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This is to certify that the

dissertation entitled
Role of Compensatory Mechanism in the Population
Dynamics of Lake Trout (Salvelinus nanaycush)
in the 0.3. Waters of Lake Superior

 

presented by

Cecilia Paola Ferrari

has been accepted towards fulfillment
of the requirements for

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ROLE OF COMPENSATORY MECHANISMS IN THE POPULATION
DYNAMICS OF LAKE TROUT (SALVELINUS NAMA YCUSH)
IN THE US. WATERS OF LAKE SUPERIOR
By

Cecilia Paola Ferreri

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

1995

ABSTRACT
ROLE OF COMPENSATORY MECHANISMS IN THE POPULATION
DYNAMICS OF LAKE TROUT (SALVELINUS NAMA YCUSH)
IN THE US. WATERS OF LAKE SUPERIOR
By

Cecilia Paola Ferreri

Lake trout (Salvelinus namaycush) populations in Lake Superior have exhibited
differing levels of abundance through time and thereby provide an opportunity in which
to study the effects of compensation on population regulation. I explored the role of
compensatory mechanisms in the population dynamics of lake trout in the Michigan and
Wisconsin waters of Lake Superior during three time periods: the pro-sea lamprey period,
prior to 1950 when lake trout were at a relatively high abundance and the fishery was the
primary source of lake trout mortality; the sea lamprey dominant period, during the 19505
and 1960s when lake trout were at a very low abundance due to sea lamprey predation
and over-exploitation; and currently, from 1985 to 1993 when wild lake trout abundance
was at a moderate level.

The role of compensatory mechanisms was evaluated using a life table approach.
Age-specific fecundity and survival schedules were incorporated into a Leslie projection
matrix to calculate the finite rate of population increase (1.). Individual growth, fecundity,
and age-0 survival rates were calculated for each lake trout population and compared
between time periods. Elasticity analyses were performed to determine the proportional

contribution of each matrix parameter to the population growth rate during the three

periods.

I found that individual growth rates, age-specific fecundity, and age-0 survival
rates changed in response to the different levels of lake trout abundance during each of
the Study periods in both Sites. Lake trout during the sea lamprey dominant period, which
experienced the lowest abundance and highest mortality levels, exhibited the fastest
individual growth rates, the highest age-specific fecundity, and the highest age-0 survival.
These high rates contributed to the relatively high production potential exhibited by lake
trout during the sea lamprey dominant period as compared to lake trout during the pro-sea
lamprey or the current periods. Survival, particularly during the pro-reproductive ages,
made a greater contribution than fecundity to the population growth rate of lake trout
during the current time period. Reducing fishing mortality, which has its greatest impact
on lake trout that are about to become mature, has a greater effect on the population

growth rate than reducing sea lamprey induced mortality by an equal percentage.

DEDICATION

In memory of my grandparents, Ruben Valencia Carillo and Marjorie Mundy de
Valencia, who through their love and by their example inspired me to strive for

excellence.

iv

ACKNOWLEDGMENTS

This publication is a result of work sponsored by the Michigan Sea Grant College
Program, project number R/GLF-37, under grant number NA89AA-D-SGO83 from the
Office of Sea Grant, National Oceanic & Atmospheric Administration (N OAA), US.
Department of Commerce, and funds from the State of Michigan. The US. Government
is authorized to produce and distribute reprints for governmental purposes
notwithstanding any copyright notation appearing hereon. Additional funding for my
doctoral studies was provided by the Michigan Agricultural Experiment Station, MSU
Minority and Women Graduate Assistantship Program, Canadian Studies Fellowship
Grant, and West Michigan Chapter Trout Unlimited.

This study would not have been possible if it were not for the hard work and
dedication of the many scientists who have worked for the National Biological Service,
the Michigan and Wisconsin Departments of Natural Resources, and the Great Lakes
Indian Fish and Wildlife Commission. I also thank these agencies for making historical
and current data regarding lake trout available to me for my dissertation research.

Needless to say, one cannot embark on a doctoral program without the support
and guidance of many talented people. I have been extremely lucky to have interacted
with people who were not only talented and dedicated, but who also were willing to
spend the time to share their insights with me. I cannot thank my major professor, Dr.
William W. Taylor, enough for all of his help, guidance, counseling, and most of all his

V

patience throughout my doctoral program. He willingly gave his time, energy, and
insights, whenever needed, to help me over the hurdles throughout my stay at Michigan
State and to create new opportunities for me to learn new things. In addition, he always
Stressed the importance of maintaining a balance between the professional and the
personal sides of life. For all of these, I am deeply grateful. One could not ask for a
better mentor!

I would also like to thank the members of my guidance committee, Dr. Tom
Coon, Dr. Don Hall, and Dr. Susan Kalisz who contributed greatly to my education at
Michigan State University, both through classroom instruction and personal consultation.

I would like to thank Mr. John M. Robertson, who was not only willing to take me
under his wing and Show me what state fisheries agencies are all about, but also freely
shared his ideas and insights regarding the science and management of fisheries. My
thanks also go to Dr. Michael J. Hansen, who gave me the opportunity to work at the
National Biological Service through a Coop-Ed program, and who shared many insights
regarding lake trout biology and graduate school. Both John and Mike were instrumental
in shaping my experience as a graduate student - I hope that our friendship will continue
to grow and prosper.

Finally, my deepest thanks goes to the people that are always there supporting us,
but who are rarely recognized - the family. To Evelyn, Kyle, and Lauren Taylor my
deepest thanks for not only inviting me into their home and lives, but also for being very
patient and understanding when I needed Dr. Taylor’s time. Finally, I am deeply grateful
to my brothers, Neil and Nicholas, and my mother, Cecilia, ‘who have always been there
to encourage me and cheer me on. They have truly been the wind beneath my wings!

vi

TABLE OF CONTENTS

LIST OF TABLES ...................................................... ix
LIST OF FIGURES ..................................................... x
INTRODUCTION ....................................................... 1
STUDY SITE AND TIME PERIODS ........................................ 7
METHODS ........................................................... 10
Leslie Matrix ...................... ' .............................. 10
Growth Comparison ............................................... 18
Population Growth Rate Comparison ................................. 19
Age-0 Survival Estimates .......................................... 23
Relative Contribution of P, and F, .................................... 23
Fishing and Sea Lamprey Induced Mortality Tradeoff .................... 24
RESULTS ............................ , ................................ 26
Mortality Comparison ............................................. 26
Growth Comparison ............................................... 29
Fecundity Comparison ............................................. 31
Population Growth Rate Comparison ................................. 33
Age-0 Survival Estimates .......................................... 37
Relative Contribution of P, and F, .................................... 41
Compensatory Scope .............................................. 44
Fishing and Sea Lamprey Induced Mortality Tradeoff .................... 48
DISCUSSION ......................................................... 54
Changes in Individual Growth ....................................... 54
Changes in Fecundity .............................................. 57
Changes in Age-0 Survival ......................................... 60
Relative Contribution of F, and P, .................................... 62
Compensatory Scope ............................................. 63
Fishing and Sea Lamprey Induced Mortality Tradeoff .................... 64

vii

MANAGEMENT IMPLICATIONS ........................................ 67

APPENDDI A: Lake Superior Lake Trout - Matrix Development ................. 70
Michigan Waters - Pro-Sea Lamprey Period ............................ 70
Michigan Waters - Sea Lamprey Dominant Period ....................... 72
Michigan Waters - Current Period .................................... 74
Wisconsin Waters - Pre-Sea Lamprey Period ........................... 75
Wisconsin Waters - Sea Lamprey Dominant Period ...................... 77
Wisconsin Waters - Current Period ................................... 78

LIST OF REFERENCES ................................................. 81

viii

Table 1.

Table 2.

Table 3.

Table 4.

Table 5.

Table 6.

Table 7.

Table 8.

LIST OF TABLES

Sources Of data used to construct the Leslie matrices for wild
lake trout populations in the Michigan and Wisconsin waters

of Lake Superior during the three study periods. ..................

Mathematical functions used to estimate age specific length,
weight, and fecundity in the Michigan and Wisconsin waters

of Lake Superior. ..........................................

Listing of parameters used to construct Leslie matrices for the
Michigan waters of Lake Superior during the three study periods.
Length is in cm, weight is in kg, P(x) is age specific survival, and

F(x) is age specific fecundity. . . .‘ .............................

Listing of parameters used to construct Leslie matrices for the
Wisconsin waters of Lake Superior during the two historical
time periods. Length is in cm, weight is in kg, P(x) is age specific

survival, and F(x) is age specific fecundity. .....................

Listing of parameters used to construct Leslie matrices in the
Wisconsin waters of Lake Superior during the current time period
for the inshore and refuge areas. Length is in cm, P(x) is age specific
survival, and F(x) is age specific fecundity; weight was not available

for this time period .........................................

Esmes of finite rate of population growth (A) of wild lake trout
in the Michigan and Wisconsin waters of Lake Superior, the bounds
of the 95% confidence interval, and the probability of getting a larger

value oft if the parameter was truly equal to 1 (Ho: i=1). ..........

Estimates of age-0 survival and of the upper and lower 95%
confidence interval bounds for wild lake trout in the Michigan and

Wisconsin waters of Lake Superior during the three time periods. . . . .

Comparison of the Observed population growth rate during each time

period and the calculated maximum possible population growth rate. .

ix

.12

.13

.15

.16

.17

.36

.38

.49

Figure 1.

Figure 2.

Figure 3.

Figrue 4.

Figure 5.

Figure 6.

Figure 7.

Figure 8.

Figure 9.

LIST OF FIGURES

Relative contribution of stocked and wild fish to the total
abundance of lake trout in the Michigan (1929-1993) and
Wisconsin (1959-1993) waters of Lake Superior. Adapted

from Hansen (1994). . . . ', ...................................

Lake Superior and the location of the study sites within the

Michigan and Wisconsin waters. ..............................

Three study periods chosen to evaluate the effects of compensation
on the population dynamics of wild lake trout in Lake Superior.
Assessment catch/effort in Michigan waters

(adapted from Hansen 1994). ...................... ' ...........

Data points used in the regression of the natural log(cpe) on year to
determine the finite rate of population growth in the Michigan waters

of Lake Superior ...........................................

Data points used to determine the finite rate of population growth

in the Wisconsin waters of Lake Superior for the three study periods .

Age specific instantaneous fishing and sea lamprey mortality
experienced by lake trout in the Michigan waters of Lake Superior

during the three study periods. ................................

Age specific instantaneous fishing and sea lamprey mortality
experienced by lake trout in the Wisconsin waters of Lake

Superior during the three study periods. ........................

Comparison of length and weight at age of lake trout in the

Michigan waters of Lake Superior during the three study periods. . . . .

Length at age of lake trout in the Michigan and Wisconsin (inshore
and refuge areas) waters of Lake Superior during the current

time period. ..............................................

..2

..8

..9

. 20

.22

.27

.28

.30

.31

Figure 10. Comparison Of weight specific fecundity of lake trout
populations during the pre-sea lamprey and current time
periods in the Michigan waters and during the current period
in the Wisconsin waters of Lake Superior. ....................... 32

Figure 11. Comparison of age specific fecundity of lake trout populations
in the Michigan and Wisconsin waters of Lake Superior during the
three study periods. ......................................... 34

Figure 12. Comparison of age specific fecundity of current lake trout
populations in the Michigan and Wisconsin (inshore and refuge
areas) waters of Lake Superior. ................................ 35

Figure 13. The 95% confidence intervals for estimates of age-0 survival in the
Michigan and Wisconsin waters of Lake Superior during the three
Study periods. Only the lower 95% confidence limit is shown for
the sea lamprey dominant period. .............................. 39

Figure 14. Projections of lake trout populations during the sea lamprey
dominant (top) and the current (bottom) periods in the Michigan
waters of Lake Superior using the age-0 survival corresponding
tothethreetimeperiods(N=100atyear l). ..................... 42

Figure 15. Projections of lake trout populations during the sea lamprey
dominant (top) and the current (bottom) periods in the Wisconsin
waters of Lake Superior using the age-0 survival corresponding
to thethreetime periods (N=100atyearl). ..................... 43

Figure 16. Elasticities (relative contribution) of age specific survival and
fecundity rates to lake trout population growth during the
pro-sea lamprey period in the Michigan and Wisconsin waters
of Lake Suprerior. .......................................... 45

Figure 17. Elasticities (relative contribution) of age specific survival and
fecundity rates to lake trout population growth during the sea
lamprey dominant period in the Michigan and Wisconsin waters
of Lake Suprerior. .......................................... 46

Figure 18. Elasticities (relative contribution) of age Specific survival and
fecundity rates to lake trout population growth during the
current time period in the Michigan and Wisconsin waters of
Lake Suprerior. ............................................. 47

Figure 19.

Figure 20.

Tradeoff between fishing and sea lamprey induced mortality
(expressed as a percent of the current value) for current lake
trout populations in the Michigan waters of Lake Superior. .......... 50

Tradeoff between fishing and sea lamprey induced mortality

(expressed as a percent of the current value) for current lake

trout populations in the inshore area of the Wisconsin waters

of Lake Superior. .......................................... 51

xii

INTRODUCTION

Lake trout (Salvelinus namaycush) in Lake Superior had an important ecological
role as a predator (Christie 1974, Ryder et al. 1981) and supported an important
commercial fishery averaging two million kg annually until 1949 (Hile et al. 1951).
Commercial yields of lake trout declined by 90% during the 19503 as a result of
overexploitation and sea lamprey (Petromyzon marinas) predation (Pycha and King
1975). Efforts to rehabilitate lake trout populations in Lake Superior began in the 19505
with stocking of hatchery reared lake trout (Lawrie and Rahrer 1973) and chemical
control of sea lampreys (Smith and Tibbles 1980). Additionally, severe harvest
restrictions were placed on the commercial fishery in 1962 in an effort to reduce lake
trout mortality (Krueger et al. 1986). Although progress toward rehabilitation of lake
trout populations has been slow, abundance of wild lake trout in the Michigan and
Wisconsin waters of Lake Superior has generally increased from 1970 to 1993 and is
currently at moderate levels (Hansen 1994). Thus, lake trout in Lake Superior have
experienced differing levels of abundance and mortality through time. Prior to 1950, lake
trout were at a relatively high abundance, during the 1950s and 19608, lake trout were at a
very low abundance due to sea lamprey predation and over—exploitation, and currently,
wild lake trout abundance is increasing toward historical levels (Figure 1). Because lake

trout populations in Lake Superior have exhibited differing levels of abundance, they

 

160
140 “ Mchiganwaters
120 —

1(1)b

 

 

 

 

 

 

 

 

 

 

e

0

g e

lllLLLJllllLllllLLlllllllllll JLJ_Ll_A_..L...

0 .
1930 1935 1940 1945 1950 1955 1960 1965 1970 1975 1980 1985 1990
Year

 

Figure 1. Relative contribution of stocked and wild fish to the total abundance of
lake trout in the Michigan (1929-1993) and Wisconsin (1959-1993) waters
of Lake Superior. Adapted from Hansen (1994).

3
provide an Opportunity in which to study the effects of compensation on population
regulation.

The idea of population compensation can be traced back to the first theories of
population growth and regulation which are attributed to the observations of Malthus,
who in 1798 observed that interactions between individuals at high densities limit
population growth and lead to stability (McFadden 1977). These observations formed the
foundation of the logistic model of population growth which implied that populations
experience negative feedback mechanisms bounding growth between limits that are
prescribed by the environment (Bellows 1981). Population compensation has been
defined as “the sum of all density-dependent phenomena that act to stabilize a
population” (Goodyear 1980). Thus, population compensation is mediated through
density-dependent factors; processes that reduce population growth at higher population
densities and increase growth at lower densities are compensatory (McFadden 197 7).
Compensatory mechanisms act through changes in growth, survival, and reproductive
rates of the individuals in the population (Chen 1987). Each of these parameters has a
range that is determined by the genetics of the individuals in the population (Phillipp et
al. 1981, Weatherly and Rogers 1978). The expression of these rates in the population is
modified by environmental conditions and determines population density. Density is a
part of the environment which feeds back on growth, survival, and reproduction to
mediate the expression of these rates within the range allowed by the population. Thus,
when density is high, growth, survival, and reproduction should occur at lower rates than
when density is low. T

The continued existence and high levels of yield of fish populations undergoing

4

exploitation are often cited as evidence of compensatory mechanisms maintaining
population viability (Goodyear 1977, 1980; McFadden 1977). However, there are limits
to the compensatory capabilities of a fish species such that each fish population has an
associated "compensatory reserve" which defines how much stress can be withstood by
the population while remaining viable (Goodyear 1977). For example, there are limits as
to how fast a fish may grow and to how fecund an individual may be. It is crucial to
consider these limits, or the range of compensation available to the population, when
assessing the impact of additional mortality on the population and how the population
will respond (Goodyear 1977). A better understanding of the role that compensation
plays in the regulation of fish populations will lead to better management of exploited.
populations (McFadden 1977).

The degree to which compensatory mechanisms are acting in a population can be
determined by comparing the population to itself during periods of differing abundance
levels. To achieve this comparison, a common unit is necessary that integrates the three
agents Of compensation, growth, survival, and reproduction, into a Single measure.
Lambda (2.), the population’s finite rate of growth, can serve as this common unit of
comparison as it is sensitive to changes in the growth, survival, and reproductive rates of
a population (Hayes and Taylor 1990). Lambda is commonly used to express the growth
rate of a seasonally breeding population and is related to the population's intrinsic rate of

increase, r, by:

A=e'

As a result, lambda greater than one indicates an increasing population, lambda equal to

5

one indicates a stable population, and lambda less than one indicates a decreasing
population (Pielou 1977). One way to interpret lambda is in terms of a percent increase
or decrease per year. For example, when lambda = 1, there is no change per year. If
lambda = 1.2, the population is increasing at a rate of 20% per year, while if lambda =
0.8, the population is decreasing at a rate of 20% per year.

Lambda is calculated from the Leslie projection matrix as the principle eigenvalue
of the matrix (Pielou 1977, Caswell 1989). The Leslie matrix explicitly incorporates age-
structure into the population (Pielou 1977) and allows for direct comparison of
population growth or decline under a wide variety of conditions (Hayes and Taylor 1990).
Further, the Leslie matrix allows for the determination of age—0 survival rates when post
age-0 survival and fecundity rates are known (Vaughn and Saila 1976). Age-0 survival is
difficult to measure in the field and is thus rarely measured for fish populations.
However, the ability to calculate age-0 survival rates is important because many
researchers believe that much of the compensation in fish populations, in terms of
responding to large losses of adults, takes place at this stage (Sissenwine et al. 1988,
Goodyear 1980). For instance, Ricker (1963) Showed that even the slightest change in
age-0 survival could lead to a large change in the abundance of the population at the time
of recruitment.

The goal of this study was to evaluate the effect of compensatory mechanisms on
the population dynamics of lake trout in Lake Superior. My specific objectives were to:

1. Determine, under different levels of abundance and mortality, if

differences occur in individual growth rates, fecundity rates, and age-0

survival rates.

6

Evaluate the relative importance of fecundity and survival in determining

the population growth rate of lake trout populations in Lake Superior.

Determine the effect of different management actions aimed at controlling
mortality of current lake trout populations in Lake Superior on their

population growth rate.

STUDY SITE AND TIME PERIODS

I evaluated the effects of compensation on the population dynamics of lake trout
in two areas of Lake Superior; one in the Michigan waters and one in the Wisconsin
waters (Figure 2). The study areas overlap the following Lake Superior Management
Zones: MI-4, MI-5, and MI-6 in Michigan waters and WI-2 in the Wisconsin waters
(Hansen 1994). These areas of Lake Superior provided the long term data sets necessary
to complete this study as they were sites of historically productive lake trout commercial
fisheries (Baldwin 1979), and lake trout populations have been monitored in these areas
by the National Biological Service for several decades (Hansen 1994). Additional
information was available that allowed me to split the Wisconsin waters of Lake Superior
into two distinct areas, the inshore and refuge areas, during the current time period only
(Wisconsin State/Tribal Technical Committee 1990). This split was important because
lake trout populations in the two areas have experienced different mortality rates as lake
trout have been protected from fishing pressure in the offshore refuge area since 1976
(Schram et al. 1995). Although fishing was not allowed in the refuge area, these lake trout
still experienced some fishing mortality due to straying out of the refuge area into
neighboring waters where fishing was still allowed (Swanson 1974).

Three time periods were selected in which to evaluate the effects of compensation

on the population dynamics of wild lake trout in Lake Superior (Figure 3). The study

_2..
\

M I CHI CAN WA TERS

  

WISCONSIN

 

 

Figure 2. Lake Superior and the location of the study sites within the Michigan and
Wisconsin waters.

periods were chosen to reflect different mortality regimes that resulted in different levels
of lake trout abundance in both areas. Wild lake trout abundance in Lake Superior was at
a relatively high level during the pro-sea lamprey period, 1929 to 1950. The commercial
fishery was the primary source of adult lake trout mortality during this period (Hile et al.
1951, Pycha and King 1975). Sea lampreys were first recorded in Lake Superior in 1946,
and by 1951, substantial numbers of spawning sea lampreys were captured in weirs
located in tributaries to Lake Superior (Lawrie 1970). Further, a steep decline in lake
trout yield was noted by 1951 as sea lampreys became abundant (Lawrie and Rahrer
1973). Thus, I selected 1951 as the beginning of the sea lamprey dominant period. Sea
lamprey populations reached peak numbers in Lake Superior in 1961 . However, in 1962,
the number of sea lampreys declined by 86% as a result of the chemical control program
which had started in 1958 (Smith and Tibbles 1980). As such, I chose 1961 as the ending

of the sea lamprey dominant period. In an effort to rehabilitate lake trout populations that

9

had been decimated by a combination of the commercial fishery and the sea lamprey, lake
trout stocking began in the early 19505 and was increased in 1958 (Krueger et al. 1986).
By 1963 stocked fish began to dominate the total catch and continued to dominate the
population dynamics of lake trout in Lake Superior until 1985 (Hansen 1994; see Figure
l). Hansen (1994) provided evidence that these hatchery-reared lake trout produced the
wild fish that have dominated the population since 1985. Therefore, I chose the years

from 1985 to 1993 to represent wild lake trout populations during the current time period.

 

160

140 P- Pie-Sea lamprey Sea lamprey Hatchery Fish Dominated Current
1929-1950 Dominant 1985-1993
120 - 1951-1961

§
V I V

 

Catch/F3011

lJleLllLlllllJlJllihAllLllllllllllLJllllLJll‘LlllllllAll ll

19!!) 1935 1940 1945 1950 1955 1960 1965 1970 1975 1980 1985 1990
Year

 

 

 

 

 

o8888

 

Figure 3. Three study periods chosen to evaluate the effects of compensation on the
population dynamics of wild lake trout in Lake Superior. Assessment
catch/effort in Michigan waters (adapted from Hansen 1994).

METHODS

Leslie Matrix

Leslie matrices were developed for wild lake trout in the Michigan and Wisconsin
waters of Lake Superior for the three time periods. The Leslie matrix parameters, age-
specific survival and fecundity rates, were estimated for each time period at each site
from published literature and reports (Table 1). The probability of survival, P,, from age

x-l to age x was calculated as:

 

where l, is the life table survivorship value at age It (Caswell 1989). Age-specific

fecundity, F, was calculated as:

F.=P.tn.

_ where m, is the life table age-specific fecundity rate (Caswell 1989). The finite rate of
population growth, A, was calculated as the principle eigenvalue of the Leslie matrix
(Pielou 1977, Caswell 1989). I calculated A for lake trout populations in the Michigan
and Wisconsin waters of Lake Superior during the three study periods and used it to
compare the growth rate of populations that exhibited different individual growth,
survival, and reproduction rates.

10

11

Lake trout populations in both study sites had a different age structure in each of
the time periods. Currently, lake trout in the Michigan waters live at least to age 24 while
during the sea lamprey dominant period, few individuals lived beyond age 12. Thus, to
facilitate comparison between time periods and sites, all matrices were extended to
include 24 years. By extending the matrix to different ages and recalculating A, I found
that this extrapolation did not affect estimates of lambda because survival probabilities
for the ages that did not appear in the population were so low that these ages did not
contribute significantly to the population growth rate.

The first step necessary to estimate age-specific fecundity (F ,) was to determine
the individual growth rate experienced by the population. Size at age data, either weight
at age or length at age, was extracted from the sources listed in Table 1. During the pre-
sea lamprey and the sea lamprey dominant time periods, size at age was extrapolated to
age 24 by fitting a power function to the data. The power function provided the highest
coefficient of association for the two historical periods because lake trout were growing
very quickly during these periods (Sakagawa and Pycha 1971). During the current time
period, however, a logarithmic function had the best fit to the data provided by the
sources in Table l. Length-weight relationships published in the sources listed in Table 1
were used to estimate the corresponding length or weight at age. Finally, weight at age
information was combined with published fecundity-weight relationships for Lake
Superior lake trout to determine age-specific fecundity rates. This value was then
multiplied by the percent of lake trout mature at that age to estimate the age-specific
fecundity of the population. The growth, length-weight, and fecundity-weight functions

used to construct the matrices are listed in Table 2.

 

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Age-specific survival rates (P,) were determined as:

~M+F+L
P =1-e(.’ ‘ ‘)

I

where M, is instantaneous natural mortality, F, is instantaneous fishing mortality, and L,
is instantaneous sea lamprey mortality. These rates and total mortality were estimated by
the sources listed in Table 1 using catch curve analysis (Ricker 1975). I assumed that
natural mortality was the only mortality factor acting on fish that were not fully recruited
to the fishery. Instantaneous natural mortality for lake trout in the Michigan and
Wisconsin waters of Lake Superior was reported as 0.2 (Sakagawa and Pycha 1971), and
this value was held constant for both sites during each period. Lake trout were fished
using a 114 mm stretch mesh gillnet which reaches peak efficiency at 51 cm (20 in) in
length (Pycha 1980). Thus, fishing‘mortality was assumed to begin significantly
impacting populations when the fish reached 51 cm length. Fishing mortality was often
determined by subtraction of the other mortality factors from a total mortality estimate.
Sea lamprey induced mortality was assumed to be zero during the pro-sea lamprey period
and was extracted from the sources listed in Table 1 for the other time periods. The
parameters, age-specific length, weight, survival and fecundity, used to construct the
Leslie matrix for lake trout populations in the Michigan waters for each study period are
listed in Table 3. For lake trout populations in the Wisconsin waters, the Leslie matrix
parameters of the historical time periods are listed in Table 4 and of the current time
period are listed in Table 5. Refer to Appendix A for a detailed description of each

matrix.

15

 

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16

 

 

 

Table 4. Listing of parameters used to construct Leslie matrices for the Wisconsin
waters of Lake Superior during the two historical time periods. Length is
in cm, weight is in kg, P(x) is age specific survival, and F(x) is age
specific fecundity.

Pre-Sea Lamprey Sea Lampre; Dominant

gge cm kg P(x) F(x) cm kg P(x) F(x)
1 13.94 0.02 0.82 0.00 10.41 0.01 0.82 0.00
2 19.16 0.05 0.82 0.00 16.00 0.03 0.82 0.00
3 22.64 0.09 0.82 0.00 22. 10 0.08 0.82 0.00
4 31.19 0.23 0.82 0.00 28.70 0.18 0.82 0.00
5 37.44 0.40 0.82 0.00 36.07 0.37 0.82 0.00
6 43.40 0.62 0.82 0.00 46.48 0.83 0.57 0.00
7 50.03 0.96 0.82 0.00 51.56 1.16 0.18 0.00
8 54.42 1.25 0.60 0.00 _ 57.91 1.68 0.18 0.00
9 60.22 1.70 0.60 0.00 68.58 2.88 0.18 174.12
10 67.22 2.38 0.60 313.48 76.45 4.08 0.18 424.17
1 1 72.07 2.95 0.60 467.59 82.30 5.15 0.18 661.45
12 78.67 3.86 0.60 1289.57 87.63 6.30 0.18 845.73
13 84.62 4.82 0.60 1794.22 94.42 7.99 0.18 1 1 18.57
14 90.38 5.90 0.60 2651.46 100.54 9.76 0.18 1404.19
15 95.98 7.09 0.60 3302.62 106.59 1 1.77 0.18 1726.78
16 101.87 8.51 0.60 4077.80 112.58 14.01 0.18 2088.16
17 107.44 10.02 0.60 4902.09 118.51 16.50 0.18 2490.15
18 l 13.06 11.71 0.60 5826.00 124.39 19.26 0.18 2934.50
19 118.63 13.57 0.60 6843.00 130.22 22.29 0.18 3422.97
20 124.18 15.61 0.60 7956.83 136.01 25.61 0.18 3957.25
21 129.70 17.83 0.60 9171.18 141.75 29.22 0.18 4539.03
22 135.19 20.25 0.60 10489.68 147.44 33.14 0.18 5169.98
23 140.65 22.86 0.60 11915.92 153.10 37.37 0.18 5851.72
24 146.08 25.67 0.60 13453.44 158.72 41.93 0.18 6585.87

 

17

Listing of parameters used to construct Leslie matrices in the Wisconsin
waters of Lake Superior during the current time period for the inshore and
refuge areas. Length is in cm, P(x) is age specific survival, and F(x) is age
specific fecundity; weight was not available for this time period.

Table 5.

 
  
 

 
 

 

 

Current - Inshore Current - Refuge

age cm P(x) F(x) cm P(x) F(x)
1 13.43 0.82 0.00 2.50 0.82 0.00
2 28.73 0.82 . 0.00 21.68 0.82 0.00
3 37.68 0.82 0.00 32.90 0.82 0.00
4 44.04 0.80 0.00 40.86 0.82 0.00
5 49.40 0.78 0.00 47.83 0.79 0.00
6 51.77 0.40 0.00 51.84 0.52 0.00
7 56.37 0.40 23.03 55 .42 0.52 25.47
8 60.49 0.40 74.32 60.30 0.52 93.95
9 62.85 0.40 129.24 . 63.50 0.52 174.54
10 62.65 0.40 477.39 65.41 0.52 744.52
1 1 66.84 0.40 841.50 68.48 0.52 1 186.28
12 68.17 0.40 906.50 72.39 0.52 1432.67
13 70.06 0.40 998.84 73.48 0.52 1501.24
14 71.69 0.40 1078.90 75.53 0.52 1630.41
15 73.22 0.40 1 153.43 77.44 0.52 1750.66
16 74.64 0.40 1223.15 79.22 0.52 1863.15
17 75.98 0.40 1288.65 80.90 0.52 1968.82
18 77.24 0.40 1350.40 82.48 0.52 2068.45
19 78.44 0.40 1408.81 83.98 0.52 2162.69
20 79.57 0.40 1464.22 85.40 0.52 2252.09
21 80.64 0.40 1516.93 86.75 0.52 2337.13
22 81.67 0.40 1567.19 88.04 0.52 2418.21
23 82.65 0.40 1615.21 89.27 0.52 2495.69
24 83.59 0.40 1661.19 90.44 0.52 2569.87

 

1 8
Growth Comparison

A regression model was developed for each time period based on a natural log
transformation of size at age in each matrix to facilitate comparison of size at age among
the different sites and times. Using analysis of covariance with contrasts (Rawlings
1988), I compared the length and weight at age among the three time periods within the
Michigan waters. 1 used the size at age data from the two historical periods in the
Michigan waters to construct the historical matrices in the Wisconsin waters since
historical age-specific length and weight information was lacking for Wisconsin lake
trout. I was able to substitute Michigan growth data for Wisconsin lake trout because
studies had indicated that lake trout in the two areas grew in a similar fashion. During the
pre-sea lamprey period, Eschmeyer et al. (1953) indicated that the annual growth
increment of adult lake trout in Wisconsin waters was similar to the growth rate exhibited
in the Michigan waters - approximately 2.1 inches per year. Additionally, the age
structure of lake trout collected in 1964, soon after the sea lamprey dominant period,
using 114 mm stretch mesh gill nets in the Wisconsin waters reported by Swanson and
Swedberg (1980) was similar to the age structure presented in Rahrer (1967) for lake
trout collected with the same gear in the Michigan waters during the same period. Since I
used the same growth data for the two sites during the pre-sea lamprey and the sea
lamprey dominant periods, I was only able to compare length at age between the two sites
during the current time period. In addition, length at age was calculated separately for
lake trout in the inshore and refuge regions of the Wisconsin waters, and growth in both
of these areas was compared to growth during the current time period in the Michigan

Waters.

19

F ecundity Comparison

Fecundity-weight regressions had been developed for the current time period in
the Michigan (Peck 1988) and Wisconsin (Schram 1993) waters and for the pre-sea
lamprey period in the Michigan waters (Eschmeyer 1955). Using the data on number of
eggs at weight presented in these publications, I recalculated the fecundity-weight
regression for each data set and calculated the 95% confidence interval for the predicted
values (Rawlings 1988) to test for differences in weight specific fecundity between the
Michigan waters pre-sea lamprey and current time periods and Wisconsin current period.

To test for differences in age-specific fecundity between time periods and sites, I
calculated age-specific fecundity using the fecundity-weight regression for those ages at
which size was known. Using analysis of covariance with contrasts (Rawlings 1988), I
compared the calculated fecundity at age of lake trout among the three time periods
within the Michigan waters and the Wisconsin waters separately, and then compared the

two areas within Wisconsin and the Michigan waters during the current time period.

Population Growth Rate Comparison

In order to complete the Leslie matrix for each period, I estimated age-0 survival;
that is, survival from egg deposition to age 1. Vaughn and Saila (1976) describe a
method for calculating age-0 survival that requires an estimate of the finite rate of
population growth (A) and a Leslie matrix that is complete except for the age-0 survival
value. Hence, the first step in calculating age-0 survival was to estimate the population
growth rate of lake trout populations in the Michigan and Wisconsin waters of Lake

Superior during each of the time periods.

20

Hansen (1994) developed estimates of wild lake trout assessment catch per unit
effort (cpe) in the Michigan waters of Lake Superior from 1929 to 1993. I used these
data to calculate the instantaneous population growth rate for each period as the slope of
the regression of the natural log of cpe against time (Figure 4; Pielou 1977). Only the
years 1958 to 1961 were used to characterize the sea lamprey dominant period. As the
average age of fish caught during these years was 6 to 7 years (Pycha 1980), these fish
had been exposed to sea lamprey induced mortality for all of their life span making these

years a better representation of the sea lamprey dominant time period than the entire time

 

 

 

 

 

 

 

 

period.
4.5
4,0- pre-larnpreylanqneycurrent .
II I ' O . .
35~'_-- ,,-. '0'.
. - ., . o
l..-
930- u. - e
g .
E25"
82m 00
EU- 00
1.0-
05*
0.0 JAAAIAALnlnanalAAAILLLALlrr11L:I1111411lirLJlnrnlJAAAnllAAran
1930 1935 1940 1945 1950 1955 1960 1965 1970 1975 1980 1985 1990
Year

Figure 4. Data points used in the regression of the natural log(cpe) on year to
determine the finite rate of population growth in the Michigan waters of
Lake Superior.

21

A time series of catch/effort such as Hansen (1994) developed in the Michigan
waters was not available for the Wisconsin waters of Lake Superior. In fact, cpe data
were not available for the historical time periods in Wisconsin waters. However, Pycha
and King (1975) indicate that commercial catch/effort in Wisconsin waters during 1937-
1948 was almost identical to that in the adjacent Michigan district MS-2. Therefore, I
used lake trout commercial catch/effort recorded in MS-2 from 1929 to 1950 (Jensen and
Buettner 1976) to represent cpe in the Wisconsin waters during the pre-sea lamprey
period. Pycha and King (1975) developed an index of lake trout abundance in the
Wisconsin waters of Lake Superior from 1949 to 1970. As in the Michigan waters, I used
only the years from 1958 to 1961 to calculate the lake trout population growth rate for the
sea lamprey dominant period. Hansen ( 1994) provided assessment cpe estimates for
stocked and wild fish during the current time period in the Wisconsin waters. The
Wisconsin State/1‘ ribal Technical Committee (1990) reported that mortality rates
calculated for wild lake trout best represent lake trout populations in the refuge area,
while mortality rates calculated for stocked fish best represent the condition of lake trout
populations outside the refuge area. Consequently, I used the cpe of stocked fish to
represent the inshore waters where fishing was allowed, and the cpe of wild fish to
represent the refuge area where fishing was not allowed. The instantaneous rate of
population growth was determined as the slope of the regression of the natural log of cpe
and the abundance index against time (Figure 5; Pielou 1977).

Finally, the finite rate of population growth (A) of lake trout in the Michigan and
Wisconsin waters of Lake superior during each time period was calculated as the antiloge

of the corresponding slope (Pielou 1977). A two—tailed Student's t test was used to

22

 

 

4.0 ~ pre-lamprey lamprey inshore refuge
I O. O Q

 

 

 

MW cpe)
8 D.’

0.5“

 

Axxnlxkx
0.0
p

3.5- O

3.0 "

 

no l#JJDL#IAALLIAAAJIALLJJ‘ALAJAIALlLLJ_LlA‘I—PA¥1L4;AAILLJA1A4ALIAA

4.0 "

10*-
25 — g
’ .-

2.0-
1 o 03

1.5 “

unna- q»)

1.0 -

 

 

 

a0 JAAAJIIAAJILL‘llLlAAlALLLJJAlllll‘llLLLJlLAAALALA ll‘AIIALLLIAL

r930 r935 1940 1945 r950 1955 1960 1965 1970 1975 1980 1985 1990
Year

Figure 5. Data points used to determine the finite rate of population growth in the
Wisconsin waters of Lake Superior for the three study periods.

23

determine if A was significantly different from 1 (Rawlings 1988), a value which would
indicate stable population numbers through time. I also calculated the 95% confidence
interval of A using the antiloge transformation of the upper and lower confidence limits
for the slope. Analysis of covariance with contrasts (Rawlings 1988) was used to
determine if the population growth rates corresponding to the different time periods were

significantly different.

Age-0 Survival Estimates
Using the estimates of A and the parameterized Leslie matrix for each time period
in both the Michigan and Wisconsin waters, age-0 survival (P0) was calculated using the

equation:

Po- A

 

k-l i
ml + Zi[(mi+l/Ai)(l-11Pj)]
r= j=

here A is the finite rate of population growth, P1 is survival at age j, and m, is fecundity
at age i, and k is the longevity of the species (Vaughn and Saila 1976). The 95%
confidence interval around P0 was approximated using the upper and lower bounds for A

in the equation for P0.

Relative Contribution of PJr and FJr
Once the Leslie matrices were completed, I determined the sensitivity of the
population growth rate to changes in age-specific survival and fecundity. I chose to use

elasticity analysis, a type of sensitivity analysis that allows one to determine the

24
proportional change in the population growth rate in response to a proportional change in
age-specific survival or fecundity (Caswell 1989). The calculated elasticities summed to
1 so that the relative contribution of matrix elements, age-specific survival and fecundity,
to the population growth rate can be directly compared (deKroon et al. 1986, Caswell
1989). Thus, matrix elements (age specific survival and fecundity) associated with higher
elasticities make a higher relative contribution to population growth rate than matrix
elements associated with lower elasticity values. Comparison of elasticities allowed me
to determine which factors were most important in determining the pOpulation growth.
The elasticity (ea) of A with respect to the matrix element oil. was calculated as:

.. - fl (LWJ' )
" A <v,w>

where w, was the right eigenvector corresponding to A, v, was the left eigenvector
corresponding to A, and <v,w> was the scalar product of the two vectors (deKroon et al.

1986, Caswell 1989).

Fishing and Sea Lamprey Induced Mortality Tradeoflr

1 evaluated the effect of different management scenarios aimed at controlling total
mortality of current lake trout populations in the Michigan and Wisconsin waters of Lake
Superior by changing either fishing or sea lamprey induced mortality to a specified
percentage of the current value in the matrix and then recalculating A. I allowed fishing
mortality to vary from 0% to 200% of its current value and explored the effect of sea

lamprey induced mortality at 0%, 50%, 100%, and 200% of the current sea lamprey

25

induced mortality rate. Additionally, by allowing both fishing and sea lamprey induced
mortality to be zero and recalculating A in this analysis, I was able to estimate the

compensatory scope, or production potential, of these lake trout populations.

RESULTS

Mortality Comparison

In the Michigan waters of Lake Superior, sea lamprey induced mortality was very
high during the sea lamprey dominant period and was still an important mortality factor
during the current time period (Figure 6). Age specific fishing mortality did not vary
greatly between the three time periods, but was an important mortality factor during each
time period. Fishing and sea lamprey induced mortality rates were of similar magnitude
during the current time period.

Sea lamprey induced mortality was not as extreme in the Wisconsin waters of
Lake Superior as in the Michigan waters, but, as in the Michigan waters, it was higher
during the sea lamprey dominant period than during the current period (Figure 7). Age
specific fishing mortality in the Wisconsin waters was dramatically greater during the sea
lamprey dominant period than during both the other periods in Wisconsin waters and the
three periods in the Michigan waters. However, lake trout that resided in the refuge area
of the Wisconsin waters during the current period experienced lower age specific fishing
mortality and equal sea lamprey induced mortality than fish that were found in the inshore
area.

Age specific fishing mortality exhibited a shift in the age of onset between the
time periods in both sites. Since lake trout were fished using 114 mm (4.5 in) stretch

mesh gill-nets that began catching fish efficiently at 51 cm (20 in; Pycha 1980) during the

26

27

 

2.5

 

 

 

 

 

2.0 *

 

 

 

 

 

1.5 _ 3

Ianprey Mortality

0.5 b

 

 

 

0.0 ‘

Age

Frgure 6. Age specific instantaneous fishing and sea lamprey mortality experienced
by lake troutin the Michigan waters of Lake'Superior during the three
study periods.

28

 

2.5

 

pie-lamprey lamprey inshore refuge

0000000 m*

 

 

2.0 —

 

1.0 l’ t .\

mung Mortality

 

 

 

 

 

 

 

 

 

Figure 7. Age specific instantaneous fishing and sea lamprey mortality experienced
by lake trout in the Wisconsin waters of Lake Superior during the three
study periods.

29
three periods, the shift in age at which fishing mortality begins to take effect indicated

that lake trout in each of the study periods reached a size of 51 cm (20 in) at different

ages.

Growth Comparison

Length and weight at age of lake trout in the Michigan waters of Lake Superior
were significantly different during each time period (P=0.001; Figure 8). Lake trout
grew faster in both length and weight during the sea lamprey dominant period than during
the pre-sea lamprey period. Further, current lake trout grew very differently than lake
trout during either of the historical periods. Current lake trout grew faster until
approximately age 8, but reached a much smaller ultimate adult size than lake trout
during the historical time periods.

In the Wisconsin waters during the current time period, lake trout in the refuge
area grew significantly longer at age than in the inshore area (P = 0.0116; Figure 9). In
addition, during the current time period, growth in length of lake trout in the Michigan
waters was not significantly different than lake trout growth in the Wisconsin inshore area
(P = 0.3058), but was significantly different than lake trout growth in the Wisconsin
refuge area (P = 0.0306). This finding was probably due to the fact that lake trout are

heavily fished in both the Michigan waters and the inshore area of the Wisconsin waters

resulting in similar growth in the two areas.

30

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 8. Comparison of length and weight at age of lake trout in the Michigan
waters of Lake Superior during the three study periods.

31

 

120

 

r MdriganlnslneRefirge

 

 

 

 

 

 

Age

Figure 9. Length at age of lake trout in the Michigan and Wisconsin (inshore and
refuge areas) waters of Lake Superior during the current time period.

F ecundity Comparison

Fecundity of lake trout between sites and time periods was compared in terms of
both weight specific and age specific fecundity. I compared the weight specific fecundity
of lake trout during the periods for which a fecundity-weight relationship was available:
the pre-sea lamprey and the current periods in the Michigan waters, and the current period
in Wisconsin waters. Weight specific fecundity was not significantly different as
indicated by the overlap in the 95% confidence intervals on’the predicted value of number
of eggs at a given weight (Figure 10). Although the 95% confidence intervals for the two

periods in the Michigan waters overlapped, current lake trout consistently have a higher

32

 

16000

 

MI Pre-lamprey MI Current W1 Current
14000 ‘~ - '0 - + ' ' * ' '

 

 

 

12000 "

 

 

Fecundity
§

 

4000 "‘

 

2000 "

 

 

 

 

 

Weight (kg)

Figure 10. Comparison of weight specific fecundity of lake trout populations during
the pre-sea lamprey and current time periods in the Michigan waters and
during the current period in the Wisconsin waters of Lake Superior.

number of eggs at a given weight.

I compared age specific fecundity between the three time periods in both sites
separately and between sites during the current time period. In the Michigan waters, age
specific fecundity was not significantly different between the pre-sea lamprey period and
the sea lamprey dominant period (P = 0.07). However, age specific fecundity during the
historical periods was significantly different from the current time period (P = 0.001 for

both comparisons; Figure 11). A similar pattern was evident in the Wisconsin waters
where fecundity at age of lake trout during the pre-sea lamprey and the sea lamprey

dominant periods were not significantly different from each other (P = 0.1612; Figure

33

11). However, age specific fecundity in both historical time periods was significantly
different from age specific fecundity calculated for both the refuge and the inshore areas
during the current time period (P = 0.0004 for the inshore area and P = 0.0016 for the
refuge area). Age specific fecundity of current lake trout populations in the Michigan
waters was not significantly different from that of current lake trout populations in the
inshore area of the Wisconsin waters (P = 0.5706) or from lake trout in the Wisconsin
refuge area (P = 0.4102; Figure 12). Likewise, the fecundity at age of lake trout currently
found in the inshore and refuge areas of the Wisconsin waters was not significantly
different (P = 0.2939).

The age at which members of the population became mature shifted between the
three time periods in both sites. Lake trout during the pre—sea lamprey period became
mature at age 10 in both sites, age 9 during the sea lamprey dominant period in both sites,
and ages 6 and 7 during the current period in the Michigan and Wisconsin waters

respectively.

Population Growth Rate Comparison
The finite population grth rates calculated for the pre-sea lamprey and current
periods in the Michigan waters and for the inshore area of the current period in Wisconsin
waters (Table 6) were all significantly less than 1 indicating that the population
abundance was declining during these periods. The population growth rate calculated
during the sea lamprey dominant period was not significantly different from 1 in either
the Michigan (P=0.0726) or the Wisconsin (P=0. 1292) waters. However, it is known

from experience that lake trout populations collapsed in Lake Superior during this time

34

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

12000
L
10000 - Michigan Waters
FEW—WW
800° ' lam
* “M
g ..m -
In .
4000 *
XIX) '-
0 1
12000
10000 r Wisconsin Waters
W
3000 ” 1m.
m
6000 — ’Efuhg‘
h L
4000 -
21!” r
0 l
0 20 25
Figure 11. Comparison of age specific fecundity of lake trout populations in the

 

Michigan and Wisconsin waters of Lake Superior during the three study
periods.

35

 

12000

 

MdrigmlnslneRefuge

1M!)-

 

 

 

 

 

 

 

Figure 12. Comparison of age specific fecundity of current lake trout populations in
the Michigan and Wisconsin (inshore and refuge areas) waters of Lake
Superior.

period. The lack of statistical significance was probably the result of having such few
data points included in the regression (N = 4) and does not negate the biological
significance of these population growth rates. The population growth rate calculated for
the pre-sea lamprey period in the Wisconsin waters was not significantly different from 1
indicating that lake trout in the Wisconsin waters of Lake Superior had a relatively stable
abundance before sea lamprey invaded the lake. In contrast, the population growth rate
calculated for the current time period in the refuge area of the Wisconsin waters was

significantly greater than 1 indicating that the population was increasing.

36

In the Michigan waters, the population growth rate during the pre-sea lamprey

period was significantly greater than the population growth rates during the sea lamprey
dominant (P=0.0335) and current (P=0.0350) periods. However, the population growth
rates calculated for the current and sea lamprey dominant periods were not significantly

different from each other (P=0.1400). In the Wisconsin waters, the population growth

rate calculated for the pre-sea lamprey period was significantly greater than the

population growth rate of current lake trout in the inshore area (P=0.0002), but was

Table 6. Estimates of finite rate of population growth (A) of wild lake trout in the
Michigan and Wisconsin waters of Lake Superior, the bounds of the 95%
confidence interval, and the probability of getting a larger value oft if the

parameter was truly equal to 1 (Ho: A=1).

 

Michigan Waters

 

 

 

 

Period _ Years A Lower Upper P>|tl
95% 95%
Pre-Sea Lamprey 1929-1950 0.972 0.962 0.983 0.000024
Sea Lamprey Dominant 1958-1961 0.836 0.671 1.041 0.072575
Current 1985-1993 0.930 0.886 0.976 0.009224
Wisconsin Waters
Period Years A Lower Upper P>ltl
95% 95%
Pre-Sea Lamprey 1929-1950 0.998 0.987 1.010 0.840974
Sea Lamprey Dominant 1958-1961 0.863 0.671 1.1 1 1 0.129232
Current - Inshore 1985-1993 0.910 0.873 0.949 0.001108
Current - Refuge 1985-1993 1.069 1.004 1.130 0.040392

 

37

significantly less than the current population growth rate in the refuge area (P=0.0042).
However, the population growth rate for the pre-sea lamprey period was not significantly
different from that during the sea lamprey dominant period (P=0.0598). Further, the
calculated population growth rate for the sea lamprey dominant period was significantly
less than the current population growth rate in the refuge area (P=0.0093), but was not
significantly different from the population growth rate of lake trout in the inshore area
(P=0.5017).

I also compared the population growth rates during the current time period
between the Michigan waters and the inshore and refuge areas of the Wisconsin waters of
Lake Superior. The population growth rate in the Wisconsin refuge area was significantly
greater than the population growth rate in the Wisconsin inshore area (P=0.0001) and in
the Michigan waters (P = 0.0002); that is, the population in the Wisconsin refuge area
was increasing while lake trout populations in the Wisconsin inshore area and in
Michigan waters were declining. The population growth rates in the Michigan waters and

the inshore area of the Wisconsin waters were not significantly different (P = 0.4918).

Age-0 Survival Estimates

Estimates of average age-0 survival for lake trout ranged from 0.00907 to 0.288 in
the Michigan waters and from 0.00430 to 0.119 in the Wisconsin waters (Table 7) of
Lake Superior. In the Michigan waters, the lowest estimate of age-0 survival was
obtained for the pre-sea lamprey period. The estimate of age-0 survival increased
dramatically during the sea lamprey dominant period, but the estimate in the current time

period was almost as low as the estimate for the pre-lamprey period. The confidence

38

Table 7. Estimates of age-0 survival and of the upper and lower 95% confidence
interval bounds for wild lake trout in the Michigan and Wisconsin waters
of Lake Superior during the three time periods.

 

 

 

 

 

 

Period Age-0 Survival Lower 95% Upper 95%

Pre-Sea Lamprey 0.00907 0.00784 0.0105

Sea Lamprey Dominant 0.288 0.0290 2.806

Current 0.0101 0.00619 0.0164
Wisconsin Waters

Period Age-0 Survival Lower 95% Upper 95 %

Pre-Sea Lamprey 0.00430 0.00363 0.00510

Sea Lamprey Dominant 0.119 ' 0.00808 1.694

Current - Inshore 0.0189 0.0120 0.0296

Current - Refuge 0.0279 0.0136 0.0517

 

intervals around the estimates of age-0 survival during the pre-sea lamprey and the
current time periods in the Michigan waters overlap indicating that these estimates were
not different (Figure 13). However, neither of the confidence intervals for the pre-
lamprey or the current periods overlap the confidence interval for the estimate during the
sea lamprey dominant era. That these confidence intervals did not overlap indicated that
the estimates of age-0 survival during the pre-sea lamprey and the current periods were A
different from the estimate of age-0 survival during the sea lamprey dominant period.
The estimates of age-0 survival in the Wisconsin waters exhibit a similar trend to
the estimates in the Michigan waters (Table 7). The lowest age-0 survival was estimated

for the pre-sea lamprey period. The estimate increased dramatically for the sea lamprey

39

 

0.06

 

 

 

 

 

 

 

4’ a/(
0.05“ l
'3
.2
t 0.04::
9
m
6
0 -4> ‘- q-
on 0.03 0
<
0.02" 0
J“ J.
0.01“ j
I
o 2 3 4. i + .
Pre-lamprey Lamprey Current Pre-lamprey Lamprey Refuge Inshore
Michigan Waters Wisconsin Waters

Figure 13. The 95% confidence intervals for estimates of age-0 survival in the
Michigan and Wisconsin waters of Lake Superior during the three study
periods. Only the lower 95% confidence limit is shown for the sea
lamprey dominant period.

dominant period and decreased in both the inshore and refuge areas during the current

time period. The confidence intervals for the estimates during the pre-sea lamprey and

the sea lamprey dominant periods do not overlap indicating that age-0 survival during the
sea lamprey dominant period was significantly higher (Figure 13). However, the
confidence interval for the estimate of age-0 survival during the sea lamprey dominant
period completely overlaps the confidence intervals around the estimates for the current
period in both the inshore and refuge areas indicating that age-0 survival was not different
during the sea lamprey dominant and the current periods. In contrast to the Michigan

waters, the confidence intervals for the estimates during the pre-sea lamprey and the

current periods do not overlap indicating that age-0 survival during the pre-sea lamprey

40

period was significantly lower than age-0 survival during the current period. In addition,
the confidence intervals for estimates of age-0 survival in the Michigan waters and the
inshore and refuge areas of the Wisconsin waters during the current time period overlap
indicating that current lake trout populations exhibit similar age-0 survival rates in the
three areas.

The age-0 survival rates estimated for the sea lamprey dominant period in the
Michigan waters were very high. To determine the effect of age-0 survival on the growth
rate of lake trout populations in the Michigan waters, the age-0 survival rates estimated
for the current and pre-sea lamprey period were substituted into the Leslie matrix
characterizing the sea lamprey dominant period and used to calculate A (Figure 14).
During the sea lamprey dominant period, lake trout populations were declining (A =
0.8361). If these fish had the same age-0 survival as lake trout in the pre-sea lamprey or
current time periods, the population would have declined at a greater rate (A = 0.6011,
0.6073 respectively). Clearly, if age-0 survival rate had not increased in response to
increased adult lake trout mortality during the sea lamprey dominant period, the
population would have declined in a more precipitous manner than observed.

Using the population dynamics observed during the current time period in the
Michigan waters, I examined the effect of increasing age-0 survival (Figure 14).
Currently, lake trout populations in the Michigan waters of Lake Superior are declining (A
= 0.930). If the current population had an age-0 survival equal to that of the sea lamprey
dominant period, the current population would increase rather than decrease (A = 1.319).
However, age-0 survival need only increase to 0.0208 from its current value of 0.0101 to

achieve stable population growth (A = 1).

41

Similar effects of age-0 survival were observed in the Wisconsin waters of Lake
Superior. Lake trout populations were declining quickly during the sea lamprey dominant
period in the Wisconsin waters. As in the Michigan waters, if age-0 survival had not
increased, lake trout populations would have declined at an even faster rate (Figure 15).
Currently, lake trout populations in the Wisconsin waters are declining in the inshore area
(A = 0.910) and are increasing in the refuge area (A = 1.069). If lake trout in the inshore
area had an age-0 survival equal to those in the refuge area, then the population would be
decreasing at a slower rate (A = 0.944; Figure 15). However, if the lake trout population
in the inshore waters had an age-0 survival similar to lake trout populations during the
pre—sea lamprey period, the population would decrease at an even faster rate (A = 0.796).
If these lake trout had an age-0 survival as high as that estimated for the sea lamprey
dominant period, the current inshore population would increasing at a rate of
approximately 9% per year (A = 1.086). However, to achieve stable population growth in

the inshore area, the age-0 survival needs to increase from 0.0279 to 0.0511.

Relative Contribution of P, and F,

Similar trends in the proportional sensitivity of the population growth rate to
changes in age-specific survival and fecundity were observed in the Michigan and
Wisconsin waters of Lake Superior. Lake trout populations in the Michigan and
Wisconsin waters during the pre-sea lamprey period were at a relatively high level of
abundance, but were declining due to heavy fishing exploitation. During this period, the
relative contribution of survival to the population growth rate was greater than fecundity

at all ages (Figure 16). Age at first maturity was reached at age 10 in both sites, and

42

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

500 - , ’
0 l n, I . A:
5 10 15 20
Year
Figure 14. Projections of lake trout populations during the sea lamprey dominant

(top) and the current (bottom) periods in the Michigan waters of Lake
Superior using the age-0 survival corresponding to the three time periods
(N = 100 at year 1). ’

 

a,

43

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Year

Frgure 15. Projections of lake trout populations during the sea lamprey dominant
(top) and the current (bottom) periods in the Wisconsin waters of Lake
Superior using the age-0 survival corresponding to the three time periods
(N = 100 at year 1).

44

survival during the pre-reproductive ages was the most significant factor contributing to
the population growth rate. During the sea lamprey dominant period, lake trout
populations declined at an even faster rate, and the age structure of the population was
truncated with few individuals living beyond age 12 in the Michigan waters and age 13 in
the Wisconsin waters (Figure 17). Age at first maturity was reached at age 9 in both sites
during this time period, and survival during the pre—reproductive ages was still very
important in contributing to the population growth rate. However, once the fish reached
maturity, the relative contribution of fecundity to the population growth rate was much
greater than survival at those ages.

During the current time period, lake trout populations in the Michigan waters and
in the inshore area of the Wisconsin waters were declining, while they were increasing in
the refuge area of the Wisconsin waters. Lake trout matured at a much earlier age than in
the historical time periods in both sites, age 6 in the Michigan waters and age 7 in the
Wisconsin waters (Figure 18). Survival of lake trout during the pre-reproductive ages
still had the greatest relative contribution to population growth, and survival was more
important than fecundity in determining population growth rate until age 11. The relative
contribution of survival and fecundity of the older lake trout in the population was nearly
identical, although it was much less than the relative contribution of either survival or

fecundity at earlier ages.

Compensatory Scope
I calculated the maximum possible population growth rate for lake trout

populations during each time period assuming that all mortality factors, other than natural

 

 

5333...”.
>. 2.50:3.-

Flgl

45

 

0.10

 

MichiganWaters

 

 

 

 

0.02 "

 

 

 

 

0.“)

 

0.10

0.08 "

WisconsinWaml-s

 

Elasticity
p
a

0.02 —

 

0.1!)

Figure 16.

 

 

Elasticities (relative contribution) of age specific survival and fecundity
rates to lake trout population growth during the pre-sea lamprey period in
the Michigan and Wisconsin waters of Lake Suprerior.

 

 

.i and}? "n-.-

|>....e.:v.=_.k

Fl;

0.10

46

 

 

 

0.08

0.06

0.02

0.(X)

Elasticity
p
a

 

Michigan Waters

 

 

 

 

 

0.10

 

0.02

0.00

Figure 17.

 

WiseonsinWaters

 

 

 

Elasticities (relative contribution) of age specific survival and fecundity
rates to lake trout population growth during the sea lamprey dominant
period in the Michigan and Wisconsin waters of Lake Suprerior.

47

 

 

0.10

 

L Survival Fecundity

Michigan Waters

 

 

0.08 "'

 

Elasticity

 

88
l
l

 

.°.°

 

Wisconsin Waters

0-08 t Inshore

 

 

 

 

01D ‘ ‘ F A
0.10

 

 

Wisermsin Waters
Refuge

0.08 '-

hone -

lastici

0.02 r

 

 

 

01X) “‘*1 ‘
20 25

 

Figure 18. Elasticities (relative contribution) of age specific survival and fecundity
rates to lake trout population growth during the current time period in the
Michigan and Wisconsin waters of Lake Suprerior.

48

mortality, were removed to determine the compensatory scope of the population. The
greatest production potential was exhibited by lake trout populations during the sea
lamprey dominant period in both the Michigan and Wisconsin waters (Table 8). If both
fishing and sea lamprey induced mortality were reduced to zero during the sea lamprey
dominant period, lake trout populations had the potential to grow at 70% per year rather
than decline at 16% per year in the Michigan waters and to grow at 59% per year rather
than decline at 14% per year in the Wisconsin waters.

During the pre-sea lamprey period, lake trout populations had the potential to
grow at 22% per year in the Michigan waters and at 17% per year in the Wisconsin waters
if fishing mortality had been completely eliminated. The production potential of current
lake trout populations in both areas was less than that of lake trout populations during the
sea lamprey dominant period and greater than that of lake trout populations during the
pre-sea lamprey period (Table 8). If both fishing and sea lamprey induced mortality could
be eliminated completely, current lake trout populations could grow at a rate of 28% per
year in the Michigan waters and at 29% annually in the inshore area of the Wisconsin
waters rather than decline by 7% and 9% annually respectively. Eliminating fishing and
sea lamprey induced mortality in the refuge area of the Wisconsin waters would allow the

population to grow at a much faster rate, 35% per year rather than the current 7%.

Fishing and Sea Lamprey Induced Mortality Tradeofi

I evaluated the tradeoff between fishing and sea lamprey induced mortality for

Current lake trout pOpulations in the Michigan waters and the inshore and refuge areas of

49

 

 

 

Table 8. Comparison of the observed population growth rate during each time
period and the calculated maximum possible population growth rate.
Time Period & Site Observed All Maximum A
Pre-Sea Lamprey

Michigan 0.972 1.221

Wisconsin 0.998 1 . 167
Sea Lamprey Dominant

Michigan 0.836 1.705

Wisconsin 0.863 1.587
Current

Michigan 0.930 1.283

Wisconsin - Inshore 0.910 1.293

Wisconsin - Refuge 1.069 1.347

 

the Wisconsin waters. In the Michigan waters, lake trout populations were declining at a
rate of 7% per year (A = 0.930) given 100% of the current fishing mortality and 100% of
the current sea lamprey induced mortality (Figure 19). Given the current level of sea
lamprey induced mortality, if fishing mortality was allowed to increase further, the
current population in the Michigan waters would decline at even faster rates. In fact,
fishing mortality would need to be reduced by approximately 35% to achieve a stable
population in the Michigan waters. In order to achieve a growing population in the
Michigan waters, fishing would need to be reduced even further given the current rates of
sea lamprey induced mortality. However, if sea lamprey induced mortality could be

reduced to one-half of its current level, fishing would only need to be reduced by 20% in

50

 

 

 

 

 

 

 

 

 

 

 

'0.20140l60‘wllm‘1201140‘1601180l2m
% fisln'ng Mty
Figure 19. Tradeoff between fishing and sea lamprey induced mortality (expressed as
a percent of the current value) for current lake trout populations in the
Michigan waters of Lake Superior.
order to attain a stable population. Further, if sea lamprey induced mortality could be
eliminated completely, fishing mortality would only need to be reduced by 1% or 2% in
order to maintain a stable population. On the other hand, given current fishing mortality
levels, if sea lamprey induced mortality doubled, the population would decrease at
approximately 13% per year, a similar rate as observed during the sea lamprey dominant
period. In order to achieve a stable population given 200% sea lamprey induced
mortality, fishing mortality would have to be reduced by over 60%. Given the current
individual growth and fecundity schedule of lake trout populations in the Michigan
waters of Lake Superior, reducing fishing mortality had a greater effect on the population

growth rate than reducing sea lamprey induced mortality. For example, if the current

fishing mortality rate was reduced by 20% given the current sea lamprey induced

51

mortality , A would increase to 0.973. On the other hand, if the current sea lamprey
induced mortality was reduced by 20% given the current level of fishing mortality, A only
increases to 0.943 - 3% per year less than when fishing was reduced by the same
percentage.

Similar trends were observed in the inshore area of the Wisconsin waters.
Currently, given 100% of the current fishing and sea lamprey induced mortality, the lake
trout population is decreasing at 9% per year (Figure 20). Given the current rate of sea
lamprey induced mortality, fishing mortality would need to be reduced by 40% to achieve

stable population growth and should be reduced even further if growing lake trout

 

 

 

 

 

 

 

 

 

 

.1.n.111.1.rrr.1.r
0.6

0 Z) 40 a) a) 1(1) 11) 140 160 18) Z!)

%Fisll'ngNh'tality

Figure 20. Tradeoff between fishing and sea lamprey induced mortality (expressed as
a percent of the current value) for current lake trout populations in the
inshore area of the Wisconsin waters of Lake Superior.

52

populations were desired. Any additional fishing pressure would cause the population to
decrease at an even faster rate. If sea lamprey induced mortality could be reduced to half
of its current rate, fishing would only need to be reduced by about 22% to allow stable
population growth. Further, if sea lamprey induced mortality could be eliminated, fishing
mortality would only need to be reduced by about 5% to achieve a stable population. As
in the Michigan waters, if sea lamprey induced mortality was allowed to double, fishing
mortality would need to be reduced by about 65% to achieve a stable population in the
inshore area of the Wisconsin waters. Reducing fishing mortality had a greater effect on
the population growth rate of lake trout in the inshore area of Wisconsin waters than
reducing sea lamprey induced mortality. For example, a 20% reduction in current fishing
mortality caused A to increase to 0.958 whereas a 20% reduction in current sea lamprey
induced mortality only caused A to increase to 0.923.

Lake trout populations in the refuge area of the Wisconsin waters were increasing
at 7% per year. Even though this area was considered a refuge, these fish still experience
fishing mortality because they stray out of the refuge area into neighboring waters where
fishing is still allowed (Swanson 1974). However, if fishing mortality could be
eliminated completely on these fish, lake trout populations in the refuge could grow at
24% per year given the current level of sea lamprey induced mortality (Figure 21). If sea
lamprey induced mortality could be eliminated as well, lake trout populations in the
refuge could grow at 35% per year. As in the Michigan waters and the inshore area of
Wisconsin waters, reductions in fishing mortality had more effect on the population

growth rate than reductions in sea lamprey induced mortality. For example, reducing

53

fishing mortality by 20% caused A to increase to 1.10 while an equal reduction in sea

lamprey induced mortality caused A to only increase to 1.08.

 

 

 

 

 

 

 

 

 

 

1.4 _
mm
_ 0%
1.3 +
.52“;
1.2 * 1(D%
‘» +
1.1 r ‘ . m
_ r = -e-
gm ' ‘ ‘ ”‘R‘
09 - i =
. ‘0
0.8 -
07 r
L
0.6 J t l r l r l 4 L 1 l l l 1 l 1 l .
0 Z) 40 60 m 100 120 140 160 18) 11)
% Fkll'nng-tality
Figure 21. Tradeoff between fishing and sea lamprey induced mortality (expressed as

a percent of the current value) for current lake trout populations in the
refuge area of the Wisconsin waters of Lake Superior.

DISCUSSION

Lake trout populations in the Michigan and Wisconsin waters of Lake Superior
have experienced different levels of abundance through time (Hansen 1994). These
different abundance levels were associated with different mortality regimes experienced
by the populations. Lake trout during the pre-sea lamprey, sea lamprey dominant, and
current periods responded to the differing levels of mortality and abundance through
changes in the following agents of compensation: individual grth rate, age-specific

fecundity, and age-0 survival.

Changes in Individual Growth

Studies have indicated that individual growth in fish is highly flexible, and
compensatory growth is probably the most commonly observed density-dependent
process (Goodyear 1980). In an overview of individual growth rates, Healy (1978a)
noted that growth rates of lake trout in the Great Lakes during 1950s were near the
maximum rate observed for lake trout throughout its range. From this observation, he
hypothesized that the rapid growth rates exhibited by these lake trout populations were a
compensatory response to increased adult mortality resulting from sea lamprey predation
and exploitation (Healy 1978a). In this study, I found that length at age of lake trout

populations was significantly different between the three study periods in the Michigan

54

55

waters of Lake Superior. Lake trout during the pre-sea lamprey and the sea lamprey
dominant periods grew in a similar manner. However, fish during the sea lamprey
dominant period grew much faster and were significantly longer at age than lake trout
during the pre-sea lamprey period. This increased growth in length of lake trout between
the pre-sea lamprey and the sea lamprey dominant period could be classified as a density-
dependent response. Lake trout during the sea lamprey dominant period experienced
excessive adult mortality which led to a dramatic decline in abundance (Pycha and King
1975). With lower densities, more food resources can become available per individual
leading to increased individual growth rates (Goodyear 1980). Thus, as lake trout
abundance declined during the sea lamprey dominant period, the individuals that survived
had more food resources available to them and were able to grow at a faster rate. A
similar trend was evident in the weight at age of lake trout in the Michigan and Wisconsin
waters of Lake Superior. Lake trout that experienced the lowest population abundance
level, during the sea lamprey dominant period, were significantly heavier at age than lake
trout that experienced higher population abundance levels during the pre-sea lamprey
period.

Lake trout during the current time period grew in a significantly different form
than lake trout of the pre-sea lamprey or the sea lamprey dominant periods. In general,
current lake trout grew longer and heavier at age than historical lake trout until
approximately eight years of age. Then, the growth rate of current lake trout slowed
dramatically, and these fish reached a much smaller total length and weight than lake
trout during the historical periods. Current lake trout in both the Michigan and Wisconsin

waters exhibited this type of growth form that was significantly different from that of

56
individuals comprising historical lake trout populations.

Differences in length and weight at age between historical and current lake trout
may be the result of a shift in the genetic make-up of lake trout populations inhabiting the
Michigan and Wisconsin waters of Lake Superior. Hansen (1994) recently provided
evidence that the wild fish currently found in the Michigan and Wisconsin waters of Lake
Superior were the progeny of hatchery reared lake trout. Historically, Lake Superior was
home for a rich variety of lake trout stocks that varied in both their appearance and in the
habitats they inhabited (Krueger and Ihssen 1995, Goodier 1981). However, many of
these stocks were lost during the 1950s and 1960s as a result of overfishing and sea
lamprey predation (Goodier 1981). In an effort to rehabilitate lake trout populations,
management agencies initiated stocking of hatchery reared lake trout into Lake Superior
in the early 1950s (Lawrie and Rahrer 1973). Releases of hatchery reared fish into the
Unites States waters of Lake Superior have been dominated by the Marquette hatchery
strain since 1958; the Marquette strain originated from Lake Superior and has been used
as the primary broodstock in the federal hatchery system (Hansen et al. 1995). The
Marquette strain was developed in the early 19505, after much of the genetic diversity of
lake trout in Lake Superior was lost (Goodier 1981). Thus, the difference in grth form
between current and historical lake trout in the Michigan and Wisconsin waters of Lake
Superior may be a consequence of comparing different genetic strains that exhibit
differences in individual growth.

On the other hand, individual growth can be as heavily influenced by
environmental characteristics such as temperature and food as by genetics (Krueger and

Ihssen 1995). Thus, the change in growth form between historical and current lake trout

57

populations may be a reflection of environmental changes that have taken place in Lake
Superior. For example, the forage base in Lake Superior has changed dramatically since
the early 1900s (Anderson and Smith 1971). Historically, lake herring and deepwater
ciscoes were the primary prey of lake trout in Lake Superior. Lake herring abundance
began to decline in the 19505 and rainbow smelt increased replacing the coregonines as
the major food source of lake trout (Dryer et al. 1965). During the 19803, rainbow smelt
abundance declined while lake herring abundance increased. However, rainbow smelt
remain the principal prey of lake trout in Lake Superior (Conner et al. 1993). Thus, the
difference in growth form between current and historical lake trout may be the result of a
shift in the quantity and quality of food resources available. Although it would be difficult
to sort out how much influence the environment or genetics had in changing the
individual growth pattern of current lake trout populations, it is clear that the individual
growth pattern of current lake trout populations is significantly different than that of

historical lake trout populations in the Michigan and Wisconsin waters of Lake Superior.

Changes in F ecundity

Density-dependent processes can affect fecundity in several ways (Goodyear
1980). First, density can affect the number of eggs spawned by a female. In high density
conditions where food is limiting, less energy is available for the production of mature
ova. Lowering population density in this situation should lead to an increase in the
number of eggs produced by surviving females. Second, since fecundity increases with

the size of the individual fish, lower densities which lead to higher growth rates and

58

larger sizes at a given age can also lead to higher age-specific fecundity. Finally, another
effect of increased growth on fecundity is a lowering of the age at which females can
become mature. Increased growth rates resulting from lower densities leads to
individuals reaching a larger size at an earlier age resulting in an earlier age at maturity
(Goodyear 1980).

Healy (1978a) hypothesized that density-dependent changes in fecundity of lake
trout populations may be an important compensatory response to increased exploitation of
adult lake trout. To determine if density-dependent processes were affecting the number
of eggs spawned by female lake trout, I compared weight specific fecundity of lake trout
during the pre-sea lamprey and current periods in the Michigan waters and during the
current period in Wisconsin waters of Lake Superior. If the number of eggs produced by
females had changed, I would have expected the weight specific fecundity of lake trout
from these three periods to be different. I found that weight specific fecundity was not
significantly different between the pre-sea lamprey and current time periods in the
Michigan and Wisconsin waters of Lake Superior. This finding was consistent with
Healy’s (1978b) finding that the average fecundity of a 55 cm lake trout from four
different Canadian lakes that varied in the amount of lake trout exploitation was
“remarkably consistent”, ranging only from 2420 - 2436 eggs. In his study, Healy
(197 8b) was not able to establish a clear relationship between exploitation and changes in
length specific fecundity. These findings seem to indicate that lake trout are genetically
programmed to produce a certain number of eggs at a givenrsize, and that this parameter
is not very flexible and does not easily change in response to changing environmental

conditions.

59

Unfortunately, I was not able to locate data concerning lake trout fecundity for the
sea lamprey dominant period when lake trout mortality was at its highest and abundance
was lowest to test for differences in weight specific fecundity. Neither total mortality
levels or abundance levels were dramatically different between the pre-sea lamprey (Z =
0.70) and the current (2 = 0.88) time periods and may explain why weight specific
fecundity was not significantly different between the two periods. However, like Peck
(1988), I found that current lake trout in the Michigan waters have consistently higher
fecundity than lake trout during the pre-sea lamprey period even though the difference
was not statistically significant. Like the differences in growth form between current and
historical lake trout, the slighfly higher weight specific fecundity of current lake trout may
be due to a shift in the genetic strain present in these waters of Lake Superior or to a
change in the environmental conditions of Lake Superior since the historical time period.

To determine the effect of individual growth rates on fecundity, I compared age-
specific fecundity of lake trout during each of the three time periods in both sites. In
contrast to weight specific fecundity, age specific fecundity was significantly different
during each of the time periods in both sites. This difference in age specific fecundity
was a reflection of the different individual growth rates exhibited by lake trout during
each period rather than a change in absolute fecundity. Lake trout during the sea lamprey
dominant period, when lake trout abundance was lowest, exhibited the fastest individual
growth, and hence the highest age-specific fecundity. Current lake trout, which grow
faster than historical lake trout at early ages but then reach a smaller ultimate size,
exhibited a higher age specific fecundity than pre-sea lamprey lake trout during earlier

ages and a lower age specific fecundity at older ages. Thus, the effects of individual

60

growth rates on fecundity were marked, and the differences in age specific fecundity can
be attributed to changes in individual growth rates.

Maturity of lake trout populations has been related to reaching a given size
(Martin and Olver 1980). Thus, faster growing lake trout can mature at younger ages
than slower growing lake trout. The shift at age of first maturity from age 9 during the
pre-sea lamprey period to age 8 during the sea lamprey dominant period in both the
Michigan and Wisconsin waters of Lake Superior was most likely a reflection of the
different individual growth rates exhibited by these lake trout. Current lake trout in both
sites begin to mature at a much younger ages than during either historical period.
Currently, lake trout mature at age 6 in the Michigan waters of Lake Superior and at age 7
in the Wisconsin waters. Although the age at maturation has changed through time, the
size at which approximately 50% of the population matures was relatively consistent
between the pre-sea lamprey and the current periods (67 cm in Michigan pro-sea lamprey
period, 61 cm in Michigan current period, and 63 cm and 65 cm in the inshore and refuge
areas of current Wisconsin respectively). That size at maturation has remained relatively
constant indicates that changes in individual growth rate are responsible for the shifting

age at maturation.

Changes in Age-0 Survival
Increasing age-0 survival has been hypothesized to be an important compensatory
response to increased adult mortality rates in fish populations (Sissenwine et al. 1988,

Goodyear 1980). For example, decreases in adult population density in species that have

61

limited spawning habitat can lead to increased survival from egg to age 1 by eliminating
bed overseeding as well as decreasing chances of cannibalism and disease (Goodyear
1980). Ricker (1963) and Sissenwine et al. (1988) showed that small changes age-0
survival can greatly influence the abundance of the recruited population in later years.
Many factors have been hypothesized to affect age-0 survival of lake trout in the Great
Lakes including the availability of suitable spawning and nursery habitat (Eshenroder et
al. 1995, Marsden et al. 1995), behavioral selection of spawning habitat by stocked fish
(Binkowski 1984), inadequate stock sizes (Selgeby et al. 1995), contaminants (Zint et al.
1995), and genetic strain differences (Krueger and Ihssen 1995). Researchers have
measured survival of lake trout from egg deposition to swim-up fry (Perkins and Krueger
1995) but have been unable to quantify survival from egg deposition to age-1. I
calculated age-0 survival of lake trout in the Michigan and Wisconsin waters of Lake
Superior during the three study periods to determine if lake trout populations exhibited a
compensatory change in age-0 survival related to changes in population abundance
through time. The age-0 survival rate calculated using the Leslie matrix reflects the
survival rate from egg deposition to age-l necessary to maintain the population at a given
rate of population growth (Vaughn and Saila 1976). The dramatic increase in the
estimated age-0 survival between the pre-sea lamprey period, when lake trout populations
were at relatively high levels of abundance, and the sea lamprey dominant period, when
excessive adult mortality caused lake trout populations to collapse, in both the Michigan
and Wisconsin waters of Lake Superior lends support to the theory that age-0 survival
may have increased in response to increased adult mortality. The existence of this

compensatory mechanism in lake trout populations was further supported by the fact that

62

substituting the age-0 survival rate estimated for either the pre-sea lamprey or the current
time period into the sea lamprey dominant period matrix caused the population in both
the Michigan and Wisconsin waters to decline even faster than was observed. Thus,
although lake trout populations may have never reached an age-0 survival as high as that
calculated for the sea lamprey dominant period, as evidenced by their continued rapid
decline, age-0 survival must have increased substantially during the sea lamprey
dominant period or the population would have declined even faster. Although these
results support the theory, the evidence is not conclusive because of the variability in the
estimates of age-0 survival and the lack of a mechanistic basis for these observations.
The age-0 survival rate estimated for current lake trout populations in the
Michigan waters of Lake Superior was almost equal to that estimated for populations
during the pre-sea lamprey period. In Wisconsin waters of Lake Superior, the age-0
survival rate estimated for current lake trout populations in the inshore and refuge areas
were not significantly different from each other, but were significantly higher than that
estimated for lake trout during the pre-sea lamprey period. If changes in age-0 survival
were compensatory, it would be expected that as lake trout densities increased, age-0
survival would decrease. Thus, this retum of current age-0 survival rates towards
historical levels as lake trout abundance has increased lends further support to the theory
that age-0 survival responds in a compensatory way to changes in population abundance

and mortality regimes.

Relative Contribution of F, and P,

Evaluation of the relative contribution of age-specific fecundity and survival

63

rates to the population growth rate can help guide the concentration of management
efforts (Crouse et al. 1987). The elasticity analysis indicates that survival, especially
during the pre-reproductive ages, was the most important factor contributing to the
population growth rate of lake trout populations in the Michigan and Wisconsin waters of
Lake Superior during the three study periods. The relative contribution of fecundity only
became more important than the relative contribution of survival to the population growth
rate during the sea lamprey dominant period in both sites. This shift was most likely a
result of adult lake trout survival being so low during the sea lamprey dominant period
that few individuals survived to maturity or beyond.

One of the assumptions used for this analysis was that natural mortality remained
constant through all study periods. However, this assumption may not be accurate as
natural mortality may act in a compensatory manner; that is, natural mortality may change
in response to population density (Backiel and LeCren 1978). This assumption needs to
be further investigated in lake trout populations. If natural mortality changes with
population density, then the estimates of natural mortality used to construct the matrices
should change accordingly. Future research should explore the implication of changes in
natural mortality rate on the relative contribution of survival to the population growth

rate.

Compensatory Scope
1 calculated the production potential of current lake trout populations during the
three study periods in the Michigan and Wisconsin waters of Lake Superior by allowing

fishing and sea lamprey induced mortality to be zero. This calculation allowed me to

64

compare the potential of these populations, in terms of individual growth and fecundity
rates, to sustain themselves under different mortality regimes. The relatively high
production potential of lake trout populations during the sea lamprey dominant period in
both sites was due to the fast individual growth rate, the high age specific fecundity, and
the high age-0 survival exhibited by these populations. Lake trout populations during that
time period were growing and reproducing as fast as possible to sustain themselves in the
face of heavy mortality regime experienced during the sea lamprey dominant period.
Lake trout populations during the pro-sea lamprey period in both the Michigan and
Wisconsin waters of Lake Superior were associated with the highest levels of abundance
and exhibited the smallest compensatory scope. The agents of compensation, growth,
survival, and reproduction were expressed at a much lower rate during the pre-sea
lamprey period than during the sea lamprey dominant period. Finally, lake trout
populations during current time period in both sites exhibited a compensatory scope that
was intermediate between the compensatory scope exhibited during the other two periods.
This intermediate production potential seems to indicate that current lake trout
populations are recovering towards historical levels of abundance. Further, my results
clearly indicated that if fishing and sea lamprey induced mortality were eliminated during
any time period in either site, lake trout populations had the capacity to increase

dramatically.

Fishing and Sea Lamprey Induced Mortality Tradeofl'
Having established that survival was the key parameter driving the population

growth rate of lake trout in the Michigan and Wisconsin waters of Lake Superior, 1

65

determined how the population growth rate of current populations would change under
different mortality regimes. In dealing with Great Lakes lake trout, managers have two
choices to control lake trout mortality: they can regulate fishing induced mortality
through fishing regulations or they can regulate sea lamprey induced mortality by altering
the sea lamprey control program. The tradeoff analysis showed that greater gains, in
terms of lake trout population growth, were made by reducing fishing mortality than by
reducing sea lamprey induced mortality by equal percentages. This finding is most likely
due to the fact that fishing mortality was greater than sea lamprey induced mortality
during the years right before maturity in all three areas. Historical and current records
indicate that lake trout tend to reach maturity at about 60 cm in length (Eschmeyer 1955,
Ebener et al. 1989). Lake trout are fished using 114 mm stretch mesh gillnets which
target lake trout that are approximately 51 cm in length (Pycha 1980). Sea lamprey, on
the other hand, are size selective predators that target the largest prey item available
(Swink 1991). Thus, fishing mortality is greatest during several of the pre-reproductive
years when survival is most important in driving the population growth rate. As a result,
reducing fishing mortality under the current scenario will have a greater impact on the
population growth rate than reducing sea lamprey induced mortality.

Given the current levels of fishing mortality in the Michigan waters and the
inshore area of the Wisconsin waters, sea lamprey induced mortality would have to be
completely eliminated for lake trout to achieve stable population growth in these two
areas. After 30 years of sea lamprey control efforts, it seems unlikely that eliminating sea
lamprey from the Great Lakes is possible. In fact, sea lamprey populations in the Great

Lakes are likely to increase rather than decrease. The Clean Water Act has improved

66

water quality in many tributaries to the Great Lakes allowing sea lamprey to use more
habitat within each tributary to spawn as well as to colonize new streams (Zint et al.
1995, Moore and Lychwick 1980). In addition, current funding policies regarding the
Great Lakes Fishery Commission's chemical control program has made it difficult for
them to maintain an adequate sea lamprey control program and clearly will not allow
them to enhance the program in response to increased sea lamprey abundances (Great
Lakes Fishery Commission 1993). If sea lamprey abundance increases due to improved
water quality in the Great Lakes, lake trout mortality can be expected to increase as well
(Ferreri et al. 1995). In this case, fishing induced mortality will have to be reduced even
further if lake trout populations are to achieve stable population growth.

In summary, I found that individual growth rates, age-specific fecundity, and age-
0 survival rates changed in response to the different levels of lake trout abundance during
each of the study periods in both sites. Lake trout during the sea lamprey dominant
period, which experienced the lowest abundance and highest mortality levels, exhibited
the fastest individual growth rates, the highest age-specific fecundity, and the highest age-
0 survival. These high rates contributed to the relatively high production potential
exhibited by lake trout during the sea lamprey dominant period as compared to lake trout
during the pre-sea lamprey or the current periods. Survival, particularly during the pre-
reproductive ages, makes a greater contribution than fecundity to the population growth
rate of lake trout during the current time period. Reducing fishing mortality, which has
its greatest impact on lake trout that are about to become mature, has a greater effect on
the population growth rate than reducing sea lamprey induced mortath by an equal

percentage.

MANAGEMENT INIPLICATIONS

This study demonstrates the importance of long-term databases to fisheries
management. Without the 60 year time series of lake trout catch per effort in Lake
Superior provided by Hansen (1994), it would have been impossible to discern changes in
lake trout abundance through time. One of the major obstacles to completing this study
was the lack of availability of historical biological data. It is critical that fisheries
management agencies collect and maintain long term databases that at the very least
include total catch, total effort, age, length, weight, and fecundity of individuals in the
population. Without such historical background data, it is difficult to effectively evaluate
the effect of management actions.

A major goal of lake trout rehabilitation in Lake Superior is the re-establishment
of self-sustaining populations (Busiahn 1990). To achieve this goal, the population
growth rate must be greater than or equal to 1 (Pielou 1977). This goal has been
accomplished in the refuge area of the Wisconsin waters by limiting fishing mortality.
The elasticity analysis showed that managers will gain the most benefit by concentrating
their efforts and policies on increasing lake trout survival in the inshore area of the
Wisconsin waters and in the Michigan waters. The tradeoff analysis where I evaluated
the consequence of reducing either fishing or sea lamprey induced mortality indicated that

managers should concentrate efforts first on reducing fishing mortality and then on

67

68

reducing sea lamprey induced mortality. However, to achieve a stable lake trout
population in either the Michigan or the inshore area of the Wisconsin waters, given
current levels of sea lamprey induced mortality, fishing mortality would have to be
reduced to 60% of its current rate. A reduction in fishing mortality of this magnitude may
not be socially or politically acceptable. Thus, managers can use the Leslie matrix
tradeoff framework to determine the optimal mix of fishing and sea lamprey control that
will ensure the sustainability of lake trout populations in the Michigan and Wisconsin
waters of Lake Superior.

The elasticity analysis showed that the population growth rate of lake trout in the
Michigan and Wisconsin waters of Lake Superior was most sensitive to changes in the
survival of lake trout to maturity. Currently, lake trout in these areas reach maturity at
approximately 60 cm in length (Ebener et al. 1989), yet they can be legally harvested at
43.2 cm (Hansen et al. 1995). In addition, lake trout fisheries utilize 114 mm stretch
mesh gillnets that are selective for lake trout that are 51 cm in length. With the current
size limit and gear, many of the lake trout caught by the fishery are immature. One way
to limit the impact of the fishery is to raise the minimum size limit of legally harvested
lake trout to over 60 cm. This action would protect lake trout during the critical juvenile
years until they reached maturity and spawned.

Another way in which managers may achieve stable lake trout populations in both
the Michigan waters and the inshore area of the Wisconsin waters is through increasing
the age-0 survival rate of these populations. My analysis showed that age-0 survival rate
in both areas must essentially double in order to achieve stable populations. Stated in this

manner, this increase seems impossible to achieve. However, the necessary increase

69

translates into one additional survivor to age 1 from every 100 eggs deposited in the
Michigan waters and two additional survivors from every 100 eggs deposited in the
inshore area of the Wisconsin waters. However, since current age-0 survival was not
significantly different from the pre-sea lamprey period in the Michigan waters and was
slightly higher than during the pre-sea lamprey period in the Wisconsin waters, it will be
less fruitful for managers to concentrate their efforts on increasing age—0 survival than on

limiting juvenile lake trout mortality.

APPENDIX

70

APPENDIX A: Lake Superior Lake Trout - Matrix Development

Michigan Waters - Pre-Sea Lamprey Period

Sakagawa and Pycha (1971) analyzed lake trout scales collected in 1948 from the
inshore waters of Lake Superior between the Keweenaw Peninsula and Munising,
Michigan. I used the weight at age data for lake trout ages 3 -16 reported by Sakagawa
and Pycha (1971) to estimate individual growth rates. Growth data for lake trout ages 0 -
2 was determined for fish collected between 1948-1952 in a study of lake trout early life
history in the same area of Lake Superior (Eschmeyer 1956). I extrapolated weight at age
to age 24 by fitting the following power function to the last four points in the series

allowing me to capture the slowing trend in growth in weight for older ages of lake trout:

Weight = 3.1513 Ageo'8909 R2 = 0.9999

According to Sakagawa and Pycha (1971), a 20 year old lake trout should weigh
approximately 28 lbs. I found, using the power function, that a 20 year old lake trout was
estimated to weigh 27.5 lbs. Thus, the power function represented the weight at age trend
well. Length at age was estimated using the length-weight relationship reported by

Sakagawa and Pycha (1971):

log(Weight) = -3.636 + 3.062 log(Length)

where Weight was in pounds and Length was in inches.
Weight-specific fecundity was estimated using data from Eschmeyer (1954) where

he collected lake trout between 1950 to 1954 to compare the fecundity of lake trout

71

caught primarily east of the Keweenaw Peninsula in Lake Superior. I used this data to fit
a regression line that described the weight-fecundity relationship for this lake trout

population:

Fecundity = -1923.39 + 832.23Weight R2=0.7774

where Weight was the weight of the fish in pounds. I estimated the age-specific fecundity
of lake trout in the Michigan waters of Lake Superior during the pre-sea lamprey period
by combining the fecundity-weight relationship with the weight at age information. The
estimated age-specific fecundity was then multiplied by a maturity schedule (percent
mature at age), reported in Eschmeyer’s (1954) fecundity study, to determine this
population's expected age-specific fecundity.

Age-specific mortality was determined as the sum of the instantaneous rates of
natural, sea lamprey, and fishing mortality. Sakagawa and Pycha (1971) estimated
instantaneous natural (M=0.2) and total mortality (Z=0.70) for lake trout during the pre-
sea lamprey period. Sea lamprey induced mortality was assumed to be zero during the
pre-lamprey period. Lake trout were fished using a 114 mm stretch mesh gillnet which
fished most efficiency at when the fish reached 51 cm (20 in) in length (Pycha 1980).
Thus, fishing mortality was assumed to begin significantly impacting populations when
the lake trout reached 51 cm length. Once fish reached this size, I estimated fishing
mortality by subtracting natural mortality from the total mortality. The length, weight,
fecundity, and survival at age used in the Leslie matrix to represent lake trout during the

pre-sea lamprey period in the Michigan waters of Lake Superior are listed in Table 2.

72

Michigan Waters - Sea Lamprey Dominant Period

Lake trout growth during the period of peak sea lamprey abundance was estimated
using data reported by Rahrer ( 1967). Fish were collected from the inshore waters of
Lake Superior between the Keweenaw Peninsula and Grand Marais, Michigan in 1953 to
determine the grth rate of lake trout in the presence of sea lamprey. I used back-
calculated lengths for ages 1 - 12 presented in Rahrer (1967) to estimate length in inches
at age for the sea lamprey dominant time period. I extrapolated length to age 24 by fitting
the following power function to the last four years in the growth series to capture the

slowing growth in length at older ages:

Length = 4.2315 Age°~8m R2 = 0.9923

Weight at age was estimated using the length-weight relationship reported in Eschmeyer
and Phillips (1965). The majority of lake trout analyzed in this study were collected fiom
the inshore Michigan waters of Lake Superior between 1953 to 1956. The reported

length-weight relationship for lake trout during this time period was:

log(Weight) = -3.765 + 3.191 log(Length)

where Weight was in pounds and Length was total length in inches.

I was not successful in locating fecundity data for this time period. Thus, I used
the fecundity-weight relationship and the maturity schedule from the Michigan waters
pre-sea lamprey period which was based on Eschmeyer’s (1955) data. This seemed
reasonable since I was examining fish populations from the same area only a few years

later and since Eschmeyer’s data was based on fish collected between 1950 and 1954, the

73

beginning of my sea lamprey dominant period. Further, in a study to determine if lake
trout fecundity changed in response to varying levels of exploitation, Healy (1978b)
found that the average fecundity of a 55 cm lake trout from four different Canadian lakes
that varied in exploitation was remarkably consistent, ranging only from 2420 - 2436
eggs.

Age-specific mortality was determined as the sum of instantaneous rates of
natural, sea lamprey induced, and fishing mortality. I assumed natural mortality was the
same as during the pre-sea lamprey period (M=0.2, Sakagawa and Pycha 1971). The only
estimate of total mortality for lake trout in the inshore Michigan waters of Lake Superior
that I could find was in Pycha (1980). Using catch curve analysis for the years 1968 -
1978, he reported annual estimates of total mortality. I chose to use the total mortality
estimate for the year 1968 (#231) as a conservative estimate of total mortality
experience by lake trout during the period of peak sea lamprey abundance. This was a
conservative estimate because the chemical control program had been effective at
significantly reducing sea lamprey abundance in Lake Superior by 1968, and total
mortality experienced by lake trout populations in the late 19505 and early 19605 was
probably even higher. Pycha ( 1980) also estimated fishing mortality during 1968
(F=0.362). Sea lamprey induced mortality was assumed to account for the difference
between total mortality and the sum of fishing and natural mortality. Since sea lamprey
prefer larger prey (Johnson and Anderson 1980), there is a gradient of sea lamprey
induced mortality with size/age of lake trout. I used the age-specific sea lamprey induced
mortality schedule reported in Ebener et al. (1989) to distribute sea lamprey induced

mortality to each age class. The length, weight, fecundity, and survival at age used in the

74

Leslie matrix to represent lake trout during the sea lamprey dominant period in the

Michigan waters of Lake Superior are listed in Table 2.

Michigan Waters - Current Period

Lake trout length at age for the current time period was estimated using data
reported in Ebener (1990). This report described the size composition of hatchery and
wild lake trout captured around the Keweenaw Peninsula from 1987 to 1989. I used the
mean length at age from ages 6 to 17 to fit a logarithmic function which allowed me to
extrapolate length at age from age 1 to age 24. During this time period, the following
logarithmic function provided a better fit to the younger age groups than a power function

and still allowed me to capture the slowing trend in growth of older lake trout:

Length = 11.405 ln(Age) + 1.408 R2 = 0.9869

where length was in inches. Weight at age was estimated using the length-weight

relationship determined on the same set of fish in Ebener (1990):

ln(Weight) = -12.0149 + 3.0917 ln(length)

where Weight was in kg and Length was in cm.

Peck (1988) studied the fecundity of both hatchery and wild lake trout collected in
the fall of 1977 - 1983 in the inshore waters of Lake Superior between the Keweenaw
Peninsula and Munising, Michigan. He found no significant differences in weight-
specific fecundity between hatchery and wild fish. Thus, I used the relationship reported

by Peck (1988) to estimate weight-specific fecundity:

wh

wei

rep

det

1131

all

UK

US

Vi

75

Fecundity = —3400 + 2450 Weight R2=0.7921

where F ecundity is the total number of eggs at a certain Weight in kg. I combined the
weight—specific fecundity information with the weight at age information to determine
age-specific fecundity. Then, I used the maturity schedule (percent mature at age)
reported by Ebener et al. (1989) to multiply the estimated age-specific fecundity to
determine the population's expected age-specific fecundity.

Age-specific mortality was determined as the sum of the instantaneous rates of
natural, sea lamprey induced, and fishing mortality. I assumed natural mortality remained
at the same level as the previous two periods (M=0.2, Sakagawa and Pycha 1971). Total
mortality was averaged from 1986—1988 in the statistical district MI-4 which included
most of the waters where fish had been collected from (2:0.88, Ebener et al. 1989). I
used the age-specific sea lamprey induced mortality caldulated by Ebener (1990) for the
sea lamprey component of total mortality. Finally, fishing mortality which began
significantly impacting the population when the fish reached 51 cm in length (Pycha
1980) was determined by subtraction of natural and sea lamprey induced mortality from
the total mortality. The length, weight, fecundity, and survival at age used in the Leslie

(matrix to represent lake trout during the current time period in the Michigan waters of

Lake Superior are listed in Table 2.

Wisconsin Waters - Pre-Sea Lamprey Period
Data on size at age for lake trout in the Wisconsin waters of Lake Superior was

not available for the pre-sea lamprey period. However, in a study of the movement of

76

marked lake trout in Lake Superior, Eschmeyer et al. (1953) indicated that the annual
growth increment of adult lake trout in the Wisconsin waters was similar to the growth
rate exhibited in the Michigan waters - approximately 2.1 inches per year. Thus, I used
the data from the Michigan waters pre-lamprey matrix to estimate size at age for lake
trout in the Wisconsin waters during this time period. I also used the same length-weight
relationship as for lake trout in the Michigan waters.

Fecundity data was not available for this site either. As I assumed that the fish
were growing in a similar manner, I used the fecundity—weight relationship and the
maturity schedule from the matrix for the Michigan waters pre-sea lamprey period.

Age specific mortality was determined as the sum of natural, fishing, and sea
lamprey induced mortality. Natural mortality was estimated as 0.2 (Sakagawa and Pycha
1971). To determine total mortality for this period, I constructed a catch curve from
information on total number of lake trout caught at Gull Island Reef in 1957 and the age
distribution of these fish (Swanson and Swedberg 1980). Total mortality was estimated
from the catch curve as 0.5173. Since most of the fish caught in 1957 were seven years
old or older, these lake trout had lived most of their lives during a period of low sea
lamprey abundance as sea lamprey did not reach peak abundance in Lake Superior until
the early 19605 (Lawrie and Rahrer 1973). Thus, sea lamprey induced mortality was
assumed to be 0 during the pre-lamprey period. Fishing mortality was determined as the
difference between total and natural mortality and was assumed to begin impacting the
population when lake trout reached a length of 51 cm (Pycha 1980). The length, weight,
fecundity, and survival at age used in the Leslie matrix to represent lake trout during the

pre-sea lamprey period in the Wisconsin waters of Lake Superior are listed in Table 3.

77

Wisconsin Waters - Sea Lamprey Dominant Period

As with the pre-sea lamprey period, size at age data was lacking for lake trout
during the sea lamprey dominant period in the Wisconsin waters of Lake Superior.
However, Swanson and Swedberg (1980) reported the age structure of lake trout collected
using 114 mm stretch mesh gill nets in the Wisconsin waters from 1964 to 1979. The age
structure reported in that study was similar to the age structure presented in Rahrer (1967)
for lake trout collected in 114 mm stretch mesh gill nets in the Michigan waters in 1953.
Since the same type of gill net was used in both areas to collect lake trout, the same size
selectivity was represented in the age structures reported indicating that lake trout in both
areas were growing in a similar fashion. Thus, I used the length at age and the length-
weight relationship for lake trout in the Michigan waters during the sea lamprey dominant
period to characterize the growth of lake trout in the Wisconsin waters. For the same
reasons, I also used the fecundity-weight relationship and the maturity schedule for lake
trout in the Michigan waters during the sea lamprey dominant period to characterize lake
trout in the Wisconsin waters. Dryer and King (1968) indicated that size at fast maturity
for lake trout in the Wisconsin waters of Lake Superior during the sea lamprey dominant
period was approximately 25 inches, the same size that Eschmeyer (1955) reported for
lake trout during the pre-lamprey period in the Michigan waters. This observation lends
further support to the assumption that lake trout in the Michigan and Wisconsin waters
were growing and maturing at similar rates during the pre-sea lamprey and the sea
lamprey dominant periods.

Age specific mortality was determined as the sum of natural, fishing, and sea

lamprey induced mortality. Natural mortality was estimated as 0.2 (Sakagawa and Pycha

78

1971). Total mortality (Z=l.7385) was estimated from a catch curve of age classes
caught in 1964 (Swanson and Swedberg 1980). Lake trout caught in 1964 were from 5 to
10 years of age and had been exposed to high sea lamprey abundances throughout their
lives. Sea lamprey induced mortality during this time period was calculated in a series of
steps. First, the percent of fish wounded by size category during 1960 (Swanson and
Swedberg 1980) was used to determine the total number of marks by size category

(Eshenroder and Koonce 1984):

marks = -ln (1 - %wounded)

Sea lamprey induced mortality (L) was then calculated as (Eshenroder and Koonce 1984):

zlfllfl
P

L

where M was the number of marks by size category, and P was the probability of a lake
trout surviving a sea lamprey attack (P=0.38; Swink and Hanson 1986). Finally, fishing
mortality started at 51 cm in length (Pycha 1980) and was calculated by subtraction of the
natural and sea lamprey induced components from the total mortality. The length,
weight, fecundity, and survival at age used in the Leslie matrix to represent lake trout
during the sea lamprey dominant period in the Wisconsin waters of Lake Superior are

listed in Table 3.

Wisconsin Waters - Current Period
The statistical district WI-2 is made up of two components, the inshore waters and

the offshore lake trout refuge. Wild lake trout have been captured only in the refuge areas

79

where fishing has not been permitted (Wisconsin State/Tribal Technical Committee
1990). Further, the Wisconsin State/Tribal Technical Committee (1990) reported that
mortality rates calculated for wild lake trout best represent lake trout populations in the
refuge area, while mortality rates calculated for stocked fish best represent the condition
of lake trout populations outside the refuge area. Thus, I chose to model lake trout in the
inshore and refuge areas separately using data from stocked fish to represent the inshore
areas and data from wild fish to represent the refuge area. Length at age for wild and
hatchery reared lake trout during the current time period in the Wisconsin waters of Lake
Superior was estimated from data reported by the Wisconsin State/Tribal Technical
Committee (1990). I used mean length at age from ages 5 to 12 to fit a logarithmic
function which allowed me to extrapolate length at age from age 1 to 24. The logarithmic
function allowed me to capture the slowing trend in growth exhibited by older lake trout.

The functions for the inshore and refuge areas were:

8.692 ln(Age) + 5.288 R2 = 0.9792
10.894 ln(Age) + 0.986 R2 = 0.9926

inshore: Length
refuge: Length

where Length was the average length in cm. I could not locate length-weight information
for these populations, so weight was not estimated.
Length-specific fecundity was estimated for both populations using the

relationship reported by Schram ( 1993):

Fecundity = -12143.3 + 24.46 Length R2=0.55

where F ecundity is the total number of eggs produced by a fish of a certain Length in mm.

This relationship was based on lake trout collected at Gull Island Shoal during 1985-

80

1989. The length-fecundity information was combined with the length at age data to
estimate fecundity at age for both populations. I used the maturity schedule reported by
the Wisconsin State/1‘ ribal Technical Committee (1990) and the estimated age specific
fecundity to estimate the population's expected age specific fecundity.

Age specific mortality was determined as the sum of the instantaneous rates of
natural, sea lamprey induced, and fishing mortality in both areas. I assumed natural
mortality remained at the same level as in the previous two periods (M=0.2, Sakagawa
and Pycha 1971). Total mortality was reported by Hansen et al. (1994) for both hatchery
and wild fish. I averaged the total mortality rate from 1985 to 1993 experienced by
hatchery fish for the inshore waters (Z = 0.916) and by the wild fish to represent the
refuge area (2 = 0.664). I used the age specific sea lamprey induced mortality calculated
by the Wisconsin Statefl‘ribal Technical Committee (1990) for hatchery and wild lake
trout for the sea lamprey component of total mortality for the inshore and refuge
populations respectively. Fishing mortality was assumed to be lower in the refuge area
than in the inshore area. Although fishing was not allowed in the refuge area, these fish
still experience fishing mortality because they stray out of the refuge area into
neighboring waters where fishing is still allowed (Swanson 1974). In both areas, fishing
mortality began impacting the population when the lake trout reached 51 cm in length
(Pycha 1980) and was determined by subtraction of the natural and sea lamprey
components from the total mortality. The length, fecundity, and survival at age used in
the Leslie matrix to represent lake trout during the current time period in the inshore and

refuge areas of the Wisconsin waters of Lake Superior are listed in Table 4.

LIST OF REFERENCES

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