DYNAMICS OF LAKE TROUT RECRUITMENT IN MICHIGAN WATERS OF LAKE SUPERIOR
by
Jessica M. Doemel
A Thesis
submitted in partial fulfillment of the
requirements of the degree
MASTER OF SCIENCE
IN
NATURAL RESOURCES (FISHERIES)
College of Natural Resources
UNIVERSITY OF WISCONSIN
Stevens Point, Wisconsin
December 2000 APPROVED BY THE GRADUATE COMMITTEE OF:
Dr. Michael J. Hansen, Committee Chair Associate Professor of Fisheries College of Natural Resources
. Szczytko Professor of Water Resources College of Natural Resources
Dr. Eric Anderson Professor of Wildlife College of Natural Resources
Mr. hades R. Bronte Gr t Lakes Fishery Analyst Green Bay Fishery Resources Office United States Fish and Wildlife Service
ii ABSTRACT
Lake Superior has been the site of an extensive restoration plan focusing on the
lake trout (Salvelinus namaycush). Historically, the lake trout was a dominant top predator in the lake and during 1913-50 supported a commercial fishery with an average
annual harvest of 2-million kg. In the 1950s, the lake trout population crashed due to
overfishing and sea lamprey (Petromyzon marinus) predation. The restoration process
·· began in the 1950s with the stocking of juvenile, hatchery-reared lake trout and controls
on sea lampreys and fisheries. In March 1996, after 3 5 years of effort, fishery managers
declared victory in their pursuit of lake trout restoration and decided to cease stocking.
The objectives were to quantify the contribution of wild and stocked lake trout to contemporary recruitment of wild lake trout and to quantify the effects of large-mesh
(114-mm stretch measure) gill net effort on wild lake trout recruitment in Michigan waters of Lake Superior.
For the first objective, Ricker stock-recruitment models were used to quantify the
contribution of wild and stocked lake trout to recruitment of wild fish. Density of wild
lake trout generally increased, whereas density of stocked lake trout generally decreased
in all Michigan managemept units of Lake Superior during 1970-1998. The density of
wild and stocked parents best described recruitment of wild lake trout during 1970-1990,
but stocked parents were only 52.2% as effective as wild parents. Recruitment rates of
wild and stocked parents declined significantly with density in all Michigan management
units. Peak recruitment was similar for wild and stocked fish, but the stocked fish
parental density needed to reach peak recruitment was twice as high for stocked parents
as for wild parents. I conclude that both wild and stocked fish have contributed to
iii recruitment of lake trout in Michigan waters of Lake Superior, but that wild fish were twice as reproductively effective as stocked fish.
For the second objective, I used a Ricker stock-recruitment model to quantify the effect of large-mesh (114-mm stretch measure) gill net effort on lake trout recruitment.
Large-mesh gill net fishing effort varied differently in all Michigan management units, but did not account for significant variation in wild lake trout recruitment. I conclude
'that current levels of large-mesh gill net fishing effort are consistent with lake trout restoration goals in Michigan waters of Lake Superior.
iv ACKNOWLEDGMENTS
This thesis would not have come without the help of many people. First, I want to thank my major advisor, Mike Hansen, who has been an endless source of support and direction. He has seen me through my ups and downs as a graduate student and as a person. It was an honor to be taught by him as an undergraduate and to work with him as a graduate student. He has opened many doors for me and for that I am forever grateful.
'special thanks also to my graduate committee, Dr. Eric Anderson, Dr. Stanley Szczytko, and Chuck Bronte, for guidance with my research.
I owe tremendous thanks to all those who made this project possible. There were
countless hours spent collecting, organizing, and maintaining the data used for this project. I feel honored to have worked on a project of this magnitude. Wisconsin Sea
Grant provided funding for this research. Joan Bratley provided database support.
Shawn Sitar provided the lake trout assessment data, as well as many hours of valuable discussion. Bill Mattes and Mark Ebener provided commercial gill net data. Wayne R
MacCallum provided the map of Lake Superior management units. Thanks to the Lake
Superior Technical Committee for allowing me to present my findings for review and
discussion at their meetings.
I also want to express my gratitude to the Marquette Biological Station. The
station provided me with time, space, and a computer so that I could work on my thesis.
Dr. Gary Klar, John Heinrich and Mike Fodale offered encouragement and advice down the final stretch. Furthermore, the station provided funding so that I could attend the
National American Fisheries Society meeting to present my thesis results.
V I also wanted to thank my friends and fellow graduate students for their support.
To Jennifer Durst, Becki Klotz, Ruth Lee, Shannon Tibbetts, Abbe Wendland, Ivy
Wendland, and Jill Gerkhe - thanks for understanding when my priorities were turned around. To Pat Schmalz., Pat Short, Kris Stepenuck, Tracy Stephens, Todd Johnson, Joel
Ernst, and several other graduate students for support and assistance when the light at the end of the tunnel wasn't always so bright. I want to personally thank Mike Wilberg for
'bearing with my frantic phone calls when I was experiencing computer problems, listening to my hour-long stories (and laughing), and for helping along the way.
Finally, I want to thank my family. From the very beginning, my parents have given me unconditional love and support. Your love has been a priceless gift. Your faith in me gave me the courage to pursue my dreams so confidently. I hope that I have made you proud. To my sister, Angela, thanks for the ''therapeutic" arguments. To my brother,
Jason, thanks for always being there for me. I also want to thank my future in-laws, Jay and Janice Richards for their support and encouragement. Caryn and Marne, thanks for the much needed tennis and piu.a nights. Ryan, thanks for being so laid back when I was so strung out. And last, but not least, I thank my fiance, Jason. You are my inspiration and my future. Thanks for always believing in me. I can't express in words how much you mean to me. I love all of you so much. My cup runneth over.
vi TABLE OF CONTENTS
ABSTRACT ...... iii
ACKNOWLEDGMENTS ...... v
LIST OF TABLES ...... viii
LIST OF FIGURES ...... x
INTRODUCTION ...... 1
Historical Background...... _ ...... 1 Restoration Efforts ...... 4 Research Objectives ...... 13
METHODS ...... 15
Study Site ...... 15 Relative Abundance ...... 16 Stock-Recruitinent...... 20 Large-Mesh Gill Net Effort ...... 23
RESULTS ...... 24
Relative Abundance ...... 24 Stock-Recruitinent ...... 24 Large-Mesh Gill Net Effort ...... 32
DISCUSSION ...... 37
Relative Abundance ...... 37 Stock-Recruitinent ...... 37 Large-Mesh Gill Net Effort ...... 39
MANAGEMENT IMPLICATIONS ...... 41
APPENDIX A-ADDITIONAL TABLES ...... 43
REFERENCES ...... 56
vii LIST OF TABLES
Table 1. Ricker stock-recruitment models ...... 21
Table 2. Comparison of nested Ricker models for significance (P~ 0.05) using extra swn of squares analysis. See Table 1 for model definitions ...... 30
Table 3. Parameter estimates for wild and stocked lake trout in Michigan waters of Lake Superior (Model 3). Wild estimates were determined by the model and stocked estimates were derived from the function (wild estimate*k). Asymptotic standard errors (ASE) are reported for the model estimates (k, wild) ...... 31
Table 4. Recruitment estimates for wild and stocked lake trout in Michigan waters of Lake Superior. Rm designates the level of peak recruitment CPE (a/l}e) and Pm designates the level of parental CPE that produces peak recruitment (1/1}). CPE was measured as the number offish caught per km of net per night normalized by a lo~ (x + 1) transformation ...... 34
Table 5. Recruit (age-7) catch per effort (CPE), parental (age-8-and-older) CPE, standard errors (SE), and number of lifts (N) for MI3 during 1970-1998. CPE was measured as the number of fish caught per km per net night normalized by a lo~ (x + 1) transformation. Dashes indicate missing data ...... 44
Table 6. Recruit (age-7) catch per effort (CPE), parental (age-8-and-older) CPE, standard errors (SE), and number oflifts (N) for MI4 during 1970-1998. CPE was measured as the number of fish caught per km per net night normalized by a lo~ (x + 1) transformation. Dashes indicate missing data...... 45
Table 7. Recruit (age-7) catch per effort (CPE), parental (age-8-and-older) CPE, standard errors (SE), and number oflifts (N) for MI5 during 1970-1998. CPE was measured as the number of fish caught per km per net night normalized by a lo~ (x + 1) transformation. Dashes indicate missing data...... · ...... 46
Table 8. Recruit (age-7) catch per effort (CPE), parental (age-8-and-older) CPE, standard errors (SE), and number of lifts (N) for MI6 during 1970-1998. CPE was measured as the number of fish caught per km per net night normalized by a lo~ (x + 1) transformation. Dashes indicate missing data...... 4 7
viii Table 9. Recruit (age-7) catch per effort (CPE), parental (age-8-and-older) CPE, standard errors (SE), and number of lifts (N) for Ml7 during 1970-1998. CPE was measured as the number of fish caught per km per net night normalized by a lo8e (x + 1) transformation. Dashes indicate missing data ...... 48
Table 10. Large-mesh (114-mm stretch measure) gill net effort (km net) in Michigan management units during 1980-1998 ...... 49
Table 11. Results of the non-linear regression for recruitment described by wild parents (Model 1). See Table 1 for model definitions ...... 50
Table 12. Results of the non-linear regression for recruitment described by stocked parents (Model 2). See Table 1 for model definitions ...... 51
Table 13. Results of the non-linear regression for recruitment described by wild parents, stocked parents, and one k (Model 3). See Table 1 for model definitions ...... 52
Table 14. Results of the non-linear regression for recruitment described by wild parents, stocked parents, and two k's (Model 4). See Table 1 for model definitions ...... 53
Table 15. Results of the non-linear regression for recruitment described by wild parents and stocked parents (Model 5). See Table 1 for model model definitions ...... 54
Table 16. Results of the non-linear regression for recruitment described by wild parents, stocked parents, one k, and large-mesh gill net effort ...... 55
ix LIST OF FIGURES
Figure 1. Yield, abundance, and intensity of commercial lake trout fisheries in Michigan waters of Lake Superior during 1929-1970, shown as percentages the 1929-1943 average, and numbers of adult sea lampreys caught at electrical barriers in index streams during 1953-1970 (Hansen et al. 1995)...... 4
Figure 2. Abundance oflake trout in Michigan waters of Lake Superior, during 1929-1993. Stocked fish are represented by the solid line and wild fish are represented by the dashed line ...... 7
Figure 3. Contours of catch per effort of age-7 stocked lake trout (numbers caught per kilometer of gill net in assessment fisheries) predicted from yearling stocking and commercial large-mesh gill net fishing effort in Michigan waters of Lake Superior (Hansen et al. 1996) ...... 10
Figure 4. Estimated relationships for Michigan management units (MB, Ml4, MIS, MI6, Ml7) of Lake Superior between number of recruits and stocked spawners, assuming no wild spawners. CPE (catch per effort) was measured as the number of lake trout caught per km per net night (Hansen et al. 1997) ...... 11
Figure 5. Lake Superior lake trout management units. U.S. management units are denoted by state; MI, Michigan; MN, Minnesota; WI, Wisconsin. Units marked by numbers only are in Canadian waters ...... 17
Figure 6. Catch.:at-age for wild lake trout in Michigan waters (MI3) of Lake Superior, 1970-1998 ...... 19
Figure 7. Geometric mean catch per effort ( CPE, fish per km per net night) of ( a) age-7 fish (recruits), (b) age-8-and-older wild fish (parental stock), and (c) age-8-and-older stocked fish (parental stock) for MI3 during 1970-1998. A break in the trend line indicates missing data...... 25
Figure 8. Geometric mean catch per effort (CPE, fish per km per net night) of (a) age-7 fish (recruits), (b) age-8-and-older wild fish (parental stock), and (c) age-8-and-older stocked fish (parental stock) for MI4 during 1970-1998 ...... 26
Figure 9. Geometric mean catch per effort (CPE, fish per km per net night) of (a) age-7 fish (recruits), (b) age-8-and-older wild fish (parental stock), and ( c) age-8-and-older stocked fish (parental stock) for MIS during 1970-1998 ...... 27
X Figure 10. Geometric mean catch per effort (CPE, fish per km per net night) of (a) age-7 fish (recruits), (b) age-8-and-older wild fish (parental stock), and (c) age-8-and-older stocked fish (parental stock) for MI6 during 1970-1998 ...... 28
Figure 11. Geometric mean catch per effort (CPE, fish per km per net night) of (a) age-7 fish (recruits), (b) age-8-and-older wild fish (parental stock), and (c) age-8-and-older stocked fish (parental stock) for Ml7 during 1970-1998. A break in the trend line indicates missing data ...... 29
Figure 12. Estimated relationships between number of recruits and spawners for (a) wild fish and (b) stocked fish. Plotted functions are based on parameters in Table 3. Recruitment CPE is age-7 fish per km per net night. Parental stock CPE is age-8-and-older fish per km per net night ...... 33
Figure 13. Large mesh (114-mm) stretch measure) gill net fishing effort during 1980-1998 for Michigan management units (Ml3-MI7) of Lake Superior ...... 35
xi INTRODUCTION
One of the most important problems in biological assessment of fisheries is the relationship between stock and recruitment (Hilborn and Walters 1992). Stock recruitment analysis examines the relationship between the spawning stock size and the ensuing recruitment of the year class produced by that spawning. Basic to any stock recruitment relationship is the fact that a fish population is limited and held at some fluctuating level by natural, density-dependent forces (Ricker 1954). Competition for food, habitat, and breeding areas are common ways in which a population can experience density-dependent mortality (Ricker 1975). However, forces that are independent of stock size also regulate fish stocks. Environmental conditions such as exposure to extreme temperatures, floods, or droughts are considered to be density-independent forces that adversely affect survival. Stock-recruitment analysis can be of great use in fisheries management, but has been scarcely used because it requires many years of continuous observations. The ability to analyze and predict stock-recruitment relationships has become an urgent issue, as the failure to maintain parental stocks at or above a critical minimum size has led to stock collapse (Gulland 1983).
Historical Background
Historically, lake trout (Salvelinus namaycush) were a dominant native predator and supported important commercial fisheries throughout the Great Lakes prior to their extirpation from all lakes by 1960 except Lake Superior (Hansen 1999). Lake trout populations in the lower Great Lakes, Erie and Ontario, declined to low levels in the late
1800s and early 1900s, peaked in the 1920s, and declined to extinction in the 1950s (Cornelius et al. 1995, Elrod et al. 1995). In the upper Great Lakes, Huron, Michigan, and Superior, lake trout stocks were reduced to low abundance by a combination of fishery exploitation and sea lamprey predation, at which time stocks collapsed through recruitment failure (Hansen 1999). Lake trout yield in Lakes Huron and Michigan declined slowly from the late 1800s to the early 1900s, while yield in Lake Superior remained relatively stable (Baldwin et al. 1979). By 1950, lake trout yield in the upper
Great Lakes had collapsed (Baldwin et al. 1979) and lake trout were absent from Lakes
Huron and Michigan by 1960 (Hansen 1999).
The lake trout is the largest of all trout species (Becker 1983) and is of natural occurrence in northern North America, but has been introduced elsewhere (Scott and
Crossman 1973). Several forms of lake trout were recognized in the Great Lakes based on fat content, morphology, location, and spawning habits (Lawrie and Rahrer 1973,
Pycha and King 1975). Morphological differentiation was nearly as great in the lake trout (Khan and Qadri 1970, Krueger and Ihssen 1995) as it was in the genus Coregonus
{Todd and Smith 1980, Smith and Todd 1984). Lake trout spend most of their lives in deep, cold waters of the Great Lakes and are most abundant between 30 and 90 m
(Eschmeyer 1957). In Lake Superior, lake trout reach maturity by age-8 (Dryer and King
1968, Peck and Sitar 2000) and spawning occurs from October to early November on rocky shoals (Becker 1983, Peck 1986). Lake trout provide no parental care of their eggs or young, as eggs are left to incubate in the crevices of rocks (Eschmeyer 1957). Adult lake trout eat primarily fish, and juvenile lake trout eat invertebrates (Dryer et al. 1965,
Conner et al. 1993). Recent surveys have reported lake trout ages that ranged from 1-42
2 years old (Schram and Fabrizio 1998), but may live up to 50 years (Martin and Olver
1980).
Three morphologically distinguishable forms of lake trout presently occur in Lake
Superior, including a lean form that inhabits waters shallower than 70 m (Pycha and King
1975), a fat form, the siscowet, that inhabits water deeper than 65 m (Eschmeyer and
Phillips 1965), and an intermediate form, the humper, that inhabits isolated offshore reefs surrounded by water deeper than 90 m (Rahrer 1965). A straight pointed snout and low body fat content characterize lean lake trout (Eschmeyer and Phillips 1965, Pycha and
King 1975). A blunt snout, high body fat content, and deep body characterize siscowet lake trout (Eschmeyer and Phillips 1965, Pycha and King 1975). A short head, convex snout, thin abdominal wall, and deep body characterize humper lake trout (Rahrer 1965).
Lake trout formed discrete spawning stocks that used tributary streams, offshore reefs, and rocky shorelines as reproductive habitat (Lawrie and Rahrer 1973, Wells and McLain
1973).
In Lake Superior, lake trout supported a substantial commercial fishery from the late 1800s through 1950, before stocks collapsed through a combination of excessive fishery exploitation and sea lamprey predation. Lake trout supported an annual harvest of
0.75 million kg in 1879, a peak harvest of 3.3 million kg in 1903, and an average harvest of 2 million kg per year during 1913-1950 (Baldwin et al. 1979). The stability oflake trout harvest during 1913-1950 implied that a sustainable annual yield had been achieved, but increased yield in Michigan waters was sustained in the 1940s through increased fishing intensity, while abundance declined (Figure 1; Hile et al. 1951). During 1949-
1952, fishing intensity increased 50%, abundance decreased 50%, and yield remained
3 350 40 5i Cl) 300 Sea en ~ Lampreys CD (¥) 250 30 ll> vI 0) I» C\I 3 0) 200 "C .... 20 a 150 ~ Cl) .... s0) -b C 100 0 Cl) 10 ~ i Cl) 50 a.. 0 0 1930 35 40 45 50 55 60 65 70 Year
Figure 1. Yield, abundance, and intensity of commercial lake trout fisheries in Michigan waters of Lake Superior during 1929-1970, shown as percentages of the 1929-1943 average, and numbers of adult sea lampreys caught at electrical barriers in index streams during 1953-1970 (Hansen et al. 1995).
4 slightly above the 1929-1943 average (Pycha and King 1975). Sea lamprey invaded Lake
Superior in the 1940s and reached peak abundance around 1960 (Klar and Weise 1994).
The collapse of Lake Superior lake trout stocks was characterized by a loss of large, old spawning adults (Lawrie and Rahrer 1973). The reduction in size and age of lake trout was supported by evidence that sea lamprey select larger, older lake trout (Fry 1953, Fry and Budd 1958, Budd and Fry 1960). Fishing intensity, yield, and abundance then declined in 1953-1961, while sea lampreys increased in abundance and preyed on remaining lake trout (Dryer and King 1968). Lake trout stocks were unable to sustain themselves in the face of intensive fishery exploitation and sea lamprey predation, and collapsed by 1962 (Pycha and King 1975, Swanson and Swedberg 1980, Pycha 1980).
Restoration Efforts
Attempts to restore lake trout stocks to Lake Superior began in 1952 with the stocking of juvenile hatchery-reared lake trout (Lawrie and Rahrer 1972, 1973). Early restoration efforts allocated yearling plantings to management units based on historic yield and available inshore habitat (LSLTTC 1986). However, annual releases of yearlings in Michigan waters were only 71 % of recommended levels (796,000/yr since
1952; Hansen et al. 1995). Chemical control of sea lampreys was implemented in 1958 and by fall 1961, sea lamprey abundance had been reduced by 87% (Smith 1971, Smith et al. 1974). In U.S. waters, numbers of spawning sea lampreys ranged higher during
1958-1961 before effective control (185,000-377,500 sea lampreys) than during 1962-
1992 after control was achieved (13,500-82,500 sea lampreys; Klar and Weise 1994).
Commercial fisheries were closed in 1962 (Pycha and King 1975), but were reopened as lake trout stocks began to recover and state and federal courts upheld tribal commercial
5 fishing rights (Hansen et al. 1995). Intensive stocking, sea lamprey control, and closure of fisheries allowed lake trout stocks to increase rapidly (Figure 2; Pycha and King
1975). Fishing mortality on lake trout was greatly reduced from 1968 to 1978 because of stringent regulations on inshore netting, but sea lamprey mortality still remained high
(Pycha 1980) and lake trout abundance began to decline as tribal fisheries became established in the 1980s (Peck and Schorfhaar 1991 ).
Progress in restoration was slower than expected because of inconsistencies in regulation among jurisdictions and growth of tribal commercial fishing (Hansen et al.
1995), which prompted the need for better coordination between management agencies. A
Joint Strategic Plan/or Management ofGreat Lakes Fisheries was developed under the direction of the Great Lakes Fishery Commission (GLFC) to help coordinate Great Lakes fishery management (GLFC 1980). Lake trout restoration in Lake Superior was developed into an inter-agency plan in 1984-1986 to set a goal for sustainable lake trout yield (2 million kg per year), define management areas, and set protocols for stocking, assessment, and reporting (LSLTTC 1986; Hansen et al. 1995). The intermediate goal of the plan was to restore recruitment in the optimal habitat areas of Lake Superior through stocking and reducing mortality. Stocking was based on the availability of quality lake trout spawning habitat, historic production, present mortality rates, and natural reproduction in an area. All agencies having jurisdiction over lake trout fisheries were charged with maintaining the total catch of lake trout so that total annual mortality was held at 50% or less. Interactions with sea lampreys, prey species, and other predators were monitored as possible impediments to rehabilitation. A large-mesh gill-net assessment fishery was coordinated to track progress of rehabilitation and aid in making
6 = •~ 250 e ~ O'I 200 .-1 d-. ~ 150 .-1 ,. . ~ , ... ~ 100 .. , , , .' ... ' ... .. , ... = ... .. I so .. :J ... -. . . . =~ t ~ 0 ~ 1929 1939 1949 1959 1969 1979 1989
Year
Figure 2. Abundance of lake trout in Michigan waters of Lake.Superior during 1929-1993. Stocked fish are represented by the solid line and wild fish are represented by the dashed line.
. 7 management decisions. Research needs were identified, as there were important pieces of information missing when the plan was developed. Progress of lake trout restoration was reported annually to the Lake Superior Committee.
As restoration progressed, reports showed that abundance of wild lake trout was increasing (Hansen 1990, Hansen et al. 1994a), though the parentage of wild lake trout was uncertain. The same reports also stated that the abundance of stocked lake trout was decreasing, despite a relatively consistent stocking rate (Hansen et al. 1994a, 1994b).
Measurement of progress toward the restoration goal set in the 1986 restoration plan was troublesome because goals were stated in terms of historic yield (2 million kg/year), which could never be evaluated because of losses to sea lampreys and unreported losses to fisheries (Bronte et al. 1995, Hansen 1996). Nonetheless, much was learned since the first lake trout restoration plan in 1986, so a revised plan was adopted in 1996. The revised plan addressed impediments to further progress in lake trout restoration in Lake
Superior and recommended future management actions based on the results of ongoing stock assessment and research (Hansen 1996). Lake trout restoration in Lake Superior evolved from a program that was dominated by stocking to a program that relied on prudent management of wild lake trout stocks.
The need to understand the dynamics oflake trout recovery in Lake Superior had become a pressing issue, so studies of restoration progress, survival, and recruitment, were initiated. In a study of progress towards restoration in Lake Superior, Hansen et al.
(1995) developed indices of stock density that showed wild lake trout were increasing in abundance, but were less abundant and more variable during 1979-1993 than during
1929-1943. These results were discouraging to fishery managers because progress was .
8 slow, but also encouraging, because wild lake trout abundance increased, even as stocked abundance declined. Lake trout of hatchery origin are now rare throughout Michigan, and are declining rapidly elsewhere. Wild fish have replaced stocked fish in most areas, and being the reproductive stocks of the future, should be protected from sea lamprey predation and fishery exploitation (Hansen et al. 1995).
In a study of stocked lake trout survival in Lake Superior, Hansen et al. (1996) showed that large-mesh gill net fishing effort was limiting survival in Michigan and
Wisconsin waters and wild lake trout predation was limiting survival in Minnesota waters. Hansen et al. ( 1996) also showed that catch per effort ( CPE) of stocked lake trout at age-7 could return to levels of the early 1970s (~20 fish/km of assessment net), if commercial gill-net fishing effort was reduced to 2.8 million meters and stocking rates were increased to 2.5 million yearlings (Figure 3). Reductions in gill-net fishing effort in
Wisconsin during 1990-1993, along with anticipated stocking levels of 186,500 yearlings, were predicted to improve survival, but not enough to increase CPE of stocked fish above 10 fish per km of assessment net. These results were discouraging for fishery managers because the CPE of stocked lake trout was generally above 20 fish per km of . assessment net during periods when stocked fish reproduced successfully.
In a study oflake trout recruitment in Lake Superior, Hansen et al. (1997) showed that stocked adult lake trout had been largely responsible for the recovery of wild lake trout, but that wild adult lake trout had contributed little to that recovery (Figure 4).
Parameters of the stock-recruitment relationship indicated that stocked lake trout had reproduced at near replacement levels, but that wild lake trout had reproduced at less than
10% of replacement levels (Hansen et al. 1997). These results were troubling for fishery
9 0.0
e 1.0 C ,g 2.0 'E -t:: 0 3.0 ffi I 4.0 a 5.0
6.0 0.0 0.5 1.0 1.5 2.0 2.5 Nurrber Stocked (ITillions)
Figure 3. Contours of catch per effort of age-7 stocked lake trout (numbers caught per kilometer of gill net in assessment fisheries) predicted from yearling stocking and commercial large-mesh gill net fishing effort in Michigan waters of Lake Superior (Hansen et al. 1996).
10 50 45 MI5 40 w a.. {.) 35
C 30 -Q) MI4 .s 25 :::::, L.. 20 0 Q) a:: 15 10 5 0 0 20 40 60 80 100120140160 Parental Stock CPE
Figure 4. Estimated relationships for Michigan management units (Ml3, Ml4, MI5, Ml6, Ml7) of Lake Superior between number of recruits and stocked spawners, assuming no wild spawners. CPE ( catch per effort) was measured as the number of fish caught per km per net night (Hansen et al. 1997).
11 managers because wild lake trout were expected to sustain stocks in Lake Superior as management moved away from dependence on stocking to prudent management of wild stocks. Nonetheless, Hansen et al. (1995) suggested that stocking be discontinued wherever wild fish dominated stocks, such as in Michigan, eastern Wisconsin, and much of Ontario. The cessation of stocking would also help to maintain genetic diversity of wild fish and protect them from hatchery diseases (Helle 1981, Ferguson 1990, Evans and Will ox 1991, Krueger and May 1991, Krueger et al. 1994). In March 1996, after 3 5 years of intensive stocking, fishery managers declared victory in their pursuit of lake trout restoration and ceased stocking most areas of Lake Superior. Wilberg (2000) compared historic and modern lake trout abundance and reported that modem ( 1984-
1998) lake trout CPE was equal to or significantly higher than historic (1929-1943) lake trout CPE in Michigan waters (Ml2-MI6) of Lake Superior. Although that analysis suggested that lake trout restoration had been achieved, forces affecting the status of lake trout in Lake Superior must still be monitored and regulated
12 · Research Objectives
My first objective was to quantify the contribution of wild and stocked lake trout
to contemporary recruitment of wild lake trout in Michigan waters of Lake Superior.
Previously, Hansen et al. (1997) showed that stocked lake trout were largely responsible
for recruitment in Michigan waters, where wild lake trout stocks recovered after 1970.
However, Hansen et al. (1997) may have reached an erroneous conclusion because their
analysis relied on aggregate stock density due to a lack of year-class specific data.
Therefore, I developed year-class specific data for my analysis, to model the relative
contributions of wild and stocked lake trout to recruitment of specific year-classes. I
expected that wild parents would be responsible for a large part of recruitment as lake
trout restoration moved away from dependence on stocking of hatchery fish. I also
expected that stocked parents would contribute to recruitment, but that they would likely
only function at a fraction of the reproduction rate of wild parents. Lastly, I believed that
lake trout populations would experience some degree of density-dependence, based on a
recent analysis that showed lake trout populations in Lake Superior may already have
reached historic levels of abundance (Wilberg 2000).
My second objective was to quantify the effects oflarge-mesh gill net fishing
effort on wild lake trout recruitment in Michigan waters of Lake Superior. Previously,
Hansen et al. ( 1996) found that declining density of stocked lake trout in Michigan waters
was significantly associated with increasing large-mesh gill net effort. That analysis was
based on the 1963-1982 year classes and cannot accurately reflect the effect of gill nets
on contemporary year classes. Consequently, I analyzed data for the years 197();.1998 to
include more contemporary year classes. I anticipated that gill-net effort would no longer
13 be an impediment to wild lake trout recruitment because gill-net fishing effort declined by 45% during 1990-1993 in Michigan waters of Lake Superior through conversion of gill net operations to trap net operations and movement of fishing operations to other
Great Lakes (Hansen et al. 1995).
14 METHODS
Study Site
Lake Superior has the largest surface area (82,414 km2) of any freshwater lake in the world, is second only to Lake Baikal in volume, and contains 100/o of the world's surface fresh water (Matheson and Munawar 1978). Lake Superior is a highly oligotrophic lake because of its unique chemical and physical characteristics. The maximum depth of Lake Superior is 405 m and it contains more than half of the water volume in the Laurentian Great Lakes (Lawrie and Rahrer 1973). The drainage basin rests primarily in the Pre-Cambrian Canadian Shield and was formed by glacial erosion
(Hough 1958, Matheson and Munawar 1978). The fish fauna of Lake Superior arose following the Pleistocene glaciation and includes 73 fish species belonging to 18 families
(Lawrie and Rahrer 1973, Lawrie 1978).
Lake Superior has the lowest annual average temperature of the Great Lakes and it is the only Great Lake for which the mean temperature does not rise above 6°C
(Bennett 1978). The clarity of Lake Superior has been noted in the past (Agassiz 1848) and is still exceptionally clear with a Secchi depth in open water of 9-15 m (Matheson and Munawar 1978). Dissolved oxygen concentrations are above 100% saturation for all months except November, and the year-round percent saturation is 101.5 ± 2.1 % (Weiler
1978). The open waters of Lake Superior are remarkably low in total dissolved solids
(--60 mg/L; Matheson and Munawar 1978, Weiler 1978).
Infertile soils and adverse climate were unfavorable for settlement and development, so Lake Superior has been minimally affected by industrial, agricultural,
15 and residential pollution (Lawrie and Rahrer 1973). However, as early as the seventeenth century, Native American maintenance fisheries were established on Lake Superior
(Lawrie and Rahrer 1972). Lake trout and lake whitefish (Coregonus clupeaformis) were harvested for subsistence and trade with fur companies throughout the eighteenth century and early nineteenth century (Lawrie and Rahrer 1973). Advancements in transportation in the nineteenth century and the opening of the Sault Ste. Marie canal allowed movement offish to Chicago, Detroit, and Cleveland (Goodier 1989) that continues to the present. Human influence on Lake Superior has not been as profound (Lawrie and
Rahrer 1973, Hansen et al. 1995) as in the lower Great Lakes (Cornelius et al. 1995;
Elrod et al. 1995, Eshenroder et al. 1995, Holey et al. 1995).
Relative Abundance
Management units in Lake Superior were based on fishery statistical districts developed by Smith et al. ( 1961) and defmed in an interagency plan that was developed in 1984-1986 (Figure 5; LSLTTC 1986). The management units were created to simplify catch reporting and data summarization (Hansen 1996). The adoption of boundaries was supported by previous studies that showed 90% of marked lake trout were generally recaptured within 80 km of the release site (Eschmeyer et al. 1953, Buettner 1961, Pycha et al. 1965, Rahrer 1968, Swanson 1973, Ebener 1990, Peck and Schorfhaar 1991).
Trends in relative abundance of lake trout were monitored with assessment gillnet fishing in five Michigan management units, MI3, MI4, MIS, MI6, and MI7, during 1970-
1998. Contracted commercial fisherman and the Michigan Department of Natural
Resources (MIDNR) conducted the assessments using standard nets of 114-mm stretched
16 Figure 5. Lake Superior lake trout management units. U.S. management units are denoted by state: MI, Michigan; MN, Minnesota; WI, Wisconsin. Units marked by numbers only are in Canadian waters.
17 measure mesh, 210/2 multifilament nylon twine, 18 meshes deep, hung on the ½ basis, and fished from late April through early June (Hansen et al. 1996). Nets were not all of the same length, so catch per effort (CPE) was defined as the number offish caught per kilometer of net. Nets were set for 1-3 riights, with 3 nights being the most frequent, so
CPE was standardized to one net-night using conversions developed from gill-net saturation studies in 1970 and 1995 (Hansen et al. 1998). The mean CPE of wild and stocked lake trout were transformed to natural logarithms and one was added to each CPE prior to transformation to adjust for zero catches. Mean CPE and 95% confidence intervals were computed for each area and year and then back-transformed into geometric means and 95% confidence intervals. Ages were determined by examining scale or otolith annuli from a random sub-sample of 20 fish per inch-class per management area.
Length and age data were compiled into age-length keys within years and management areas, which were then applied to the length-frequency for the entire catch within each area and year to determine age composition (Ricker 1975). All hatchery-reared lake trout were marked by removal of a fin before stocking in Lake Superior, so scale-ages were validated by matching the fin clip observed on individual fish to the year-class in which that fin-clip was used to mark fish before stocking (Hansen et al. 1994a).
The CPE of age-7 wild lake trout was used as an index of recruitment and the
CPE of age-8 and older lake trout was used to index of spawning stock density. The CPE of age-7 wild lake trout was used to index recruitment because catch curves showed that lake trout are fully recruited to the assessment gear beginning at age-7 (Figure 6; Pycha
1980). Spawning stock density was indexed by the abundance of age-8 and older lake trout because 50% of females reached sexual maturity at age-8 (Peck and Sitar 2000).
18 C' :I ~ 1500 1A• """-C ...CP 1000 i s:I 500 -=~ u•
3 4 5 6 7 8 9 10 11 12 13 14 15
Age(years)
Figure 6. Catch-at-age for wild lake trout in Michigan waters (MI3) of Lake Superior, 1970-1998.
19 The CPE of spawning-aged lake trout was paired with the CPE of recruits eight years
later, because lake trout spawned in the fall of any year would hatch in spring of the next year and reach age-7 eight years after spawning (Krueger et al. 1986; Hansen et al.
1995a). To account for this time lag, spawning stock CPE for 1970-1990 was matched with recruit stock CPE for 1978-1998.
Stock-Recruitment
The contribution of wild and stocked lake trout to recruitment of wild fish in Lake
Superior was tested using the Ricker (1975) stock-recruitment model:
where R is recruitment, S is the parental stock, a describes recruits-per-spawner near the origin (the density-independent parameter), and~ describes the rate at which the stock recruitment curve bends over as stock size increases (the density-dependent parameter).
The model can be modified to include both wild (W) and stocked (S) parents, each with a corresponding a and ~ {Table 1). When fit to data from all management units simultaneously, the models ranged in complexity from 10 parameters (Model 1) to 20 parameters (Model 5). Model 1 evaluated the contribution of wild parents only, Model 2 evaluated the contribution of stocked parents only, and Models 3 through 5 evaluated the relative contributions of wild and stocked parents.
Models 3 and 4 included a parameter k that allowed stocked fish to be modeled as constant equivalents of wild fish. The parameter k was used as a way to parsimoniously describe the relative efficiency of wild and stock parents. Stocked fish all came from the
20 Table 1. Ricker stock-recruitment models.
Model Equation Description
Ricker stock-recruitment function based on wild parents; density-dependence.
2 Ri=asSie•PsSi Ricker stock-recruitment function based on stocked parents; density-dependence.
3 Ri=a(Wi + kSi)e•P 4 R=a(Wi + kaSi)e•P 5 R=(a.wWi + a.sSi)e•PwWi-pssi Ricker stock-recruitment function in which wild and stocked fish have their own density-independent and their own density-dependent terms. 21 same hatchery brood fish and wild fish likely came from a mixed parentage, so wild and stocked lake trout could be some constant equivalent of one another, no matter where they lived and reproduced. Consequently, estimates for alpha and beta could vary among units because habitat varies among units, but wild and stocked fish might be relatively similar in all areas. Thus, k links the fish to one another among units. Model 3 included one k for both density independence and density dependence, whereas Model 4 included one k for density-independence (ka) and another k for density-dependence (kb). Model 5 allowed for different reproductive success for wild and stocked parents and for different density-dependence for wild and stocked fish. Parameter estimates and asymptotic standard errors were obtained numerically using a Gauss-Newton iterative algorithm (Systat 1992). Optimal fit of the parameter estimates were ensured by using a variety of starting values for each model solution. Each time the number of variables and parameters was increased, the model was tested to determine whether the additional variable(s) and parameter(s) led to a significantly better fit (P ~ 0.05) by 'extra sums of squares' F-tests (Bates and Watts 1988). I estimated management parameters describing peak recruitment and the parental density that produced peak recruitment from density independent and density dependent parameters for the most parsimonious stock-recruitment model. Peak recruitment, Rm, was estimated as ..!!.... for wild and stocked fish in each management unit, where a was f3e the density-independent parameter and p was the density-dependent parameter from the stock-recruitment model (Ricker 1975, Hilborn and Walters 1992). The parental density, Pm, needed to produce peak recruitment was estimated for wild and stocked fish in each 22 management area by ..!_, where p was the density-dependent parameter from the stock- p recruitment model (Ricker 1975, Hilborn and Walters 1992). Large-Mesh Gill-Net Fishing Effort Large-mesh gill net fishing effort was examined as a possible source of mortality that may have limited recruitment, in addition to stock size and density-dependence. The best model describing recruitment was selected from Models 1-5, and then modified to include gill net effort. For example, for Model 5, the modification to include gill net effort (Xi) would be: where all other terms are as previously described. To determine the amount of large mesh gill-net fishing effort that age-7 lake trout faced during their pre-recruit years, catch curves were used to develop weights for effort in years between spawning and recruitment (Figure 6). For example, if 15% of the pre-recruit catch was age 4, 400/o was age 5, and 45% was age 6, then the effort in those years would be multiplied by the proportion of catch and summed to give the total effort faced during pre-recruitment years. To determine the best model describing lake trout recruitment, the model that included large-mesh gill-net fishing effort was tested against the best model of recruitment without gill net effort using 'extra sum of squares' F-tests (Bates and Watts 1988). 23 RESULTS Relative Abundance Density of wild lake trout generally increased, whereas density of stocked lake trout generally decreased, during 1970-1998 in all Michigan management units of Lake Superior (Figures 7-11). Consequently, stocked lake trout were more numerous than wild lake trout during 1970-1985, while wild lake trout were more numerous than stocked lake trout during 1986-1998. Trends in abundance of wild and stocked lake trout were similar in all Michigan management units during 1970-1998. Wild parental CPE and recruitment CPE was generally very low early in the time series and increased without trend as dependency moved away from stocking and natural reproduction carried on. Stocked parental CPE decreased throughout the time series and will be replaced by wild lake parents as restoration progresses. Recruitment CPE and wild parental CPE were highest in MI5 and MI6 and stocked parental CPE was highest in MI4 and MI5. Stock-Recruitment Recruitment of age-7 wild lake trout during 1978-1998 was best described by density of age-8-and-older wild and stocked parents during 1970-1990, with stocked parents represented as a constant fraction of wild parents (Model 3; Table 2). Recruitment rates were significantly greater for wild lake trout than stocked lake trout, and changed with density of both wild and stocked parents {Table 3). Recruitment rates of wild lake trout (aw) ranged from 0.726 recruits per parent in MI3 to 3.777 recruits per parent in MI6. Stocked parents were half as productive as wild parents (k=0.522), so recruitment rates of stocked parents (as) ranged from 0.379 recruits per parent in MI3 to 24 20 (a) 1970 1975 1980 1985 1990 1995 Year 50 (b) 40 t: ~ 30 i-;; 20 u 10 0 -1----=-+---_.l-+-----+-----+-----I------1970 1975 1980 1985 1990 1995 Year 150 (c) t: 100 ~ i u-;; 50 1970 1975 1980 1985 1990 1995 Year Figure 7. Geometric mean catch per effort (CPE, fish per km per net night) of (a) age-7 fish (recruits), (b) age 8-and-older wild fish (parental stock), and (c) age-8-and-older stocked fish (parental stock) for MI3 during 1970-1998. A break in the trend line indicates missing data. 2S 35 (a) 30 t: 25 !S t+-i 20 15 itu u 10 5 0+--==-----+-----+-----+-----+----+---- 1970 1975 1980 1985 1990 1995 Year 60 (b) 50 ] 40 t+-i i 30 utu 20 10 0 -1----""'11!!!'!::::.....__+------+------+-----+-----+---- l970 1975 1980 1985 1990 1995 Year 150 (c) t: 100 ig i utu 50 0 --I-----~---+----+--~-...... ---..---- 1970 1975 1980 1985 1990 1995 Year Figure 8. Geometric mean catch per effort (CPE, fish per km per net night) of (a) age-7 fish (recruits), (b) age 8-and-older wild fish (parental stock), and (c) age-8-and-older stocked fish (parental stock) for Ml4 during 1970-1998. 26 100 (a) 80 1970 1975 1980 1985 1990 1995 Year 120 (b) 100 ] 80 (-i-< i 60 u~ 40 20 0 --l---~=-l------1------1------1------1------1970 1975 1980 1985 1990 1995 Year 120 (c) 100 80 60 40 20 0 -l------+-----1------+-____:_~~---llllll!!!f!!~~-- 1970 1975 1980 1985 1990 1995 Year Figure 9. Geometric mean catch per effort (CPE, fish per km per net night) of (a) age-7 fish (recruits), (b) age 8-and-older wild fish (parental stock), and (c) age-8-and-older stocked fish (parental stock) for MIS during 1970-1998. · 27 80 (a) t: 60 ~ i 40 ~ u 20 1970 1975 1980 1985 1990 1995 Year 60 (b) 50 t: 40 ~ i 30 u~ 20 10 ol---~~~::__-~~i_---l-___'.__.!_~----l---- 1970 1975 1980 1985 1990 1995 Year 120 (c) 100 80 60 40 20 0 -+-----l------l------l---____i__:~-....-.!!!!!!!!~~!'!!!!!'!!!1-- 1970 1975 1980 1985 1990 1995 Year Figure 10. Geometric mean catch per effort (CPE, fish per km per net night) of ( a) age-7 fish (recruits), (b) age 8-and-older wild fish (parental stock), and (c) age-8-and-older stocked fish (parental stock) for MI6 during 1970-1998. 28 25 (a) 20 1970 1975 1980 1985 1990 1995 Year 40 t: 30 ~ i 20 'tis u 10 0 ...l....-_!'!!""':..__-4--___---l------l------+------l---- l970 1975 1980 1985 1990 1995 Year 120 (c) 100 80 60 40 20 0 _j____ +-- ___:__~-----l-~~-__,..-~------1970 1975 1980 1985 1990 1995 Year Figure 11. Geometric mean catch per effort (CPE, fish per km per net night) of (a) age-7 fish (recruits), (b) age 8-and-older wild fish (parental stock), and (c) age-8-and-older stocked fish (parental stock) for MI7 during 1970-1998. A break in the tren~ line indicates missing data. 29 Table 2. Comparison of nested Ricker models for significance (P::;; 0.05) using extra sum of squares analysis. See Table 1 for model definitions. Sum of Degrees of Mean F Ratio p Source Squares Freedom Square Extra parameters 17.343 1 17.343 42.830 0.000 Model3 34.014 84 0.405 Model 1 51.357 85 Extra parameters 15.282 1 15.282 37.740 0.000 Model3 34.014 84 0.405 Model2 49.296 85 Extra parameters 0.017 1 0.017 0.042 0.838 Model4 33.997 83 0.410 Model 3 34.014 84 Extra parameters 2.138 9 0.238 0.559 0.826 Model 5 31.876 75 0.425 Model3 34.014 84 Extra parameters 2.121 8 0.265 0.624 0.755 Model5 31.876 75 0.425 Model4 33.997 83 Extra parameters 1.652 5 0.330 0.807 0.548 Gill net effort 32.362 79 0.410 Model3 34.014 84 30 Table 3. Parameter estimates for wild and stocked lake trout in Michigan waters of Lake Superior (Model 3). Wild estimates were determined by the model and stocked estimates were derived from the function (wild estimate*k). Asymptotic standard errors (ASE) are reported for the model estimates (k, wild). a ~ Management Unit k Wild ASE Stocked Wild ASE Stocked All 0.522 0.148 MI3 0.726 0.278 0.379 0.045 0.015 0.023 MI4 1.328 0.423 0.693 0.035 0.009 0.018 MIS 1.424 0.433 0.743 0.020 0.006 0.010 MI6 3.777 1.486 1.972 0.095 0.025 0.050 Ml7 2.140 1.132 1.117 0.070 0.037 0.025 31 1.972 recruits per parent in MI6. Recruitment rates of wild and stocked parents declined significantly with increased density in all Michigan management units, though density dependence of stocked lake trout recruitment (Ps) was only half that of wild parents (Pw) in all units. Stock-recruitment curves for wild and stocked lake trout parents were shaped differently in each Michigan management unit (Figure 12). The level of parental density that would produce peak recruitment was attained in all management units for wild fish and stocked fish, with the exception of MIS for stocked fish during 1970-1998. Hence, the level of peak recruitment was attained in all management units during 1970-1998 {Table 4). Peak recruitment was similar for both wild and stocked fish, but the parental density to reach peak recruitment for stocked fish was twice that of wild fish. Peak recruitment from the stock-recruitment function was lowest in MI3 and highest in MIS. The parental density that would produce peak recruitment from the stock-recruitment function was lowest in MI6 and highest in MIS. Large-Mesh Gill Net Effort Large-mesh (114-mm stretch measure) gill-net fishing effort did not explain significant variation in recruitment, beyond that which was explained by wild and stocked parents {Table 2). Large-mesh gill-net fishing effort varied differently in each Michigan unit during 1980-1998 (Figure 13). Gill net effort was highest in MI4, next highest in MI3 and MI7, lower in MI6, and lowest in MIS. Gill net effort in MI3 peaked in 1986, plummeted shortly after, and fluctuated slightly until 1996 when effort rose again. Gill net effort in MI4 generally increased from 1985 to a peak in 1990, fell 32 30 (a) MI5 25 w e_, 20 C: -Q) s 15 :::l ...0 Q) 10 a:: 5 0 0 20 40 60 80 100 Parental Stock CPE 30 (b) MI5 25 w e_, 20 C: -Q) MI4 15 ·5s ...0 Q) 10 a:: 5 0 0 20 40 60 80 100 Parental Stock CPE Figure 12. Estimated relationships between number of recruits and spawners for (a) wild fish and (b) stocked fish. Plotted ftmctions are based on parameters in Table 3. Recruitment CPE is age-7 fish per km per net night Parental stock CPE is age-8-and-older fish per km net per net night 33 Table 4. Recruitment estimates for wild and stocked lake trout in Michigan waters of Lake Superior. Rm designates the level of peak recruitment CPE (a/pe) and Pm designates the level of parental CPE that produces peak recruitment (lip). CPE was measured as the number of fish caught per km of net per night normalized by a loge (x + 1) transformation. Rm= a/Pe Pm=l/P Management Unit Wild Stocked Wild Stocked MB 5.935 6.062 22.220 43.478 MI4 13.959 14.164 28.571 55.556 MIS 26.194 27.335 50.000 100.000 MI6 14.627 14.510 10.526 20.000 MI7 11.247 11.107 14.286 27.027 34 300 MI3 800 MI4 250 i ]' 600 0 200 0 c 150 ~,_, 400 t: 100 t: iil iil 200 ~ 50 ~ 0 0 1980 1985 1990 1995 2000 1980 1985 1990 1995 2000 Year Year 60 MIS 120 MI6 ] 50 ]' 100 0 40 0 80 0 ,_,.... 30 c 60 t: 20 t: 40 ig iil 20 w 10 ~ 0 0 1980 1985 1990 1995 2000 1980 1985 1990 1995 2000 Year Year 300 Ml7 ]' 250 200 ~ 150 ~ 100 ~ so 0 1980 1985 1990 1995 2000 Year Figure 13. Large-mesh (114-mm stretch measure) gill net fishing effort during 1980-1998 for Michigan management units (Ml3-M17) of Lake Superior. 35 sharply until 1995, and then leveled off after a slight increase in 1996. Gill net effort in MIS fluctuated throughout the period, reached its peak in 1990, and dropped off by 1995, but began to increase again in 1997. Gill net effort in MI6 rose sharply from 1980 to 1983 and then generally declined over time. Gill net effort in Ml7 increased from 1980 to 1990, generally decreased from 1990 to 1995, and increased again after 1996. 36 DISCUSSION Relative Abundance My results show that wild lake trout abundance generally increased and stocked lake trout abundance generally decreased during 1970-1998. My depictions of lake trout abundance early in the period showed that stocked fish were present and wild fish were rare, which was noted by earlier studies (Lawrie and Rahrer 1973, Lawrie 1978, Maccallum and Selgeby 1987, Hansen et al. 1995). My results also show that wild lake trout became more numerous than stocked lake trout during the 1980s, which was also noted by Maccallum and Selgeby (1987), Peck and Schorfhaar (1994), and Hansen et al. (1995). My results show that contemporary wild lake trout abundance has slightly increased or fluctuated without trend and that stocked fish have become rare, which was supported by Peck and Sitar (2000). In fact, wild lake trout now make up over 80% of populations in all Michigan areas (Peck and Sitar 2000). Stock-Recruitment My results suggest that wild lake trout were more reproductively effective than stocked lake trout in Michigan waters of Lake Superior during 1970-1998. In contrast, Hansen et al. ( 1997) found that stocked lake trout reproduced at near-replacement rates and that wild lake trout reproduced at 10% or less of replacement levels. I found that recruitment rates for wild fish were nearly 300 times higher than recruitment rates estimated by Hansen et al. (1997) and recruitment rates of stocked fish ranged from 0.5 to 1.5 times of the recruitment rates estimated by Hansen et al. ( 1997). However, the analysis by Hansen et al. ( 1997) relied on aggregate stock density and did not include 37 contemporary data beyond 1993, whereas my analysis used age-specific data from 1970- 1998. Peck ( 1986) found that fecundity of contemporary hatchery and wild lake trout was similar, which suggests reproductive rates of stocked and wild fish should be similar. Differences in reproductive rates may be explained by the inability of stocked fish to locate optimal spawning habitat. Krueger et al. ( 1986) found that wild adult lake trout produced significantly greater numbers of recruits in the Apostle Islands because stocked fish were less able to locate offshore spawning reefs and shoals and therefore were reproductively less effective than wild lake trout. A tagging experiment revealed that nearly 100% of native lake trout on Gull Island Shoal returned to the principal spawning grounds, but only 58.6% of hatchery-origin lake trout returned to the spawning grounds (Swanson 1973). The inability of hatchery fish to home in on optimal spawning areas may greatly reduce their spawning potential (Swanson 1973). In contrast, Walters et al. (1980) suggested that stocked fish should be as reproductively successful as wild fish for maintaining progress toward lake trout recovery. My results suggested that lake trout abundance in all Michigan management units was high enough for density-dependence to occur. This is evidenced by the downward trend in abundance shortly after the peak recruitment was reached in all management units. Hilborn and Walters (1992) described density-dependence as a compensatory change in reproduction, where the number of recruits per spawner decreases as stock size increases, as is evident in my results for all Michigan management units. Evans and Willox (1991) examined lake trout stock-recruitment relationships in several small inland Ontario lakes and found that density-dependent cannibalism limited recruitment. In Lake Superior, cannibalism has previously been noted, but only as newly stocked lake trout in 38 the stomachs of adult lake trout (Conner et al. 1993). Bronte et al. (1995) suggested that density-dependent survival in lake trout populations would likely be related to available spawning habitat. Wilberg (2000) demonstrated that lake trout abundance in most Michigan management units is at least as high now as during 1929-1943, when lake trout stocks were thought to be sustained at their highest density. This may explain the surprising result from my analysis that lake trout stocks are now experiencing density dependent survival from spawning to recruitment. In contrast to my results, Schram et al. (1995) found that the lake trout population at Gull Island Shoal, Wisconsin, had not yet been affected by density-dependent survival. However, Gull Island Shoal did not recover .as rapidly as near-shore locations, and therefore had the capacity to increase later in time. Large-mesh gill net effort My results suggest that large-mesh gill net fishing effort was not a significant factor limiting recruitment of wild lake trout during 1980-1998, in contrast to Hansen et al. (1996), who found that large-mesh gill net fishing effort was inversely related to survival of the 1963-1982 year-classes of stocked lake trout in Michigan and Wisconsin waters of Lake Superior. Estimates of by-catch of lake trout during the late 1960s indicated that use of large-mesh gill nets would inhibit lake trout restoration (Schorfhaar and Peck 1993). As a result, agencies promoted the use of trap nets to reduce non-target mortality. Differences between my results and those of Hansen et al. (1996) may be attributed to conversions from gill nets to trap nets and movement of fishing operations to other Great Lakes, which reduced gill net effort by 45% during 1990-1993 (Hansen et al. 1995). Also, I included contemporary gillnet fishing effort in my analysis, which 39 reflects the downward trend in gill-net fishing effort since the 1980s, and thereby reduces the effect of fishing effort on lake trout recruitment. 40 MANAGEMENT IMPLICATIONS Restoration of self-sustaining lake trout stocks is the primary objective of all fishery management agencies involved with lake trout rehabilitation in Lake Superior. Naturally reproducing lake trout stocks have been reestablished in most areas of Lake Superior, but progress in the other Great Lakes has not been as positive. Decisions to rehabilitate or maintain stocks through stocking must evaluate new evidence that suggests that stocked lake trout are only 52.2% as reproductively·effective as wild lake trout. Wild lake trout stocks have replaced most of the hatchery fish in Lake Superior. However, the parentage of wild lake trout recruits in Lake Superior is uncertain, which raises important questions about genetic diversity of wild lake trout. Modem lake trout stocks may not be able to reproduce at similar levels as historic native lake trout stocks. Krueger and lhssen (1995) documented a loss of genetic diversity in Lake Superior due to the stocking of hatchery strains of lake trout. Poor survival, low juvenile recruitment, and inefficient habitat use are three biological situations that may arise from a loss of genetic diversity (Burnham-Curtis et al. 1995). Also, the forage base in Lake Superior has changed (Lawrie and Rahrer 1972) and lake trout now prey heavily on exotic rainbow smelt (Osmerus mordax), rather than native lake herring (Coregonus artedi; Dryer et al. 1965; Conner et al. 1993). Furthermore, lake trout must now compete with other, mostly exotic, species of trout and salmon for food (Bronte et al. 1995). Large-mesh gill net fishing effort did not explain significant variation in wild lake trout recruitment, so I conclude that current levels of large-mesh gill net fishing effort are consistent with lake trout restoration goals. However, commercial fisheries should be 41 monitored and regulated to ensure that levels of large-mesh gill net fishing effort do not return to levels that previously limited lake trout survival in Lake Superior. Lake trout abundance and mortality should continue to be monitored in all Michigan management units, to verify that stock density and survival remain within limits that will ensure wild lake trout stocks can be sustained in the future. Much has changed in Lake Superior since lake trout restoration began, and therefore, lake trout management should focus on current conditions in Lake Superior, which will require fishery managers to prudently manage wild lake trout stocks within natural limits of reproductive potential. Recent results suggest that the future of lake trout restoration is promising, but efforts must not be relaxed as the fate of Lake Superior lies in the hands of those that use and manage this grand resource. 42 APPENDIX A ADDITIONAL TABLES 43 Table 5. Recruit (age-7) catch per effort (CPE), parental (age-8 and older) CPE, standard errors (SE), and number of lifts (N) for MI3 during 1970-1998. CPE was measured as the number of fish caught per km per net night normalized by a lo~ (x + 1) transformation. Dashes indicate missing data. Year Recruit SE Wild SE Lifts (N) Stocked SE Lifts (N) CPE parental CPE (wild) parental CPE (stocked) 1970 0.000 0.000 0.078 0.155 4 1971 0.073 0.098 0.084 0.117 4 1.573 0.783 7 1972 0.858 0;690 0.322 0.189 3 2.410 0.495 3 1973 0.920 0.395 0.690 0.430 13 3.016 0.348 12 1974 0.550 0.478 1.273 0.439 16 2.604 0.511 17 1975 0.790 0.534 1.344 0.575 12 1.177 0.480 13 1976 1.138 0.544 1.724 0.648 16 3.754 0.717 18 1977 1.653 0.717 2.315 0.817 10 4.460 0.539 10 1978 0.718 0.430 1.582 0.559 15 2.807 1.442 22 1979 0.920 0.812 1.287 1.122 6 3.318 1.114 6 1980 1.621 0.853 1.841 0.679 8 3.916 0.679 8 1981 1.985 0.574 2.515 0.521 8 3.910 0.254 8 1982 1.578 0.279 2.598 0.689 8 4.119 0.286 8 1983 1.938 0.303 2.331 0.158 7 3.515 0.145 7 1984 2.675 0.301 3.397 ·0.330 4 4.427 0.643 4 1985 4.206 0.331 5 1986 2.525 0.911 12 1987 2.053 0.648 2.526 0.533 11 2.115 0.797 14 1988 1.157 0.716 2.290 0.726 24 1.373 0.647 24 1989 2.528 0.500 3.043 0.474 21 0.933 0.430 15 1990 1.349 0.734 3.205 0.720 22 0.660 0.401 16 1991 1.314 0.625 2.947 0.746 31 0.496 0.273 22 1992 1.527 0.411 2.006 0.502 27 0.545 0.186 11 1993 1.583 0.625 2.095 0.587 31 0.604 0.306 15 1994 1.762 0.770 2.678 0.820 29 0.570 0.165 13 1995 1.712 0.710 2.042 0.678 30 0.694 0.516 16 1996 1.667 0.565 1.882 0.610 30 0.581 0.261 16 1997 1.512 0.634 2.283 0.593 30 0.392 0.204 12 1998 1.336 0.635 1.935 0.954 16 0.602 0.027 2 44 Table 6. Recruit (age-7) catch per effort (CPE), parental {age-8 and older) CPE, standard errors (SE), and number of lifts (N) for MI4 during 1970-1998. CPE was measured as the number of fish caught per km per net night normalized by a lo&: (x + 1) transformation. Dashes indicate missing data. Year Recruit SE Wild SE Lifts (N) Stocked SE Lifts (N) CPE parental CPE ( wild) parental CPE (stocked) 1970 0.157 0.317 0.293 0.423 13 1971 0.185 0.216 0.274 0.324 33 3.368 1.3 44 1972 1.008 0.522 0.381 0.354 14 2.85 0.693 26 1973 1.446 0.673 1.263 0.455 15 3.706 0.596 15 1974 0.960 0.501 1.647 0.568 34 3.507 0.556 35 1975 0.921 0.530 1.353 0.612 19 1.662 0.626 19 1976 1.225 0.532 1.789 . 0.661 34 4.313 0.668 38 1977 1.664 0.451 2.262 0.571 25 4.633 0.705 25 1978 1.365 0.672 2.141 0.911 27 4.225 0.906 29 1979 1.513 0.605 1.448 0.656 15 3.825 0.905 29 1980 3.053 0.672 2.683 0.768 21 4.013 0.533 21 1981 3.300 0.548 3.211 0.589 25 3.535 0.772 25 1982 2.318 0.819 2.888 0.736 33 3.203 0.762 33 1983 2.134 0.706 2.501 0.740 41 2.957 0.582 41 1984 2.633 0.408 2.815 0.511 24 2.959 0.673 24 1985 2.415 0.670 2.883 0.875 9 3.055 0.776 21 1986 3.260 0.456 2.703 0.451 12 2.880 0.709 22 1987 3.053 0.537 2.810 0.456 16 1.665 0.571 27 1988 3.079 0.967 3.009 0.832 61 1.237 0.738 60 1989 2.873 0.746 2.404 0.780 79 0.901 0.480 65 1990 3.035 0.517 3.767 0.639 40 0.835 0.488 44 1991 3.033 0.719 3.305 0.658 46 0.462 0.339 40 1992 2.913 0.490 3.243 0.492 36 0.689 0.327 30 1993 2.316 0.752 2.959 0.634 39 0.703 0.357 33 1994 1.477 0.788 2.733 0.893 28 0.523 0.221 22 1995 1.913 0.889 2.558 0.886 30 0.744 0.419 23 1996 2.649 0.415 2.527 0.518 30 0.615 0.378 22 1997 2.660 0.695 3.076 0.712 30 0.524 0.381 27 1998 1.929 0.596 2.546 0.520 18 0.510 0.192 15 45 Table 7. Recruit (age-7) catch per effort (CPE}, parental (age-8 and older) CPE, standard errors (SE), and number of lifts (N) for MIS during 1970-1998. CPE was measured as the number of fish caught per km per net night normalized by a log, (x + 1) transformation. Dashes indicate missing data. Year Recruit SE Wild SE Lifts (N) Stocked SE Lifts (N) CPE parental CPE ( wild) parental CPE (stocked) 1970 0.165 0.27 0.272 0.437 9 1971 0.579 0.371 0.545 0.396 7 4.402 0.356 8 1972 1.193 0.54 0.517 0.246 7 4.151 0.424 8 1973 1.964 0.937 1.746 0.886 9 3.614 1.565 8 1974 1.03 0.765 1.571 0.991 21 3.475 1.118 25 1975 1.954 0.847 2.307 1.234 10 3.47 1.537 10 1976 2.064 0.831 2.748 0.959 32 3.513 1.868 32 1977 2.396 0.877 2.986 0.943 21 3.634 1.897 22 1978 2.269 0.657 3.227 0.779 27 2.719 1.889 28 1979 2.225 0.677 2.926 0.729 16 3.404 1.816 16 1980 3.255 0.942 2.754 0.786 12 4.057 0.258 12 1981 3.5 0.467 2.584 0.401 10 3.496 0.402 10 1982 4.074 0.513 2.517 0.54 10 3.013 0.369 10 1983 3.253 0.403 3.535 0.298 16 2.728 0.469 16 1984 3.111 0.692 3.39 0.294 8 3.554 0.378 8 1985 3.615 0.533 4.4 0.153 3 4.092 0.225 5 1986 3.946 0 4.353 0 1 3.871 0.711 5 1987 3.916 . 0.236 3.929 0.37 5 2.273 0.73 8 1988 3.859 0.696 3.189 1.194 14 1.271 0.973 14 1989 3.448 0.483 4.115 0.531 21 1.115 0.713 20 1990 0.497 0.595 1.989 0.919 14 0.779 0.456 21 1991 3.84 0.513 3.469 0.521 18 0.695 0.506 17 1992 3.181 0.72 3.558 0.528 24 1.208 0.618 23 1993 26.44 0.417 3.812 0.457 24 0.932 0.518 23 1994 3.117 0.604 3.746 0.466 20 0.753 0.367 20 1995 3.037 0.653 3.545 0.42 20 1.368 0.696 20 1996 3.287 0.861 3.323 0.755 22 1.366 0.478 22 1997 3.161 0.817 4.08 0.637 20 0.939 0.395 19 1998 2.251 2.251 2.935 0.696 46 0.438 0.266 34 46 Table 8. Recruit (age-7) catch per effort (CPE), parental (age-8 and older) CPE, standard errors (SE), and number of lifts (N) for MI6 during 1970-1998. CPE was measured as the number of fish caught per km per net night normalized by a lo~ (x + 1) transformation. Dashes indicate missing data. Year Recruit SE Wild SE Lifts (N) Stocked SE Lifts (N) CPE parental CPE (wild) parental CPE (stocked) 1970 0.252 0.419 0.556 0.573 8 1971 0.305 0.256 0.493 0.42 6 4.294 0.481 7 1972 2.158 0.121 1.289 0.323 2 4.403 0.098 2 1973 1.366 0.493 1.097 0.373 10 2.875 0.77 12 1974 1.101 0.488 1.585 0.528 14 3.307 0.515 14 1975 1.388 0.754 1.666 0.7 14 3.32 0.734 15 1976 1.403 0.5 1.996 0.558 24 3.404 0.423 24 1977 1.783 0.614 2.159 0.715 25 3.124 0.757 26 1978 1.207 0.545 1.929 0.704 30 2.415 0.592 30 1979 1.26 0.565 1.751 0.635 26 2.186 0.612 26 1980 2.01 0.614 1.326 0.794 19 2.418 0.561 20 1981 3.409 0.77 1.631 0.934 3 3.146 0.335 3 1982 2.231 1.274 2.427 1.161 10 3.154 0.876 10 1983 1.891 0.338 1.943 0.374 12 2.122 0.594 12 1984 2.504 0.612 2.901 0.501 8 2.981 0.419 8 1985 2.407 0.604 3.034 0.47 8 2.484 0.723 8 1986 2.679 0.702 1.964 0.489 2 2.695 2.313 3 1987 3.114 0.576 2.932 0.593 8 1.413 0.746 8 1988 2.121 0.835 0.735 0.943 12 1.266 0.983 12 1989 2.228 0.601 3.391 0.642 14 0.713 0.458 11 1990 0.464 0.588 1.933 0.911 15 0.674 0.488 24 1991 2.866 0.728 3.188 0.697 28 0.653 0.416 14 1992 2.869 0.678 3.407 0.696 26 0.895 0.611 20 1993 3.124 0.675 3.632 0.766 16 1.432 1.060 13 1994 2.566 0.802 2.875 1.06 25 0.925 0.560 16 1995 2.598 1.133 3.031 1.216 12 0.958 0.581 9 1996 3.655 0.79 3.367 0.81 6 1.235 0.944 6 1997 2.506 0.858 3.506 0.674 12 0.880 0.328 9 1998 2.155 0.357 3.069 0.499 18 0.471 0.296 11 47 Table 9. Recruit (age-7) catch per effort (CPE), parental (age-8 and older) CPE, standard errors (SE), and number of lifts (N) for Ml7 during 1970-1998. CPE was measured as the number offish caught per km per net night normalized by a lo~ (x + 1) transformation. Dashes indicate missing data. Year Recruit SE Wild SE Lifts (N) Stocked SE Lifts (N) CPE parental CPE (wild) parental CPE (stocked) 1970 1.159 0 0 0 2 1971 0.367 0.38 0.449 0.416 11 4.357 1.001 5 1972 0.831 0.47 0.513 0.365 6 3.69 0.521 6 1973 1.764 0.486 1.263 0.439 5 3.578 0.463 5 1974 1.307 0.577 1.761 0.628 8 3.597 0.293 8 1975 2.303 0.655 2.403 0.642 5 3.958 0.405 5 1976 1.988 0.596 2.626 0.615 31 3.395 0.641 32 1977 2.316 0.866 2.738 0.912 19 3.276 0.926 20 1978 1.534 0.463 2.16 0.523 31 2.511 0.647 32 1979 1.102 0.412 1.932 0.597 14 20.63 0.508 15 1980 3.005 0.318 2.613 0.253 9 2.29 0.6 9 1981 2.671 0.527 2.549 0.72 10 3.04 0.459 10 1982 1.933 0.688 2.634 0.641 18 2.811 0.592 18 1983 2.362 0.529 3.032 0.477 7 3.008 0.403 7 1984 2.897 0.253 3.513 0.146 6 3.513 0.264 6 1985 2.059 0.606 6 1986 2.135 0.916 2.642 0.692 4 1.362 0.487 12 1987 2.408 0.528 2.786 0.638 11 1.185 0.645 11 1988 2.18 0.888 2.213 0.745 25 0.636 0.646 12 1989 2.623 0.586 3.165 0.693 19 0.689 0.200 12 1990 0.703 0.251 6 1991 2.38 0.822 2.822 0.537 24 0.531 0.231 9 1992 1993 2.36 0.599 2.764 0.422 16 0.563 0.125 9 1994 2.048 0.366 3.057 0.386 7 0.903 0.445 2 1995 2.259 0.592 2.668 0.543 16 0.684 0.263 3 1996 2.959 0.565 3.129 0.498 16 0.641 0.306 13 1997 2.139 0.53 3.029 0.566 16 0.513 0.260 10 1998 1.774 0.562 2.044 0.634 16 0.572 0.000 2 48 Table 10. Large-mesh (114-mm stretch measure) gill net effort (km net) in Michigan management units during 1980-1998. Year MB MI4 MIS MI6 MI7 1980 0.0 0.0 0.0 140.5 0.0 1981 0.0 0.0 0.0 466.8 266.4 1982 0.0 0.0 0.0 759.0 187.9 1983 0.0 0.0 0.0 1104.6 690.2 1984 501.0 0.0 0.0 943.1 641.5 1985 2305.7 1362.3 0.0 692.0 1511.9 1986 2828.0 4871.3 84.0 489.5 1635.1 1987 975.3 3353.1 330.0 403.6 1584.2 1988 1461.8 5709.5 292.0 516.9 1654.5 1989 735.6 6872.8 132.0 595.0 1810.6 1990 776.6 6696.4 538.0 542.8 2509.7 1991 905.2 6171.4 142.5 276.8 2129.4 1992 1559.4 5413.4 420.0 477.9 1280.7 1993 1375.3 3962.8 392.0 199.9 965.4 1994 1267.8 2868.7 127.0 346.3 1174.2 1995 1066.4 1529.2 113.4 109.7 752.6 1996 792.0 2096.4 161.4 249.9 319.1 1997 1340.2 2389.0 102.3 137.8 1036.5 1998 1729.5 2202.7 280.3 267.9 917.8 49 Table 11. Results of the non-linear regression for recruitment described by wild parents (Model 1). See Table 1 for model definitions. NONLIN MODEL RECRUITS7=LOG(((MI3*A3+MI4*A4+MIS*AS+MI6*A6+MI7*A7)*(EXPWILD)), *EXP(-(MI3*B3+MI4*B4+MIS*BS+MI6*B6+Mi7*B7)*(EXPWILD))+l) ESTIMATE/ ITER= 500 START= 1, 1, 1, 1, 1, .1, .1, .1, .1, .1, GN 20 iterations Dependent variable is RECRUITS? zero weights, missing data or estimates reduced degrees of freedom Source Sum-of-Squares df Mean-Square Regression 570.783 10 57. 078 Residual 51.357 85 0 .604 Total 622.140 95 Mean corrected 60.. 580 94 Raw R-square (1-Residual/Total) 0.917 Mean corrected R-square Cl-Residual/Corrected) 0.152 R(observed vs predicted) square 0.356 Wald Confidence Interval Parameter Estimate A.S.E. Param/ASE Lower < 95%> Upper A3 3.061 1.227 2.495 0.622 5.500 A4 5.702 1.742 3.274 2.240 9.165 AS 5.027 1.340 3.751 2.362 7 .692 A6 4.120 1.173 3.513 1. 788 6 .452 A7 5.521 2.443 2.260 0.663 10.379 B3 0.148 0.035 4.174 0.078 0.219 B4 0.100 0.021 4.869 0.059 0.141 BS 0.045 0.008 5.695 0.030 0.061 B6 0.100 0.027 3.700 0.046 0.154 B7 0.144 0.038 3.781 0.068 0.219 50 Table 12. Results of the non-linear regression for recruitment described by stocked parents (Model 2). See Table 1 for model definitions. NONLIN MODEL RECRUITS7=LOG(((MI3*A3+MI4*A4+MIS*AS+MI6*A6+MI7*A7)*(EXPCLIPCPE8)), *EXP(-(MI3*B3+MI4*B4+MIS*BS+MI6*B6+MI7*B7)*(EXPCLIPCPE8))+1) ESTIMATE/ ITER=S00 START= l,l,l,l,l,-1,-l,-l,-l,-l,GN 15 iterations Dependent variable is RECRUITS? Zero weights, missing data or estimates reduced degrees of freedom Source Sum-of-Squares df Mean-Square Regression 588.909 10 58.891 Residual 49.907 90 0.555 Total 638.816 100 Mean corrected 62.893 99 Raw R-square (1-Residual/Total) 0.922 Mean corrected R-square (1-Residual/Corrected) 0.206 R(observed vs predicted) square 0.351 Wald Confidence Interval Parameter Estimate A.S.E. Param/ASE Lower < 95%> Upper A3 0.866 0.292 2.965 0.286 1.446 A4 1.448 0.424 3.417 0.606 2.291 AS 4.310 1.396 3.087 1.536 7.084 A6 3.237 0.899 3.601 1.451 5.023 A7 2.886 0.835 3.455 1.227 4.546 B3 0.042 0.009 4.491 0.023 0.061 B4 0.030 0.007 4.080 0.015 0.044 BS 0.047 0.009 5.442 0.030 0.064 B6 0.070 0.012 6.044 0.047 0.093 B7 0.059 0.009 6.258 0.040 0.077 51 Table 13. Results of the non-linear regression for recruitment described by wild parents, stocked parents, and one k (Model 3). See Table 1 for model definitions. NONLIN MODEL RECRUITS7=LOG(((MI3*A3+MI4*A4+MIS*AS+MI6*A6+MI7*A7)*(EXPWILD+EXPCLIPCPE8*K)), *EXP(-(MI3*B3+MI4*B4+MIS*BS+MI6*B6+MI7*B7)*(EXPWILD+EXPCLIPCPE8*K))+l) ESTIMATE/ ITER=S00 START= 1,1,1,1,1,1,-.s,-.s,-.s,-.s,-.S,GN 10 iterations Dependent variable is RECRUITS? Zero weights, missing data or estimates reduced degrees of freedom Source Sum-of-Squares df Mean-Square Regression 588.126 11 53.466 Residual 34.014 84 0.405 Total 622 .140 95 Mean corrected 60.580 94 Raw R-square (1-Residual/Total) 0.945 Mean corrected R-square (1-Residual/Corrected) 0.439 R(observed vs predicted) square 0.442 Wald Confidence Interval Parameter Estimate A.S.E. Param/ASE Lower < 95%> Upper A3 0. 726 0.278 2.607 0.172 1.280 A4 1.328 0.423 3.137 0.486 2.170 AS 1.424 0.433 3.286 0.562 2.286 A6 3 .777 1.486 2.541 0.821 6.732 A7 2.140 1.132 1.892 0.110 4.390 K 0.522 0.148 3.527 0.228 0.817 B3 0.045 0.015 2.999 0.015 0.075 B4 0.035 0.009 3.713 0.016 0.054 BS 0.020 0.006 3.224 0.008 0.033 B6 0.095 0.025 3.779 0.045 0.145 B7 0.070 0.025 2.747 0.019 0.120 52 Table 14. Results of the non-linear regression for recruitment described by wild parents, stocked parents, and two k's (Model 4). See Table 1 for model definitions. NONLIN MODEL RECRUITS7=LOG(((MI3*A3+MI4*A4+MIS*AS+MI6*A6+MI7*A7)*(EXPWILD+EXPCLIPCPE8*KA)), *EXP(-(MI3*B3+MI4*B4+MIS*B5+MI6*86+MI7*B7)*(EXPWILD+EXPCLIPCPE8*KB))+l) ESTIMATE/ ITER=S00 START=l,1,1,1,1,1,-.5,-.5,-.5,-.5,-.5,1,GN 14 iterations Dependent variable is RECRUITS? Zero weights, missing data or estimates reduced degrees of freedom Source Sum-of-Squares df Mean-Square Regression 588.143 12 49.012 Residual 33.997 83 0.410 Total 622.140 95 Mean corrected 60.580 94 Raw R-square (1-Residual/Total) 0.945 Mean corrected R-square (1-Residual/Corrected) 0.439 R(observed vs predicted) square 0.442 Wald Confidence Interval Parameter Estimate A.S.E. Param/ASE Lower < 95%> Upper A3 0.691 0.295 2.342 0.104 1.277 A4 1.263 0.468 2.698 0.332 2.195 AS 1.362 0.491 2.771 0.384 2.339 A6 3.632 1.556 2.334 0.536 6. 727 A7 2.100 1.120 1.875 0.128 4.328 KA 0.565 0.236 2.398 0.096 1.034 B3 0.045 0.015 2.962 0.015 0.075 84 0.035 0.010 3.616 0.016 0.054 BS 0.020 0.006 3.088 0.007 0.033 86 0.094 0.025 3.700 0.043 0.144 B7 0.070 0.025 2.738 0.019 0.120 KB 0.534 0.156 3.435 0.225 0.844 53 Table 15. Results of the non-linear regression for recruitment described by wild parents and stocked parents (Model 5). See Table 1 for model definitions. NONLIN MODEL RECRUITS7=LOG((((MI3*AW3+MI4*AW4+MIS*AWS+MI6*AW6+MI7*AW7)*(EXPWILD))+((MI3*AS3+ MI4*AS4, +MIS*ASS+MI6*AS6+MI7*AS7)*(EXPCLIPCPE8))), *EXP( ((MI3*BW3+MI4*BW4+MIS*BWS+MI6*BW6+Mi7*BW7)*(EXPWILD))+((MI3*BS3+MI4*BS4+MIS*BSS +MI6*BS6+MI7*BS7)*(EXPCLIPCPE8)))+1) >ESTIMATE/ ITER=S00 START= 1,1,1,1,1,1,1,1,1,1,-.s,-.s,-.s,-.s,-.s,-.s,-.s, .s,-.s,-.S,GN 64 iterations Dependent variable is RECRUITS? zero weights, missing data or estimates reduced degrees of freedom Source Sum-of-Squares df Mean-Square Regression 590.264 20 29.513 Residual 31.876 75 0.425 Total 622.140 95 Mean corrected 60.580 94 Raw R-square (1-Residual/Total) 0. 949 Mean corrected R-square (1-Residual/Corrected) 0.474 R(observed vs predicted) square 0.479 Wald Confidence Interval Parameter Estimate A.S.E. Param/ASE Lower < 95t> Upper AW3 0.934 0.867 1.078 -0.793 2.662 AW4 1. 964 0.852 2.307 0.268 3.661 AWS 1. 967 0.833 2.361 0.307 3.627 AW6 3.651 3.051 1.197 -2.427 9. 728 AW7 1.147 1.138 1.008 -1.119 3.413 AS3 0.365 0.226 1.618 -0.084 0.814 AS4 0.373 0.206 1.810 -0.037 0.784 ASS 0.463 0 .440 1.052 -0.413 1. 338 AS6 1.767 1.282 1.378 -0.787 4.321 AS7 2.023 1. 518 1.332 -1.002 5.048 BW3 0.077 0.051 1.507 -0. 025 0.179 BW4 0.053 0.014 3.748 0.025 0.081 BWS 0.025 0.011 2.333 0.004 0.047 BW6 0.082 0.038 2.140 0.006 0.158 BW7 0.049 0.043 1.143 -0.037 0.135 BS3 -0.016 0.014 -1.100 -0.044 0.013 BS4 -0.007 0.007 -0.985 -0.022 0.007 BSS -0.007 0.013 -0.504 -0.033 0.020 BS6 -0.051 0.013 -3.865 -0.077 -0.025 BS7 -0.048 0.016 -2.978 -0.080 -0.016 54 Table 16. Results of the non-linear regression for recruitment described by wild parents, stocked parents, one k, and large-mesh gill net effort. NONLIN MODEL RECRUITS7=LOG(((MI3*A3+MI4*A4+MIS*AS+MI6*A6+MI7*A7)*(EXPWILD+EXPCLIPCPE8*K)), *EXP(-((MI3*B3+MI4*B4+MIS*BS+MI6*B6+MI7*B7)*(EXPWILD+EXPCLIPCPE8*K)), -((MI3*G3+MI4*G4+MIS*GS+MI6*G6+MI7*G7)*(EFFSUM)))+l) ESTIMATE/ ITER=S00 START= 1, 1, 1, 1, 1, 1, - . 5, - . 5, - . 5, - . 5, - . 5, - .1, - .1, - .1, - .1, - .l,GN 12 iterations Dependent variable is RECRUITS? Zero weights, missing data or estimates reduced degrees of freedom Source Sum-of-Squares df Mean-Square Regression 589.779 16 36.861 Residual 32.362 79 0.410 Total 622.140 95 Mean corrected 60.580 94 Raw R-square (!-Residual/Total) 0.948 Mean corrected R-square (!-Residual/Corrected) 0.466 R(observed vs predicted) square 0.468 Wald Confidence Interval Parameter Estimate A.S.E. Param/ASE Lower < 95\-> Upper A3 0.850 0.336 2.528 0.181 1.519 A4 1.373 0.460 2.987 0.458 2.288 AS 1.497 0.469 3.193 0.564 2.431 A6 4.148 1. 990 2.084 0.187 8.110 A7 2.745 1. 825 1.504 -0.888 6 .377 K 0.512 0.147 3.471 0.218 0.805 B3 0.039 0.015 2 .612 0.009 0.068 B4 0.035 0.010 3.630 0.016 0.055 BS 0.016 0.007 2.441 0.003 0.030 B6 0.097 0.025 3.837 0.047 0.148 B7 0.076 0.027 2.781 0.022 0.130 G3 0.328 0.266 1.231 -0.202 0.858 G4 0.016 0.078 0.203 -0 .139 0.170 GS 8.162 5.599 1.458 -2.983 19.306 G6 0.126 0.534 0.237 -0.936 1.189 G7 0.156 0.299 0.521 -0.440 0.751 55 REFERENCES Agassiz, L. 1850. Lake Superior: its physical character, vegetation, and animals. Gould, Kendall and Lincoln, Boston. Baldwin, N. S., R. W. Saalfeld, M.A. Ross, and H.J. Buettner. 1979. Commercial fish production in the Great Lakes 1867-1977. Great Lakes Fishery Commission Technical Report 3. Bates, D. M. and D. G. Watts. 1988. 'Nonlinear regression analysis and its applications.' (John Wiley and Sons: New York). 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