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This is to certify that the
thesis entitled
Dynamics of Lake Trout (Salvelinus namaycush)

Size and Age Structure in Michigan Waters
of Lake Superior, 1971—1995

presented by

Christopher T. Weeks

has been accepted towards fulfillment
of the requirements for

Master of Science degree in Fish. & Wildl.

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DYNAMICS OF LAKE TROUT (Salvelinus namaycush)
SIZE AND AGE STRUCTURE IN MICHIGAN WATERS OF
LAKE SUPERIOR, 1971-1995
By

Christopher Todd Weeks

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

MASTER OF SCIENCE

Department of Fisheries and Wildlife

1997

ABSTRACT
DYNAMICS OF LAKE TROUT (Salvelinus namaycush)
SIZE AND AGE STRUCTURE IN MICHIGAN WATERS OF
LAKE SUPERIOR, 1971-1995
By

Christopher Todd Weeks

Lake trout (Salvelinus namaycush) were a native predator species in the upper
Great Lakes but were nearly driven to extinction through combined efl‘ects of fishery
exploitation and predation from sea lamprey (Petromyzon marinas). The Great Lakes
Fishery Commission was established in 1956 between Canada and the United States to
develop coordinated programs of research in the Great Lakes for lake trout restoration
and sea lamprey controL Rehabilitation efforts, including stocking, reduced harvest rates,
and sea lamprey control, have had some success in Lake Superior, where presently, wild
lake trout outnumber stocked lake trout in annual harvest. In addition, survival of stocked
lake trout in the lake appears to have been drastically reduced over time. These events,
among others, have led to discussions by some fishery managers and researchers on
whether lake trout in Lake Superior should now be considered rehabilitated.

To explore the dynamics of wild and stocked lake trout during the recovery
period, I developed a statistical catch-at-age model for lake trout in Michigan waters of
Lake Superior over 1971-1995, and fit the model to age-length composition data obtained
from fisheries and non-fishery based sources, survey catch per unit effort (CPUE), and
total harvest. My goal was to obtain a comprehensive assessment of growth, mortality,

and abundance. I modeled wild and stocked lake trout independently and compared a

constant growth version of the model to a time-varying growth version. The time-varying
growth version showed a significantly better fit to the data than the constant growth
version (P<0.005) for both wild and stocked lake trout. Estimates of abundance of wild
lake trout age-7 and older indicated a decline from 1988-1995. Estimates of total annual
mortality of age-7 and older wild fish exceeded 45% each year except 1993 over the same
time period. Mortality estimates indicate that fishing was the major source of mortality for
lake trout age-5 and older. Based on results from stock assessment models for
management unit MI4, if sea lamprey induced mortality is not reduced, and fishing
intensity remains at 1990-1994 levels, wild lake trout stocks will continue to decline.
These results suggest that lake trout populations in Michigan waters of Lake Superior

cannot self-sustain themselves under the mortality rates they experienced from 1990- 1994.

This work is dedicated to my dad, Richard,
who by taking a young boy fishing and hunting,

instilled in him the spirit of nature.

iv

ACKNOWLEDGMENTS

I would like to thank the Red Cliff Band of Lake Superior Chippewas and the
United States Fish and Wildlife Service (USFWS) Sport Fish Restoration Program for
contributing financial support for this research. I would also like to thank members of the
Lake Superior Technical Committee for their expertise and advice, particularly Richard
Schorfliaar and Jim Peck (MIDNR), Bill Mattes (GLIFWC), and Mark Ebener
(COTFMA).

I give my sincere thanks to the faculty of Michigan State University, Fisheries and
Wildlife department, and my committee members, Dr. Dan Hayes and Dr. Don Hall, for
their insights into biological sciences. I also thank my fellow graduate students, including
Darren Benjamin, Kristi Klomp, Ann Krause, and Mike Rutter, for sharing their
perceptions, knowledge, and camaraderie. I especially thank my mentors, Dr. Jim Bence
and Harry Westers, for their wisdom and dedication to fisheries research, and for helping
to point my soul toward a truly meaningful path.

Finally, I cannot nearly express the gratitude and love I have for my wife, Ianthe,

and family, Jacob, Chad, and Kendra, for they’re faith, love, and support.

TABLE OF CONTENTS

LIST OF TABLES .................................................... viii
LIST OF FIGURES .................................................... x
INTRODUCTION ..................................................... 1
METHODS .......................................................... 7
Study area ...................................................... 7
Data sources .................................................... 8
Data summarization .............................................. 10
Population assessment model ....................................... 11
Model description ............................................... 12
Abundance .................................................... 13
Mortality 1983-1995 ............................................. 14
Natural mortality .......................................... 14
Fishing mortality .......................................... 14
Lamprey mortality ......................................... 16
Mortality 1971-1982 ............................................. 17
Growth ....................................................... 18
Age-length compositions .......................................... 18
Survey estimates ................................................ 19
Harvest estimates ................................................ 20
Ageing error ................................................... 21
Objective function ............................................... 24
Model simulation ................................................ 26
RESULTS .......................................................... 27
Comparison of TVG and CG models ................................ 27
Wild lake trout CG and TVG model comparison .................. 28
Stocked lake trout CG and TVG model comparison ............... 32
Model responses to peaks in observed CPUE .................... 33
Stocking versus recruitment ................................. 35
Lake trout time-varying growth model results ......................... 38
Fit of wild lake trout TVG model predictions to observed data ............. 39

Wild lake trout assessment CPUE ............................. 39

Wild lake trout mean length-at-age ............................ 41

Wild lake trout age compositions from spring assessments .......... 45

Wild lake trout harvest ..................................... 46

Fit of stocked lake trout TVG model predictions to observed data .......... 47
Stocked Lake trout assessment CPUE ......................... 47

Stocked lake trout mean length-at-age ......................... 48

Stocked lake trout age compositions from spring assessment ........ 49

Stocked lake trout harvest .................................. 49

Growth, recruitment, mortality, selectivity, and abundance of lake trout in MI4 52

Wild lake trout growth ..................................... 52

Wild lake trout recruitment .................................. 52

Wild lake trout mortality .................................... 55

Wild lake trout selectivity ................................... 56

Lake trout spawner abundance ............................... 59

Stocked lake trout growth .................................. 59

Stocked lake trout recruitment ............................... 62

Stocked lake trout mortality ................................. 64

Stocked lake trout selectivity ................................ 67
DISCUSSION ....................................................... 69
Time-varying growth effects on lake trout assessment .................... 70

Wild lake trout mortality ........................................... 71
Stocked lake trout mortality ........................................ 75
Progress of lake trout restoration .................................... 76
Suggestions for future research ..................................... 77
Managing toward the long term goal ................................. 78
APPENDIX - ADDITIONAL TABLES .................................... 81
LIST OF REFERENCES ............................................... 89

LIST OF TABLES

Table 1. Age-specific natural mortality rates (MO) used in the population assessment
model for MI4 of Lake Superior. Values were estimated by Sitar (1996) using an
SCAA model for lake trout in Lake Huron. ........................... 15

Table 2. Methods used to age samples of lake trout from MI4 of Lake Superior by
Michigan DNR assessments and commercial sampling from 1971-1995. ..... 22

Table 3. Stock recruitment model with parameter estimates and asymptotic errors for
lake trout in MI4. Variable definitions: W,- = estimated total number of wild lake
trout eggs produced in year i, and S,- = estimated total number of stocked lake
trout eggs produced in year i. Parameter estimates were obtained fiom
unpublished results. ............................................. 72

Table 4. One hundred year projected values of recruitment (number), spawner
abundance, and total annual yield (both in Kg) of lake trout in MI4 of Lake
Superior. The 1994 estimate of fishing intensity (f) was used as a baseline value.

............................................................. 74
Table 5. Model ageing error matrix for 1971-1988 based on lake trout samples from
Michigan waters of Lake Superior, 1993-1995. True ages determined from
finclips of stocked lake trout. Coded ages determined by scale annuli. Data
supplied by Michigan Department of Natural resources. .................. 81

Table 6. Model ageing error matrix for 1989-1994 based on lake trout samples from
Michigan waters of Lake Superior, 1993- 1995. True ages determined from
finclips of stocked lake trout. Coded ages determined by scale annuli up to age-8
and by otoliths age-9 and older. Data supplied by Michigan Department of Natural
resources. .................................................... 82

Table 7. Fitted parameters from statistical catch-at-age constant growth (CG) and time-
varying growth (TVG) models for wild and stocked lake trout in MI4. . . . . 83

Table 8. Fitted parameters from statistical catch-at-age constant growth (CG) and time-
varying growth (TVG) models for wild and stocked lake trout in MI4. Values
with and asterix (*) were set at zero since no fish were stocked in that particular

year .......................................................... 84

Table 9. Fitted parameters from statistical catch-at-age constant growth (CG) and tirne-
varying growth (TVG) models for wild and stocked lake trout in MI4. ....... 85

Table 10. Commercial harvest, mean weight, recreational harvest, and total harvest of
lean lake trout in MI4 of Lake Superior, 1983-1994. The 1990 commercial
harvest was determined from the average mean weight from the two adjacent
years. The recreational harvest prior to 1987 is estimated as the mean recreational
harvest from 1987-1989. Data provided by Great Lakes Indian Fish and Wildlife
Commission and Michigan Department of Natural Resources. ............. 86

Table 11. Observed (obs.) and predicted (pred.) harvest (in numbers) from time-varying
growth models for wild and stocked lake trout in MI4. Observed data obtained
from Michigan Department of Natural Resources and the Great Lakes Indian Fish
and Wildlife Commission. ........................................ 86

Table 12. Number of gill net lifts, mean catch per unit effort (CPUE), coefficient of
variation (CV) of CPUE from individual years, and variation of mean CPUE all
years combined for wild and stocked lake trout caught in spring assessments in
MI4 of Lake Superior from 1971-1995. Data from Michigan Department of
Natural Resources. ............................................ 87

Table 13. Number of gill net lifts, mean catch per unit efiort (CPUE), coefficient of
variation (CV) of CPUE from individual years, and variation of mean CPUE all
years combined for wild and stocked lake trout caught in summer assessments in
MI4 of Lake Superior from 1985-1995. Data from Michigan Department of
Natural Resources. ........................................... 88

LIST OF FIGURES

Figure 1. Lake trout management areas in Lake Superior. U.S. management areas are
denoted by state: MI, Michigan; MN, Minnesota; WI, Wisconsin. Areas marked
by numbers only are in Canadian waters. .............................. 3

Figure 2. Linear regression of mean coded ages from scales to fincoded (true) ages of
lean lake trout caught in the spring assessment in Michigan waters of Lake
Superior from 1993- 1995. Data from Michigan Department of Natural Resources
............................................................. 23

Figure 3. Linear regression of mean coded ages from otoliths to fincoded (true) ages of
lean lake trout caught in the spring assessment in Michigan waters of Lake
Superior fiom 1993-1995. Data from Michigan Department of Natural Resources.

............................................................ 23

Figure 4. Recruitment estimates from constant growth (CG) and time-varying growth
(TVG) models of wild lake trout in MI4 of Lake Superior, 1971-1995.
Recruitment after 1990 was set equal to the estimate for 1990 because one year-
olds after 1990 were never large enough to be adequately sampled. ......... 29

Figure 5. Observed and predicted catch per unit effort (CPUE) of wild lake trout in MI4
spring assessments of Lake Superior, 1971-1995. CPUE is defined as the number
of lake trout caught in 1.0 km of gill net, standardized to net-nights. Predictions
were made using constant growth (CG) and time-varying growth (TVG)
population assessment models. .................................... 30

Figure 6. Mean instantaneous mortality rates of wild lake trout ages 5-10 in MI4 of
Lake Superior, 1971-1995, from constant growth (CG) and time-varying growth
(TV G) models. The horizontal line represents a total annual mortality rate of
45%. ........................................................ 31

Figure 7. Actual numbers of hatchery-reared lake trout stocked and recruitment estimates
of stocked lake trout from constant growth (CG) and time-varying grth (TVG)
models for MI4 of Lake Superior. .................................. 32

Figure 8. Mean instantaneous total mortality rate estimates of stocked lake trout ages
5-10 in MI4 of Lake Superior, 1971-1995. Estimates were made using constant
growth (CG) and time-varying growth (TVG) assessment models. The horizontal
line corresponds to a total annual mortality rate of 45%. ................. 33

Figure 9. Observed and predicted catch per unit effort (CPUE) of stocked lake trout in
MI4 spring assessments of Lake Superior, 1971-1995. CPUE is defined as the
number of lake trout caught in 1.0 km of gill net, standardized to net-nights.
Predictions were made using constant growth (CG) and time-varying growth
(TVG) population assessment models. ............................... 35

Figure 10. Observed and predicted values of catch per unit effort (CPUE) for stocked
lake trout from the summer assessment in MI4 of Lake Superior, 1985-1994.
CPUE is defined as the number of lake trout caught in 1.0 km of gill net,
standardized to net-nights. ..................................... 37

Figure 11. Observed and predicted values of catch per unit effort (CPUE) for wild lake
trout from the summer assessment in MI4 of Lake Superior, 1985-1994. CPUE is
defined as the number of lake trout caught in 1.0 km of gill net, standardized to
net-nights. ................................................ 40

Figure 12. Logo-based residuals from model predictions of spring assessment catch per
unit efiort (CPUE) of wild lake trout in MI4. ......................... 40

Figure 13. Observed and predicted mean total length for age 7-9 wild lake trout from
spring assessments in MI4 of Lake Superior. ......................... 42

Figure 14. Length specific selectivity patterns estimated for spring and summer
assessments and fishery harvest of wild lake trout. ...................... 43

Figure 15. Standardized residuals for spring assessment age compositions of age 7- 10
wild lake trout in MI4. Standardized residuals equals (observed) minus (predicted)
proportions at age divided by estimated standard deviation. ............... 44

Figure 16. Loge-based residuals from model predictions of spring assessment catch per
unit effort (CPUE) of stocked lake trout in MI4. ....................... 47

Figure 17. Observed and predicted mean total length for age 7-9 stocked lake trout from
spring assessments in MI4 of Lake Superior. ........................ 50

Figure 18. Standardized residuals for spring assessment age compositions of age 7-10
stocked lake trout in M4. Standardized residuals equals (observed) minus
(predicted) proportions at age divided by estimated standard deviation. ...... 51

Figure 19. L-infinity estimates from constant growth (CG) and time-varying growth
(TVG) models for wild lake trout in M4. ............................ 53

Figure 20. Recruitment (age-1) and abundance at age-7 estimates for 1970-1989 year
classes of wild lake trout in M4. ................................... 54

Figure 21. Instantaneous mortality rates based on mean 1990-1994 model estimates for
wild lake trout, ages 1- 15. Mortality components: M0 = natural mortality, ML =
sea lamprey induced mortality, F = fishing mortality, and Z = total mortality. The
horizontal dashed line represents a total annual mortality rate of 45%. ....... 56

Figure 22. Instantaneous mortality rates averaged across ages 5- 10 for wild lake trout in
M4, 1983-1995. Mortality components: M. = sea lamprey induced mortality,
F = fishing mortality, and Z = total mortality. The horizontal line represents a total
annual mortality rate of 45 %. ...................................... 57

Figure 23. Fishing intensity estimates for wild and stocked lake trout in M4 of Lake
Superior, 1983-1995. .......................................... 58

Figure 24. Wild, stocked, and total spawner abundance estimates of lake trout in M4,
1971-1995. ................................................... 60

Figure 25. L-infinity estimates from constant growth (CG) and time-varying growth
(TVG) models for stocked lake trout in M4. ........................ 61

Figure 26. Estimates of recruitment (age-1) and abundance at age-7 of stocked lake trout
and the actual number of lake trout planted in M4 of Lake Superior for 1970-
1988 year classes. .............................................. 63

Figure 27. Instantaneous mortality rates based on mean 1990-1994 model estimates for
stocked lake trout, ages 1-15. Mortality components: MO=Natural mortality,
M;sea lamprey mortality, F=fishing mortality, and Z=total mortality. The
horizontal dashed line represents a total annual mortality rate of 45%. ....... 65

Figure 28. Instantaneous mortality rates of stocked lake trout averaged across ages 5-10.
Mortality components: M;sea lamprey induced mortality, F=fishing mortality,
and Z=total mortality. The horizontal line represents a total annual mortality rate
of 45%. ...................................................... 66

xii

Figure 29. Length specific selectivity patterns for spring and summer assessments and
fishery harvest of stocked lake trout. ................................ 68

Figure 30. Yield and spawner abundance projections for lake trout in M4 of Lake
Superior based on (a) fishing intensity rate equal to that estimated for 1994
(f =0.67), and (b) fishing intensity rate reduced 32% (f =0.45) from the 1994f
estimate. Projections in year 0 correspond to the year 1995. .............. 73

Figure 31. One hundred year projections of recruitment (numbers), spawner abundance,
and total annual yield (both in Kg) of lake trout in M4 using the 1994 estimate of
fishing intensity (f = 0.67) as a baseline value. ........................ 74

INTRODUCTION

Lake trout were dominant predators in Lake Superior but stocks were driven to
extinction or extremely low levels in the 1950's through combined effects of fishing and
predation by sea lamprey (Pycha and King 1975; Walters et al. 1980). Effective chemical
control of sea lampreys, intensive stocking of hatchery-reared lake trout, and a
cooperative lake trout rehabilitation plan between state, tribal, and international agencies,
have helped restore naturally-reproducing populations of lake trout in most areas of Lake
Superior in the 1990's. However, present abundances of inshore stocks are only 50-60%
of historic abundances or the rehabilitation goal (Hansen et al. 1995).

Commercial fishing in Lake Superior is thought to have originated along the
southern shores of Lake Superior in the 17th and 18th centuries by Native Americans
(Nute 1944; Warren 1957). Lake trout harvest was less than 1 million kg in 1879,

1 increased to a peak of 3 million kg in 1903, and averaged 2 million kg per year from 1913
to 1950 (Baldwin et aL 197 9). Improvements in gear efficiency and increased fishing
intensity in the 1940's and 1950's, combined with invasion of the sea lamprey beginning
1946, caused native lake trout populations to collapse (Pycha and King 1975; Walters et
al. 1980; Hile et a1. 1951). Management agencies initiated a sea lamprey control program

beginning in 1953. Initially mechanical and electrical barriers were used to prevent

2

upstream passage of spawn-run sea lampreys (Lawrie and Rahrer 1973). Sea lamprey
abundance peaked between 1958-1961, but dropped 87% in 1962 when the chemical
toxicant 3-trifluormethyl-4-nitrophenol (TFM) was proven to be an effective treatment to
control sea lamprey abundance (Smith and Tibbles 1980).

Thousands of hatchery-reared lake trout were planted annually into Lake Superior
starting 1947 in Ontario, in 1952 for Wisconsin and Michigan, and in 1962 for Minnesota.
During the 1960's these fish increasingly dominated inshore lake trout catches, accounting
for 95% of the trout taken in most areas (Lawrie and Rahrer 1973). Stocking of lake
trout became intensive throughout the 1960's after methods to control sea lamprey
became feasible. The commercial fishery for lake trout was closed lake-wide in 1962, and
remained closed until the 1970's when abundances began to increase and tribal fishing
rights were confirmed (Pycha and King 1975; Hansen et a1 1995).

A Joint Strategic Plan for Management of the Great Lakes Fisheries (also known
as SGLFMP), developed by fishery management agencies and the Great Lakes Fishery
Commission (GIfC), called for fish communities based on self sustaining stocks,
supplemented by stocking where necessary (GLFC 1980). Objectives for lake trout
restoration in Lake Superior were established by an inter-agency plan in 1984-1986 by the
Lake Superior Lake Trout Technical Committee (LSL'I'I‘C). The plan’s long term goal is
to achieve a sustainable lake trout yield of 2 million kg per year. The plan also defined
management areas within Lake Superior (Figure 1), for reporting, lamprey control,
assessment and research, and set protocols for stocking of lake trout and non-native

salmonines (LSLTI‘C 1986).

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Presently in Lake Superior three distinct morphological forms and/or behavioral
variants exist; leans, fats (siscowets), and humpers, although increasing evidence suggests
that cross-breeding takes place between variants (Burnham-Curtis and Smith 1994;
Goodier 1981). Lean lake trout have slender bodies, low body fat, and are characteristic
of inshore waters less than 73 meters (40 fathoms) in depth. Siscowets have stout bodies,
a high fat content, and are usually found in water deeper than 90 meters (50 fathoms).
Humpers have been described as deep bodied with a thin abdominal wall, an intermediate
fat content, and have been found isolated above offshore shoals separated by deep water
(Rahrer 1965). Lake trout rehabilitation in Lake Superior has emphasized recovery of
lean lake trout, referred herein as “lake trout”; however, there are plans to develop fishery
and assessment objectives for each of the three lake trout forms historically caught in Lake
Superior (GLFC 1996).

Lake trout are slow growing fishes and can be long lived. In Lake Superior, lake
trout have been reported to reach maturity between the ages of 6 and 11 (Peck 1979;
Ebener 1990; Ferreri 1995). Spawning times and sites differ between variants, but leans
normally spawn between late September and early November on gravel beaches and rocky
shoals in waters 2-37 meters in depth (Eschrneyer 1955). Some populations of lake trout,
possibly now extinct, migrated up tributaries as far as 2 miles to spawn (Loftus 1958).
Long range migration of lake trout in Lake Superior is rare; tagging studies of wild and
stocked lake trout indicate that most fish remain within a 81 km of release points or
planting sites (Pycha et aL 1965; Rahrer 1968; Swansen 1973; Ebener 1990).

The Lake Superior Technical Committee (LSTC) has estimated that a target of

5

36-101 million recruits per year is required to achieve the rehabilitation goal of 2 million
kg annual sustainable harvest (GLFC 1996). One strategy adopted by management
agencies is to limit total mortality to 45% because model simulations of spawner
abundance decreased when mortality exceeded 45% but increased when mortality was
below that level (GLFC 1996; Technical Fisheries Review Corm'nittee 1992). Presently,
“Total Allowable Catch” (TAC) models are used by commercial fishery management
agencies to set annual harvest rates for individual management districts (Ebener et al.
1989). TAC models project yields of hatchery fish based on total mortality limits, the
numbers of fish stocked, and estimated mortality rates. Similar calculations are done for
wild lake trout, with wild recruitment estimated from the proportion of wild lake trout
caught in assessment surveys.

Questions remain regarding the best management strategies for lake trout in Lake
Superior. An important question is whether a total mortality rate of 45% is the optimal
level for building and sustaining lake trout populations in Lake Superior. Even with an
established target mortality rate, determination of TAC's following previously established
procedures requires estimates of survival at young ages and an estimate of the ratio of
marked hatchery fish to unmarked wild fish (Ebener et aL 1989). Estimates of early life
survival are subject to potential error and are based on limited data. Furthermore,
management agencies have decided to discontinue stocking throughout most US. waters
of Lake Superior because recent analyses indicate that additional stocking of "lean"
hatchery fish is doing little to promote restoration (Hansen et al. 1994; Roger Gordon,

US. Fish and Wildlife, and M. Ebener, Chippewa/Ottawa Treaty Fishery Management

6

Authority, pers. comm). Without information on the catch rate of hatchery fish of
"known" abundance to calibrate catch rates of native fish, the current method of
estimating absolute recruitment of naturalized fish will no longer be feasible. Thus, there
is a need to develop estimates of absolute recruitment that are independent of known
hatchery releases and estimates of their survival.

The goal of this research was to assess recent population dynamics of lake trout in
Michigan waters of Lake Superior in order to provide guidance for managing lake trout
populations. The objectives of this project were to:

1. Develop an age/size structured stock assessment model for lake trout in an
example area of Lake Superior, designed to be fitted to age and length
composition data from the fisheries and other sources, estimates of total
fishery removals, and relative indices of abundance (e. g., catch per unit effort
from assessment fisheries).

2. Estimate abundance, recruitment, growth, and mortality rates by fitting the
model.

3. Estimate the relationship between recruitment and lake trout spawning stock
size based on the stock assessment results described under objective two, and

use this relationship to evaluate management strategies.

METHODS

5mm

Under the inter-agency lake trout restoration plan, Lake Superior is divided into
specific geographic areas for reporting, assessment, and research (Figure l), which are
modified from the statistical districts established by Hile (1962). I examined assessment
and creel data from the Michigan Department of Natural Resources (MIDNR), in addition
to harvest and biological sampling data from the Great Lakes Indian Fish and Wildlife
Commission (GLIFWC) and the Chippewa/Ottawa Treaty Fishery Management Authority
(COTFMA) for Michigan waters of Lake Superior, M2 - M8. The first step in the
model building process was to identify a nominal stock of lake trout subjected to similar
recruitment, growth, and mortality rates. Based on data collected from 1980 to the
present, stocks within Lake Superior Management zones M4, M5, and M6 were
separately, or collectively, a good target population for this study (R. Schorfhaar,
Michigan Department of Natural Resources, and W. Mattes, Great Lakes Indian Fish and
Wildlife Commission, pers. comm).

The decision to model M4, separately, as the initial target population was based
on a number of issues. TAC models have reported different estimates of lamprey induced

mortality rates across all management areas M2-M6 (Ebener et al 1989). In addition,

8

commercial harvest quotas were established on a management unit basis, and total
harvests have been noticeably different over time between management areas (Mattes et
a1. 1996; Peck and Schorfhaar 1994). Based on mark-recapture of spawning stocks
around the Keweenaw Peninsula, Ebener (1990) reported that a greater number of the fish
tagged in M4 were recaptured in M4 than trout tagged in other units. Finally, the
geographic region of Keweenaw Bay suggests that stocks in M4 are isolated from
surrounding areas, and, thus, a likely candidate for being approximated by a closed

population model.

W

I compiled data from the Michigan DNR spring assessment 1971-1995, summer
assessment 1985-1995, and creel survey 1985-1995, in addition to the commercial fishery
harvest and sampling data 1983-1995, for M4 of Lake Superior. Spring assessments
targeting cornmercial-size (17 inches and greater) lake trout were performed by
commercial contractors or state-owned operators in the spring (April-lune), using nylon
114-mm (4.5-4.6 in) stretched-mesh gill nets, fished for approximately 3 nights at depths
of 20-40 fathoms. From 197 l- 1987 scale samples were taken from a lake-wide subsarnple
of lake trout with a target of 40 fish per inch group. Ages were determined from the
scales and applied to an age-length key to estimate the age-length compositions. From
1988-1994 scales and/or otoliths were taken from all fish sampled for subsequent ageing.

The summer assessment was designed primarily as an assessment of pre-recruit

(to fishery) lake trout. They were performed from July-August by Michigan DNR

9
personnel using nylon graded-meshed gill nets (300-ft panels of 2.0-, 225-, 2.5-, 2.75-,
3.0-, and 3.5-in stretch-measure mesh), fished approximately 24 hours at depths of 15-40
fathoms. All lake trout caught in the assessments were measured to the nearest 0.1 inch
and checked for fin clips and lamprey wounds or scars. Total dressed and round weights
were recorded and individual round weights were obtained periodically to evaluate length-
weight relationships (Peck and Schorfhaar 1994; Peck and Schorfhaar 1991).

Commercial catch and effort data were obtained from catch reports submitted by
commercial fisherman 1983-1995. Fisherman were required to record date of lift, total
feet of gill net lifted, material of net, mesh size, location of lift, and pounds of each species
caught (in round or dressed weights). Age-length compositions and length-weight
relationships were derived from biological monitoring of catches, several times a month by
the Bad River, Keweenaw, and Red Cliff Fisheries Departments, and the Great Lakes
Indian Fish and Wildlife Commission (Ebener 1986; Mattes et al. 1996). Numbers of lake
trout were obtained by dividing the commercial harvest dressed weight by the mean
dressed weight per lake trout from commercial samples. Michigan DNR creel survey data
1987-1994 provided the observed recreational harvest. The catch from 1983-1986 was
based on the mean recreational harvest from 1987-1989. The mean recreational harvest
was approximately 16% of the total harvest and similar size ranges of fish appeared in
both fisheries. I concluded that little would be gained from modeling both fisheries
independently, and combined recreational harvest with commercial harvest to obtain the

observed total harvest.

10

Dalmatian

Catch per unit effort, as an index of relative abundance, and age composition were
determined for each year in each data-set. Catch-per-unit-efi‘ort (CPUE) was defined as
the number of lake trout caught in 1.0 km of gill net. Because net sets varied in duration,
CPUE was standardized to net-nights using corrections derived from controlled
fishing in 1970. A set of one night duration was the equivalent of 1.00 net-night, two
nights duration - 1.52 net-nights, three or more nights duration - 1.80 net-nights (Curtis et
al., unpublished manuscript). Hatchery reared lake trout were all fin clipped prior to
stocking so distinctions between stocked and wild lake trout were made on the presence
or absence of a fin clip. Age compositions and CPUE were determined separately for
stocked and wild lake trout. I assumed variation in CPUE was constant for individual
lifts; hence year to year variation in CPUE was caused by the number of lifts per year.
Observed CPUE and corresponding coefficient of variation (CV) of mean CPUE are
listed in tables (4 and 5) for the spring and summer assessments. To reduce model
complexity, I also assumed that assessment data came from simple random samples. I
realize, however, that assessments may be more systematic than random because they may
target areas where fish tend to be caught. Also, weather conditions often dictate when
assessments can be conducted. Treating individual gill net sets from spring and summer
assessments as random samples, however, may lead to biased estimates of variances for
CPUE, and the CPUE index itself, depending on the extent and nature of spatial
correlation (see Discussion: Suggestions for future research).

Both the spring assessment and commercial sampling were inconsistent in

11

reporting undersized lake trout (less than 17 inches). According to W. Mattes
(pers.comm.), fish less than 17 inches are not included in total harvest reports. Where
applicable, I subtracted the CPUE of fish less than 17 inches from the total survey CPUE
to include only larger fish in observed CPUE.

Age-length compositions were calculated in two ways depending on data sources.
For the spring assessment and the commercial fishery, length-classes started with a length
of 17 inches (43.2 cm), and spanned over 2 inch length bins. Since all fish caught in both
the commercial fishery and the spring assessment were age-3 or older, proportions of lake
trout less than age-3 were set to zero. For summer assessments catches of fish less than 9
inches were combined as were fish greater than 24 inches; fish between 9-24 inches were

grouped in one inch intervals.

Warm

The lake trout population assessment model for M4 was similar to the “stage 2"
stock synthesis model developed by Methot (1990), although I developed my own model
application using Excel version 5 .0 software. This model is an implementation of the
statistical catch-at-age analysis (SCAA) and incorporates auxiliary information from
different sources. This approach models the age structure of the population but defines
fishery selectivity patterns as explicit functions of length. In essence, this model simulates
the population dynamics, fishery and data collection processes, and estimates a suite of

parameter values so that the model produces the best possible match with observed

l2

quantities. Advantages of this modeling approach for lake trout in Lake Superior are:

. SCAA models integrate fishery assessment age composition data to estimate
patterns of removals of the population and provide information on year-to-year
recruitment (Fournier and Archibald 1982; Deriso et al. 1985; Methot 1990).

0 Modeling selectivity as a function of length rather than age has the potential to
reduce bias associated with time varying growth rates.

a Wild and stocked lake trout populations can be modeled independently of one
another by estimating recruitment of both wild and stocked fish during model

fitting.

1 I l l l . .
The M4 lake trout assessment model is a cohort survivorship model applied over
a time series (1971-1995), based on data collected from assessment and fishery harvest
information, and adapted to both wild and hatchery-reared stocks. Abundance estimates
of age-1 fish to a cohort represent recruitment from either natural reproduction or
numbers of “viable” stocked yearlings and are parameters directly estimated during the
model fitting. The model predicts the numbers-at-age surviving to the following year and
keeps track of each cohort throughout the time series. A growth submodel estimates
mean total length and dynamically tracks changes in length over time. Auxiliary sources
of data are modeled independently based on selectivity patterns as specific functions of
length, rather than age, to assess time-varying growth affects. The model addresses bias

associated with errors in ageing techniques by transforming true age compositions to what

12

quantities. Advantages of this modeling approach for lake trout in Lake Superior are:

a SCAA models integrate fishery assessment age composition data to estimate
patterns of removals of the population and provide information on year-to-year
recruitment (Fournier and Archibald 1982; Deriso et al. 1985; Methot 1990).

. Modeling selectivity as a function of length rather than age has the potential to
reduce bias associated with time varying growth rates.

0 Wild and stocked lake trout populations can be modeled independently of one
another by estimating recruitment of both wild and stocked fish during model

fitting.

Wu

The M4 lake trout assessment model is a cohort survivorship model applied over
a time series (1971-1995), based on data collected from assessment and fishery harvest
information, and adapted to both wild and hatchery-reared stocks. Abundance estimates
of age-1 fish to a cohort represent recruitment from either natural reproduction or
numbers of “viable” stocked yearlings and are parameters directly estimated during the
model fitting. The model predicts the numbers-at-age surviving to the following year and
keeps track of each cohort throughout the time series. A growth submodel estimates
mean total length and dynamically tracks changes in length over time. Auxiliary sources
of data are modeled independently based on selectivity patterns as specific functions of
length, rather than age, to assess time-varying growth affects. The model addresses bias

associated with errors in ageing techniques by transforming true age compositions to what

13

we expect to see in the harvest or surveys. Harvest, effort, and age-length composition
estimates are compared to observed quantities using a maximum likelihood approach. A

numerical search is done for the set of parameter estimates that maximizes the likelihood.

Ahrradmcc
Numbers at age (a) and year (y) of the population were determined by the
exponential mortality equation:

Na +1,y+1 = N

a.y

e -Za. y (1)
where Z was the instantaneous mortality rate equal to the sum of natural mortality (M0)
plus lamprey mortality (ML) plus fishing mortality (F):

Z“ = M0“ + ML M + FM (2)
Abundance at ages 2-15 in 1972-1995 were calculated from equation (1). Recruitment
(the number of age-1 fish), and initial abundance at ages 2-7 for wild fish (ages 2-8 for
stocked fish) in 1971 were parameters estimated during the model fitting. Abundance of
wild lake trout older than age-7 and stocked lake trout older than age-8 in 1971 were set
equal to zero, reducing the number of parameters required by the model, justified by the
small percentages of older lake trout caught in spring assessments in the 1970's.
Recruitment estimates of stocked fish were compared to the actual number stocked to

assess survival of hatchery-reared lake trout.

14
W
The model calculated age-specific total instantaneous mortality fiom equation (2),
and also calculated age-length stratified values for mortality in 1983-1995 by:

Z” , = M0,, + ML,y + f, S, (3)
where f, was fishing intensity in year y and S, was the length specific selectivity of the

commercial fishery. Values for Z,, x, were required to determine harvest age-length

compositions comparable to observed values from commercial sampling data.

Natural mortality

I defined natural mortality (M 0 ) as the mortality experienced by the population in
absence of fishing and sea lampreys. I assumed natural mortality did not vary over the
' time period 1983-1995 for both wild and stocked fish, and I used the age-specific values
of M0 reported by Sitar (1996) , estimated from a SCAA model of lake trout in Lake

Huron (Table 1).

Fishing mortality

Projections of abundance at age required age specific fishing mortality (F a, y), while
predictions of age-length compositions of the harvest required estimates of length specific
mortality (F ,_ ,). Fishing mortality was calculated in terms of length categories and then

converted to a function of age:

Fy’, = fy S, (4)

15

Table 1. Age-specific natural mortality rates
(MO) used in the population assessment model
for M4 of Lake Superior. Values were
estimated by Sitar (1996) using an SCAA model

 

 

 

for lake trout in Lake Huron.
id MO
1 0.6663 9 0.1001
2 0.3184 10 0.1000
3 0.1716 11 0.1000
4 0.1235 12 0.1000
5 0.1077 13 0.1000
6 0.1025 14 0.1000
7 0.1008 15 0.1000
8 0.1003
21 FL): Na,y,I _
FM 2.2, N... 5 2,5,1-

(5)

where a was the target age in the range of age-classes (k), and Paw was the proportion of
fish in age class, a, length class, I , and year, y. The model calculated selectivity values for
each source using a garnma-type function described by Deriso et al (1985):

l“em

S =
l maxj( few) (6)

 

where l was the midpoint of the length bin, or and [3 are selectivity coefficients estimated

during the model fitting, and max,- ( ) selects the length category (i) that maximizes the

16

function and defines the length category with a selectivity equal to 1.0.

Lamprey mortality
I used spring assessment data on lamprey wounding rates to estimate instantaneous
lamprey-induced mortality rates from a submodel in the Lake Superior lake trout TAC

model (Ebener et al. 1989). Mean wounds per fish were calculated by:

 

_ _ l y
Wily _ (7)

where W, , was the number of wounds recorded per fish of length-class (i) in year (y) and
n, , was the number of fish sampled. Lamprey-induced mortality rates were determined

fiom Eshenroder and Koonce (1984):

 

(8)

 

 

Probabilities of survival from a sea lamprey attack, P8 ,, were reported by Grieg et al.
(1992): 0.35 for 432-533 mm lake trout, 0.45 for 534-635 mm lake trout, and 0.55 for

636 mm or greater lake trout. Length specific mortality rates were converted to age

specific mortality rates by:

n i
ML =2. E—U— ML,”

my
1’ "My (9)

17

where i is the target length-class in the range of length-classes (1) (Ebener et al. 1989).
The lamprey submodel assumes that the wounds per fish from spring assessments
were representative of attacks that occurred the previous year, and that lamprey-induced

mortality was the same for both wild and hatchery-reared lake trout (Ebener et al. 1989).

W

The period 1971-1982 differs from later years in that neither harvest, commercial
sampling, nor summer assessment data were available. Over this time series the model
relied entirely on spring assessment information. Simulation trials using the relationships
described in equations (2) and (3) failed to predict mortality events required to match
large fluctuations in observed abundance from spring assessments. I therefore combined
the effects of M 0 and F together into a new parameter (ZW) for the fishable population,
and allowed the model to estimate Z”, over specified time intervals from 1971-1982 to
best match the spring assessment CPUE:

Z

a.y

= ZMFM + Z! (10)

a. y
Values of Z", for ages 1-4 were constant and equal to the natural mortality values used in
the later years because these fish were too small to be caught in significant numbers by the
fishery. Zm estimates for ages 5- 15 were grouped into periods of equivalent mortality
rates during simulation trials based on two objectives: (1) annual mortality rates were
combined for as many years as possible in attempt to reduce the number of parameters
required by the model, and (2) spring assessment CPUE estimates fitted by the model

peaked in close apprordmation to observed values.

18
Grinch
Mean length at age for age-1 fish in 1971-1995 and ages 2-15 fish in 1971 was

determined by the von Bertalanffy equation:

" -k(l -t

LU = Looy-l (l—e 0’) (11)
Mean length for ages 2-15 in 1972-1995 were calculated by adding growth predicted by
the von Bertalanffy equation in incremental form to the mean length of that cohort:

_ - _ _,, (12)
L = La—r,y—1Jr (Lwy-l-La—l.y~l ) “—3 )

a,y

k and to were growth parameters estimated by the model, and t was set at 1 year. Values
of L, , theoretical maximum length, represented yearly growing conditions and were
estimated during the model fitting process. Thus, a large estimated L, represented
favorable growing conditions and a larger incremental growth rate than a smaller L, . If
predicted growth increments from equation ( 12) were less than zero, an increment of zero
was used. I also modeled growth using time-varying values of k rather than L, , but this

did not improve the model fit.

5 -l I . .
The proportion of the population (Pa, ,, ,) of age (a) in length class (I) and year (y)
was based on a normal distribution about the mean length for that age. I assumed a

constant coefficient of variation in lengths about their age specific mean (Ricker 1975),

l9

and the CV was estimated during the model fitting. Proportions falling in specific length
categories (described in the section titled Data summarization) were then calculated from

a normal cumulative distribution function.

W

The model predicted abundance at age of the population at the beginning of each
year (Equation 1) and followed the numbers surviving to the appropriate time interval of
both spring and summer assessments by:

N

a. y+t

= NH e 42W (13)
Abundance at time t = 0.3 estimated the size of the population at approximately the
midpoint of the spring survey (May 15th), and abundance at t = 0.59 represented the
population at the midpoint of the surmner survey (August 2nd). Numbers at age in a given
length class were calculated as:

Na,y+t,l = Na,y+tPa (14)

,y,l
N,_ N, values were multiplied by the appropriate selectivity function estimates (Equation
6) to predict the age-length compositions expected in the assessments:

na,y+t,l = Nam: S i (15)
Where necessary, these values were transformed to coded age-length compositions to
predict observed data (see later section titled Aging error). Proportions were then
determined by:

__ "my +t,I

pa.y+r,l — Elzk "Ly”.l (l6)

 

20

Spring and summer assessment CPUE’s were estimated by multiplying survey age-length

compositions by catchability, q, and summing over all ages and lengths:

Ky : q 2120 na,y+t,l (17)

Hmtnstirnates
Numbers at age in the beginning of the year (Equation 1) were multiplied by the
age-length proportions in the population, Pa, ,, ,, using equation (14) to obtain age-length

compositions, N, y, ,, in the population. Harvest at age and length was determined by the

 

Baranov catch equation:
F I ‘2
Canal = Z" (NW - N.,,,,e W) (18)
a,y,l

where 2,. L, was determined from equation (3), F L, from equation (4). Total harvest was

obtained by summing the age-length composition of the harvest over all ages and lengths:
Cy = Z, Ea Cm, (19)

Fincodes were used to age hatchery-reared lake trout from 1984-1989; all remarnm' ' g

harvest estimates required ageing error transformations to coded ages of harvest.

21

Proportions of the harvest age-length compositions were determined after ageing error

 

(if required):
Ca. .1 (20)
pa. .1 = y
y cy
Arnhem

Ageing techniques used by assessment and commercial fishery management
personnel are listed in Table (2). Beginning in 1989 ageing methods changed fi'om scales
only, to scales for fish less than 23 inches and otoliths for fish 23 inches and greater, based
on Johnson and MacCallum’s (1987) results that lean lake trout older than age-8 were not
mowing suficiently to form annuli on scales. I examined 1993- 1995 assessment data
collected across all Michigan management units and compared the recorded ages of lake
trout aged independently by two or more different methods: scales, otoliths, and fincodes.
From these data I constructed a combination of ageing error transition matrices used by
the model, relating true ages (fincoded) to coded ages (recorded age by either scale or
otolith method) in attempt to reduce bias associated with ageing error.

The first matrix was applied to wild lake trout over the period 1971-1988, prior to
the use of otoliths (Appendix). The probability that a fish of true age (P, a) was coded age
c was based on a normal distribution described by the standard distribution about the mean
coded age for ages 4-8. For example, for a fish with a true age of 4, the probability that it
was correctly coded as age-4 was taken as the probability the fish was aged

between 3.5 and 4.5, based on the distribution of recorded ages from scale readings of

22

Table 2. Methods used to age samples of lake trout from M4 of Lake Superior by
Michigan DNR assessments and commercial sampling from 1971-1995.

 

 

 

S Iin source Pen'od Lake trout A ei Method Reference
Michigan DNR 1971 - 1995 Stocked Fincodes + subsamoles Peck and Schorfhaar (1994)
of scales and otoliths
1971 - 1988 Wild Scales
1989 - 1995 Wild < 23 in. Scales
Wild 23+ in. Otoliths
Commercial 1984 - 1989 Stocked Fincodes M. Ebener (pers. comm.)
1984 - 1989 Wild Scales
1990 - 1995 Any < 23 in. Scales B. Mattes (pers. comm.)
Any 23+ in. Otoliths

 

 

age-4 fincoded lake trout caught in spring assessments. Sample sizes for true ages above

8 were small or non existent, so probabilities were based on a normal distribution about

the coded age obtained from a linear remession of mean coded ages to true ages (Figure

2) and a standard distribution of 1.25, the mean standard deviation for fincoded ages 9-15

for which data existed.

The second matrix transformed true ages to coded ages for wild lake trout and

commercial samples of stocked lake trout in 1989-1995. This matrix was identical to the

first matrix through age-8. For ages 9 and above, probabilities are based on a normal

distribution about the coded age obtained from a linear remession of mean otolith age to

fincode age and a standard distribution equal to that for an 8 year old fish (0 = 0.82)

(Figure 3). The transition matrices converted estimates of numbers at true age to an

expected coded age by:

na.y+t,lx Ta : ca.y,l

(21)

where n, M, was the estimated true age-length composition in year (y) fi'om assessments

 

23

I aura: 2.2088
R I 0.822.

 
 
  

Coded ages
‘ t5

ONO-56C

I 10 12 14 1B 18
Trueages

0 2 4 0

Figure 2. Linear remession of mean coded ages from scales to fincoded (true) ages of
lean lake trout caught in the spring assessment in Michigan waters of Lake Superior from
1993-1995. Data from Michigan Department of Natural Resources.

y = 0.782x + 1.6302
n2 -.- 0.9454

Coded can

 

duh-5.5
OMhOOONfiO

2 3 4 5 6 7 a 9101112131415161718
Trueages

Figure 3. Linear remession of mean coded ages from otoliths to fincoded (true)
ages of lean lake trout caught in the spring assessment in Michigan waters of Lake
Superior from 1993-1995. Data from Michigan Department of Natural

Resources.

24
or harvest, T, was the ageing error transition matrix containing individual Pm’s, and Ca. y',
was the coded age-length composition in year (y). For the commercial harvest age
compositions, C, L, (Equation 18) can be substituted for n, L, in equation (21) to obtain

observed coded age predictions in the harvest.

01"fi'

The M4 lake trout model estimated a suite of parameter values describing the
population dynamics and compared observed values to the model’s expected values using
a log-likelihood approach similar to that of Methot (1990). The objective function was
sum of the log-likelihoods from each of the model’s components:

LM=L,+L,+L3+L,+L,+L6 (22)
where L , and L2 were the likelihood functions for the spring and fall assessment CPUE,
respectfully, L 3 was the total harvest, L, and L, were the age-length compositions of the
spring and summer assessments, and L, was the age-length composition of the harvest.
This objective function was maximized by forward differencing of parameters in
log-space using a quasi-Newton algorithm.

The model assumed log-normal distributions for assessment CPUE and total

harvest. Log-likelihood components L, , L2, and L 3 were calculated from:

2

 

A
[ml-fl ~
L = -0.5 2; y + 1n -—1——
“f [ W271)

25

where Ay was the predicted assessment CPUE and total harvest in year y (K, and C,
respectively), A'ywas observed assessment CPUE and total harvest in year y, and oywas
the assessment CPUE and total harvest standard error on a log-normal scale in year y.
Values for 0 were calculated from the coefficient of variation from each data source (Law

and Kelton 1982) using:

(24)

 

o = J1n[(C.V.)2 +1]

The model assumed that the CV. of the total harvest was constant and based on a 1%
error in the reporting of true harvest (C.V. = 0.01).
Likelihood functions for assessment and harvest age-length compositions, L, , L5,

and L, were calculated from a multinomial error structure:

 

J!
L=X J £02m ,ln(pa ,)+X ln "
y y a.y. .y. y na.y.l!na+l.y.l!oocnj‘y.l!na.y.l+l'!ooona'y.k! (25)

where pa, ,D, was the estimated proportions of age-length compositions in assessments and
harvest and p’, x, was observed proportions. Also in equation (25): J was the effective
sample size, n was the age-length composition, j was the number of age classes, and It was
the number of length classes, all observed in the assessments and commercial biological
sampling. Efiective sample sizes were set to a maximum of 100 individuals so that large

sample sizes would not dominate the model’s fit (Fournier and Archibald 1982).

26

Mammalian

The M4 model was adapted to assess wild and hatchery-reared lake trout
independently and compare constant mowth to time-varying mowth. Simulation one, the
reduced model, assumed a constant mowth rate described by a single estimate of L, over
the entire time series. The constant mowth (CG) model required 24 less parameters
(yearly L, values) than the second simulation, the time-varying mowth (TVG) model
I used the likelihood ratio test statistic: 2[L(9) - L(00)] , to compare the fit of both
models to observed data (Seber and Wild 1989). In this test, L(0) and L(00) were the
total log-likelihood values (Lw) from the time-varying mowth and constant mowth

models, respectfully.

RESULTS

The time-varying mowth versions of both wild and stocked lake trout models fit
data significantly better than the constant mowth versions (P<0.005 for both). Temporal
patterns in mortality and recruitment were similar between the TVG and CG versions,
except for larger peaks in recnritment in the late 1970's and in mortality between
1981-1982 for the CG versions of both wild and stocked lake trout models. I conclude
that the driving force behind the differences between the CG and TVG models were
responses to peaks in observed CPUE. First, I present the contrasts between the TVG
and CG versions of both wild and stocked lake trout models. For the time-varying mowth
models, I then compare estimates to observed data and present population level patterns
for wild and stocked lake trout. Estimated parameters for all versions of the M4 lake

trout model are in the appendix.

WM

Both wild and stocked lake trout constant mowth models estimated periods of
much higher recruitment followed by higher mortality rates than the time-varying mowth
models. This general pattern appears to be a differential response by the two models to

spikes in observed spring assessment CPUE, which was the only data source available

27

28

during the period that major differences between the CG and TVG models occurred. Both
CG and TVG model predictions matched observed harvest closely. This result is not
surprising given the large weight errors in predicted harvest were given during model
fitting. Summer assessment CPUE predictions fit well with observed values fiom both CG
and TVG models, but were modeled only over the short time series of available data

(1985-1995).

Wild lake trout CG and TVG model comparison

For wild lake trout, recruitment estimates in 1975-1977 (Figure 4) were
substantially higher for the CG model than the TVG model. Age-1 fish in 1975-1977
were 4-6 year-olds in 1980, and 5-7 year-olds in 1981, which were peak years in spring
assessment CPUE. Thus, the CG model required much higher rates of recruitment in
order to match the large spike in observed CPUE than the TVG model (Figure 5).

Observed wild CPUE in the spring assessment dropped dramatically in 1982 to
approximately 50% of the 1981 peak value (Figure 5). This resulted in high estimates of
total instantaneous mortality (Z) in 1981 and 1982 (Figure 6). The CG model required
higher mortality rates than the TVG model over this period to reduce a larger population
produced from higher recruitment estimates in 1975- 197 7. After 1983, mean total
mortality rates from the two models followed similar trends, although mortality estimates

were slightly meater for the time-varying mowth model.

29

 

 

500-

TO; 450-:

C 400- +CG

g 350- +TVG

.2 300-

5 .

can 250‘ '

s 200- ' \

e \,

:5 150- . z \

g 100_ .f.‘ .\

I 50‘ l
Oiiiiiili+iiiiii+iiiiiii
1971 1975 1979 1983 1987 1991 1995

Year

Figure 4. Recruitment estimates from constant mowth (CG) and time-varying mowth
(TVG) models of wild lake trout in M4 of Lake Superior, 1971-1995. Recruitment after
1990 was set equal to the estimate for 1990 because one year-olds after 1990 were never
large enough to be adequately sampled.

30

fififlfloumwul
—-+——— TVG

CPUE

 

 

197 1975 1979 1W3 1%7 1991 19%
Year

Figure 5. Observed and predicted catch per unit efiort (CPUE) of wild lake trout in M4
spring assessments of Lake Superior, 1971-1995. CPUE is defined as the number of lake
trout caught in 1.0 In of gill net, standardized to net-nights. Predictions were made using
constant mowth (CG) and time-varying mowth (TVG) population assessment models.

31

1.2 “r

1.4.

0.8 if

N 0.6

 

0.4

   

 

0.2 -

 

 

0 r I I T 17 r ‘7 17 f

1971 1975 1979 1 1987 1991 1995
Year

I I T r T f t I l I f I ]

Figure 6. Mean instantaneous mortality rates of wild lake trout ages 5- 10 in M4 of
Lake Superior, 1971-1995, from constant mowth (CG) and time—varying mowth (TVG)
models. The horizontal line represents a total annual mortality rate of 45%.

32

  

 

 

1600 'F o
A 1400 _, n # Stocked
/ \
_._

é. as... o-d 1‘ EV:

I -o—
3: 1000 1- I l
E
0
E
.2:
3
r
r:

1971 1975 1979 1983 1987 1991 1995
Year

Figure 7. Actual numbers of hatchery-reared lake trout stocked and recruitment estimates
of stocked lake trout from constant mowth (CG) and time-varying mowth (TVG) models
for M4 of Lake Superior.
Stocked lake trout CG and TVG model comparison
Recruitment (age-1) estimates for hatchery-reared fish (Figure 7) showed little
resemblance to the actual number of yearling lake trout planted in M4. My estimates of
recruitment for both constant and time-varying mowth models were well above planting
levels prior to 1979. After 1979 this is reversed and recruitment estimates dropped to
very low levels.
Total instantaneous mortality estimates (Z) of stocked lake trout, averaged over
ages 5-10, peaked in 1981-1982, when once again the CG model’s estimates were much
higher than the TVG model’s estimate (Figure 8). This scenario is similar to that seen for

wild lake trout in that increased mortality was required to “kill off” excess fish left-over

33

_0_ CG
—-O—TVG

.4
a:
1
l

 

 

 

Year

Figure 8. Mean instantaneous total mortality rate estimates of stocked lake trout ages
5-10 in M4 of Lake Superior, 1971-1995. Estimates were made using constant mowth
(CG) and time-varying mowth (TVG) assessment models. The horizontal line
corresponds to a total annual mortality rate of 45%.

from high recruitment years. After 1983, total mortality estimates were similar between

the TVG and CG versions of the model.

Model responses to peaks in observed CPUE

Parameter estimates of both wild and stocked lake trout models were strongly
influenced by peaks in observed spring assessment CPUE. Rapid increases followed by
rapid decreases in observed CPUE coincided with elevated recruitment estimates five to
six years prior to a peak in observed CPUE and higher estimates of mortality rates during

the years observed CPUE declined than in earlier years. For wild lake trout, the elevated

34

recruitment value estimated for 1975 (Figure 4) preceded a large increase in observed
CPUE values for 5, 6, and 7 year olds in 1979-1981 from the spring assessment

(Figure 5). This was followed by elevated total mortality estimates (Figure 6) for wild fish
in 1981-1982, as spring assessment observed CPUE rapidly declined. Similarly, for
stocked lake trout, recruitment estimates were high in 1971-1977 (Figure 7) in order to
match the 1976-1981 peak in observed CPUE (Figure 9), and estimated mortality rates
rose in 1981-1982 (Figure 8), when observed CPUE of stocked lake trout fell.

My results indicate that the primary difierences between the CG and TVG models
for both wild and stocked lake trout were responses to peaks in observed spring
assessment CPUE, mainly much higher recruitment leading to higher mortality rates for
the CG model than the TVG model. Since selectivity was modeled as a constant function
of length, either increased recruitment or increased mowth rates could produce an
increase in predicted CPUE. Parameters of the CG model could only respond so as to
match large peaks in observed CPUE through changes in recruitment and mortality rates.
The TVG model allowed fish to mow faster at some times than at others. This allowed a
larger peak in CPUE for a given amount of recruitment because these fish could more
rapidly enter into the most highly selected sizes, and suffer less mortality in the process.
Another consequence of rapid mowth occurs at older ages when size exceeds the length
of maximum selectivity, and CPUE falls with time, not only because abundance is
declining but also because selectivity is declining. Therefore, the TVG model required less

recruitment and subsequently less mortality to match large peaks in observed CPUE.

35

 

 

 

1971 1975 1979 1983 1987 1991 1995

Figure 9. Observed and predicted catch per unit effort (CPUE) of stocked lake trout in
M4 spring assessments of Lake Superior, 1971-1995. CPUE is defined as the number of
lake trout caught in 1.0 km of gill net, standardized to net-nights. Predictions were made
using constant mowth (CG) and time-varying mowth (TVG) population assessment
models.

S tacking versus recruitment

In the stocked lake trout model I estimated recruitment (age-1) over time rather
than using the actual numbers of yearlings stocked in the lake as known values. This was
the same formulation I used for the wild lake trout model, for which I had no means of
comparing recruitment estimates to the actual number of wild recruits. Since I assumed
that natural mortality was fixed over all ages, and only natural mortality was operating at

younger ages (1-3), changes in mortality for younger ages over time would show up as

36

time-varying recruitment. Model estimates of recruitment can therefore be considered
“viable recruitment”, and discrepancies between estimated recruitment trends and trends in
stocking imply a change in survival from yearling plantings to ages that were present in
sampling (about age-4 and older).

Using the CG model, I estimated an increase in recruitment from the 1971 year
class through the 1977 year class followed by a sharp decline to much lower recruitment
levels that persisted starting with the 1979 year class. With the TVG model, I also
estimated a sharp decline in recruitment from the 1977 to the 1979 year class and low
recruitment for all subsequent year classes. Estimates from the two models differed in that
the TVG model recruitment estimates were not increasing, but were relatively stable for
1971 through 1977 year classes. In contrast with the increasing trend in recruitment over
the 1971-1977 year classes I estimated using the CG model, there was no such trend in
actual numbers of yearlings stocked. Hence, if the trend I estimated using the CG model
reflects reality it implies an increase in subsequent early life survival. I have found no
independent reasons to suspect that early life survival should have increased over these
year classes, and take this non-intuitive pattern as an additional reason to prefer the TVG
model

After 1979, my estimates of recruitment dropped well below the actual numbers of
lake trout planted in M4. Low values for CPUE from the summer assessment of stocked
lake trout (Figure 10), and discrepancies between low recruitment estimates and the actual

numbers of yearlings planted in M4 after 1979, suggest that in the later years the actual

37

 

 

 

1985 1987 1989 1991 1993

Year

Figure 10. Observed and predicted values of catch per unit effort (CPUE) for stocked
lake trout from the summer assessment in M4 of Lake Superior, 1985-1994. CPUE is
defined as the number of lake trout caught in 1.0 lnn of gill net, standardized to net-nights.

natural mortality rates suffered by young stocked lake trout were higher than those I used
in the model.

The results from fitting the stocked lake trout model call into question the
assumptions I made in both models concerning mortality rates of young lake trout,
primarily ages 1-3. Over this age intervaL I assumed constant and known natural
mortality and that other mortality sources were trivial. For wild fish, I was unable to
separate variations in recruitment at age-1 from variations in mortality between age-1 and

age-3. Hence, variations in estimated recruitment, which nominally occurs at age-1, could

38
be resulting from time-varying mortality after that age. Clearly for stocked fish such
variation is occurring following planting as yearlings, as indicated by the mismatch

between recruitment estimates and the actual numbers of stocked fish.

 

Based on the likelihood ratio test, the TVG model produced a significantly better
fit than the CG model for both wild and stocked lake trout. In order to evaluate the
uncertainty in mortality estimates from the TVG model, I calculated a 90% confidence
interval for a single parameter, namely fishing intensity (I) from 1991. I fixed f in year
1991 at values both above and below the original estimate, and refit the model for each
fixed value off. I continued this procedure until I obtained values of f in year 1991 that
resulted in total maximum likelihood values (Lm) approximately equal to the upper and
lower bound of the 90% confidence interval. The upper and lower bounds were based on
a Chi-square distribution using the likelihood ratio test statistic: 2[L(0) - L(00)] , where
L(0) was the total log-likelihood for the fixed values off and L(00) was the total log-
likelihood for the original estimate (Seber and Wild 1989). The 1991 estimate of fishing
intensity (13,91) was equal to 0.675 and the 90% confidence interval for f1991 was 0.549 to
0.776.

In the following sections I present results fiom the wild and stocked lake trout
TVG models for M4. I compare model predictions of CPUE, mean length-at-age, and
age-compositions to observed values obtained from spring assessment data because it

spans a much longer time-series than fishery sampling or maded-mesh survey data. I also

39

compare model predictions of harvest to observed harvest, present estimates of
parameters describing mowth, mortality, survey and fishery selectivity, and estimates of

spawner abundance of Wild and stocked lake trout in M4.

 

Wild lake trout assessment CPUE

Predictions of assessment CPUE from the wild lake trout TVG model matched the
general long term trends in observed CPUE, but did not match shorter-tenn variations.
For the spring assessment, model predictions of CPUE (Figure 5) appeared to be
responding to the 1979-1981 and 1986-1991 peaks in observed CPUE, but fell short of
peak observed values. The model predictions matched the modest decline in summer
assessment observed CPUE from the mid 1980's to the 1990's (Figure 11), but was not
challenged meatly by the summer assessment data because large and rapid changes in
CPUE did not occur.

N 0 clear patterns were observed in log-scale residuals between TVG model
predictions and observed spring assessment CPUE (Figure 12), suggesting the model fit
observed data well. The only exception may be a short series of positive residuals for the
period 1977-1982, which were probably an indication of how the model had difficulty

matching the spike in observed CPUE.

80 -- -0bserved
+ Predicted

    

CPUE
8

 

 

Figure 11. Observed and predicted values of catch per unit effort (CPUE) for wild lake
trout from the summer assessment in M4 of Lake Superior, 1985-1994. CPUE is defined
as the number of lake trout caught in 1.0 km of gill net, standardized to net-nights.

Residuals

 

Year

Figure 12. Log-based residuals from model predictions of spring assessment catch per
unit efl'ort (CPUE) of wild lake trout in M4.

41

Wild lake trout mean length-at-age

One important area in which predictions from the TVG and CG models differ is in
mean length-at-age. The TVG model allows mean length-at-age of the population to vary
over time in response to time-varying mowth, providing it with much meater latitude for
changing predicted length-at-age than is available to the CG model I compared
predictions of mean length-at-age for 7-9 year-old lake trout from the TVG model to
observed values caught in spring assessments (Figure 13). I chose to use ages 7-9 in this
comparison because lake trout in Lake Superior reportedly become fully selected to the
fishery and mature over these ages (Peck 1979; Ebener 1990), and the spring assessment
was the selected data source because it provided the longest time series of available data.
The model appeared to follow trends in observed mean length-at-age reasonably well, but
did not match rapid changes in mean length-at-age well This suggests either the model
was constrained from matching large changes in size that really did occur, or the model
successfully reduced excess variation, or “noise”. Predictions of mean length-at-age for
age-7 and possibly age-8 after 1984 tended to be higher than observed values. This was
probably due to a complex interaction between model mowth rates and predicted CPUE.
The model needs to account for the large increase in observed spring assessment CPUE
that began in 1984 and extended into the 1990's. Mean total lengths for age-7 and age-8
lake trout range between 19 and 23 inches. This size range also corresponded to the
steeper part of the selectivity curve for wild lake trout (Figure 14). Increased mowth
rates in 1984 caused age-7 and age-8 fish to become more selected, and hence, increased

CPUE. After 1984 trends in estimated mean length-at-age followed trends in observed

42

Age-7 WIId Lake Trout

8

-—Obcerved
-e— Predcted

N
&
1

Mean total length (Inches)
3 R3

 

 

18 T I I j I I I mm I I I I I I I I I I I I I I I

1971 1975 1979 1983 1987 1991 1995

Age-8 Wild Lake Trout

‘ ’A
24- ¢ .

Mean total length (Inches)

 

 

m I I w 1 I I I I r I I I I I I rfiiil I I I I I I

1971 1975 1979 1983 1987 1991 1995

Age-9 Wild Lake Trout

 

 

 

Mean total length (Inches)
9

m I I I I I I I l I I I I I I I I I T I 1 I I W 1
1971 1975 1979 1983 1987 1991 1995
Year

Figure 13. Observed and predicted mean total length for age 7-9 wild lake trout from
spring assessments in M4 of Lake Superior.

43

+Spring assessment

 

 

O
.l
+-
a
.0-
1

 

db
qt-
‘-

1 1
I V T

19 20 22 24 26 29 30 32
Total length (In)

 

 

 

8 10 12 14 16 18 20 22 24

Total length (In)

Figure 14. Length specific selectivity patterns estimated for spring and summer
assessments and fishery harvest of wild lake trout.

7T IAge7
6 " “968

 

 

 

 

 

 

 

 

 

 

 

Standardized residuals
N

 

 

 

1975 1979 1983 1987 1991

 

Shudlllllud reeldmle

 

 

1973 1977 1981 1985 1989 1993
Year

Figure 15. Standardized residuals for spring assessment age compositions of age 7-10
wild lake trout in M4. Standardized residuals equals (observed) minus (predicted)
proportions at age divided by estimated standard deviation.

45

mean length-at-age quite well but at a slightly higher level, which appears to be mainly due

to the increase in mowth that occurred between 1984 and 1985.

Wild lake trout age compositions from spring assessments
I examined standardized residuals of lake trout caught in spring assessments

(Figure 15). Standardized residuals were defined by :

pa,y+t,l Observed _ pa,y+t,l Predicted

6
where pay,” was the proportion at age and length in the assessments and the fishery (see

 

 

Equation 16), 6=mew Predimd (1 — pm,” Predicted) / nef, and n,,is the effective sample
size. These residuals show that the time-varying mowth model underestimated
proportions of age-8 lake trout, as indicated by generally positive residuals, but residuals
for older ages were randomly distributed with few outliers. Residuals for age-7 fish
tended toward the negative side, but were much closer to zero. These results suggest that
assumptions about ageing error of 7 and 8 year-old fish may require further attention.

One possibility is that the model’s values for ageing error result in an overlap, or
“leaking”, of age-8 fish into age-7 fish. I further explored this problem by combining
age-7 and age-8 fish into a single age-class within the objective function of the model.
Increases in the multinomial log likelihood functions L,, L 5, and L6 resulted in large
increases in the overall log likelihood (Equation 26). Residuals for combined ages 7 and 8
still tended to be positive but were much closer to zero with fewer outliers than the
residuals for the individual age-8 age-class. Parameter estimates from the combined

age-7 and age-8 model, however, remained similar to those estimated when age-7 and

46

age-8 were not combined in the objective function. Thus, combining ages 7 and 8 in the
objective function improved patterns in the residuals of spring assessment but had very

little affect on parameter estimates of the population.

Wild lake trout harvest

Model predictions of harvest matched observed harvest quite closely in all cases
(Appendix). The low value assumed for error in reporting harvest (CV = 1 %) forced this
close fit. In an ideal world reported harvest could be considered a known quantity since it
is based on required reporting rather than sampling. In Lake Superior total commercial
harvest is determined by transforming the total dressed weight of the reported harvest to
numbers-at-age of wild or stocked lake trout based on sampling, and recreational harvest
is determined through creel census. By-catch from commercial fisheries are likely to
induce errors in reporting. Hence, the assumed CV of 1% is probably optimistic, but no
hard data is available for fixing the CV at a higher level I chose a low error rate since this
is consistent with how harvest is treated in many catch-at-age models, where it is assumed
known. It would be valuable to determine empirically the actual error rate in reported

harvest.

47

 

Residuals (log scaled)
I o A

 

t i
-3 -. i
1971 1975 1979 1983 1987 1991

Year

Figure 16. Loge-based residuals from model predictions of spring assessment catch per
uniteffort (CPUE) of stocked lake trout in M4.

 

Stocked Lake trout assessment CPUE

Stocked lake trout made a simlificant contribution to the recovery of naturally
reproducing wild stocks and lake trout rehabilitation in Lake Superior throughout the
1970's (Hansen et al in press). In the 1980's, however, CPUE of the fish planted into the
lake dropped significantly. The stocked lake trout TVG model followed general patterns
in the observed trend in spring assessment CPUE (Figure 9). Closer examination
indicates some lack of fit; residuals showed a prolonged period of positive residuals from
1976 to 1986 followed by a period of negative residuals (Figure 16). CPUE predictions
were nearly always less than observed values from 1976-1986, and were meater than
observed values from 1987-1994. The overall decline in observed CPUE from

1976-1994, then, was meater than the decline in predicted CPUE. This lack of fit occurs

48

because estimates of mortality were not high enough to allow the model predictions to
match the overall decline in observed CPUE. In the model, natural mortality was constant
by assumption, and sea lamprey mortality rates varied only in response to observed
wounding patterns. Only fishing mortality rates could be altered during the model fitting
process in order to match the observed CPUE patterns, but this response was constrained
by a need to match harvest levels. Hence, the pattern in residuals reflects a balancing of
errors during 1976-1986 and 1987-1994 so that the residuals in neither time period is as
large as they would be if the model had matched observed quantities during only one of
the time periods.

Observed and predicted summer assessment CPUE values for stocked fish were
much lower that those of wild lake trout and declined from 1985-1994 (Figure 10). The
majority of the fish caught in the summer assessment range between ages 4-6 (13-18
inches length). When compared to the numbers of lake trout stocked in M4, the low
observed CPUE in summer assessments indicates low survival rates for fish less than
4 years of age, or 13 inches in length. This is dealt with by the model by low estimates of

recruitment.

Stocked lake trout mean length-at-age

Mean length-at-age estimates of stocked lake trout were compared with observed
values from spring assessment data (Figure 17). These results were similar to those of
wild lake trout in that incremental changes in predicted mean length-at-age were nearly

always less than changes in observed values. Modeled mean length-at-age estimates were

49

almost always meater than observed values after 1982. The model therefore tended to
mow fish faster to a larger size-at-age than what was actually observed through and after
the rapid decline in CPUE. The reason for this lack of fit is unclear, but I believe it to be
related to the lack of fit seen for spring assessment CPUE data. Without the changes in
mowth leading to the lack of fit in mean length-at-age, the pattern in residuals seen for

CPUE might be even meater.

Stocked lake trout age compositions from spring assessment

The stocked lake trout model tended to underestimate the proportions of age-7
and age-8 fish caught in the spring assessment prior to 1983 (Figure 18). The model also
appeared to overestimate proportions of age-5 fish prior to 1985 and age-6 fish after
1990. This lack of fit is probably related to the model not being able to mimic the decline
in CPUE from the spring survey by increasing mortality rates. With natural and sea
lamprey mortality rates fixed, and fishing mortality limited based on relationships with
observed harvest, the model was forced to change other parameter (mowth, selectivity,
etc...) estimates, and this would have influenced the lack of fit between estimated and

observed age compositions.

Stocked lake trout harvest
As in the case for wild lake trout, harvest estimates for stocked fish matched

observed harvest closer than any other variable in the model (Appendix).

50

Age-7 Stocked Lake Trout

8

M
r.

 

Iantotal length (Indies)

 

 

18 l l J l
1 I I T I I ‘f I I I I T I T I I I T ‘7' I

1972 1976 1980 1984 1988 1992

N
fi
1

R3

 

IIOInanIlongfllflnchee)

 

 

B

1972 1976 1980 1984 1988 1992

l 4 .I

8 B

 

Ill-htohllongfllflnchee)
R

 

8 IS

I I l
I I I I I I I I I I I l I I I I I I I

1972 1976 1980 1984 1988 1992

Figure 17. Observed and predicted mean total length for age 7-9 stocked lake trout from
spring assessments in M4 of Lake Superior.

51

 

 

 

 

3 oAge-S
P e
g 2-- ‘ ° 0 A996
0

1 . - .

O I o . l .2 l W Jr 1 I T $ 9 r rfi
E _1 o ‘ o e 2 . 9 o o

‘ . 0 o 0 ° o 0 e .
O O

-3 . O

.4 O

1971 1975 1979 1983 1987 1991 1995
a 8 AAg9'7
g 5 A ANS-'8
g 4 A ‘ A ‘ A
g2 ‘ A?“§ff“:£ “‘7 ‘A
h 0 k I I T l I fit I T: A A H I I H

-2 A A A A

.4

1971 1975 1979 1983 1987 1991 1995

YOU

Figure 18. Standardized residuals for spring assessment age compositions of age 7 - 10
stocked lake trout in M4. Standardized residuals equals (observed) minus (predicted)
proportions at age divided by estimated standard deviation.

52

10.1.1. 91.1.1115! H'IA.‘ V.) IA 2.1. 3.0 -1131; 0 ,Er' !0 .1 U"

Wild lake trout growth

One of the unique features of this assessment model not present in previous lake
trout models for the Great Lakes was that a mowth submodel was used to explore the
effects of time-varying mowth on the population. The model estimated annual mowth
conditions by finding annual values of L-infinity (L,) using von Bertalanffy equations
(11 and 12). Estimated mowth conditions for wild lake trout were relatively constant
during 1971-1980, varied meatly and appeared to decrease in the early 1980’s, and have
increased since 1985 (Figure 19). The period of large variations in L, came right after the
1979-1981 spike in large-mesh CPUE of wild lake trout. This was also the period that
observed spring assessment CPUE for stocked fish went from peak values into the large
decline. The combination of these factors suggests that a density dependence effect may

have triggered large changes in mowth rates.

Wild lake trout recruitment

Historically, CPUE of age-7 lake trout has been used as a relative index for
recruitment of a particular year-class. I compared the TVG model estimates of
recruitment (age- 1) to estimates of abundance at age-7 for the corresponding year-class.
Figure (20) shows general correspondence between abundance at age-1 and age-7 for the
same year class, but the relationships between age-1 and age-7 were not constant. This
suggests that time-varying mortality between age-4 and age-7 influences recruitment to

age-7. Since recruitment estimates are based on “seeing” those fish in the data, which

L-lnflnlu an.)

 

53

 

l 1 1 l
I

T T W 1' I

1985 1990

I I I I I fir I I I I

1975 1980
Year

Figure 19. L-infinity estimates from constant mowth (CG) and time-varying mowth
(TV G) models for wild lake trout in M4.

54

 

Ago-7 abundance ( x 1,000)

 

 

300 +Aga-1 7a
_‘ -0—Aga-7
§ 250-- " ‘0
fi. .1-
e zoo -- 5°
\-
~- 40
§ 150 .. , '
s ' - “"’
100 ~~ - -
E - . -- 20
8 w .- . . . . I Jun '0
K /O\./0 . .
0 f : I 4 v : . ‘f T . .L . . 4. a ‘r a a 0
1970 1975 1980 1985 1990
Year class

Figure 20. Recruitment (age-1) and abundance at age-7 estimates for 1970-1989 year
classes of wild lake trout in MI4.

55

start at age-4, the lower bound of the age range for which I have evidence of time-varying

mortality is age-4.

Wild lake trout mortality

Mortality of lake trout in Lake Superior varies in intensity over time and across
ages. I estimated the various components of total mortality over time and ages, and
fishing intensity over time, to assess the overall mortality suflered by lake trout in MI4.
Age-specific mortality is presented based on mean 1990-1994 model estimates
(Figure 21). Total mortality was broken down into components of natural, sea lamprey,
and fishing mortality. Fishing was estimated to be the primary component of lake trout
mortality in MI4.

I plotted sea lamprey, fishing, and total mortality estimates, averaged across ages
5-10, from 1983-1995 (Figure 22) to assess how mortality has changed over time.
Estimates of sea lamprey mortality varied slightly but remained less than 0.11. Total
mortality estimates increased from about 0.2 in 1983 to above 0.7 in 1988, primarily due
to increased fishing mortality. Since 1990, mean instantaneous total mortality estimates
have averaged 0.62 (total annual rate of 46.4%). Fishing intensity (fy) estimates for wild
lake trout (Figure 23) followed the same trend as the total mortality estimates, and

fluctuated much less than those for stocked lake trout.

56

Instantaneous rate
9 9 9 P 9 9 9
G.) A 0| 9 V w b

p
to

 

Age

Figure 21. Instantaneous mortality rates based on mean 1990-1994 model estimates for
wild lake trout, ages 1-15. Mortality components: M0 = natural mortality, ML = sea
lamprey induced mortality, F = fishing mortality, and Z = total mortality. The horizontal
dashed line represents a total annual mortality rate of 45%.
Wild lake trout selectivity
Summer assessment selectivity had a dome shape relationship to length
(Figure 14), starting and ending near zero and rising to a peak selectivity value at a total
length of 15 inches (38.1 cm). In contrast, spring assessment and fishery selectivity
patterns had a less pronounced dome and were nearly asymptotic functions of length.
Similarities between selectivity patterns in the spring assessment and the fishery suggest
that the assessment and fishery appear to be targeting similar size-classes of wild lake
trout. This is expected because the gear used in the spring assessment is similar to that

used in the fishery.

57

<3 c:
a, -q
\\ Pd

0444-

 

Instantaneous rate

 

 

O

L

'1' '
qr-
1D

1982 1984 1986 1988 1990 1992 1994 1996

Figure 22. Instantaneous mortality rates averaged across ages 5-10 for wild lake trout
in M14, 1983-1995. Mortality components: ML = sea lamprey induced mortality,

F = fishing mortality, and Z = total mortality. The horizontal line represents a total
annual mortality rate of 45%.

58

 

 

1.2 -— .
' +Wlld
1.0 -- -0—Stocked
z: .
2 0.8 -~ - ‘- ~° . ‘ ‘
‘2 \
- 0.6 -- " -
g o ‘/ 0
g 0.4 ~-
u.
0.2 -- .
0.0 T . . . , . . . .
192 1% 1990 1994
Year

Figure 23. Fishing intensity estimates for wild and stocked lake trout in MI4 of Lake
Superior, 1983-1995.

59

Lake trout spawner abundance

I multiplied estimates of lake trout abundance-at-age by the female maturity rates
reported by Ebener et al. (1989), and summed these to obtain estimates of the available
spawning stock of lake trout in MI4 over time (Figure 24). Available spawning stock
increased to a peak of 130,000 spawners in 1977 and consisted primarily of stocked lake
trout. Spawner abundance declined sharply until 1984, when it appeared to have leveled
ofi at around 43,000 individuals (33% peak value), based on the 1984-1988 average.
Since 1988, total spawner abundance estimates have been declining, and consists almost
entirely of wild fish. Model estimates indicate that spawner abundance was dominated by
stocked lake trout through the 1970's and into the early 1980's, but declined drastically
beginning 1978 and has not recovered from the large decline. Estimates of wild lake trout
spawner abundance increased from extremely low levels in the early 1970's to a peak value

of 35,000 in 1988 and declined during the 1990's.

Stocked lake trout growth

In initial attempts at fitting the stocked lake trout model, L, parameters were
estimated to be many magnitudes greater than maximum lengths normally observed in
surveys. Apparently, the model estimated unrealistic growth rates so that fish could
become fully selected as quickly as possible by the fishery in order to match excessive
mortality rates associated with stocked lake trout. I therefore constrained L, values to a

maximum of 40 inches (101.6 cm). Resulting L, values are shown in figure (25). The CG

—0— Wild

 

 

 

Year

Figure 24. Wild, stocked, and total spawner abundance estimates of lake trout
in MI4, 1971-1995.

model estimated an L, value equal to the maximum constraint of 40 inches. The TVG

61

    
 

 

 

45
40
«~35
£30-
£25»
520*
h
:15--
.310» """ CG
5..
0 ..T4...+.fi.e ..:...4...fi:
1971 1975 1979 1983 1987 1991 1995
Year

Figure 25. L-infinity estimates from constant growth (CG) and time-varying growth
(TVG) models for stocked lake trout in MI4.

model showed improvement with L, estimates “bound’ at the 40 inch constraint in only 4
years out ofthe 25 year time series. The 1971-1995 meanL, estimate for stocked lake
trout was 33.5 inches, and the mean value for wild lake trout was 27.3 inches. If these
model estimates actually reflect growing conditions, this would indicate overall better
growth for stocked fish than wild fish. As discussed earlier, however, residual patterns in
age compositions suggested that the stocked lake trout model tended to increase the
growth rates and over select for younger lake trout than older fish to match the decline in
CPUE (see section titled Stocked lake trout age compositions). For stocked lake trout the
values estimated for L, are influenced by assumptions about mortality rates, and as

discussed above these assumptions may be incorrect. Hence the differences between L,

62

estimated for stocked and wild lake trout may not be truly indicative of differences in
growth, because the estimates for L, from the stocked model may be unreliable, especially

in more recent years.

Stocked lake trout recruitment

Model estimates of recruitment and of age-7 abundance had markedly different
trends for the 1970-1977 year-classes (Figure 26). Furthermore, neither recruitment nor
age-7 abundance estimates followed the temporal pattern in the actual numbers of yearling
fish that were planted. This suggests that mortality has varied over time for stocked lake
trout between the ages of l and 7, and that survival from age-l to age-7 decreased rather
dramatically between the 1970 and 1976 year classes. This decline in survival experienced
by stocked lake trout from 1971-1977 appears to have been caused by factors other than
sea lamprey because estimates of sea lamprey induced mortality declined over that time
period. Beginning with the 1978 year-class, estimates of recruitment at age-1 and
abundance at age-7 tracked one-another closely but were at much lower levels than earlier
years, and neither appear to follow the trend of the actual number of fish stocked in MI4.
These results clearly suggest that natural mortality rates for stocked lake trout are time-

varying and survival of young stocked fish have decreased considerably since 1971.

63

       

 

 

 

 

 

 

600 _ —#Stocked 1 80
l +Age-1
500 “ -o-Age 7abundance "7° 3‘
A 960 '_-
§ 400 . x
a "50 V
; h
v 300 «~40 %
E

5 200 - T”

«20
100 ~ g

.10

0 v 1 r I I v v I r + r . ° 1 v 0

1970 1975 1980 1985 1990

Year class

Figure 26. Estimates of recruitment (age- 1) and abundance at age-7 of stocked lake
trout and the actual number of lake trout planted in MI4 of Lake Superior for 1970-

1988 year classes.

Stocked lake trout mortality

A target mortality rate for stocked lake trout was not specified within the lake
trout rehabilitation goal for Lake Superior (GLFC 1996), but my estimates suggest that
wild and stocked fish experience difl'erential fishing mortality. Mean instantaneous
mortality estimates for stocked fish, averaged from 1990-1994, were above 45 % for fish
age-8 and older (Figure 27). Both wild and stocked fish mean total mortality estimates
for this time period peaked at age- 12 but were higher for stocked lake trout (Z = 1.0) than
for wild fish (Z = 0.83). Differences in total mortality estimates between wild and
stocked fish were due to fishing since sea lamprey and natural mortality rates were equal
for wild and stocked fish.

Mortality estimates of stocked lake trout, averaged across ages 5-10, were broken
down into components of total mortality (Figure 28). Total annual mortality for these
ages went above 45%, but to a much lesser degree than those of age-7 and older from
1990-1994. This figure indicates that time-varying mortality appears to be driven
primarily by mortality due to fishing. Fishing intensity (f,) rates estimated for stocked fish
(Figure 23) were much higher than those for wild fish from 1983-1987, and during these
years fy estimates for stocked lake trout varied greatly. Variations in estimates of fishing
intensity and fishing mortality rates suggest that the fishery fished harder for stocked lake

trout than for wild fish during the mid 1980's.

65

d
d ie
I J
I fl
3 _1 i N

P
on
m

 

hat-Mallow: rate
9 a
A a:

 

P
N
'1' 1.!

 

*
.4 a. w: ;‘_

   

Figure 27. Instantaneous mortality rates based on mean 1990-1994 model estimates for
stocked lake trout, ages 1-15. Mortality components: MO=Natural mortality, ML==sea
lamprey mortality, F=fishing mortality, and Z=total mortality. The horizontal dashed line
represents a total annual mortality rate of 45 %.

iflB‘fll‘llflflOOUO rate

1 T
0.9 ..
0.3 a
0.7 --

0.6

 

 

0.5 +
0.4 -~
0.3 “r
0.2 u-
0.1 ._

 

 

Figure 28. Instantaneous mortality rates of stocked lake trout averaged across ages 5-10.
Mortality components: ML=sea lamprey induced mortality, F=fishing mortality, and
Z=total mortality. The horizontal line represents a total annual mortality rate of 45%.

67

Stocked lake trout selectivity

Summer assessment selectivity patterns estimated for stocked lake trout
(Figure 29) were similar to those estimated for wild fish but peaked at 16 rather than 15
inches. Estimated selectivity patterns for the spring survey and the fishery differed from
one another. The selectivity pattern estimated for the spring survey for stocked lake trout
was dome-shaped and similar to the pattern estimated for wild fish. In contrast, the
selectivity pattern for the fishery increased asymptotically with increasing size. These
results suggest that the spring survey and the fishery may be targeting difierent size-ranges
of stocked lake trout. This pattern, however, may be confused by low levels in abundance

of stocked lake trout and overall difficulties in fitting the stocked lake trout model.

68

1.4
1.2

0.8
0.6
0.4 + Spn'ng assessment
0.2 -0- Fishery
0 . : i 1r : : . .
1a 20 22 24 as 28 30 32
Total length (In)

Solocthlly

    

 

 

 

 

a 10 12 14 16 18 20 22 24
Total length (In)

Figure 29. Length specific selectivity patterns for spring and summer assessments and
fishery harvest of stocked lake trout.

DISCUSSION

Lake trout rehabilitation efforts in Lake Superior have led to considerable progress
toward establishing naturally reproducing wild stocks, but, current harvest rates may be
too high to allow stocks to sustain themselves. Based on results from a time-varying
growth statistical catch-at-age (S CAA) model for lake trout in MI4, wild lake trout stocks
are presently declining. Increased abundances of wild fish in the 1970's and 1980's, and
reduced survival of stocked lake trout led to the decision by management agencies to
eliminate stocking throughout most of Lake Superior. Observed CPUE values from
1985-1994 summer assessments in MI4 indicate that abundance of young wild fish was
declining (Figure 11). Population assessment model estimates for MI4 indicated that
spawner abundance has been declining since 1988 (Figure 24). Estimates also show that
the 1990-1994 mean annual mortality rate of wild lake trout age-7 and older is above 45%
(Figure 21). In the following sections I will discuss time-varying growth effects on lake
trout, and how progress in lake trout restoration might be limited by fishing mortality and

current stock recruitment relationships in the lake.

69

70

 

Assessment and commercial sampling data obtained for lake trout in Lake Superior
have indicated that growth of lake trout has varied over time. Lake trout growth rates
have been used as an indicator of fishery potential and ecosystem health, but variation in
ageing and sampling of lake trout have precluded detailed assessment of the effects that
time-varying growth has on the fitness of lake trout populations (Healey 1978; Marshall et
al. 1987). I have developed a lake trout population assessment model that utilizes age and
length composition data from assessment and commercial sampling to estimate abundance,
recruitment, growth, and mortality. I then compared a time-varying growth version of the
model to a constant growth version, and showed that the TVG model showed a
significantly better fit than the CG model for both wild and stocked lake trout in MI4.

The greatest discrepancy between the CG and TVG models appeared to be responses to
peaks in observed spring assessment CPUE prior to 1983. Since commercial sampling and
harvest information first became available beginning 1983, and prior to 1983 only spring
assessment data was available, discrepancies between the CG and TVG model may have
been a result of limited data before 1983. After 1983, the constant growth model
appeared to perform as well as the time-varying growth model While this does suggest
that reasonable results can be obtained from less complicated constant growth SCAA
models, changes in lake trout growth occurring since 1983 may not have been substantial
enough to cause disparities between the CG and TVG models. I believe that the results
from the MI4 model indicate that time-varying growth can be important, and the TVG

model provides useful information about lake trout populations not provided by previous

71

lake trout assessment models for Lake Superior. The time-varying growth model fit 24
additional parameters than the constant growth model. A drawback to the time-varying
growth model is that the model fitting process took 36-72 hours to obtain a solution on a
Gateway P5-150 (Pentium) computer, which was about twice the amount of time required
by the constant growth model. Thus, when considering the use of constant versus time-
varying growth models as management tools, managers should consider possible tradeoffs

between model precision, model complexity, and computer processing time.

EC] 1 l I 1'
One of the strategies developed by the LSTC was to limit harvest of
spawning-sized lake trout (fishz 25 in.) so that total mortality is less than 45% per year
(GLFC 1996). I used a stock recruitment model (Table 3) similar to Hansen et al.
(in press) together with results from the wild lake trout model for MI4 to examine whether
a target mortality rate of 45% would result in increased lake trout abundance. I estimated
recruitment in 1995 and all subsequent years based on the relationship to spawning stock
in January of the previous year, and projected estimates of abundance and yield out
100 years. Estimates of yield and spawner abundance dropped toward zero when fishing
intensity (I) value is equal to the 1994 estimate (Figure 30). I then held selectivity
constant and reduced f until total annual mortality (A) was lowered to 45% for age-ten
fish (a 32% reduction inf), because present total allowable catch (TAC) models specify a
female maturity of 100% beginning at age-10 (Ebener et al. 1989) (see Figure 30). For

this scenario, yield and spawner abundance increased asymptotically. I repeated these

72
Table 3. Stock recruitment model with parameter estimates and asymptotic
errors for lake trout in MI4. Variable definitions: W,- = estimated total number of
wild lake trout eggs produced in year i, and S ,- = estimated total number of
stocked lake trout eggs produced in year i. Parameter estimates were obtained
from unpublished results.

 

 

 

Equation Description

R, = (awWi + asSi) e ‘BWW‘ as. “Multi-species” Ricker stock
recruitment function
Asymptotic

Parameter Estimate standard error

aw 0.01 18 0.005136

as 0.00204 0.00067 1

[3W 1.01 x10‘8 2.05 x10'8

BS 8.60 x10'9 3.35 x10'9

 

projections for reduced values off (ranging 5-50% of the 1994 value) and estimated that
a 30-40% reduction in fishing intensity from that estimated for 1994 would optimize the
projected yield (Table 4, Figure 31).

The results from the stock recruitment projections clearly imply that wild lake
trout stocks will decline if fishing pressure is not reduced below 1990-1994 average.
These results agree with the findings of P. Ferreri (1995), who reported a finite rate of
population growth (A) for wild lake trout in Michigan waters of Lake Superior to be less
than one (A=0.930), indicating a decreasing population. Ifmy estimates of mortality are

realistic, then current management practices do not appear to have efl’ective control over

73

 

 

 

 

35?

l

 

iii?

Biomass (Kg)

 

 

 

Figure 30. Yield and spawner abundance projections for lake trout in MI4 of Lake
Superior based on (a) fishing intensity rate equal to that estimated for 1994 (f =0.67), and
(0) fishing intensity rate reduced 32% (f =0.45) from the 1994 f estimate. Projections in
year 0 correspond to the year 1995.

74

Table 4. One hundred year projected values of recruitment (number), spawner
abundance, and total annual yield (both in Kg) of lake trout in MI4 of Lake Superior.
The 1994 estimate of fishing intensity (f) was used as a baseline value.

 

 

 

 

 
  

  
    

   

 

 

F'mhing Reduction from Recruits Spawner Yield Note
intensity (f) f 1994 (%) (number) biomass (Kg) (Kg)
0.67 0 9.150 1.510 2.659 SCAA estimate for 1994
0.65 3 17,190 2,851 4.791 SCAA estimated 1990-1994 average
0.60 10 65,796 1 1.264 16.836
0.57 15 138,298 24.987 34.089
0.53 20 232.066 45.601 56,370 Total mortality (A )=45% for age-7
0.50 25 318,988 69,348 77,223
0.47 30 384,106 92,689 92,576
0.45 32 407.162 103.127 97,769 Total mortality (A )=45% for age-10
0.43 35 428.748 1 14.780 102.385
0.40 40 457,51 1 135 .985 107,779
0.37 45 473,600 156,596 109,605
0.33 50 479.276 176.707 108.424
180 T can
\
160 4 ‘" 45°§
-\ .
§ 140 -- ‘0‘“
._ m5.
V: 720 “ :06
x 300
g 100 ~- 5
L250
‘6
II 80 “ E
2 2°":
E 6'0 “ + Spawner abundance ,_ mm
o
u _ .0.
Q 40 Yield J» 100
— Recruitment 8 e-1
204 (a ) -50
0 .L i : 4 t t t t a

 

0 5 10 15 20 25 30 35 4o 45 50
96 Reduction in f from 1994 estimate

Figure 31. One hundred year projections of recruitment (numbers), spawner abundance,
and total annual yield (both in Kg) of lake trout in MI4 using the 1994 estimate of fishing
intensity (f = 0.67) as a baseline value.

75

compliance of the 45% mortality goal for spawning lake trout. Another concern is that
small changes in fishing intensity (i.e. 20%) resulted in opposite trends of either increasing

or deceasing yields. Establishing total mortality targets below 45 % may actually provide

higher long term yields.

WW!

Changes in survival of young stocked lake trout were probably the result of
intensive fishing and environmental responses to over 30 years of stocking. When
stocking was initiated in the 1960's, wild abundance was low, and stocked lake trout
survived well because there was little competition and/or predation from wild fish. Early
plants of stocked lake trout in Michigan waters of Lake Superior successfully spawned on
inshore spawning reefs. Over-exploitation of lake herring appears to be responsible for a
dramatic reduction in the forage base in the early 1980's (Selgeby 1992), and increasing
numbers of wild fish competed for food and habitat with stocked lake trout. As a result,
survival and growth for both wild and stocked fish began to decline in the early 1980's.
Repeated years of stocking must have influenced the entire lake ecosystem As forage
base levels were reduced, wild lean stocks and siscowet populations may have preycd
more heavily on young lake trout. Survival rates of young stocked lake trout may be less
than those of wild fish simply because they are easier for predators to locate and capture.
If supplemental stocking is required in the future, managers should examine different

stocking approaches (timing and location of plants, size/age of fish at release, etc.).

76

W

The long term goal set by the Lake Superior Technical Cormnittee (LSTC) is to
achieve a sustainable lake trout yield of 2 million kg per year - the average annual yield in
1929-1943 (GLFC 1996). One way to assess progress toward the long term goal is to
measure or estimate the number of recruits that are produced by the spawning stock in an
individual management area (GIFC 1996). The LSTC has estimated that 3.6 million
recruits per year lake-wide is required to produce the annual yield of 2 million kg, based
on a natural mortality rate of 0.12. Using total surface area of lean lake trout habitat in
Lake Superior, this breaks down to 305,444 recruits required for MI4 annually. I
estimated the mean number of recruits from 1986-1990, the last 5 years that recruitment
was estimated, and obtained a value of 141,788, or 46.4% of the objective estimated by
the LSTC. Thus, if we were able to double our present levels of recruitment, we should
be within 10% of the long-term restoration goal for MI4. Projections based on the stock
recruitment relationship for MI4, however, indicate that a 45 % reduction in fishing
mortality would maximize both recruitment and yield (Table 7) at 437, 600 recruits and a
yield of 109,600 Kg. The ratio of the area of MI4 (1,430 Km”) to the area of the lake
(16,856 Km”) is approximately 8.5%. Using this as a scaling factor, I estimate the
maximum lakewide sustainable yield as 1.3 million Kg.

According to the restoration plan, achievement of the target level of recruitment
would suggest that the long-range goal for lake trout restoration in that area has been
achieved (GIFC 1996). However, results from the SCAA and stock recruitment models

for MI4 produced much less yield and spawners per recruit than those predicted using a

77

constant natural mortality of 0.12. In my model I used age-specific mortality rates
reported by Sitar (1996) ranging from 0.66 for age-1 fish to 0.10 for fish age-5 and older.
Predictions from the wild lake trout model appeared to fit observed data well suggesting
that the assumed mortality rates were reasonable. Results from my stocked lake trout
model suggested that natural mortality may have changed over time. A wide range of
natural mortality estimates (excluding sea lamprey induced mortality) have been previously
reported for lake trout in Lake Superior: 0.26 by Pycha (1980), 0.10-0.25 by Sakagawa
and Pycha (1971), and 0.31 for wild fish by Ebener (1990). Accurate estimates of natural
mortality are essential for predicting allowable harvests, and establishing restoration

targets based on a single natural mortality rate of 0.12 appears questionable.

W11

Results from the statistical catch-at-age models for lake trout in MI4 were based
on a method similar to Methot’s (1990) stock synthesis approach. This approach uses a
maximum likelihood function to fit model estimates to observed data. CPUE and harvest
variance estimates are internalized in the log-likelihood objective function, and act as
weighting factors to the overall solution. In the MI4 model, I assumed spring and summer
assessment data came from simple random samples. According to J. Peck, Michigan DNR
(pers. com.), assessments targeted fixed locations spread out over the study area each
year, with replicate samples at each location. Treating fixed stations, spread out in space,
as random samples may result in an overestimation of the variance in CPUE. In addition,

assessment data may also contain cluster (year and station) effects which could bias

78
variance estimates for CPUE. It is also possible that use of fixed stations leads to biased

trends in CPUE indices, if the fixed stations are not representative of the entire study area.
Future research should examine possible temporal and spatial correlations caused by the
sampling design.

A common assumption used in catch-at-age and VPA models is that catch is
known (Hilborn and Walters 1992; Bence et aL 1993). In the MI4 model, I assumed that
the coefficient of variation (CV) in reported harvest to be 1.0%. M. Ebener, COTFMA
(pers. com), suggested that the error rate in reported harvest was probably higher than the
1.0% CV that I used for the MI4 fishery. Model simulations based on a 15% error rate
showed similar mortality estimates to the original model (1.0% error rate), but nearly
doubled the width of the 90% confidence interval of the fishing intensity estimate in 1991.
Accuracy of reported harvest appears to greatly aflect the reliability of the model results.
Fishery management agencies need to stress the importance of accurate catch reports and

determine methods to reduce under reporting of harvest.

W

The target yield called for by the restoration plan was based on the 1929-1943
average annual yield. Two critical biological events have taken place within the lake since
that time period: (1) sea lampreys invaded the lake in the late 1940's (Pycha and King
1975), and (2) the forage base for adult lake trout has significantly changed over time
(Bronte and Hoff 1996; Selgeby 1992; Dryer et al. 1965). Chemical treatments of TFM

has proven to be an eflective method for killing ammocoetes, but after 30 years of

79

treatment sea lampreys remain a substantial mortality source of lake trout in the Great
Lakes. Lake herring was historically the primary prey item of lake trout but was replaced
by rainbow smelt, an exotic to the Great Lakes, as the major food of lake trout in the
1970's (Dreyer et al. 1965; Bronte 1992). Annual harvest of both lake honing and
rainbow smelt in US waters have declined well below historic levels (Selgeby 1992).
Presently, lake trout management in Michigan waters of Lake Superior appears to
be focused on maximizing harvest rates while maintaining total mortality rates of 45%.
Uncertainties associated with estimating natural and lamprey mortality rates, stochastic
environmental events, time varying growth and mortality, sampling and ageing error,
etc. . . . , can distort estimates of mortality from true mortality rates experienced by the
population. Management objectives have not resulted in increasing wild lake trout stocks
in MI4 through 1990's. If total annual mortality of lake trout is to remain a rehabilitation
objective, fishery managers need to carefully analyze two critical issues: (1) is the
objective mortality rate currently being met, and if not, how can compliance be enforced;
and (2) will the mortality rate objective lead to lake trout restoration. Projections for MI4
indicated that a total annual mortality rate equal to 45% for age-7 fish (greater than 45%
for fish older than age-7) slightly increased yields. However, when mortality was reduced
below 45% for age 7-9 fish (equal to 45% for age-10 fish) the projected yield was nearly
double that produced when mortality was equal to 45% for age-7 (Table 7, Figure 31).
Finally, to achieve the long term goal of the restoration plan, conditions within
Lake Superior must be similar, or better, to the conditions that existed before the invasion

of sea lamprey and before major changes occurred in the forage base. Whether this goal is

80

realistic or not is debatable, but the direction of the long term goal seems appropriate in
that it implies that fishery management agencies should continue to conduct scientific

research, control harvest, reduce sea lamprey induced mortality, and improve lake trout
habitat. Total restoration of lake trout in Lake Superior may not be possible unless sea

lamprey are eradicated and harvest of lake trout and forage fish is strictly controlled.

APPENDIX - ADDITIONAL TABLES

 

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R8... mi... mum... $8... 88... 3...... 83... m8... .8..... .. .. o

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2.8... 6.8... 8...... 6...... 88... 38... .8... 9...... 88... 88... 88...

m8..... 58... 2.8... 3.... 58... R8... 88... 8...... 8...... £8...

«.8... 28... ER... .5... «3.... 8...... 38... ..

88... 8...... new... 8...... 88... ..

88... 84.... 8o... mama... 3...... ..

.8..... 8...... 32.... 8.... 88...

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81

82

 

 

58... 88... 8...... 82... 2...... 88... .. .. .. .. .. .. .. .. .. 2
88... 82... .34... 22.... 88... 88... .8..... o .. .. .. o .. .. .. e.
88... 8...... 8.... 03.... «8... 28... 88... .. .. .. .. .. .. .. .. 2
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o .. .8..... 58... 88... .22. use... 3...... 88... 88.. .. .. .. .. .. a.
o .. .. 88... 3...... 84.... 89... .3”... 8...... 3.... .8..... .. .. o .. o
.. .. .. .. 28... 28... 3...... 2e... 92... 85.. 38... .. .. .. .. m
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.. .. .. .. o .. 88... 2...... can... one»... 3...... .. .. .. .. o
o .. .. .. .. .. .. ...8... 2...... 48... mm... 88.. .. .. .. m
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38... .e 68.58.... 88 .880 .82. 83 62.8.. .e .28.. as. 8858.... 82 ea... «8.88. 8.8.8
8.3 me 222.. 59:22 So... 8.95... So... 83 no 33.. 33-33 8.. x32: .95 memo? .282 6 03am.

 

83

Table 7. Fitted parameters from statistical catch-at-age constant growth (CG) and time-

varying growth (TVG) models for wild and stocked lake trout in MI4.

 

   
 

 

0.213

Estimates
WiH CG Wild TVG SIOCKOG 0G SIOCKOG TVG

 

 

 

to gowth mmeters 0.699 0.637 -1.940 -0.640
L-int (71) L-intinity 26.661 26.799 39.997 32.292
L-int (72) 26.661 29.052 39.997 35.671
L-int (73) 26.661 25.167 39.997 33.424
L-lnt (74) 26.661 27.204 39.997 33.416
L-int (75) 26.661 29.704 39.997 37.267
L-mt (76) 26.661 30.059 39.997 36.461
L-int (77) 26.661 29.302 39.997 31.515
L-1nt (78) 26.661 31.619 39.997 39.997
L-int (79) 26.661 27.694 39.997 31.269
L-mt (60) 26.661 31.096 39.997 31.760
L-int (61) 26.661 19.369 39.997 39.963
L-inl (62) 26.661 29.164 39.997 36. 066
L-int (63) 26.661 16.119 39.997 12.671
L-int (64) 26.661 32.165 39.997 29.019
L-int (65) 26.661 22.006 39.997 35.299
L-int (66) 26.661 24.026 39.997 33.977
L-ini (67) 26.661 23. 965 39.997 27.029
L—inl (66) 26.661 27.590 39.997 33.663
L-int (69) 26.661 27.691 39.997 31.610
L-int (90) 26.661 26.524 39.997 36.262
L-int (91) 26.661 25.645 39.997 32.676
L-int (92) 26.661 27. 915 39.997 29. 460
L-ini (93) 26.661 27.650 39.997 39. 997
L-int (94) 26.661 29.236 39.997 39.997
L-int (95) 26.661 34.500 39.997 34.615
8 Variation in age-length composition

CV-a+ bx (use) 0.165 0.136 0.166 0.172

 

 

84

Table 8. Fitted parameters from statistical catch-at-age constant growth (CG) and time-
varying growth (TVG) models for wild and stocked lake trout in MI4. Values with and
asterix (*) were set at zero since no fish were stocked in that particular year.

 

Parameter DTmnption

Estimates
Wild CG Wild TVG CG TVG

 

 

 

M1 (71) Age-1 dandance 23370 14694 513642 342321
Nut (72) 34367 25662 906642 618452
N.-1 (73) 25540 13428 641903 641903
N..1 (74) 66942 22964 789603 494094
N.-1 (75) 458481 179561 1206935 643597
Nat-1 (76) 231380 145903 1196081 547962
N..1 (77) 325681 115978 1549675 672214
”ad (78) 92265 83990 612599 389516
"ad (79) 135443 115451 110593 107729:
N... (80) 93479 140509 63443 62255.
No.1 (81) 114549 111850 67304 65613
N..1 (82) 229045 235093 55292 54052
Nut (83) 230276 223563 33267 33142
Na-t (84) 166126 145268 " 0 * 0
Na-t (85) 261182 266635 54677 50673
N..1 (86) 280070 246658 36311 32121
N..1 (87) 175500 152247 23765 21167
NM (88) 115894 101033 40590 36637
N..1 (89) 98653 79444 34130 24331
Na-l (90) 190928 129558 " 0 " 0
N..2 (71) Abmthnce age-2 12192 8923 838589 561414
N..a (71) Abundance age-3 9866 6886 494764 337333
Ned (71) Abundance age-4 10813 8050 383526 292384
N..s (71) Abmdance age-5 6316 4537 165399 134693
N..e (71) Abmdance age-6 1300 1032 118237 104871
N.-7 (71) Abmdance age-7 449 368 31527 31527
N..a (71) Abmdance age-8 54322 54322
alpha w Selectivity tmction 1.769 1.646 1.771 1.740
beta m parameters 0.298 0.263 0.192 0.251
dpha em 37.509 35.523 20.129 21.303
beta GM 2.337 2.230 1.197 1.293
alpha F 27.466 25.387 0.775 0.390
beta p 1.207 1.067 1.23E-47 1.23E-47
Q m Catchability 4.92E-04 5.70E-04 6.37E-04 5.02E-04
EM 4.79E-04 4.91 E-04 1.64E-04 2.16E-04

 

 

85

Table 9. Fitted parameters from statistical catch-at-age constant growth (CG) and time-

varying growth (TVG) models for wild and stocked lake trout in MI4.

 

WIUCG WildTVG StockedCG StockedTVG

 

 

 

 

Fishing intensity

1 (85) 0.182 0.195 0.521 0.441

1(86) 0.340 0.456 1.510 1.165
t (87) 0.261 0.363 0.606 0.458
t (86) 0.622 0.927 1.023 0.667
t (89) 0.700 0.902 1.094 0.800
t (90) 0.699 0.776 1.206 0.822
1 (91) 0.596 0.657 1.286 0.782
t (92) 0.506 0.592 0.662 0.446
t (93) 0.453 0.539 0.760 0.591

t (94) 0.519 0.666 1.242 0.846
ZMF (71 -72) Combined natural and fishing 0.306 0.285
ZMF (71 -80) mortality (age-5 and older) 0.100 0.100

ZMF (7374) 0.578 0.430
2m: 05%) 0.443 0.262
ZMF (77—60) 0.477 0.487
ZMF (81-62) 0.942 0.626 1.395 1.039]

 

86

Table 10. Commercial harvest, mean weight, recreational harvest, and total harvest of
lean lake trout in MI4 of Lake Superior, 1983-1994. The 1990 connnercial harvest was
determined from the average mean weight from the two adjacent years. The recreational
harvest prior to 1987 is estimated as the mean recreational harvest from 1987-1989.
Data provided by Great Lakes Indian Fish and Wildlife Commission and Michigan
Department of Natural Resources.

 

Year Commercial Fishery Recreflonal Total
Total Camh Mean Total Catch Trap Net Catch Harvest
(dressed wt in lbs) Weifi ()bs) (numbers) Incidentd (numbers)

 

1%3 15900 4.03 3941 9166 13107
1%4 91725 3.00 $601 9166 39767
135 49132 3.70 13273 45 9166 22484
1%6 1M1 3.77 $028 38 9166 45232
137 75346 3.34 22548 22 4675 27244
138 133756 2.75 47501 8319 55820
1M9 119283 2.89 41321 14504 55825
1990 1 44899 50459 1 1 $06 54076
1991 1 08315 2.86 3791 5 6 5866 43787
1992 $671 3.30 26239 1 4789 31029
1993 77152 3.55 21736 40 4898 26674
1994 76295 2.91 2621 1 40 6051 m

 

Table 11. Observed (obs.) and predicted (pred.) harvest (in numbers) from time-
varying growth models for wild and stocked lake trout in MI4. Observed data
obtained from Michigan Department of Natural Resources and the Great Lakes
Indian Fish and Wildlife Commission.

 

 

 

rYear Wild obs. Wild prod. Stocked obs. Stocked pred.
harvest harvest harvest harvest
1933 3130 3130 9977 9931
1934 3309 3303 31453 31579
1935 10113 10111 12372 12374
1936 22164 22166 23063 23120
1937 20223 20231 7017 7023
1933 46373 46931 3942 3926
1939 43347 43315 6973 6972
1990 47557 47517 6519 6507
1991 37521 37505 6266 6251
1992 27402 27404 3627 3625
1993 22399 22414 4275 4275
1994 26367 26367 5936 5932

 

 

87

Table 12. Number of gill net lifts, mean catch per unit effort (CPUE), coefficient of
variation (CV) of CPUE fron_1_i_ndividual years, and variation of mean CPUE all
years combined (CV mean =CV divided by W ) for wild and stocked lake trout
caught in spring assessments in MI4 of Lake Superior 60111 1971-1995. Data from
Michigan Department of Natural Resources.

 

 

 

Year # Lifts Wild lake trout r Stocked lake trout
Mean CPUE CV CV mean Mean CPUE CV CV mean
1971 43 1 .072 0.960 0.097 45.461 0.903 0.1 17
1972 25 3.670 0.609 0.127 69.068 0.910 0.154
1973 15 5.630 0.627 0.164 119.73 0.604 0.199
1974 34 4.786 0.581 0.109 87.399 0.531 0.132
1975 19 4.553 0.580 0.145 84.264 0.776 0.176
1976 36 6.717 0.684 0.106 121.209 0.768 0.128
1977 24 9.974 0.590 0.129 140.195 0.503 0.157
1978 29 14.623 0.866 0.118 117.323 0.634 0.143
1979 14 34.631 0.552 0.169 1 12.963 0.564 0.205
1980 21 45.075 0.492 0.136 102.533 0.549 0.168
1961 25 41 .363 0.510 0.127 63.673 0.784 0.154
1982 33 23.345 0.597 0.110 47.832 0.792 0.134
1983 41 17.990 0.567 0.099 35.905 0.554 0.120
1984 24 19.622 0.393 0.129 31 .036 0.617 0.157
1985 21 24.881 0.658 0.138 23.637 0.722 0.168
1966 22 41.231 0.511 0.135 17.288 0.769 0.164
1987 27 33.724 0.483 0.122 5.303 0.680 0.148
1988 60 39.370 0.717 0.082 4.050 0.907 0.099
1989 79 28.517 0.674 0.071 3.784 0.860 0.086
1990 48 41.137 0.741 0.092 3.418 0.841 0.111
1991 46 36.850 0.672 0.093 2.721 1.044 0.113
1992 36 28.522 0.483 0.106 3.173 0.836 0.128
1993 40 22.024 0.624 0.100 2.795 1 .000 0.122
1994 32 16.001 0.767 0.1 12 2.446 0.899 0.136
1995 30 25.366 0.709 0.116 4.342 1.176 0.140
Mean: 0.634 Mean: 0.769

 

 

 

88

Table 13. Number of gill net lifts, mean catch per unit efiort (CPUE), coefiicient of
variation (CV) of CPUE__from individual years, and variation of mean CPUE all years
combined (CV mean =CV divided by (fiffi ) for wild and stocked lake trout caught in
summer assessments in MI4 of Lake Superior from 1985-1995. Data from Michigan
Department of Natural Resources.

 

 

  

 

 

     

 

 

 

Year 1r Lifts Wild lake trout l Stocked lake trout
___MemE _C__ CV_m_ean Me_E CV _ CV mean
1966 13 66.996 0.764 0.204 8.194 0.601 0.239
1987 14 50.998 0.676 0.197 5. 580 1 .063 0.230
1988 14 71.996 0.731 0.197 4. 687 0. 845 0. 230
1989 14 48.171 0. 824 0.197 4. 687 0. 758 0. 230
1990 14 50.124 0.633 0.197 3.906 1.017 0.230
1991 14 47.650 0.632 0.197 4. 557 1.014 0.230
1992 14 42. 833 0.731 0.197 4.947 1 .016 0.230
1993 14 53.900 0.925 0.197 3.255 0.962 0.230
1994 14 35.152 0.741 0.197 3.645 0.941 0.230
Mean: 0.737 0.862

 

 

 

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