure 7a). Statoliths were aged for a proportion of the population (N=30 statoliths, l9
sea lamprey aged), and the model estimates including bias-corrected age and length
indicated that 40% of the animals were age-1, and age-2 and age-3 animals each made up
30% of the population (Table 9). With length and age information included, the model
estimated proportion-at-age to consist of fewer age-1 animals and more age-3 animals
compared to using length information only (Table 9, Figure 7b). Adding the statolith
information substantially increased the precision of the model’s estimate of the
proportion-at-age-l, as evidenced by a comparison of likelihood proﬁles for the

proportion-at-age-l estimate, with and without age information included (Figure 8).

Discussion

Prior to this study, the interpretation of annuli formation on statoliths had only
been demonstrated for a single year’s growth. Using statoliths from “known-age”
populations, readers observed that annuli are often difﬁcult to visualize, resulting in a
substantial bias in our age interpretations. Our estimates of APE for all age
determinations using the Crystal Bond method (22.5-46.3%) and the Immersion Oil
method (14.7-35.3%) were much higher than those reported by Beamish and Medland
(1988) (28-52%) and Hollett (1998) (08-24%) for sea lampreys. However, their error
rates were obtained by using mean age rather than true age as the reference age, which
means they only assessed precision, not bias. Volk (1986) also reported a low incidence
of error (i.e., high precision) in repeated sampling of the same statolith from sea
lampreys. Our APE estimates based on mean age as the reference, using the Crystal

Bond method (1 1-15.6%) or the Immersion Oil method (9.1-20.5%) are closer to those of

49

 

Beamish and Medland (1988) and Hollett (1998) but are still higher, suggesting lower
overall precision in my study. However, the exclusion of statoliths for which age could
not be assigned (Beamish and Medland 1988) or that were considered ambiguous (Volk
1986, Hollett 1998) may have resulted in higher estimated precision in those studies. I
did not exclude statoliths whose interpretations were ambiguous from our analysis, but
only excluded those that were unreadable (broken or burnt). The average percent error
observed in this study was similar to those reported by Meeuwig and Bayer (2005) for
Paciﬁc lampreys (Lampetra tridentata) (16.7%) and western brook lampreys (Lampetra
richardsoni) (33%) in a study in which precision in statolith aging was assessed and
statoliths that were ambiguous or difﬁcult to read were not excluded.

Both the Immersion Oil and Crystal Bond methods produced a similar pattern of
how statolith interpretations differed from the true age between streams, with bias and
precision similar on average between the two streams. I observed greater bias on average
in age interpretations of statoliths from Ogemaw Creek, the warmer, high-alkalinity
stream, and results suggests that statolith readers will tend to overestimate younger ages
in fast-growing populations. Lower bias was observed in ages estimated by statoliths
from the cold, low-alkalinity stream, and proportion-at-age estimates based on length-
frequency information for ages 3 and 4 were far from the true proportion-at-age, but were
considerably improved when age composition was included (Table 8). However,
determining proportion-at-age for a population based on statolith interpretation for a
sample of animals will be imprecise even if these estimates are unbiased or bias-
corrected, particularly if the sample size is small. This may explain why, for Ogemaw

Creek, proportion-at-age estimates based on length-frequency information were not

50

improved when age composition data was included (Table 8). If, by chance, the sample
of animals that are aged using statoliths deviates from the true age composition, addition
of these data to the estimation model will not increase the accuracy of the proportion-at-
age estimates. This would not be expected in the long run, however.

Model estimates of proportion-at-age for the Grafton Creek population revealed
greater precision in the proportion-at-age-l estimate using bias-corrected age and length.
The estimate using all available information was more precise, with the 95% conﬁdence
interval much smaller than that obtained using length only (Figure 8). Addition of
statolith age composition data would also affect estimates of other demographic
parameters. For example estimates of the abundance of age-1 larvae for Grafton Creek in
2006 were 683 versus 470 when using only length versus using length and bias-corrected
age information. Similarly, the estimated annual survival rate (minimum variance
unbiased assuming selectivity is l for all ages) (Chapman and Robson 1960) increased
from 0.618 to 0.661 when statolith data were included. In streams with greater numbers
of sea lamprey these differences would be even larger. By including a direct aging
method independent of size, we can analyze individual variability in the data, and our
ability to investigate important life history parameters is greatly improved (Volk 1986).
More precise age estimates will reduce the propagation of error through the assessment
and management process (Morison et al. 2005).

The use of a calciﬁed structure to provide age estimates is subject to error from
two major sources: (1) error inherent in the structure itself, and (2) error in the process of
interpreting its incremental structure (Campana 2001). Producing and preserving quality

in statolith samples should decrease both types of errors. Study animals were frozen

51

prior to statolith removal in this study, and statoliths were sometimes lost or broken in the
extraction or mounting process. I chose to freeze animals, as it had been learned that
statoliths would disintegrate when animals were preserved in formalin. However
freezing animals for long periods dried out some samples, which made statolith
extraction difﬁcult and increased the brittleness of the statoliths. Another study
investigating statolith microchemistry preserved sea lamprey in ethanol for up to one year
and had no samples whose statoliths were difﬁcult to extract or brittle, especially in
contrast to their frozen samples (Carrol Hand, University of Windsor, Windsor, Ontario,
personal communication). Methods of preserving animals for statolith evaluation and
extraction should be compared to determine the method that results in the best quality
samples over varying time periods; using animals collected from “known-age” streams
would also determine if bias in aging differs with preservation method.

It is a more laborious process to include the growth dynamics of a population of
ﬁsh by extracting and evaluating statoliths and correcting for bias in aging, than to simply
interpret length-frequency distributions to determine proportion-at-age of a population,
but the additional effort can result in substantially improved estimates. This study used
an objective, likelihood-based model to estimate proportion-at-age, and determined that
model estimates are more precise when including bias-corrected age and length
information to estimate proportion-at-age. By including more data on age distribution
besides length-frequency information, such as bias-corrected age information we are also
more likely to approximate the true age distribution. Aging sea lamprey using length-
frequency distributions requires large sample sizes, and older age-classes are often

difﬁcult to discriminate due to overlapping length distributions (Barker et al. 1997).

52

Barker et al. (1997) found that in low-alkalinity streams sea lamprey statoliths are diverse

in size, banding patterns, and presence within and among populations, which emphasizes

the importance of using length-frequency distributions in combination with statoliths

aging to verify assigned ages. The current study improved both methods of sea lamprey

aging by verifying statoliths as a method of aging with measured bias, and creating and

testing an objective, likelihood based statistical model to estimate proportion-at-age using

both length-frequency and age information.

To improve ammocoete age-assessments based on results of this study, a standard

protocol for estimating age composition of sea lamprey in streams is suggested:

1.

A random sample of sea lamprey (at least 100 animals) should be

collected from throughout a stream.

All animals should be properly preserved (frozen or preserved in ethanol)

then measured to the nearest millimeter, and a random subsample of sea
lamprey (at least 25 animals) should be set aside for statolith extraction.
Statoliths should be extracted as described in the methods and prepared
and evaluated using either the Immersion Oil or Crystal Bond method.

A length-frequency histogram should be prepared and the number of age-
classes in a stream should be determined and included in the statistical
model using length-frequency information and knowledge of the treatment

history of the stream.

. Using the length-frequency histogram, starting values for the statistical

model parameters Ll, being the mean length of the youngest age class, and

LM, being the mean length of the oldest age class, should be determined

53

and included in the statistical model along with length-frequency
information.

Observed proportion-at-age should be determined based on statolith
evaluation and included in the statistical model. The appropriate aging
error matrix created in this study should be included in the statistical
model to correct the bias in statolith aging.

The statistical model should be used to estimate proportion-at-age based
on the included information, and sensitivity of the model estimates to the
starting values of L1 and LM should be explored. The resulting estimates
can then be used as inputs to other modeling or assessment activities that

contribute to the effective management of Great Lakes sea lampreys.

54

Table 1. Descriptive statistics of the sea lamprey in
the entire sampled population of the “known-age”
streams, N=number of sea lamprey.

 

Total Length (mm)

 

True Year
age(years) Collected N Mean SE Min Max

Big Garlic River

 

 

1 2003 65 33 0.50 25 53
2 2004 177 57 0.74 36 86
3 2005 127 61 0.76 43 98
4 2006 81 84 1.21 65 107
Ogemaw Creek
1 2004 92 50 0.76 34 81
2 2005 99 90 1.00 69 1 19
3 2006 73 112 1.80 80 155

Table 2. Descriptive statistics of the sea lamprey
from the “known-age” streams whose statoliths
were examined in 2006, N=number of statoliths.

 

Total Length (mm)

 

_gge(years) N Mean SE Min Max
Big Garlic River

 

 

 

1 1 1 32 0.55 29 35
2 13 55 2.37 41 70
3 15 66 1.56 61 79
4 15 85 2.48 68 97
Ogemaw Creek
1 14 47 1.54 39 54
2 15 89 1.78 75 97
3 15 106 4.72 80 155

55

Table 3. Bias and precision of age estimates by
two readers using statoliths from sea lampreys
sampled from the “known-age” streams in
2006, N=number of statoliths.

 

 

 

 

 

 

Bias Precision
Reader APE SE N APE SE
Big Garlic River
1 31.6 5.8 54 11.6 1.97
2 29.9 4.2 54 16.6 2.65
Ogemaw Creek
1 34.5 6.6 44 20.5 3.12
2 30.7 5.0 44 18.0 2.47

Table 4. Descriptive statistics of the sea lamprey
whose statoliths were examined in three rivers in
2005, N=number of statoliths.

 

 

 

 

 

 

 

 

 

 

 

 

 

Crystal Bond
Total Lengt_h (mm)
True
_age(years) N Mean SE Min Max
Big Garlic River
1 4 31 1.25 28 34
2 13 55 2.58 36 67
3 20 63 2.20 50 92
Ogemaw Creek
1 15 55 2.84 43 81
2 26 93 2.1 1 71 1 19
Bowmanville Creek
N/A 22 89 2.08 67 1 17
Immersion Oil
Total Lergth (mm)
True
jge(years) N Mean SE Min Max
Big Garlic River
1 6 32 0.31 31 33
12 65 2.11 53 77
3 8 67 7.34 43 98
Ogemaw Creek
1 9 52 1.88 40 57
8 83 2.36 78 98
Bowmanville Creek
N/A 9 83 3.51 65 94

56

Table 5. Bias and precision of the Crystal
Bond and the Immersion Oil methods
evaluated in 2005, N=number of statoliths.

 

Crystal Bond

Bias Precision
Reader APE SE N APE SE
Big Garlic River
1 25.2 3.42 37 15.6 2.03
2 22.5 3.58 37 15.3 2.13
Ogemaw Creek
1 37.8 6.94 41 13.0 1.94
46.3 7.54 41 11.0 1.69

 

 

 

 

 

Immersion Oil
Bias Precision
Reader APE SE N APE SE
Big Garlic River
1 16.7 3.73 26 12.2 3.01
2 14.7 3.93 26 9.1 2.57
Ogemaw Creek
1 35.3 8.85 17 17.7 3.19
2 25 8.3 17 16.0 2.35

 

 

 

 

 

 

Table 6. Aging error matrix used to remove bias from
the observed proportion-at-age determined by statolith
aging when three age-classes are present.

 

 

Statolith Age
1 2 3
1 0.59375 0.171429 0
True Age 2 0.1875 0.4 0.533333

3 0.21875 0.428571 0.466667

Table 7. Aging error matrix used to remove bias from the
observed proportion-at-age determined by statolith aging when
four age-classes are present.

 

 

Statolith Age
1 2 3 4
1 0.59375 0.171429 0 0
True Age 2 0.1875 0.4 0.275862 0
3 0.21875 0.428571 0.241379 0.5
4 0 0 0.482759 0.5

57

Table 8. The true proportion-at-age and proportions-
at-age estimated by the model for the two “known-
age” streams from information only on length, and
when using both bias-corrected age and length.

 

Estimated by Estimated by

 

 

 

Age using length using length and
Class True only bias-corrected age
Big Garlic River
1 0.145 0.129 0,144
2 0.393 0.420 0.404
3 0.282 0.031 0.279
4 0.180 0.420 0174
Ogemaw Creek
1 0.349 0.328 0.317
2 0.375 0.356 0.343
3 0.276 0.316 0.340

Table 9. Grafton Creek proportions-at-age determined by information
only on length, only on bias-corrected age, and using both bias-
corrected age and length (N=19 sea lamprey aged).

 

 

Length only Bias-corrected Bias-corrected

Age Class age only age and length
1 0.577 0.390 0.399
2 0.264 0.427 0.292
3 0.159 0.183 0.309

58

     

Big Garlic River

Ogemaw Creek

Figure 1. Location of streams in which 1 established “known-age” sea lamprey
populations.

59

N=450

 

 

 

 

 

Number of Fish

 

 

 

 

 

20 110

Length (mm)

Figure 2. Length-frequency distributions for all ages combined and for ages 1, 2, 3 and 4
are shown for the Big Garlic River “known-age” sea lamprey population after four years
of sampling. Sea lamprey lengths range from about 20 to 110 mm and N indicates the
total number of sea lamprey sampled.

60

N=264

All Ages

    

Age 1

 

 

 

 

.C
.9
u.
’5
5 Age 2
.Q
E
3
2
Age 3
30 Length (mm) 160

Figure 3. Length-frequency distributions for all ages combined and for ages 1, 2, and 3
are shown for the Ogemaw Creek “known-age” sea lamprey population after three years
of sampling. Sea lamprey lengths range from about 30 to 160 mm and N indicates the
total number of sea lamprey sampled.

61

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0 . 0
1 2 3 4 1 2 3 4

g, B
< <
‘— C:
h

g S
(U (U
a: an
O: m

 

 

 

 

 

 

 

 

 

 

 

2 2 .
d) ——
_ 0
1 1 - —
0 4 0 -
1 2 3 1 2 3
Known Age

Figure 4. Age bias plots constructed from statoliths evaluated in 2007 from the two
“known-age” streams that were aged by two readers. Panels a and b show the average
age coded by each reader compared to the true age when evaluating the Big Garlic River
population. Panels c and d show the average age coded by each reader compared to the
true age when evaluating the Ogemaw Creek population. Error bars indicate 95%
conﬁdence intervals surrounding the mean age assigned by each reader to the true age.

62

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

3 . a 3
2 - 2 _ __
0 —-1—
—— 1
1 1
0 4 o 2 . m
m 1 2 3 o 1 2 3
0’ a)
< <2
‘- N
L h
8 s
(U (U
a) d)
o: o:
d
3 Z c 3 - _/
cl 0
2 » —— 2
_ I
ll #_
1 i 1 "
0 4 o -
1 2 3 1 2 3
Known Age

Figure 5. Age bias plots constructed from statoliths evaluated in 2005 from the Big Garlic
River sea lamprey population that were aged by two readers. Panels a and b show the
average age coded by each reader compared to the true age when using the Crystal Bond
method. Panels c and d show the average age coded by each reader compared to the true
age when using the Immersion Oil method. Error bars indicate 95% conﬁdence intervals
surrounding the mean age assigned by each reader to the true age.

63

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

3 r
__ i—
0 a __ b
2 _ 2 - ——
0
0
1 1 .
a) 0 ‘ 0 ‘
O) 1 2 8, 1 2
< <
‘: N
m h
g 8
0 8
05 o:
3 - 3 .
c 0 d
2 - 2 l.
0
1 1 __
0 0 .
1 2 1 2
Known Age

Figure 6. Age bias plots constructed from statoliths evaluated in 2005 from the Ogemaw
Creek sea lamprey population that were aged by two readers. Panels a and b show the
average age coded by each reader compared to the true age when using the Crystal Bond
method. Panels c and d show the average age coded by each reader compared to the true
age when using the Immersion Oil method. Error bars indicate 95% conﬁdence intervals
surrounding the mean age assigned by each reader to the true age.

64

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0.1 a" .,,_7i 7 3- i- _[ 3.5
0 09 , Proportion-at-age
0.577 + 3
35 0-08 1 0.264 a
1 0.07 4 0-159 .. 2.5
.D
5 0.06 «
g «i 2 g
0
_.I 0.05 1 5
u
_l
2 1i 1 5 o-
0.04 -I a
E 5
'0; 0.03 '1 H. _ ‘l ' T 1 8
I” : .' ‘ i
0.02 1 n "11.,$ l
H Hi i-. l T 0-5
0.011 \ ,, 1"“ I
l l . .
o 20 so 100 120
Length (mm)
L Age1——Age2----Age3—---Data|
0-1 T ‘ 7 ' ‘ “" " ""‘W’im‘ﬁ' "’ 1r- 35
0.09 . Age Proportion-at-age
1 0.399 ‘" 3
,, ”8‘ 2 0.292 b
2' our 3 0.309 ._ 2.5
>0
.0
0.06 . ‘3.
5 ~ 2 1:
3’ 3
o 0.05 4 ..
-' a
'0‘; r 1.5.:
a- 0.04 4 §
5 o
“003— I'll I U , .1
1'3 ' . ' . \.‘ i' 1 r ' l. '
0.02 “ ' ' ‘ " J ' 1L. n -l [i . l
" " | "u' Iiwl‘i " ' ~05
‘ ' ' - I II 11. .' I 1 '
0.01 — j l-\ , .I , . _ I
'J "I \ l" "-
I l h | \| i . 'l . ' ‘ J
o 1 i I I A ‘- __1_1_i__ o
o 20 80 100 120
Length (mm)
L Age1——Age2----Age3—---Datal

 

 

Figure 7. The actual length-frequency data for the Grafton Creek sea lamprey population
is shown in gray with the approximate age-class distributions outputted by the model
indicated as age 1, age 2, and age 3. Panel (a) shows the age-class distributions
approximated by the model using only length information, and panel (b) shows
approximations of the model using both length and bias-corrected age information.
Proportions-at-age estimations are shown in the right-hand comer of each panel.

65

 

 
 
 
 

 

 

 

 

 

4 a
‘6
o 3
:E
E 2 95% conﬁdence limits
:3 lower 0.131
1 upper 0.712
O
0.0 0.2 0.4 0.6 0.8 1.0
Proportion-at—age-1 estimate
5
4 b
'0
° 3
,2 95% conﬁdence limits
E 2 lower 0.159
'3 upper 0.538
1
0 . . L A 4
0.0 0.2 0.4 0.6 0.8 1.0

Proportion-at-age-1 estimate

Figure 8. Likelihood proﬁles for the model estimates of proportion-at-age-l for the
Grafton Creek sea lamprey population when using a) only length information and b)
when using both length and bias-corrected age information. 95% confidence limits for
the estimates are shown in the lower right-hand comer of each panel.

66

Chapter 3

COMPARING SEA LAMPREY CONTROL STRATEGIES USING
STOCHASTIC RECRUITMENT DYNAMICS AND ASSESSMENT
UNCERTAINTY IN A SEA LAMPREY DECISION MODEL

Abstract

Incorporating density-independent recruitment variation and assessment
uncertainty into sea lamprey (Petromyzon marinas) management models is important to
facilitate a realistic comparison of the effectiveness of lampricide and adult (alternative)
control strategies. Using recent data on recruitment and larval assessment uncertainty, a
more realistic simulation model for an actual Great Lake was developed. This model
simulates the existing sea lamprey control program for Lake Michigan and allows
comparison of the effect of using only lampricide control to combinations of both
lampricide and adult control methods (hybrid strategy). The sensitivity of the model to
adult control costs and the effective proportion of spawners reduced by adult control was
tested, using the current sea lamprey control budget for Lake Michigan. Assuming our
best estimates of adult control costs and efﬁcacy, results suggest that increasing adult
control efforts at the expense of lampricide use will result in an increased abundance of
sea lamprey. Adult control costs must be reduced and efﬁcacy of adult control must be
increased for a hybrid strategy to compare favorably to using only lampricide control.
Sea lamprey pheromones may help reduce the proportion of effective spawners in each
stream reach and decrease adult control costs, if pheromones can be inexpensively
synthesized and applied. This modeling exercise was designed to effectively compare

sea lamprey control strategies for the Great Lakes Fishery Commission which desires to

67

reduce reliance on lampricide control, and increase the role of adult control methods in

controlling sea lamprey.

Introduction

The Great Lakes Fishery Commission (GLFC), in a recent mission statement,
expressed the desire to achieve 50% of sea lamprey control (Petromyzon marinus)
suppression with technologies alternative to lampricides, while reducing lampricide use
by 20% (GLFC 2001). Extensive tests on the environmental safety of the two
lampricides used by the Commission, TFM and Bayluscide, have revealed no long-term,
detrimental effects to the ecosystem (Hubert 2003, Dawson 2003), and when effective,
lampricide applications are believed to remove between 95 and 99% of the ammocoetes
from treated streams (William Swink, US. Geological Survey, Hammond Bay Biological
Station, unpublished data). Even though stream applications continue to be remarkably
successful, public apprehension about pesticides and rapidly escalating lampricide costs
compelled the Commission to ﬁnd alternatives to lampricide control (GLF C 2001).
Methods alternative to lampricide control use adult trapping (Mullett et al. 2003), barriers
(Hunn and Youngs 1980, Lavis et al. 2003), and release of sterile males (Twohey et al.
2003a). Pheromones (Li et al. 2003, Sorensen and Vrieze 2003) also are being explored
as a future alternative to lampricides. The available alternative methods all seek to
reduce the number of adult spawners to decrease subsequent recruitment, and thus are
referred to here as adult control methods.

The effectiveness of adult control methods depends on the ability to overcome

recruitment variation; to reduce spawners to the point where few or no high recruitment

68

events will occur. The relationship of sea lamprey spawning stock to the number of
resulting recruits is highly variable at a wide range of spawning stock sizes, but high
recruitment events (>200 age-1 larvae per 100m2) were not observed when spawner
abundance was below 0.2 females per 100m2 (see chapter 1). Therefore, results suggest
that adult control methods can be effective at trying to ensure low recruitment of sea
lamprey populations if managers reduce spawner abundance to this value or below.
However, we currently have very little information on the costs of adult control methods,
and whether annual application of adult control methods on some streams could be cost-
effective, or more effective at reducing the long-term adult sea lamprey population than
lampricide use on some streams. Using a hybrid strategy in which lampricides are still
used but at a substantially lower frequency on streams where adult control is applied, has
been suggested as the majority of lampricide treatment expenditures each year are
directed to a small number of large rivers (Brege 2003). Considerable savings may be
achieved by directing adult control efforts at these rivers, but there are still many
unanswered questions about the costs and efficacy of adult control.

The effectiveness of lampricide control depends on selecting the streams for
treatment that will kill the most parasitic juveniles (transformers) per dollar spent. Since
1995 the GLFC has used a model, the Empiric Stream Treatment Ranking (ESTR)
program (Christie et al. 2003), to rank stream reaches each year for lampricide treatment
by using data from larval assessments to make short-term projections of the abundance of
parasitic juveniles in each stream reach. This model fails to address the signiﬁcant
variability and uncertainty inherent in the stream ranking process (Hansen et al. 2003),

uncertainty that is introduced through both measurement error (i.e., inaccurate estimates

69

of larval habitat and abundance), and process error (i.e. inaccuracies in parameter
estimates for growth rates and probability of metamorphosis) (Steeves 2002, Treble
2006). Consequently, there is concern about the accuracy of the estimates of abundance
that it produces and thus the choice of streams for lampricide treatment (Steeves 2002).

To evaluate control strategies in the Great Lakes the GLF C has used models of
sea lamprey population dynamics (Greig et al. 1992). Models are valuable tools for
ﬁsheries management but can misinform managers if they fail to account properly for
process error, measurement error, and model uncertainty (Schnute and Richards 2001).
For example, in the past, models used by the GLFC have not included density-
independent recruitment variation (e. g. Koonce et al. 1993), a form of process error,
when modeling sea lamprey population dynamics. Deterministic sea lamprey
management models that do not explicitly incorporate density-independent recruitment
variation will substantially overestimate the beneﬁts of adult sea lamprey control options
that rely on reducing adult reproductive success (Jones et al. 2003). A more realistic sea
lamprey population model that accounts for recruitment variation and assessment
uncertainty, and allows for the evaluation of a range of sea lamprey control strategies is
what is needed to estimate the cost and effort at which adult control becomes a viable
complement or alternative to lampricide control.

The objectives of this chapter were; (1) to develop a realistic model of sea
lamprey population dynamics for a Great Lake (Lake Michigan) that allowed simulation
of both lampricide and adult control; (2) to use this model to assess the relative
performance of management strategies that differed in the allocation of control resources

between lampricide control, which targets ammocoetes, and adult controls, which target

70

adult sea lampreys; and (3) to determine the sensitivity of the results from objective 2 to
alternative assumptions about adult control costs and the proportion of spawner reduction

achieved by adult control.

Methods
Description of the model

A stochastic age-structured population model was used to forecast equilibrium
parasitic sea lamprey abundance for Lake Michigan. The current model was derived
from the whole-life cycle model previously described in Jones et al. (2003). The model
is organized into several sub-model areas each described below, with deﬁnitions for all
parameters provided in Tables 1 and 2. The complete set of sea lamprey-producing
streams for Lake Michigan was explicitly represented in this model, following the data
structure used in the ESTR database (Gavin Christie, Great Lakes Fishery Commission,
Ann Arbor, MI, personal communication), which divides large streams into reaches for
which independent lampricide treatment decisions can be made. Overall, the model is
designed to forecast and compare the effect of different control strategies on the future

abundance of parasitic sea lampreys in Lake Michigan.

Larval habitat

Each stream reach was characterized by its length, average width, and the area of
two types of habitat suitable for larval sea lamprey production, all determined from
habitat surveys. The total amount of larval habitat was then calculated from reach area

and suitable habitat coverage

71

Aizvi-wi-(pli+p2i-r’) (1).
Type I habitat was deﬁned as areas of ﬁne sand and silt and is preferred by larval
lampreys, while Type II habitat was deﬁned as areas of coarser sand that is acceptable for
larval lampreys. Type II habitat was weighted less heavily than Type I habitats based on

observed differences in sea lamprey density in these two habitat types (Slade et al. 2003).

Sea lamprey life cycle Simulation

Adult sea lamprey do not home to natal streams (Bergstedt and Seelye 1995),
therefore spawning sea lampreys were allocated to stream reaches for spawning based on
two rules: (1) the area of larval habitat in each reach, as streams with the greatest
discharge have been found to accommodate the largest number of spawning-phase sea
lampreys if other environmental factors are favorable (Mullett et al. 2003, Morman et al.
1980) and (2) the abundance of larvae in each reach, as lamprey have been shown to be
attracted to a migratory pheromone released by stream-dwelling ammocoetes (Sorensen
and Vrieze 2003). In all of the simulations used in this analysis, the two rules were given
equal weight, and spawning sea lampreys were assumed to be positively related to both

available larval habitat and larval abundance

A, L,
SIZSA'i—Z'l'SP ——le (2).

Spawners were divided into those that migrate based on the area of larval habitat
S A = NA ' pA (3):
and those that migrate based on the abundance of larvae in each reach

5,. = NA — s, (4).

72

The estimate of larval habitat area combined with the density of spawning female
sea lamprey was used to calculate recruitment of age-1 larvae following a stochastic

Ricker stock-recruitment function

(S.,,-p/> .
— . +8

1'

Lu; 261' S"; ”1709 Al (5).

The parameters for this relationship were estimated using data from 90 stream-years of
sea lamprey stock-recruitment data (see chapter 1). We found empirical evidence of
differences in this relationship for streams categorized a priori by sea lamprey control
agents as regular (reg) or irregular (irr) sea lamprey producers (see chapter 1) and thus,
used different a and ,8 parameters for the two groups of streams (Table 1). Regular
producers are streams subjected to a reliable cycle of lampricide treatments (i.e., they
have been treated every 3, 4, or 5 years, depending on the stream). Irregular producers
are subjected to a less consistent cycle of treatment. We also assumed that density—
independent recruitment variation among streams was not correlated over time (no
common “year effects”) based on our empirical analysis (see chapter 1). The empirical
model related spawner numbers to age-l abundance, so the number of age-O sea lamprey
from age-1 abundance was back-cast using an annual survival rate assumed constant

among ages and stream reaches

 

L _ Ll,l,l
i,0,t _ (6),
S L
The model was age-structured and growth of larval sea lamprey was calculated as
lug =a-s€,-aa’g,+€0 (7).

73

Season length and average daily growth estimates for each stream reach were obtained
from the ESTR database. In addition, each cohort of larval sea lamprey was subdivided
into a set of nine length bins, with the proportion of the cohort in each length bin

characterized by a normal distribution with a ﬁxed mean and coefﬁcient of variation
6 i,a,b : 61,0 (1 + CV6 . db) (8)

This change from the Jones et al. (2003) model was made to enable application of a
length-dependent logistic model of metamorphosis, as is used in the ESTR system for
forecasting future production of metamorphosing sea lampreys. The probability of
metamorphosis depends on the length of the sea lamprey at the end of the previous year.

The proportion of larvae from a given length bin to transform was calculated as

(ﬂ +ﬂ we )
t e 0 l b

p, = (1 + etﬂowrewl) (9).

 

The number of transformers estimated by the model in each reach was then calculated by

6 9
T.- =Z(L,-..-p”°Zp;) (10).
0:1 1):]

Application of sea lamprey control

A method analogous to the stream selection procedure utilized in the sea lamprey
control program (Christie et al. 2003) was used to determine which stream reaches to
treat in any given year of the simulation. Each year, stream reaches were ranked

according to the number of transformers that would be removed from next year’s

74

parasitic population, per dollar of treatment cost. Stream reaches with large populations
of large ammocoetes (i.e., those likely to metamorphose into parasites within a year) and
modest treatment costs were ranked highest (Jones et al. 2003). If a reach was selected
for TFM treatment, the entire larval population in that reach was reduced based on a

reach-speciﬁc survival from chemical treatment
Lu 2 Li,t—I 'Sc (11)-

Each year, reaches were treated in rank order, from highest to lowest, until the budget
apportioned to lampricide control was utilized.

The number of parasites that enter the lake each year was calculated from the
number of transformers last year that survived treatment in treated streams and the total
number of transformers present in untreated streams

M N
P: :(ZTu—I 'Sc; + ZTj.t—I)’Sr (12).
i=1 1' =M +1
The total number of spawners predicted in the lake next year is the number of parasites

surviving the parasitic phase this year

NA =P-s. (13).

HI I j

The model included an additional source of parasitic sea lampreys, called the
“untreatable pool” which was intended to represent production of sea lampreys from
sources that are not presently vulnerable to lampricide control (e. g., lentic areas).
Population dynamics (reproduction, larval grth and survival, etc.) in the untreatable
pool followed the same rules as for the treatable stream reaches, as did the allocation of

spawning sea lamprey to this compartment. The size (larval habitat area) of the

75

untreatable pool was deﬁned as a proportion of the overall area of larval habitat in the
entire lake (10% was used in the current simulations).

Adult control was simulated by reducing the population of effective spawning
females by a ﬁxed percentage, relative to the predicted size of the spawning run in stream

reaches

Mame/7;. = (St, r9f )(1- s.) (14).

To be effective, controls directed at reducing sea lamprey spawning success would have
to be applied annually because, unlike a lampricide treatment that affects all year classes
of ammocoetes present in a reach at the time of treatment, an adult control action only
affects a single year class (Jones et al. 2003).

Chemical control was applied over the entire infested length of a stream reach if a

stream reach was selected for treatment (e. g., total stream area)
AS, =V1'W; (15).
For this reason, chemical control costs for the model were assumed to be a function of

total stream reach area
Cci : ci +uci °ASi (16)-
Chemical control costs were obtained from recent data on lampricide costs for each

stream reach. Linear regressions were performed on lampricide costs (C a. ) vs. total

stream reach area (AS,)to obtain values for ﬁxed cost ( f C,- ) and unit cost (“a ) per unit of

stream reach area using Statistica 7.0 (StatSoft, Inc. 2004).

76

Adult control reduces the effective spawning population and attempts to reduce
the total number of larvae produced by a stream reach; therefore adult control costs were

assumed to be a function of larval habitat

Cai :fai +uai .At' (17)
Adult control costs were obtained from recent data on barrier costs (average annual cost

over 50 years) for a subsample of Lake Michigan streams. A linear regression was

performed on barrier costs (C0,) vs. larval habitat (A, ) to obtain values for ﬁxed

cost ( f a,- ) and unit cost (um) per unit of larval habitat area using Statistica 7.0 (StatSoft,

Inc. 2004).

Inclusion of uncertainty
Recruitment variation was added to the model using the a" term in the stock-

recruitment equation (equation 9), based on the observed residual variation in ln(R/S)
from my empirical analysis (see chapter 1).

For lampricide control, uncertainty in the stream reach selection process was
simulated by adding an error term to the actual abundance of sea lamprey expected to

transform and become parasites in the following year in each reach

Tobsl. =TI. +8? (18).

8; ~ F(O,ch)

The error was drawn independently for each stream reach from a gamma distribution

with a CV of 1.71 , which was derived from an analysis of uncertainty in the larval

77

assessment procedures currently used to rank reaches (Steeves 2002). This mimicked the
uncertainty in the larval assessment process that is used to rank reaches for TFM
treatment.

Model calibration and simulations

The model was calibrated using recent observations of adult sea lamprey
abundance and recent control expenditures, and by assuming that the adult sea lamprey
population in Lake Michigan is roughly in equilibrium with recent control expenditures.
The size of the untreatable pool was set to give plausible sea lamprey abundances at very
high control expenditures. Then, I adjusted the survival rate of larval sea lampreys (the
model was sensitive to this value and the true value is unknown) until the median
forecasted adult sea lamprey abundance for long-term (100 year) simulations using a
budget corresponding to recent control expenditures reasonably matched observed adult
abundance for recent years.

All model simulations were run for 100 years to allow sea lamprey spawner
abundance to reach an equilibrium state prior to the ﬁnal years of the simulation when
model estimates were evaluated. Each simulation was repeated 100 times to capture
uncertainty due to density-independent recruitment variation and assessment error. The
same sequence of random numbers was applied to each set of simulations, so that the
differences among sets of simulations were not inﬂuenced by random variations among
sets. For each set of simulations the median number of resulting spawners for each year
over 100 simulations was recorded. The ﬁnal outcome indicator was then the average of

the median number of spawners for the ﬁnal ten years of the simulation. Additionally, I

78

recorded the number of times each of the ten largest streams were treated with lampricide
in the 100-year cycle.

I assessed the performance of control strategies by varying the allocations of an
overall control budget between lampricide and adult control. Management scenarios
using only lampricide, only adult control, and a combination of both control methods
were explored. Total cost of integrated sea lamprey management was the combined cost
of chemical and adult control, not to exceed the current (2006) sea lamprey control
budget for Lake Michigan which was $2.06 million dollars.

Initially, I considered an adult control strategy in which an 88% effective
reduction of spawners was achieved, comparable to the adult control success achieved
recently in the St. Mary’s River (Gavin Christie, Great Lakes Fishery Commission, Ann
Arbor, Michigan, personal communication). To simulate increasing levels of adult
control, I added streams (consisting of all the stream’s reaches) to the adult control
program by starting with the largest (i.e., most expensive) stream ﬁrst, and reducing the
funds available for lampricide control by the costs of applying adult control to that
stream. With an overall control budget of $2.06 million and adult control costs of
$3 9500+ $0.06 - larval habitat area, applying adult control to the Muskegon River (largest
stream in the Lake Michigan watershed, 2.67 million m2 of larval habitat) reduces the
budget available for lampricide control to $1.86 million ($2.06 million - $199,545 for
Muskegon River adult control). Then I added the second largest stream and further
reduced the lampricide budget accordingly. Adding a second stream (Manistique, 2.23

million m2) further reduces the lampricide budget to $1.69 million.

79

My rationale for selecting the largest streams ﬁrst was that these are the most
expensive streams to treat with lampricide. If treatment frequency can be reduced on
these streams the lampricide control costs may be much lower to achieve the same lake-
wide level of chemical control. I continued this progressive addition of large streams to
the adult control program for up to ten streams, and costs of adult control were increased
according to the total larval habitat area affected.

I assessed the sensitivity of the performance of different adult control budgets to
two key variables. First, I varied the percent reduction in spawners achieved in each
stream by adult control. I successively increased the percent reduction of spawners by
2% from the initial value of 88% until reaching a point at which some adult control did
better than lampricide control. Second, I varied the unit cost of adult control per m2 of
larval habitat. I successively decreased the unit cost of adult control by $0.01 from the
initial value of $0.06 until I reached the point at which some adult control did better than
lampricide control. Finally, I combined assumptions of reduced costs of adult control
with a simultaneous increase in the percentage of spawners reduced, as described above,
to ﬁnd a point at which at least some adult control was equally effective as lampricide
control alone in reducing spawning lamprey populations. I evaluated the performance of
different strategies by comparing the long-term reductions of spawners achieved in the
lake, and by comparing the number of times the ten largest streams were treated with
lampricide.

To determine how sensitive the outcomes are to the stock-recruitment parameters,
I evaluated the model results when applying adult control to a set of regular sea-lamprey

producing streams compared to applying adult control to a set of irregular sea-lamprey

80

producing streams of similar total area (and total cost of adult control). I looked for
evidence to support the claim that regular sea lamprey-producing streams are less
susceptible to adult control because they require greater reductions in spawner numbers,
on average, to achieve target recruitment levels (see chapter 1). I evaluated whether four
sets of regular sea lamprey-producing streams of similar total size and total cost to
irregular sea lamprey-producing streams produced noticeably more spawners on average
when adult control was applied in long-term simulations, and determined the frequency

of lampricide applications in the ten largest streams.

Results

Visual inspection of the relationship between lampricide costs and stream reach
area (Figure 1) suggested a different relationship for small and large streams, with unit
costs increasing much more rapidly with area for smaller streams. Accordingly I divided
the data into two groups of streams and ﬁt separate regressions to each group (Figure 1,
Table 2). After trying a range of cut-offs between small and large reaches, the best-ﬁt
regression lines occurred when small reaches (sm) were regarded as having a stream area
of less than 400,000 m2, with large reaches (lg) having a larger stream area. The best-ﬁt
line that described the ﬁxed and unit costs of adult control based on larval habitat area,
was the same for all stream reaches (Figure 2, Table 2). The ﬁt of the adult control cost
data to a regression line was poor (Adjusted R2= 0.56). The ﬁt of the lampricide control
data to a regression line for small streams was good (Adjusted R2=0.82), while the ﬁt for

large streams was poor (Adjusted R2: 0.56) (Figures 1 and 2).

81

At the initial costs of adult control of $39500 + $0.06 - larval habitat, and an 88%
spawner reduction, at no point did adult control perform better than lampricide control
(Figure 3a). In fact, unit costs of adult control at this level of spawner reduction would
have to be reduced to $0.01 per m2 of larval habitat to perform better than lampricide
control (Figure 3b). In this case, if we treat the largest stream with adult control ﬁrst, at a
cost of $39500 + $0.01 - larval habitat, and use the rest of the budget for lampricide
control, the median number of spawners in the lake can be reduced compared with using
only lampricide control (Figure 3b).

Employing the costs of adult control of $39500 + $0.06 - larval habitat, the %
reduction of spawners by adult control must be increased from 88% (Figure 4a) to 100%
to do better than only using only lampricide control (Figure 4b). Under this scenario, I
observed that by treating at least two of the largest streams with adult control, adult
control does better or is almost equally as effective as only lampricide control in reducing
the long-term number of spawners in the lake (Figure 4b).

By simultaneously increasing the % spawners reduced initially by adult control
and decreasing the initial unit cost of adult control I found a few hybrid scenarios (using
both adult and lampricide control) that perform better than using only lampricide control
(Figure 5). By decreasing the unit cost of adult control by half (to $0.03) and increasing
the spawner reduction to 94%, which was achieved in the St. Mary’s River in 2002, we
can do better than using only lampricide control by treating two or six of the largest
streams with adult control (Figure 5a). By increasing the spawner reduction to 96% and
at a unit cost of $0.04, we can treat the three largest streams with adult control and reduce

the long-term number of spawners compared to using only lampricide control (Figure

82

5b). As the proportion of spawners reduced in each stream reach by adult control is
increased, the frequency of lampricide treatments needed in the targeted stream reaches is
reduced (Table 3).

When applying adult control to only regular sea-lamprey producing streams
compared with applying adult control to only irregular sea-lamprey producing streams of
similar total area and cost, results indicated that the number of spawners produced in
long-term simulations was very similar between the stream types (Table 4). When adult
control was applied to irregular streams the frequency of lampricide treatments on the

seven largest regular sea lamprey-producing streams was higher in all cases (Table 4).

Discussion

Comparing the true effectiveness of adult controls to lampricide control requires
the incorporation of density-independent recruitment variation and larval assessment
uncertainty estimates, and is dependent on model parameters such as cost and
effectiveness of adult control. Using my best estimates of adult control costs and the
efﬁcacy that can be achieved by adult control, results suggest that increasing adult control
efforts at the expense of lampricide use will result in an increased abundance of sea
lamprey. Results suggest that it would be unrealistic for adult control to compare
favorably to lampricide control by either just reducing costs of adult control or just
increasing the proportion of effective spawners that can be reduced by adult control. To
compare favorably to lampricide control, adult controls costs must be minimized and the
proportion of effective spawners that can be reduced by adult control must be increased.

If this can be achieved, the treatment of a few large streams with adult control was

83

observed to be an option for a successful hybrid strategy. in which lampricides are still
used but at a substantially lower frequency on streams where adult control is applied
(Table 3). Adult control on the two largest streams. assuming we can achieve a cost of
$39500 + 0.04 per m2 of larval habitat costs $0.275 million. while lampricide treatments
currently cost over ﬁve times as much. Considerable savings may be achieved by
directing adult control efforts at these streams. provided increased etliciency and reduced

costs of adult control.

Sea lamprey pheromones hold considerable promise as a tool to enhance trapping
efﬁciency (Wagner et al. 2006, Johnson et al. 2006), which suggests that the spawner
reduction targets implied by these model results may be achievable. lfchemica]
attractants could be inexpensively synthesized, then the proportion ofeﬁ‘ective spawners
reduced by adult control could be increased at a reasonable cost (Li et al. 2003). The
initial 88% effective reduction of spawners used in the model was based on adult control
success achieved recently through trapping and sterile male release in the St. Mary‘s
River, with recent reductions recorded at up to 94%. Trapping efﬁciency on Lake
Michigan streams in 2005 ranged from 11-85% with an average trapping efficiency of
41%, on streams with no releases of sterile males. Besides the option of substantially
increasing trapping efﬁciency through the use of pheromones in these streams, effective
spawner reduction can still be achieved through other uses of pheromones. Recent
modeling research found that rapid suppression of sea lamprey populations could be
achieved by the combined application of the current level of trapping in the Great Lakes

and release of pheromone-enhanced sterile males (Klassen et al. 2005).

84

 

When adult control was applied to only regular sea lamprey-producing streams
and only irregular sea lamprey-producing streams of similar total size and total cost.
similar numbers of spawners were produced in all cases. The Ricker alpha parameter.
which describes average survival when spawner abundance is close to zero, of regular sea
lamprey-producing streams is three times higher than that of irregular sea lamprey-
producing streams (Table l-log scale). Therefore, a regular sea lamprey-producing
stream produces more recruits than an irregular sea lamprey-producing stream from the
same size spawning population. This suggests that sea lamprey populations in irregular
streams would be more vulnerable to all control measures, as the ability of the population
to replace itself is reduced compared with regular streams. Results between adult control
on regular and irregular sets of streams may be similar because treating irregular sea
lamprey-producing streams with adult control could be very effective, but lampricide
treatments must then be focused on productive streams (regular) less susceptible to
lampricide control (Table 4), and thus the model estimates similar numbers of sea
lampreys produced as in the regular stream sets. Treating regular sets of streams with
adult control should be less effective, but lampricide treatments are applied, in this case at
a more equal proportion on regular and irregular sea lamprey-producing streams, and
since irregular streams are more susceptible to control measures the model estimates
similar numbers of sea lampreys as produced in the irregular stream sets (Table 4). We
do no better by applying adult control to those streams more susceptible to control efforts
(irregular streams), due to the trade-off of applying lampricide control to streams less

susceptible to control efforts (regular streams).

85

This model mimicked the sea lamprey control program for Lake Michigan and
compared sea lamprey control strategies on the basis of cost in dollars and the long-term
number of spawners produced. In this model, uncertainty in sea lamprey assessment
procedures was characterized, and meta-analytic techniques were used to gather stock-
recruitrnent data used in the life cycle simulation in an attempt to reduce the biological
basis of uncertainty (Myers and Mertz 1998) and make the model more realistic. This
model has, and should continue to be improved through input from sea lamprey
managers, and can help in guiding sea lamprey managers in an integrated pest
management program. But, ideally these results could provide the basis for the
delineation of management experiments for individual streams (Jones et al. 2003) or for
Lake Michigan as a whole. Experimenting with sea lamprey control strategies within an
adaptive management framework on one of the ﬁve Great Lakes would provide greater

understanding and the ultimate test of management strategies.

86

Table 1. Parameters, their assumed values, and state variables used in the sea lamprey
population model.

 

 

 

 

ﬁmbol Deﬁnition Assumed value
i Reach
a Age
1; Length bin(9) to hold each cohort of
larval sea lamprey
t Year
Habitat
AS, Stream area varies by reach
A,- Larval habitat area varies by reach
v,- sea lamprey infested length of stream varies by reach
w,- mean width of stream varies by reach
p1,. proportion of type I larval habitat varies by reach
(preferred)
p 2 r proportion of type II larval habitat varies by reach
(acceptable)
r, index of type 2 habitat suitability, 0.38
relative to type 1
Sea lamprey life cycle simulation
NA, Number of spawners in lake State variable
S L, Spawning sea lamprey abundance State variable
P, Number of parasites in lake State variable, initially 100,000
Tm, Transformer abundance State variable
Lm, Larval sea lamprey (ammocoete) State variable
abundance
a0 initial age-0 larval density 1 per m2
m a Age-speciﬁc probability of 0(2),.2(3),.4(4).7(5),1.(6)
metamorphosis
PA proportion of spawners allocated by 0.5
area
S p spawners to be allocated by area 50% of spawners in lake
SA spawners to be allocated by 50% of spawners in lake
pheromone
a Ricker model parameter reg=4.815, irr=3.754
B Ricker model parameter reg=0.1616, irr=0.1473
5L annual survival during ammocoete 0.395

phase

87

Table 1(continued).

 

Sm
51‘
p”
pl
Bo
13]

survival during transformation phase
survival during parasitic (juvenile)
phase

proportion of females

proportion of larvae transforming into
parasites

upper lakes logistic transformation
curve parameter

upper lakes logistic transformation
curve parameter

0.75
0.75

0.5
varies

0.1343101

-19.22319

 

 

age

88

Growth
Cm larval length varies by reach and age
SE,- season length varies by reach
adg, average daily growth varies by reach
Co initial length in millimeters 20
db "distance" of length bin b from mean varies by bin
length
pb probability of being in a length bin ~(-04(1),-07(2),-12(3),-17(4),-20(5),
Uncertainty terms - 1 7(6),.12(7),.07(8),.04(9))
g". variance of process error in larval reg=2.99, irr=3.24
recruitment to age-1
8T error on transformer abundance ~ ”0,1 -71)
ch coefﬁcient of variation of transformer 1.71
abundance
CVt coefﬁcient of variation of length at 0.33

Table 2. Parameters, their assumed values, and state variables used in applying sea

lamprey control.

 

 

Symbol Deﬁnition Assumed value
Cc,- Cost of chemical control (dollars) State variable
Ca,- Cost of adult control (dollars) State variable
fci ﬁxed cost of chemical control (dollars) sm=8000,1g=60000
uci Unit cost of chemical control (dollars) sm=0.52,1g=0.12
fa,- ﬁxed cost of adult control (dollars) Initial=39500
uai Unit cost of adult control (dollars) Initial=0.06
Sc survival from chemical treatment varies by reach(<0. 1)
Sr reduction of effective female spawners by adult Initial=0.88

control
Momsem, Effective number of female spawners varies

Table 3. Comparison of the number of times the ten largest streams were treated with
lampricide under only lampricide control and when using different levels of adult

 

 

control.
Adult Adult Adult
control control control
88% 94% 96%
spawner spawner spawner
Lampricide reduction reduction reduction
control $0.04 unit $0.04 unit $0.04 unit
only cost cost cost
Times Times Times Times
Larval treated treated treated treated
habitat / 100 year / 100 year / 100 year / 100 year
River Name area (m2) cycle cycle cycle cycle
Muskegon 2,667,426 22.45 6.37 4.01 3.03
Manistique 2,231,677 18.65 4.10 2.95 2.24
Pere Marquette 1,791,364 28.06 13.85 12.22 11.67
Big Manistee 1,600,131 26.6 14.66 13.31 12.8
St. Joseph 1,099,377 21.93 9.42 7.96 6.98
White 959,531 32.66 17.40 16.68 15.41
Ford 697,880 17.16 4.78 3.37 2.21
Cedar 579,338 24.52 10.91 9.77 8.62
Kalamazoo 527,311 24.60 11.17 9.74 8.6
Whiteﬁsh 435,059 23.94 11.26 9.40 8.51

89

Table 4. Detailed data on the comparison of treating four similar sets of regular sea

lamprey-producing streams and irregular sea lamprey-producing streams with adult
control.

 

 

 

 

 

Number of
Area of Spawners Number of lampricide
larval produced lampricide treatments on
habitat to Cost of when sea treatments on the three
which adult applying lamprey the seven largest
control was adult control largest regular irregular
Streams applied control was streams in a streams in a
set (m2) (dollars) applied 100-year cycle 100-year cycle
Regular
1 4,067,901 402,074 190,191 130.9 58.1
2 3,826,555 348,093 206,619 132.3 57.9
3 3,330,234 318,314 194,683 132.7 59.3
Imular
1 4,041,065 400,464 215,946 155.7 33 .6
2 3,858,367 350,002 215,946 155.7 33.6
3 3,331,055 278,863 191,454 159.9 44.1

90

955

/ O
; /
8E5 ’
O /

’ z
3 7E5_ /
e : ,
o 6E5’ / 0
g _ /
§ 555_ /

/

(D , O o
‘U
Q 4E5 O /
E
m 3E5’
._l

2E5

 

155 ’

 

 

Stream reach area

Figure 1. The regression of lampricide cost data for all streams in the model against the
total stream reach area. The resulting line equations provide the cost structure inputted
into the model of Total cost=ﬁxed cost + unit cost - stream reach area. The ﬁxed cost
used in the model was adjusted to be slightly below the lowest lampricide control cost.
Small stream reaches (<400,000m2), illustrated by closed circles and the solid line, were
found to follow a different linear relationship than large stream reaches (>400,000m2),
illustrated by open circles and the dashed line. The resulting line equations were 8000 +
0.52 - stream reach area and 60000 + 0.12 - stream reach area for small and large streams,
respectively.

91

1.2E5

 

 

O
155-
t’.’
«.6
"a
3 80000
a
0)
O
2
g 60000-
C
O
0
E
-~ 40000
E
£3
<
20000 +0
0

 

0 2E5 4E5 6E5 8E5 1E6 1.2E6 1.4E6 1.6E6

Larval habitat area (m2)

Figure 2. The regression of adult cost data for a subsample of streams in the model
against the total larval habitat area. The resulting line equation provides the cost structure
inputted into the model of total cost=ﬁxed cost + unit cost - larval habitat area. The
resulting line equation, illustrated by the solid line, was 39500 + 0.06 ' larval habitat area.

92

Median Spawners (Thousands)

Median Spawners (Thousands)

 

 

 

 

 

 

400 —
10
. O
350 E 9
5 o
300 - 0 Z
4 5
250 ~ ' ' a
1 2 3
200 - . ‘ '
150 [
100 1 r + 1 r 1 1
0 200 400 600 800 1000 1200
Cumulative Cost (Thousands)
400 -
350 ~
300 -
250 - b
8 10
200 - 3 4 6 7 ' 2 .
. 5 o o
150 -—°-'-' '
100 ‘ ‘ ‘ ' ' ‘
0 200 400 600 800 1000 1200
Cumulative Cost (Thousands)

Figure 3. The median number of spawners produced versus the cumulative cost of adult
control when using adult control costs and spawner reductions achieved by adult control
of a) $39500 + $0.06 - larval habitat area and 88%; and b) $39500 + $0.01 - larval habitat
area and 88%. The horizontal line in each graph represents the median number of
spawners resulting from the application of only lampricide control. The number next to
each point represents the number of streams treated by adult control; one to ten of the
largest streams received adult control, added in order of decreasing size.

93

 

 

 

 

 

 

’u? 400 -
'2 10
g 350- 8 9 '
.2 5 . o
l" 300 ' o 7
T; 4 5 '
L. C
E 250- ° 3
2 3
£1 200 - l ' '
5
'6 150-
CD
2
100 ‘ ‘ L . 1 .
0 200 400 600 800 1000 1200
Cumulative Cost (Thousands)
’6? 400 r
'O L
c .
a 350L
8 :
E 300 L
9
2 250- b
3
g :
a, 200r 6 7
c: 1 2 5 8
$3150- - = 3 3="*3‘.°
0 . O
E
100 ‘ ' ‘ ‘ ' e
0 200 400 600 800 1000 1200
Cumulative Cost (Thousands)

Figure 4. The median number of spawners produced versus the cumulative cost of adult
control when using adult control costs and spawner reductions achieved by adult control
of a) $39500 + $0.06 - larval habitat area and 88%; and b) $39500 + $0.06 ' larval habitat
area and 100%. The horizontal line represents the median number of spawners resulting
from the application of only lampricide control. The number next to each point
represents the number of streams treated by adult control; one to ten of the largest
streams received adult control, added in order of decreasing size.

94

 

 

 

 

 

 

 

 

g 400 -
C
g 350-
O
.C t
L“, 300 r
9
“g 250 r
a
$200,» 1 345 78210
s E - 2 . ' 6 ' ’ '
._ . C
E 150:
100 . . 1 . . .
0 200 400 600 800 1000 1200
Cumulative Cost (Thousands)
g 400
C
g 350.-
0 .
C .
L‘, 300 -
<3 .
“g 250 E b
as :
.3200.- 2 3 4 3:?310
g i 1 o . 0 i ‘
=5 150: ' '
m .
2 100’ - - e . - . . -
O 200 400 600 800 1000 1200
Cumulative Cost (Thousands)

Figure 5. The median number of spawners produced versus the cumulative cost of adult
control when using adult control costs and spawner reductions achieved by adult control
of a) $39500 + $0.03 - larval habitat area and 94%; and b) $39500 + $0.04 ' larval habitat
area and 96%. The horizontal line in each graph represents the median number of
spawners resulting from the application of only lampricide control. The number next to
each point represents the number of streams treated by adult control; one to ten of the
largest streams received adult control, added in order of decreasing size.

95

MANAGEMENT RECOMMENDATIONS

Observed sea lamprey stock-recruitment data for 90 stream-years (chapter 1)
suggests to management a proposed adult (alternative) control target of 0.2 females- 100
m'2 of larval habitat in streams is required to reasonably ensure success of adult control
strategies. Recruitment variation occurs at all spawner abundances, however, so there is
no “ideal” reference point, but no high recruitment events were seen below 0.2
females- 100 m'z, so this serves as a reasonable target. If this adult control target is to be
achieved by trapping spawning-run sea lampreys then trapping efﬁciency must
signiﬁcantly increase from current levels across the basin. Since sea lamprey
pheromones have been shown to effectively attract and capture sea lampreys in traps,
thereby increasing trapping efﬁciency in ﬁeld trials, pheromone strategies should be
integrated into existing management techniques provided this can be done at a reasonable
cost

Using the simulation model research (chapter 3) as a guide, the best test of
management strategies would be provided by designing management experiments and
dovetailing this research with the design of the pheromone ﬁeld trials to get at critical
uncertainties concerning current adult control methods and adult control using
pheromones. The simulation model results highlight that comparisons of different
management strategies using combinations of lampricide and adult control depend
critically on developing better estimates of the costs of adult control, and of determining
the achievable levels of efﬁcacy for adult control strategies. Management experiments

and the pheromone ﬁeld trials could be designed to answer questions from this

96

 

dissertation, such as the magnitude of spawner reductions that could be achieved with
existing adult control and pheromone-enhanced trapping, the level of age-1 recruitment
that would be cost-effective to achieve with existing adult control and pheromone-
enhanced trapping, and the true costs of adult control with and without pheromones.

To answer these questions adult control managers on a stream would characterize and
estimate the sea lamprey spawning run, trapping efﬁciency, larval habitat area controlled
(i.e., area upstream of barrier or trap), recruitment-at-age-l the following fall, and costs
required to implement adult control. Many of these metrics are measured yearly by sea
lamprey managers, so coordinating the estimate of all these measures in experimental
streams should be feasible and contribute signiﬁcantly to improving adult sea lamprey
control.

The simulation model suggested we did no better by applying adult control to
streams more susceptible to control efforts (lower survival of recruits), due to the trade-
off of having to apply more lampricide control to streams less susceptible to control
efforts; thus management experiments should focus adult control on the largest streams in
the basin where lampricide costs are high and adult control may help reduce the
frequency of treatments in these large steams and most likely reduce the amount of
lampricide used basin-wide. Again, this presumes that the cost-effectiveness of adult
control will be greater on these large streams due to economies of scale (i.e., ﬁxed costs
will not increase in proportion to stream size).

The objective, likelihood-based statistical model to estimate proportion-at-age
(chapter 2) should be used by managers, as it is an improvement over subjectively

assigning age-classes based on length-frequency data. Including information on the

97

"—-

growth dynamics of populations by aging a subsample of animals using statoliths will
further improve assessments. Accurate age-assessment is important to measure
inﬂuential life history characteristics such as recruitment, growth rate, and mortality rate
to improve our estimates of the productivity of sea lamprey populations and improve sea
lamprey control, so the standard protocol outlined in chapter 2 should be implemented in
the sea lamprey management program.

A fair comparison of control options should also consider the relative
environmental costs of the control options as well as their beneﬁts (McLaughlin et al.
2003). Social, environmental, and non-target costs and beneﬁts should be a consideration
when comparing sea lamprey control strategies, and not just costs and beneﬁts in dollars.
Pressure to use alternatives to lampricide control has increased due to public concern
about pesticide use and rising costs of lampricides, however costs of adults control
measures such as non-target effects of barriers and possible transmission of aquatic
pathogens resulting from conducting the sterile-male-release technique should also be

considered when comparing sea lamprey control strategies.

98

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