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This is to certify that the
thesis entitled

TEMPORAL AND SPATIAL TRENDS IN SISCOWET (SALVELINUS
NAMAYCUSH) ABUNDANCE AND BIOLOGY FOR MICHIGAN
WATERS OF LAKE SUPERIOR

presented by

Melissa Teniente Mata

has been accepted towards fulﬁllment
of the requirements for the

MS. degree in Fisheries and Wildlife

 

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Date

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TEMPORAL AND SPATIAL TRENDS IN SISCOWET (SAL VELIN US NAMA YCUSH)
ABUNDANCE AND BIOLOGY FOR MICHIGAN WATERS OF LAKE SUPERIOR

By

Melissa Teniente Mata

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

2009

 

“1.“..-

ABSTRACT

TEMPORAL AND SPATIAL TRENDS IN SISCOWET (SAL VELIN US NAMA YCUSH)
ABUNDANCE AND BIOLOGY FOR MICHIGAN WATERS OF LAKE SUPERIOR

By

Melissa Teniente Mata
The siscowet form of lake trout (Salvelinus namaycush) is the most abundant of three
lake trout morphotypes found in Lake Superior of the North American Laurentian Great
Lakes, but published information on their population dynamics and biology is limited. I
investigated spatial patterns, temporal patterns, or both, in abundance and life history
attributes of siscowet lake trout across Michigan waters of Lake Superior based on data
collected during 1970 through 2006. I assessed temporal patterns in siscowet lake trout
abundance based on data from a long-term survey that targeted the lean lake trout
morphotype, because data from a survey targeting siscowet was more limited. In order to
develop an index of siscowet abundance from these data, I used delta-lognormal models.
I emphasize both the abundance results and the modeling methodology, which is
generally applicable for non-target species. My results agree with previous reports that
siscowet densities increased substantially during the 1980-2006 period, and show that the
rate of increase decreased since about 2000. The most striking spatial and temporal
differences in life history were for length-at-maturity and condition (mass at length). In
eastern Michigan waters, siscowets matured at smaller sizes and were in better condition
than in waters further to the west. In most areas there was a decline in condition and
length-at-age, and an increase in length-at-maturity after 1999, coinciding with when the

rate of increase in siscowet density appeared to be decreasing.

 

 

ACKNOWLEDGEMENTS

Thank you Shawn Sitar (MDNR), Mark Ebener (CORA), Bill Mattes (GLIF WC),
Matt Symbal (Red Cliff Fisheries Department), and all other personnel that collected and
provided data for this project. This project wouldn’t have started without your
collaboration and efforts in creating a siscowet database and ﬁnding all available data for
siscowet lake trout. I thank my committee members Mike Jones and Andrew McAdam
who contributed their thoughts and guidance throughout my academic career and during
the development of this thesis.

To my advisor Jim Bence, I don’t even think there are words to describe how
lucky and grateful I am to have you as an advisor. Even though, I may have ﬂoundered a
bit by taking on little more than I can chew from time to time. You never tried to change
my mind, and let me venture into several different areas while attending Michigan State
University (MSU). I’m grateful that you allowed me to ﬁgure my way out and discover
my limits. Once again, thank you for ﬁnally emailing me back and giving me this
opportunity to work with you and attend MSU. This will be one of the few deﬁning
moments in my life. Thank you.

Finally I would like to thank my family, which consists of my ﬁance' Eric and our
dog Honey. This has been an adventure for the both of us, while struggling to ﬁnd
employment to be close or working long distance. They have both endured through
many of my departures while I further my academic career and I’m grateful for their
patience. If there were times I felt discouraged, Eric was always there to pick me up

when I truly needed encouragement and support.

iii

 

m1. _ ..

TABLE OF CONTENTS

LIST OF TABLES .................. ' ................................................................. v i
LIST OF FIGURES ..................................................................................... ix
THESIS INTRODUCTION & SUMMARY ...................................................... 1
Summary of Chapter 1 ............................................................. 4

Summary of Chapter 2 ............................................................. 6

Concluding Remarks and Connection Between Chapters 1 and 2 ........... 8

References ................................................................................... 10

CHAPTER 1

DEVELOPING AN INDEX OF ABUNDANCE FOR SISCOWET LAKE
TROUT (SAL VELIN US NAMA Y C USH) USING A NON-TARGET SURVEY
FOR MICHIGAN WATERS OF LAKE SUPERIOR

Abstract ...................................................................................... 13
Introduction .................................................................................... l 5
Methods ...................................................................................... 19
Assessment Fishery Data ......................................................... 19
Delta Approach Overview ....................................................... 20
Modeling the probability of occurrence for a non-zero catch ............... 22
Modeling the catch rate for positive catches ................................... 23
Model selection procedure ....................................................... 24
Constructing indices of abundance and standard errors ..................... 26
Results ....................................................................................... 28
Model Selection for the probability of occurrence for
a non-zero catch (p) ...................................................... 28
Model Selection for the catch rate for positive
catches (In(CPUE)) ...................................................... 28
Important ﬁxed and random effects ............................................. 29
Trends in the probability of occurrence for a non-zero catch (p) ........... 29
Trends in the catch rate for positive catches (ln(cpue)) ...................... 30
Trends in Standardized Catch Rate (Index of annual
abundance = (ln(p)+ln(cpue)) ........................................... 30
Comparative Analysis ............................................................ 31
Discussion ................................................................................... 31
Acknowledgements ........................................................................ 36
References ................................................................................... 60

iv

 

 

__r_. -_...

CHAPTER 2

SISCOWET BIOLOGY ACROSS REGIONS AND OVER TIME IN MICHIGAN
WATERS OF LAKE SUPERIOR

Abstract .................................................................................... 63
Introduction .................................................................................. 64 -
Methods .................................................................................... 67
Assessment Fishery Data ........................................................ 67
General Analysis Procedures ................................................... 70
Age and size composition ....................................................... 7O
Mortality ........................................................................... 71
Length-at-50% maturation ....................................................... 72
Mass-Length Relationship —- Condition Indices ............................... 73
Modeling time-vary growth ...................................................... 76
Results ........................................................................................ 80
Age and size composition ........................................................ 80
Mortality ........................................................................... 81
Length-at-50% maturation ....................................................... 82
Model Selection for the mass-length relationship ............................ 82
Predicted Mass at 450 mm and 700 mm as condition indices ............... 83
Growth and length-at-age ........................................................ 85
Discussion ................................................................................... 86
Acknowledgements ........................................................................ 91
References ................................................................................. 1 15

 

 

 

LIST OF TABLES

Table 1.1. Speciﬁc years, number of years, number of grids, and number of gill-net sets
included in this analysis for siscowet lake trout index of abundance for Michigan water of
Lake Superior ........................................................................................ 37

Table 1.2. Combinations of random effects considered in models for both the probability
of occurrence for non-zero catch and catch rate (CPUE) for positive catches. The random

terms are deﬁned as follows: 5yg year by grid interaction, )1 yd year by depth
interaction, Agd grid by depth interaction and Pygd year by grid by depth

interaction ............................................................................................ 38

Table 1.3. Combinations of ﬁxed effects considered in models for both the probability of
occurrence for a non-zero catch and catch rate (CPUE) for positive catches. The ﬁxed

effects are deﬁned as a y is the year effect, ﬁg is the grid effect, and cod is the depth
effect .................................................................................................. 39

Table 1.4. Unique candidate models with number of estimated parameters (K), Akaike’s
information criterion differences (AAIC, 0 = best model) and AIC weights for both the
probability of occurrence for a non-zero catch and catch rate for positive catches
submodels for M13 .................................................................................. 40

Table 1.5. Unique candidate models with number of estimated parameters (K), Akaike’s
information criterion differences (AAIC, 0 = best model) and AIC weights for both the
probability of occurrence for a non-zero catch and catch rate for positive catches
submodels for M14 .................................................................................. 41

Table 1.5 (cont’d) .................................................................................... 42

Table 1.6. Unique candidate models with number of estimated parameters (K), Akaike’s
information criterion differences (AAIC, 0 = best model) and AIC weights for both the

probability of occurrence for a non-zero catch and catch rate for positive catches
submodels for M15 .................................................................................. 43

Table 1.6 (cont’d) .................................................................................... 44
Table 1.7. Unique candidate models with number of estimated parameters (K), Akaike’s
information criterion differences (AAIC, 0 = best model) and AIC weights for both the

probability of occurrence for a non-zero catch and catch rate for positive catches
submodels for M16 .................................................................................. 45

vi

 

 

Table 1.8. Unique candidate models with number of estimated parameters (K), Akaike’s
information criterion differences (AAIC, O = best model) and AIC weights for both the
probability of occurrence for a non-zero catch and catch rate for positive catches
submodels for M17 ................................................................................. 46

Table 1.9. Unique candidate models with number of estimated parameters (K), Akaike’s
information criterion differences (AAIC, 0 = best model) and AIC weights for both the
probability of occurrence for a non-zero catch and catch rate for positive catches
submodels for M15 for the second data selection procedure .................................. 47

Table 1.9 (cont’d) .................................................................................... 48

Table 1.10. Unique candidate models with number of estimated parameters (K), Akaike’s
information criterion differences (AAIC, 0 = best model) and AIC weights for both the
probability of occurrence for a non-zero catch and catch rate for positive catches
submodels for M16 for the second data selection procedure .................................. 49

Table 1.11. Unique candidate models with number of estimated parameters (K), Akaike’s
information criterion differences (AAIC, O = best model) and AIC weights for both the
probability of occurrence for a non-zero catch and catch rate for positive catches
submodels for M17 for second data selection procedure ....................................... 50

Table 2.1. Number of observations (N) on individual siscowet included for each analysis
by survey and zone for Michigan waters of Lake Superior .................................... 92

Table 2.2. All possible combinations of random effects considered in models for mass-
length relationship that included all ﬁxed effects. Model shorthand notation is used to
indicate which random effects are included in the model (e. g., length*year indicates that a
random interaction of length and year was included). For the actual model

see equation 3 ........................................................................................ 93

Table 2.3. All possible combinations of ﬁxed effects for mass-length relationship that
were considered and used with best random effects model. Model shorthand notation is
used to indicate which effects are included in the model (e. g., year indicates an effect of
year was included, and length*zone that an interaction of length and zone was included).
For the actual model see equation 3 ............................................................... 94

Table 2.4. Estimated observation error (among individual variation not explained by age
or year) used for each analysis for modeling time varying von Bertalanffy growth model.
Zones are deﬁned as combination of management units: zone 1 is M12 and M13, zone 2

is M14, zone 3 is M15 and M16 and zone 4 is M17 ............................................. 95

Table 2.5. Length distribution (mm) summary statistics for siscowet lake trout for each
survey, time period, and zone from samples collected during 1996-2006. Statistics are
denoted by: sample size (N), minimum (min), maximum (max), mean, and standard
deviations (std) ........................................................................................ 96

vii

 

 

Table 2.6. Age (years) distribution summary statistics for siscowet lake trout for each
survey, time period, and zone from samples collected during 1996-2006. Statistics are
denoted by: sample size (N), minimum (min), maximum (max), mean, and standard
deviations (std) ....................................................................................... 97

Table 2.7. Estimates of instantaneous rates of total mortality (Z) for each survey by zone
and period and 95% conﬁdence intervals (denoted by lower and upper bounds for
intervals) ............................................................................................. 98

Table 2.8. The number of siscowet sampled (N) and length-at-50% maturity (L50, mm)
with 95 % conﬁdence intervals in parentheses for each zone and temporal period for

survey 2. Zones are deﬁned as combination of management units: zone 1 is M12 and

M13, zone 2 is M14, zone 3 is M15 and M16 and zone 4 is M17. Period 1 includes
years < 2000 and period 2 includes years > 1999 ............................................... 99

Table 2.9. Unique candidate models for random effects in mass-length models with

number of estimated parameters (Np), AIC differences (AAIC, 0 = best model), and AIC

weights for the mass-length relationship model for each survey. All ﬁxed effects were
included in all models ...................................................................................................... 100

Table 2.10. Unique candidate mass-length models containing ﬁxed effects and the best
random effects model (lowest AIC in Table 2.1) with number of estimated parameters

(Np), AIC differences (AAIC, 0 = best model), and AIC weights for the mass-length

relationship model for each survey. Fixed effects are not italicized and random effects
are italicized ........................................................................................ 1 01

Table 2.10 (cont’d) ................................................................................. 102

Table 2.11. List of alternative growth models for model comparison based on deviance

information criteria (DIC), number of estimated parameters ne, and ADIC is the

differences between DICs with the best model (lowest DIC). When parameters were
allowed to vary over time they followed a random walk model (see text) ............... 103

viii

 

 

 

 

LIST OF FIGURES

Figure 1.1. Lake trout management units of Lake Superior (Hansen et al. 1995b). The
letter abbreviations denote U. S. waters by state MN — Minnesota, MI — Michigan, and
W1 -— Wisconsin, and numbers represent Canadian waters. Bolded management units
were the ones that supplied data used in this paper ............................................. 51

Figure 1.2. Proportion of gill-net sets that caught at least one siscowet from the
standardized spring lean lake trout survey from 1975-2006 ................................... 52

Figure 1.3. Probability of occurrence of a non-zero catch of siscowet from the spring lean
lake trout survey for ﬁve Michigan management units in Lake Superior during 1975-2006
(solid circles joined by dashed line). The open circles show years that did not catch any

siscowet for each unit ............................................................................... 53

Figure 1.4. Estimated log-scale catch per unit effort (CPUE) for siscowet positive catches
from the lean lake trout survey for ﬁve Michigan management units in Lake Superior
during 1975-2006 (solid circles joined by dashed line). The open circles show years that
did not catch any siscowet lake trout ............................................................. 54

Figure 1.5. Estimated standardized catch rates (loge scale) of siscowet lake trout from the
spring lean lake trout survey for ﬁve Michigan management units in Lake Superior
during 1975-2006 (solid circles joined by dashed line). The open circles show years that
did not catch any siscowet lake trout ............................................................. 55

Figure 1.6. Estimated probability of occurrence of a non—zero catch of siscowet from the
spring lean lake trout survey for ﬁve Michigan management units in Lake Superior
during 1975-2006 for best (ﬁlled circles) and second best (open circles) selected models
using AIC. When only one symbol is visible for a year (open circle) then the two
estimates are identical .............................................................................. 56

Figure 1.7. Estimated log-scale catch per unit effort for siscowet from the spring lean
lake trout survey for ﬁve Michigan management units in Lake Superior during 1975-2006
for best (ﬁlled circles) and second best (open circles) selected models using AIC. When
only one symbol is visible for a year (open circle) then the two estimates are identical...57

Figure 1.8. Estimated standardized catch rates for siscowet from the spring lean lake
trout survey for ﬁve Michigan management units in Lake Superior during 1975-2006 for
best (ﬁlled circles) and second best (open circles) selected models using AIC. When only
one symbol is visible for a year (open circle) then the two estimates are identical. . . . .....58

Figure 1.9. Relative abundance (CPUE) of siscowet lake trout in commercial ﬁsheries in
all area US. and Canadian waters of Lake Superior during 1950-1989 (from Bronte et al.
2003) .................................................................................................. 59

ix

 

 

 

Figure 2.1. Lake trout management units of Lake Superior (Hansen et al. 1995). The
letter abbreviations denote U. S. waters by state MN — Minnesota, MI - Michigan, and
W1 — Wisconsin, and numbers represent Canadian waters. Bolded management units
were the ones that supplied data used in this paper ........................................... 104

Figure 2.2. Length-frequency distributions for siscowet lake trout sampled in survey 1
for each period and zone. Left panels are for period 1 and right panels are for period 2.
Zones are deﬁned as combination of management units: zone 1 is M12 and M13, zone 2
is M14, zone 3 is M15 and M16, and zone 4 is M17. Period 1 includes years < 2000 and
period 2 includes years > 1999 .................................................................. 105

Figure 2.3. Length-frequency distributions for siscowet lake trout sampled in survey 2
for each period and zone. Leﬁ panels are for period 1 and right panels are for period 2.
Zones are deﬁned as combination of management units: zone 1 is M12 and M13, zone 2
is M14, zone 3 is M15 and M16, and zone 4 is M17. Period 1 includes years < 2000 and
period 2 includes years > 1999 .................................................................. 106

Figure 2.4. Length-frequency distributions for siscowet lake trout sampled in survey 3
for each period and zone. Left panels are for period 1 and right panels are for period 2.
Zones are deﬁned as combination of management units: zone 1 is M12 and M13, zone 2
is M14, zone 3 is M15 and M16, and zone 4 is M17. Period 1 includes years < 2000 and
period 2 includes years > 1999 .................................................................. 107

Figure 2.5. Age-frequency distributions for siscowet lake trout sampled in survey 1 for
each period and zone. Leﬁ panels are for period 1 and right panels are for period 2.
Zones are deﬁned as combination of management units: zone 1 is M12 and M13, zone 2
is M14, zone 3 is M15 and M16, and zone 4 is M17. Period 1 includes years < 2000 and
period 2 includes years > 1999 .................................................................. 108

Figure 2.6. Age-frequency distributions for siscowet lake trout sampled in survey 2 for
each period and zone. Left panels are for period 1 and right panels are for period 2.
Zones are deﬁned as combination of management units: zone 1 is M12 and M13, zone 2
is M14, zone 3 is M15 and M16, and zone 4 is M17. Period 1 includes years < 2000 and
period 2 includes years > 1999 .................................................................. 109

Figure 2.7. Age-frequency distributions for siscowet lake trout sampled in survey 3 for
each period and zone. Left panels are for period 1 and right panels are for period 2.
Zones are deﬁned as combination of management units: zone 1 is M12 and M13, zone 2
is M14, zone 3 is M15 and M16, and zone 4 is M17. Period 1 includes years < 2000 and
period 2 includes years > 1999 .................................................................. 110

 

 

Figure 2.8. Predicted logarithm of masses at 450 (on left) and 700 mm (on right) total
' length for siscowet lake trout in three different surveys for each zone from 1990 to 2006.
The zones are denoted by: solid circle zone 1; open circles zone 2; solid upside-down
triangle zone 3; open triangle zone 4. The vertical line represent the lake-wide average of

loge (mass) within each survey and length class .............................................. 11 1

Figure 2.9. Length at age (mm) estimated by (mean of posterior distribution) nonlinear
von Bertalanffy model that allowed parameters to vary over time (see text) for three
selected ages ........................................................................................ 112

Figure 2.10. Length at age (mm) estimated (mean of posterior distribution) by nonlinear
von Bertalanffy model that allowed parameters to vary over time (see text) for age 6 and
age 20. The ﬁrst four lower lines are predicted values for age 6 and top four lines
correspond to age 20 siscowet.............. ...................................................................... 113

Figure 2.11. Estimated standardized catch rates (loge scale) of siscowet lake trout from

the spring lean lake trout survey for ﬁve Michigan management units in Lake Superior
during 1975-2006 (solid circles joined by dashed line). The open circles show years that
did not catch any siscowet lake trout (reproduced from Chapter 1) ......................... 114

xi

 

 

 

THESIS INTRODUCTION & SUMMARY

Lake Superior is the largest of the Laurentian Great Lakes and is the only one to
contain lake trout (Salvelinus namaycush) morphotypes other than the lean. Three

morphotypes are widely distributed in Lake Superior: the lean, the siscowet or “fat”, and

 

the humper (Khan and Qadri 1970; Lawrie and Rahrer 1973; Pycha and King 1975).
These morphotypes are distinguished by facial characteristics, body fat content, habitat
depth, and spawning time.

The siscowet morphotype of lake trout, the focus of this study, usually inhabit

 

offshore water at depths greater than 80 m and have a deep, stout body high in fat content
making them less desirable to commercial ﬁsheries (Eschmeyer and Phillips 1965; Khan
and Qadri 1970; Pycha and King 1975; Burnham-Curtis 1993; Moore and Bronte 2001;
Bronte 1993). Nevertheless, siscowet contributed 27% of the lake trout harvest from
1929 to 1961, with the lean form making up most of the remainder (Bronte and Sitar
2008). Lean lake trout tend to inhabit inshore water at depths less than 80 m, have a
salmon-like appearance, and are currently the only commercially targeted lake trout
(Eschmeyer and Phillips 1965; Pycha and King 1975). Humper lake trout are
distinguished from the other forms by inhabiting deep offshore reefs and through their
deep-bodied shape with thin abdominal walls (Eschmeyer and Phillips 1965). Several
additional variants have been reported as being extant, but only near Isle Royale in the
north-central part of the lake (Moore and Bronte 2001). Signiﬁcant genetic differences
exist among these three morphotypes, but they do not warrant species or subspecies

distinctions (Burnham-Curtis 1994; Krueger and Ihssen 2005). Phenotypic differences

 

 

appear to be adaptations to their respective environments (Henderson and Anderson
2002).

Historically, lake trout were a dominant predator in the Lake Superior ﬁsh
community, and they supported a substantial commercial ﬁshery that yielded an annual
average of 2.0 million kg from 1913 to 1950 (Hansen et al. 1995). During the 19505,
lake trout abundance declined drastically because of excessive commercial ﬁshing and
predation by sea lamprey (Petromyzon marinus). Sea lamprey invaded Lake Superior in
the 19405, and their abundance increased in the late 19505, reaching peak levels in 1961
(Smith 1971). Commercial yield of lake trout declined by more than 90% from 1952 to
1962, which resulted in closure of lake trout commercial ﬁsheries in 1962 (Pycha and
King 1975).

Lake trout rehabilitation and management efforts focused primarily on lean lake
trout populations, despite the ecological importance of both siscowet and humper
morphotypes of lake trout (Horns et al. 2003). Lean lake trout stocks increased rapidly in
the 19705 and 19805, in response to the commercial ﬁshery closure, stocking of yearling
hatchery-reared lean lake trout, and sea lamprey control. Commercial lake trout ﬁsheries
reopened in Wisconsin and Michigan in 1970 and 1980, respectively, as their stocks
increased (Hansen et al. 1995). Although not the focus of restoration efforts, siscowet
and humper lake trout stock levels increased in the 19805, primarily due to sea lamprey
control.

Recent reports indicate that siscowet densities have been much higher than those

of lean lake trout for the past 30 years. Commercial catch per unit effort (CPUE) data

. . . . . . . -l .
indicate that Slscowet densmes increased steadily from >20 kg-km net in the early

 

19505 to about 250 kg-km.l net in the late 19905 (Bronte et al. 2003). In addition,

increases in by-catch of siscowet lake trout in the sport ﬁsheries, which targeted lean lake
trout, has also been observed since the early 19905 (Bronte et al. 2003). Based on both
spring and summer lean lake trout surveys, Sitar et al. (2007) showed that siscowet lake
trout relative abundance, doubled during 1993 -2000 from surveys during 1985-1992. In ..
contrast, lean lake trout relative abundance during 1993-2000 was below their average F

relative abundance during 1983-1992. Ebener (1995) also showed that in 1995 siscowet

 

lake trout made up 72% of the total predator biomass in western Lake Superior compared l
to 21% for lean lake trout.

Given the previous emphasis of research and management on lean lake trout
populations and evidence of the high abundance and potential ecological importance of
the other forms, there is a growing recognition of a need to develop objectives for each of
the three lake trout forms that were historically (1929 — 1943) widely distributed in Lake
Superior (Burhnam-Curtis 1993; Bumham-Curtis and Smith 1994). Concerns have been
expressed about potential ecological effects of the siscowet form on the lean form
(Bronte et al. 2003; Bronte and Sitar 2008), and recently their has been a renewal of
interest in harvesting siscowet (Bronte and Sitar 2008) because they contain high levels
of omega-3 fatty acids (Wang et al. 1990; Bronte and Sitar 2008), which could be used
for pharmaceutical needs. Additional knowledge of their biology and population
dynamics could be useful in deﬁning sustainable harvest levels. There is also some
interest in re-introducing deep water forms, such as siscowet lake trout, to other Great

Lakes. Improved understanding of their biology could be informative for such efforts.

 

In this thesis I explore both temporal trends in relative abundance of siscowet lake
trout in different areas of Michigan’s waters of Lake Superior (chapter 1), and spatial and
temporal patterns in their life-history and biology (chapter 2). In ﬁsheries management
information on year-speciﬁc abundance is often crucial for making decisions. In addition
to evaluating trends in abundance, it is also important to understand the life history and
biology of a ﬁsh. For example information on maturity at age, mass-at-length, and
length-at-age could be used in calculations of per recruit reference points and could be
informative on sustainable levels of ﬁshing (Quinn and Deriso 1999). Furthermore, it
would be useful to evaluate the extent to which life-history characteristics vary spatially
and over time as this might provide clues to whether stocks in Lake Superior are
approaching biological limits or whether if the siscowet form were introduced into other
lakes its biology might differ from what has been seen in particular areas of Lake
Superior. This latter topic points out the usefulness of evaluating both relative abundance
and life history of a ﬁsh.

Summary of Chapter 1

CPUE is widely used as an index of abundance, in part because time series of
catch and effort information are frequently available from commercial, recreational or
assessment ﬁsheries. For instance, in Michigan’s waters of Lake Superior a spring gill-
net survey that targets lean lake trout has collected catch and effort information since
1959 and a gill net survey that targets siscowet form lake trout has collected catch and
effort information for ﬁve survey years (but with many fewer sites sampled each year

than the survey targeting lean lake trout) during 1996-2006 in most areas.

In chapter 1, I report on efforts to develop an index of abundance based on ﬁtting
statistical models to “standardize” CPUE data from the spring gill-net survey that targets
lean lake trout. I chose not to use the survey that targeted siscowet form lake trout
because of its shorter time-series, fewer sampled years, and fewer sample sites for each
year. Catch and effort standardization methods are widely used to account for factors
other than abundance that inﬂuence CPUE through the use of statistical models, such as
general linear models or generalized linear models. Such catch and effort standardization
generally should be used in developing an index of abundance based on data unless the
data arise from a fully randomized design. When using raw CPUE (a ratio of total catch
to total effort or a simple average of the ratio over samples for annual or longer periods)
as an index of abundance in such situations, instead of estimates based on statistical
modeling, it is known that there are various factors other than abundance that could
inﬂuence the expected CPUE. Changes in such factors, when not accounted for, could
either add unnecessary noise to the index or lead to a violation of the basic assumption
for using CPUE as an index of abundance, that CPUE is directly proportional to
abundance.

For the spring lean lake trout survey, catches of siscowet form lake trout are
essentially by-catch. By-catch species tend to have CPUE data that are highly skewed to
the left with a high proportion of zero catches. Such data are common for non-target
species in both surveys and ﬁsheries. This type of data leads to difﬁculty in modeling
CPUE and alternative statistical methods are needed to address such problems. A
modern method that is commonly used in marine systems to analyze such CPUE data is

called the delta approach (Lo et al. 1992; Vignaux 1996; Ortiz et al. 2000; Ortiz et al.

2004). This method essentially involves modeling both the probability of a non-zero
catch and the CPUE given a positive catch and then taking the product of these as an
index of abundance. I adopted this approach and the delta-lognormal model speciﬁcally,
to analyze the siscowet form CPUE observations from the lean lake trout survey.

In chapter 1, I emphasize both the modeling methodology and what the results tell
us about changes in siscowet relative abundance over time. My approach illustrated the
usefulness of statistical standardization, random effects to account for correlations, and
information theoretic model selection methods, as well as the value of the delta approach
for analyzing by-catch data where zeros are common.

My results agree with previous reports that siscowet densities increased
substantially during the 1980-2006 period, and show that the rate of increase decreased
since about 2000. Given the use of statistical modeling for CPUE standardization and the
use of the lean lake trout survey data, my results provide further evidence of substantial
increases in siscowet densities during the l980-2006 period, based on a different suite of
data and assumptions than previous assessments based primarily on raw CPUE from
ﬁshery data. My results also show a decrease in the rate of increase since about 2000.
My analyses were done separately for ﬁve different lake trout management areas in
Michigan’s waters, and roughly similar patterns were seen across areas.

Summary of Chapter 2

In chapter 2, I focused on biological characteristic that would be important to
ﬁsheries management in the future. The biological characteristics I chose were age and
size composition, mortality, maturation, condition, and growth. These are key

demographic factors that can inﬂuence spawning stock biomass, recruitment, and yield

potential. Some limited basic biology and life history attributes of siscowet form lake
trout have been described in previous studies, for example, siscowet lake trout have an
estimated Brody growth coefﬁcients (K) ranging from (0053-0080), ﬁrst maturity near
age 8, and mass-speciﬁc fecundity has been estimated at 1025 eggs/kg (Carlander 1970;

Peck 1988; Kitchell et al. 2000; Miller and Schram 2000). However, there is still much

 

,.—

more to be learned about their life history. My study is the most comprehensive
investigation of siscowet life history and the ﬁrst to look simultaneously at age and size
composition, condition, growth, maturation, and mortality of siscowet in Lake Superior.
The objective for this chapter was to examine all these aspects of biology/life
history together, and for each biological measure describe temporal and spatial variation
and determine whether the measures are related to siscowet density. The sources of
information for this chapter included several ﬁsh surveys primarily targeting leans or
siscowets that use gill-nets with either ﬁxed or varying mesh sizes. Available siscowet
data I used start as early as 1990 and extend through 2006, where for most analyses I
created time periods: period 1 is a time block for the 19905 and period 2 is a time block
for the 20005. During the19905 there was general increase in siscowet abundance,
whereas during the 20005, increases were still occurring but at a declining rate potentially
approaching an asymptote (Chapter 1, Bence et al. manuscript). Therefore, one objective
of my study was to identify whether siscowet biology has changed during these periods
when large changes in abundance took place. In addition, I was interested in identifying
whether there were spatial differences in siscowet biology within the Michigan waters

represented in the survey data I used (Management units M12 through M17, Chapter 1,

Figure 1.1). To evaluate this I looked for differences among zones consisting of one or
more management units.

Various statistical techniques were used to evaluate temporal and spatial patterns
in life history and biological parameters, in addition I looked at several different gear
types that targeted either lean or siscowet lake trout. While the details differ among
analyses and from Chapter 1, again I rely on statistical models, incorporation of
appropriate random effects, and information theoretic methods for model selection.
Regardless of the type of gear used, the temporal and spatial trends observed were
consistent. In general, I saw a shift toward older and longer siscowet from period 1 to
period 2. Siscowet lake trout are pre-dominantly maturing at larger sizes and both
condition and growth were declining over time. A particularly interesting ﬁnding was for
siscowet lake trout in zone 4 (M17), the most eastern part of the lake 1 evaluated, which
had different results compared to the other areas. Siscowet lake trout in zone 4 matured
at smaller size, were in better condition, and were longer at younger ages.

Concluding Remarks and Connection Between Chapters 1 and 2

In general, I found that both the population dynamics and several life history
attributes for siscowet lake trout have been changing through time. Several life history
attributes underwent substantial changes of the type one would expect as compensatory
responses as siscowet densities approached their highest levels. This may be an
indication of a cause and effect relationship between siscowet densities and the growth
and condition declines and the associated changes in the maturity schedule. These results

provide a new in depth look at siscowet abundance and siscowet biology, considering

spatial and temporal differences and will contribute to furthering our knowledge of

siscowet lake trout.

References

Bence, J .R., J. Nieland, and Mata, M. T. Draft manuscript (Appendix C). Estimates of the
productive capacity of siscowet lake trout in Michigan waters of Lake Superior.

Bronte, C. R. 1993. Evidence of spring-spawning lake trout in Lake Superior. Journal of
Great Lakes Research 19: 625-629.

Bronte, C. R, Ebener, M. P., Schreiner, D. R., DeVault, D. S., Petzold, M. M., Jensen, D.
A., Richards, C., and Lozano, S. J. 2003. Fish community change in Lake
Superior, 1970-2000. Canadian Journal of Fisheries and Aquatic Sciences 60:
1552-1574.

Bronte, C. R., and Sitar, S. P. 2008. Harvest and relative abundance of siscowet lake trout
in Michigan waters of Lake Superior, 1929-1961. Transactions of the American
Fisheries Society 137: 916-926.

Burnham-Curtis, M. K. 1993. lntralacustrine speciation of Salvelinus namaycush in Lake
Superior: and investigation of genetic and morphological variation and evolution
of lake trout in the Laurentian Great Lakes. Doctoral dissertation. University of
Michigan, Ann Arbor.

Bumham-Curtis, M. K., and Smith, G. R. 1994. Osteological evidence of genetic
divergence of lake trout (Salvelinus namaycush) in Lake Superior. Copeia: 943-
850.

Carlander, K. D. 1970. Handbook of freshwater ﬁshery biology, volume 1. Iowa State
University Press, Ames.

Ebener, M. 1995. Bioenergetics of predatory ﬁsh in western US waters of Lake Superior.
Report prepared for the Red Cliff Band of Lake Superior Chippewas, Red Cliff
Fisheries Department, Bayﬁeld, Wisconsin.

Eschmeyer, P. H., and Phillips, Jr. A. M. 1965. Fat content of the ﬂesh of siscowet and
lake trout from Lake Superior. Transactions of the American Fisheries Society 94:
62-74.

Hansen, M. J ., Peck, J. W., Schorﬂiaar, R. G., Selgeby, J. H., Schreiner, D. R., Schram, S.
T., Swanson, B. L., MacCallum, W. R., Bumham—Curtis, M. K., Curtis, G. L.,
Heinrich, J. W., and Young, R. J. 1995. Lake trout (Salvelinus namaycush)
populations in Lake Superior and their restoration in 1959-1993. Journal of Great
Lakes Research 23 (Supplement 1): 152-175.

Henderson, B. A., and Anderson, D. M. 2002. Phenotypic differences in buoyancy and
energetics of lean and siscowet lake char in Lake Superior. Environmental
Biology of Fishes 64: 203-209.

10

Horns, W. H., Bronte, C. R., Busiahn, T. R., Ebener, M. P., Eshenroder, R. L., Gorenﬂo,
T., Kmieck, N., Mattes, W., Peck, J. W., Petzold, M., and Schreiner, D. R. 2003.

Fish-community objectives for Lake Superior. Great Lakes Fishery Commission
Special Publication 03-01: 1-78.

Khan, N. Y., and Qadri, S. U. 1970. Morphological differences in Lake Superior lake
char. Journal of the Fisheries Research Board of Canada 27: 161-167.

Kitchell, J. E, Cox, S. P., Harvey, C. J., Johnson, T. 8., Mason, D. M., Schoen, K. K.,
Aydin, K., Bronte, C., Ebener, M., Hansen, M., Hoff, M., Schram, S., Schreiner,
D., and Walters, C. J. 2000 Sustainability of the Lake Superior ﬁsh community:
interactions in a food web context. Ecosystems 3: 545-560.

Krueger, C. C, and Ihssen, P. E. Review of genetics of lake trout in the Great Lakes:
history molecular genetics, physiology, strain comparisons and restoration
management. 1995. Journal of Great Lakes Research 21(1):348-363.

Lawrie, A. H., and Rahrer, J. F. 1973. Lake Superior: a case history of the lake and its
ﬁsheries. Great Lakes Fishery Commission Technical Report 19.

Lo, N.C, Jacobson, L.D., and Squire, J. L. 1992. Indices of relative abundance from ﬁsh

spotter data based on delta-lognormal models. Canadian Journal of Fisheries and
Aquatic Sciences 49: 2515-2526.

Miller, M. A. and Schram, S. T. 2000. Growth and contaminant dynamics of Lake
Superior lake trout. Journal of Great Lakes Research 26: 102-111.

Moore, S. A., and Bronte, C. R. 2001. Delineation of sympatric morphotypes of lake trout
in Lake Superior. Transactions of the American Fisheries Society 130: 1233-
1240.

Ortiz, M., and Arocha, F. 2004. Alternative error distribution models for standardization
of catch rates of non-target species from a pelagic longline ﬁshery: billﬁsh
species in the Venezuelan tuna longline ﬁshery. Fisheries Research 70: 275-297.

Ortiz, M., Legault, C. M., and Ehrhardt, N. M. 2000. An alternative method for
estimating bycatch from the US. shrimp trawl ﬁshery in the Gulf of Mexico,
1972-1995. Fishery Bulletin 98: 583-599.

Peck, J. W. 1988. Fecundity of hatchery and wild lake trout in Lake Superior. Journal of
Great Lakes Research 14: 9-13.

Pycha, R. L., and King, G. R. 1975. Changes in the lake trout population of southern

Lake Superior in relation to the ﬁshery, the sea lamprey and stocking, 1950-1970.
Great Lakes Fishery Commission Technical Report 28.

ll

 

 

-'

Quinn, T. J ., II, and Deriso, R. B. 1999. Quantitative ﬁsh dynamics. Oxford University
Press, New York.

Sitar, S. P., Bronte, C. R., Ebener, M. P., Mattes, W. P., Petzold, M, Schram, S. T., and
Schreiner 2007. Lake trout. Pages 49-61 in M. P. Ebener, editor. The state of Lake
Superior in 2000. Great Lakes Fishery Commission Special Publication 07-02,
Ann Arbor, Michigan.

Smith, B. R. 1971. Sea Lamprey in the Great Lakes of North America. Pages207-247 in
The biology of lampreys. Academic Press, New York.

Vignaux, M. 1996. Analysis of spatial structure in ﬁsh distribution using commercial
catch and effort data from the New Zealand hoki ﬁshery. Canadian Journal of
Fisheries and Aquatic Sciences 53: 963-973.

Wang, Y. J, Miller, L. A., Perren, M., and Addis, P. B. 1990. Omega-3 fatty acids in
Lake Superior ﬁsh. Journal of Food Science 55: 71-76.

12

 

CHAPTER 1
ABSTRACT
DEVELOPING AN INDEX OF ABUNDANCE FOR SISCOWET LAKE TROUT
(SAL VELIN US NAMA Y C USH) USING A NON-TARGET SURVEY FOR MICHIGAN
WATERS OF LAKE SUPERIOR
By
Melissa T. Mata
Siscowet lake trout are the most abundant form of lake trout in Lake Superior.

Published information on siscowet population dynamics is largely based on commercial
ﬁshery data. A survey to speciﬁcally sample siscowet lake trout was not started until
1996, is done only every third year, and samples relatively few locations within each
management unit in Michigan waters. In this paper we assess temporal patterns in
siscowet form lake trout abundance in Michigan waters of Lake Superior based on data
from a long-term lake trout survey that targeted the lean form. Although siscowets are
regularly caught in the lean lake trout survey, there were high proportions of zero catches
in some years and highly skewed positive catch data. In order to develop an index of
siscowet abundance from these data, we used delta-lognormal models. This approach
involves ﬁtting two submodels, one for the proportion of non-zero (positive) catches, and
one for the catch per unit effort (CPUE) conditional on the catch being non-zero, and
estimating the unconditional CPUE for each year as the product of the estimated
proportion of non-zero catches and the conditional CPUE. We developed these statistical
models for ﬁve of the eight management units within Michigan, with the other units not

having sufﬁcient data to estimate a useful time-series of indices. We considered year,

grid (a ﬁxed sample site), and depth of the gill-net as potential factors to include in the

13

models and selected among alternative models using Akaike Information Criterion (AIC).
We emphasize both modeling methodology as an example of such methods for ﬁsh
species of interest from a non-target survey, and the results that provide further evidence
of substantial increases in siscowet densities during the 1980-2006 period, with a

decrease in the rate of increase since about 2000.

14

 

Introduction

Lake Superior is the largest of the Laurentian Great Lakes and is the only one to
contain lake trout (Salvelinus namaycush) morphotypes other than the lean. The siscowet
morphotype of lake trout, the focus of this study and one of the three morphotypes
distributed lake-wide, usually inhabit offshore water at depths greater than 80 m and have
a deep, stout body high in fat content making them less desirable to commercial ﬁsheries
(Eschmeyer and Phillips 1965; Khan and Qadri 1970; Pycha and King 1975; Bumham-
Curtis 1993; Moore and Bronte 2001; Bronte 1993). Nevertheless, siscowet contributed
27% of the lake trout harvest from 1929 to 1961 (Bronte and Sitar 2008).

Historically, lake trout were a dominant predator in the Lake Superior ﬁsh
commmtity, and they supported a substantial commercial ﬁshery that yielded an annual
average of 2.0 million kg from 1913 to 1950 (Hansen et al. 1995). During the 19505,
lake trout abundance declined drastically because of excessive commercial ﬁshing and
predation by sea lamprey (Perromyzon marinus). Sea lamprey invaded Lake Superior in
the 19405, and their abundance increased in the late 19505, reaching peak levels in 1961
(Smith 1971). Commercial yield of lake trout declined by more than 90% from 1952 to
1962, which resulted in closure of lake trout commercial ﬁsheries in 1962 (Pycha and
King 1975).

Lake trout rehabilitation and management efforts focused primarily on lean lake
trout populations, despite the ecological importance of both siscowet and humper
morphotypes of lake trout. Lean lake trout stocks increased rapidly in the 19705 and
19805, in response to the commercial ﬁshery closure, stocking of yearling hatchery-

reared lean lake trout, and sea lamprey control. Commercial lake trout ﬁsheries reopened

15

 

in Wisconsin and Michigan in 1970 and 1980, respectively, as their stocks increased
(Hansen et al. 1995). Although not the focus of restoration efforts, siscowet and humper
lake trout stock levels increased in the 19805, primarily due the sea lamprey control
efforts. Observations of increasing catch per unit effort (CPUE) of siscowet lake trout for
commercial lake trout and Whiteﬁsh ﬁsheries during the 19805 and early 19905 led to the
development of the Lake Superior Technical Committee (LSTC) lake-wide siscowet
surveys. These surveys were initiated in 1996 and 1997 throughout Lake Superior and
are conducted every three years in an attempt to document siscowet densities and verify
that the observed increasing catch per unit effort in the commercial ﬁshery was in fact
reﬂecting increases in siscowet stocks.

In addition to data from this survey, there is substantial biological and catch per
unit effort information on siscowet lake trout obtained by various standardized
assessment ﬁsheries throughout Michigan waters of Lake Superior. These standardized
surveys primarily targeted the inshore lean lake trout; siscowet and humper lake trout
were considered incidental catch. However, siscowet lake trout have been caught
commonly in these surveys for several decades, providing relevant information on time
trends of abundance for siscowet lake trout.

Evaluations of relative abundance, based largely on (CPUE) in ﬁshery and survey
samples, suggest that siscowet densities have been increasing since the 19605 and have
been much higher than those of lean lake trout for the past 30 years (Bronte et al. 2003;
Sitar et al. 2007; Bronte and Sitar 2008). Ebener (1995), based on commercial ﬁshery
data, concluded that siscowet lake trout made up 72% of the total predator biomass in

western Lake Superior compared to 21% for lean lake trout in 1995. CPUE for siscowet

l6

increased from >20 kg-km-l net in the early 19505 to about 250 kg-km-l net in the late

19905 (Bronte et al. 2003). In addition, by—catch of siscowet lake trout increased after the
early 19905 in the sport ﬁsheries, which targeted lean lake trout (Bronte et al. 2003).
Sitar et al. (2007) reported that CPUE of siscowet lake trout doubled from 1985-1992 to
1993-2000, based on a summer survey that targets smaller sizes of lean lake trout. In
comparison, lean lake trout CPUE from this survey during 1993-2000 was below the
average CPUE for 1983-1992.

There is now a need to broaden lake trout management efforts and develop
speciﬁc objectives for siscowet and humper morphotypes as well as for lean lake trout
(Horns et al. 2003). All three of these lake trout morphotypes were historically (1929 -—
1943) caught in substantial numbers in Lake Superior (Burnham-Curtis 1993; Bumham-
Cm‘tis and Smith 1994), and are currently widely distributed in the lake. Given the high
abundance of siscowet lake trout in Lake Superior, interest in their biology and
population dynamics has increased.

The purpose of this paper is to i) develop an index of abundance for siscowet lake
trout utilizing the spring lean lake trout survey data and ii) describe trends in relative
abundance over time and space. The siscowet survey provides samples from only ﬁve
sample years starting in 1996, and thus provides limited information on long-term trends.
In contrast, the spring lean lake trout survey contains catch and effort information since
1959, and siscowet lake trout have been consistently caught in these surveys since the
late 19705. Our approach contrasts with and builds upon past efforts in evaluating trends
in siscowet abundance in several ways. Results presented by Bronte et al. (2003 and

2008) are based upon commercial ﬁshery data, and such trends can be inﬂuenced by

17

changing ﬁshing power and ﬁshing behavior (Hilbom and Walters 1992). In addition,
Bronte et al. (2003 and 2008) and Sitar et al. (2007) based their evaluations of temporal
changes in siscowet abundance upon raw CPUE (a ratio of total catch to total effort for
annual or longer periods). Such aggregate measures of CPUE can be inﬂuenced by
changes in ﬁshing or sampling locations or other factors. Although sampling locations
tend to be more constant for surveys than for a ﬁshery, there have been some inter-annual
differences in sampling locations for the lean lake trout surveys due to logistics (e.g.,

weather conditions) and to intentional design changes. Patterns resulting from such

 

changes can be confounded with actual abundance changes. Fortunately, a “catch-effort
standardization” approach based upon statistical modeling can account for some variation
due to such factors and produce less biased estimates of relative abundance and a more
reliable assessment of uncertainty (e. g., Maunder and Punt 2004).

One challenge for developing a statistically-based index of abundance for non-
target catch and effort is that the data are skewed to the left with a high proportion of zero
catches (Stefansson 1996; Ortiz et al. 2000). This adds to the usual need to account for
variation due to factors such as changes in sampling locations. Such standardization of
catch and effort is most commonly accomplished through the use of general linear
models, generalized linear models, or related approaches on catch and effort data
(Maunder and Punt 2004), and here we applied both of these types of models to CPUE
data. In addition, we implemented a delta approach to address statistical issues stemming
from the relatively high frequency of zero catches. The delta approach is widely used in

modeling CPUE where there is a high proportion of zero catches, as is often the case for

18

non-target species in both survey and ﬁshery data (Lo et a1. 1992; Vignaux 1996; Ortiz et
al. 2000; Ortiz et al. 2004).
Methods
Assessment Fishery Data

We analyzed data based on samples collected in Michigan’s waters of Lake
Superior by the Michigan Department of Natural Resources (MDNR), Chippewa Ottawa
Resource Authority (CORA), and Great Lakes Indian Fish and Wildlife Commission
(GLIF WC) (Figure 1.1). These data came from a standardized spring gill-net survey that
has been conducted since 1959. Only data archived electronically were used, limiting our
analysis to 1975 through 2006 overall. Michigan (MI) waters of Lake Superior are
divided into eight management units, and the end year for individual management units
was either 2005 or 2006. The primary purpose for this survey was to provide an index of
abundance for lean lake trout. Sampling occurred during April through June at ﬁxed
stations, using large mesh gill-nets (4.5 inch stretched mesh), and set on the bottom
across contours targeting depths from 30 — 250 feet (ft). Data collected for each gill-net
set include: date, length of gill-net set, water depth at start and end of the set,
management unit, number by species of ﬁsh caught, and other descriptive and
quantitative biological variables.

The catch of siscowet represented 4.6% of the total lake trout catch by numbers
for this assessment period. There was a total of 3310 gill-net sets conducted, of which
1211 captured at least one siscowet. The proportion of lake trout catch that was siscowet

ranged over years from 2% to 86%, showing a generally increasing pattern (Figure 1.2).

19

 

Siscowet were regularly caught in the surveys, however there were a large
proportion of zeros catches, especially in earlier years, and the positive catch data were
highly skewed. To achieve our objective of developing an index of siscowet abundance
from these data, we needed to account for the distribution of the data. To this end we
used a delta approach, which involved ﬁtting two “submodels”.

Delta Approach Overview
We applied the delta approach separately for ﬁve of the eight management units.

At this spatial scale the populations are likely to be experiencing different recruitment

 

and survival patterns over time. Thus a combined analysis was not considered, because
we believed that complex interactions involving management unit would make the results
of such an analysis difﬁcult to interpret and reduce or preclude statistical beneﬁts such as

increased power to detect common patterns. For two units, M11 and M12, we did not

 

develop models because there were no siscowet catches. We did not include a third
management unit (M18) because data were available for only four years, which we found
to be insufﬁcient for describing temporal trends in abundance. Brieﬂy, the idea is to
model CPUE as the product of the probability of occurrence for a non-zero catch and
CPUE for positive catches, and use estimates of these two components for a given year to
obtain indices of abundance. CPUE is expressed as the number of ﬁsh caught per
kilometer of gill-net set. Duration of gill-net sets varied, and thus CPUE was
standardized to account for varying soak time and the inﬂuence of net saturation prior to
analysis (Hansen et al. 1998).

More speciﬁcally, we used a delta-lognormal model to estimate annual indices of

abundance for siscowet lake trout. This involved developing statistical submodels for the

20

two components (probability of occurrence for a non-zero catch and CPUE for positive
catches). The probability of occurrence for a non-zero catch naturally follows a Bernoulli
distribution. For the second component, CPUE given positive catches was assumed to
follow a lognormal distribution because positive CPUE data were highly skewed.
Parameters for each submodel were estimated using either generalized linear models or
generalized linear mixed models (GLMs or GLMMs), by using “1m”, “glm” or “lmer”
procedures in R version 2.4.0.

Our statistical submodels for the probability of occurrence for a non-zero catch or
CPUE given positive catches potentially included year, grid (3 ﬁxed sample site), and
depth of the gill-net set as ﬁxed effects. Depth was treated as a ﬁxed categorical effect.
A gill-net is classiﬁed as shallow if the maximum of the start and end depths of a gill-net
set was <=150 ft, as deep if the minimum was > 150 ft, and as intermediate if otherwise
(i.e., if 150 R was between the maximum and minimum). We deﬁned depth as a
categorical variable with just three levels because typical gill-net sets spanned a broad
range of depths. Our models also potentially included all possible interactions of these
ﬁxed effects as random effects. Grid is treated as a ﬁxed effect because the ﬁxed
sampling locations represented by these grids were chosen based on historical ﬁshing, in
a non-random fashion. Depths of samples were also not randomly selected and ﬁsh in
general tend to have deﬁned depth distributions, hence this factor was treated as ﬁxed.
Our focus here is to estimate relative abundance in each year, and identify potential
systematic trends over the study period. Hence we also model year as a ﬁxed effect, but
recognize that modeling year as a random but temporally correlated effect is a reasonable

alternative. Our modeling of the interactions of ﬁxed effects as random, contrasts with

21

the more usual treatment of these as ﬁxed in the context of a manipulative experiment.
The idea here is that these interactions reﬂect short-terrn and/or smaller spatial scale
variations in distribution that are unpredictable and thus can be viewed as if random. For
example, we are treating the year by grid interactions as reﬂecting chance variations in
the distribution of ﬁsh that inﬂuenced CPUE at the speciﬁc grid and time of sampling.
Note that another way of viewing these random interactions is that including them is
equivalent to imposing non-independence in the residual error among the gill-net sets
representing the combination of factors represented by the interaction, for a model that
does not include such random interactions. Our ﬁnal submodels and associated indices
did not include all these potential ﬁxed and random effects, as we ﬁrst went through a
model selection process to avoid an over-parameterized model.
Modeling the probability of occurrence for a non-zero catch

Parameters for the submodel for the probability of occurrence for a non-zero catch
were estimated based on data for each gill-net set, where observations were classiﬁed as
“1” if at least one siscowet was caught or “0” if no siscowet caught. The analysis
assumes that the classiﬁed observations are independent realizations of Bernoulli random
variables, with probability p of success of catching a siscowet for a given combination of
years, grid and depth as deﬁned by effects in the model. There were often multiple
observations (n) for each combination of effects and hence we modeled the number of

non-zero catches as binomial, using a generalized linear mixed effect model and a logit

link function (McCullagh and Nelder 1989; Schall 1991; Venables and Dichmont 2004).

The fully (saturated) mixed effects model for the logit [g()] of the probability [pi] of non-

zero catches for the ith observation from year y, grid g, and depth stratum d is:

22

 

[11 g(pi)= loge(pi/(1-pi))=ay +ﬂg +("d +5yg +7rd ”Ed +pygd

where a), is the effect for year, 13g is the effect for grid, and is the effect for depth, Byg is
the random interaction for year and grid, yyd is the random interaction for year and depth,

Agd is the random interaction for grid and depth, and Pygd is the random interaction for

year by grid by depth. All random effects were assumed to be normally distributed with
a mean of zero and a variance estimated by the model.

Sparse data are known to cause convergence issues and unreliable estimates for
this type of model (Collett 2003), which we found to be true for these data also in
preliminary analyses. Consequently we restricted our analysis to years where both zero
and non-zero (positive) catches were made for a management unit, and to grids that were
sampled in at least three years (Table 1.1).

Modeling the catch rate for positive. catches

A second submodel was constructed using data for gill-net sets that caught at least
one siscowet. The response variable is the catch rate, which we also refer to as catch per
unit effort (CPUE), for an individual (ith) gill-net set for a given year y, grid g, and depth
stratum d. Given our assumption of lognormal CPUE for positive catches, data were log-

transformed, and the fully (saturated) mixed effects model is:
[2] loge(CPUE,°) = p + ay + ,Bg +wd +5yg + de + Agd + Pygd +ci

where p is the overall mean, try is the effect for year, [lg is the effect for grid,
cod is the effect for depth, Syg is the random interaction for year and grid, yyd is the

random interaction for year and depth, lgd is the random interaction for grid and depth,

23

Pygd is the random interaction for year and grid by depth, and s,- is the unexplained

residual error.
Model selection procedure

We considered models simpler than the fully saturated one. To this end we ﬁt all
possible models that allowed any combination of ﬁxed effect and random effect terms
included in the fully saturated model, provided the ﬁxed effect of year was included. We
focused on models that included a year effect because our objective was to calculate an
annual index of abundance, and this is only possible for models that included such an
effect. We also considered an intercept only model, with no ﬁxed effects, in order to
assess whether there was evidence for changes in CPUE from year to year. There were
16 different candidate models for random effects (Table 1.2), and ﬁve different candidate
models for ﬁxed effects (Table 1.3), leading to a total of 80 possible models. However,
many random effects had variances that converged on zero, and hence a number of
models became effectively identical to more parsimonious models. We only report
results for those models that are unique and also do not report results for the intercept
only model, which was always the worst based on AIC (see below).

Final models for each management unit were selected using Akaike’s information
criterion (AIC) (Burnham and Anderson 1998):
[3] AIC = -2 log L(0) + 2K,
where log L(0) is (maximum) log-likelihood, and K denotes the number of parameters in
the model. Model selection was accomplished using R 2.4.0, using both AIC and log-
likelihood built in function. For models that included random effects we used the R lmer

functions, and for ﬁxed effect models we used the glm function for the binomial

24

 

component and the lm function for the CPUE for positive catches component (the lmer
function requires at least one random effect). We subtracted two from the AIC results
obtained using 1m because the residual variance is counted as a parameter for K in the
AIC calculation for 1m, but is not included in the calculation of K by lmer. Maximum
likelihood (ML) techniques were used for model ﬁtting when comparing all models. All
models were comparable within each management unit because there was no missing

data and all models used the same response variable. In addition, for each model we

calculated AAIC; (AAICi = AICi — AlCmin), where i is the model index, and Akaike

weights (Burnham and Anderson 1998). The model selection procedure was applied
separately for both the probability of occurrence for a non-zero catch and the catch rate
(CPUE) given positive catches, resulting in one best overall model (with two separately
selected components).

We conducted a comparative analysis to evaluate how an alternative data
selection procedure would inﬂuence results. Our alternative data selection procedure was
to again require that each year contain both zero and non-zero catches, but that each grid
needed to be sampled in at least eight different years (instead of the three years we
required in the base analysis). Only three of the ﬁve management units were re-analyzed
based on this procedure (M15 thru M17), because for the other units all grids that were
sampled at least three times were also sampled at least eight times. Once we had applied
the alternative data selection procedure we repeated the complete model selection process
and compared both the selected model and the resulting trends in abundance indices with

those that resulted from the base analysis.

25

For the best CPUE for positive catches model, a frequency histogram of the
residuals and a quantile-quantile plot were examined to evaluate whether there were
substantial departures from the assumed normal error distribution (on the transformed
scale).

Constructing indices of abundance and standard errors

An index of annual abundance was deﬁned based on combining least square
means (LSMs) for year obtained from the best submodels for the probability of
occurrence for a non-zero catch and catch rate given a positive catch. The index of

abundance is deﬁned as:

[4] Index of annual abundance = loge( p ) + loge(CPUElpositive catches),

where i) is the estimated probability of occurrence for a non-zero catch (capturing a

siscowet = “success”) and CPUElpositive catch is the catch per unit effort (catch rate)

given a positive catch. Both of these components are estimated for each year for average

values of the explanatory variables (other than year). The loge( p ) component of the

annual index of abundance was constructed by ﬁrst converting the LSMs from the
binomial model, which was on the logit scale, to a probability scale. From equation 1 we

have:

p(6,X) )2,“ ~

5 L = ‘ = é,X =1 . X
[1 SM 509) g(p( )) oge[1_p(6’X) ﬂ

Where g() is the logit link function, 63 is the vector of estimated parameters (a and B), a

is the intercept, and B is a vector of slope coefﬁcients, and it is understood that this

equation is for a given year. By deﬁning f2 = p(é, X) we are emphasizing that the

26

estimated probability depends upon the estimated parameters and the row vector of
explanatory values. Here, for calculation of LSMs, X represents average values of the
explanatory variables, except for year which is set to the year of interest. Solving

equation 5 for the estimated probability leads to:

 

. _ ~ = exp(LSM)
[6] p _p(9’X) 1+exp(LSM)'

Variances for estimates of loge(p) (squared standard errors) were calculated using

a simpliﬁed form of the delta method (Seber, 1982, p. 8):

 

 

 

2
Var(loge( 13)) = Var(h(LSM)) = (w) Var(LSM) , where
h(LSM) = loge exPlLSM) , mm”) = 1 , and Var(LSM) was
1 + exp(LSM ) 6LSM 1 + exp( LSM)

obtained by squaring the standard errors for the LSMs.
The standard errors for the ﬁnal standardized CPUE estimates are just the square

root of the variances for the index, and these variances are obtained as the sum of the

variances for the two components: Var(lndex) = Var(loge( p )) +Var(loge(CPUE |

positive catches)). Var(loge( 13)) is obtained as described above, and Var(loge(CPUE |

positive catches)) is the squared standard error for the LSMs for GLMs or GLMMs for
the positive catches.

LSMs for both submodels and their standard errors were constructed in SAS
version 9.1 (SAS 2003), because within R’s lmer function you can not extract the mean

square error that is needed to calculate the standard errors for the LSMs. SAS was not

27

used for model selection because PROC GLIMMIX uses a pseudo-likelihood and
associated pseudo AIC values which should not be compared across models
(Schabenberger personal communication, 2007). The conversion from the logit to the p
scale (expression [5]) is done automatically within SAS (with appropriate speciﬁcation of
options), but is not automatically calculated within R. We veriﬁed that the results
matched what we obtained by our own calculations for the same model using R.

Results

Model Selection for the probability of occurrence for a non-zero catch (p)

The ﬁnal models that best explained the probability of occurrence for a non-zero
catch varied slightly across all management units (Tables 1.4-1.8). In general, however,
the best model included both year and depth ﬁxed effects. Models for M14 and M15
differed from the other units by also including a year by grid by depth random interaction
(Table 1.5 and 1.6). Each management unit had at least one competing model that was
within 2 AIC units, indicating that these models also had substantial support (Tables 1.4-
1.8). These competing models did not share a common model structure across
management units, in contrast to what we saw for the best models.

Model Selection for the catch rate for positive catches (In(CPUE))

The best model for the catch rate for positive catches included year, grid, and
depth ﬁxed effects for three out of ﬁve management units. The models for the remaining
two management units did not include the grid ﬁxed effect (Tables 1.4-1.8). Four of the
management units also had at least one competing model that received substantial
support, and 50% of those models also included year, grid, and depth ﬁxed effects. In the

second data selection procedure, where we required that a grid be sampled in at least

28

eight years, two management units (M15 and M16) that previously included both year and
depth ﬁxed effects in the best model for the ﬁrst data selection procedure, now also
included a grid ﬁxed effect as the overall best model (Tables 1.9-1.10).
Important ﬁxed and random effects

Year was present in all the models and all these models were better (lower AIC)
than an intercept only model with no ﬁxed effects. Based on AIC we were able to
conclude that depth was an important factor, since all the best models included a depth

ﬁxed effect. Most models that included a depth ﬁxed effect were within six AIC units of

 

the best model, except for two probability of occurrence of non-zero catch models in
M14. Alternatively, models that did not include a depth ﬁxed effect had an AIC from 6 to
85 units more than the AIC for the best model. The grid ﬁxed effect was included in four
out of 10 best models, and two additional best models in management units M14 and M15
(one for each unit) included random interactions involving grid, although grid was not
included as a ﬁxed effect in those models. Overall, however, relatively few random
effects were included in the best models, with 80% of the best models including no such
effects.

Trends in the probability of occurrence for a non-zero catch (p)

We describe these trends on the probability scale (p) instead of on the log-scale to
aid in the interpretation. In 82% of the year by management unit combinations during the
period 1975 through 1985 siscowet were not captured and the probability of occurrence
for 50% of those years when siscowet was captured was less than 0.1. The probability of
occurrence during 1986-1995 varied across management units but there was generally a

trend of increase during the early 19905. The probability of occurrence for a non-zero

29

catch was highest in M13 and M15, with an average probability of 0.58. During the 1996
through 2006 period the probability of non-zero catch increased and then leveled off in
all management units, with an average upper level of 0.75 (Figure 1.3). In M14, the
average probability during this period was 0.88. The average probability of occurrence
increased from 0.30 in the 1975-1985 period to 0.97 in the 1996-2006 period.

Trends in the catch rate for positive catches (In(cpue))

The trends observed for the catch rate for positive catches (on a log-scale) was
slightly different from the trends observed in the probability of occurrence for a non-zero
catch. The ﬁrst (1975-1985) period was similar, in that it had the lowest average of
-0.23. The general patterns of increase and leveling off for the catch rate resembled
trends observed for the probability occurrence (Figure 1.4). However, patterns for catch
rate diverged for some units during 1986-1995 from the patterns seen for the probability
of occurrence. The year with the maximum catch rate (for positive catches) occurred
during this middle period for M13 and M15 (Figure 1.4). In contrast, catch rates for M14
and M16 have their highest averages during the last period (1996-2006) (Figure 1.4). The
increase in siscowet catch rate between the ﬁrst (1975-1985) and last (1996-2006)
periods averaged 1.60 on a natural log-scale, corresponding to nearly a ﬁve-fold increase.
Trends in Standardized Catch Rate (Index of annual abundance = (ln(p)+ln(cpue))

In Michigan waters of Lake Superior, our siscowet index of abundance was near
zero or siscowets were not caught at all between 1975 and 1985, except for M16 (Figure
1.5). The trends in the index varied across management units, but there was a general
pattern of increase from 1986-1995 and a leveling off at a higher level from 1996-2006

(Figure 1.5). In M16 our abundance index average was higher than in the other units and

30

 

' l

did not show the same temporal pattern. From 1975 to 1985, the index was higher than
in the other management units and declined from 1979 to 1985 (Figure 1.5). As seen
previously in other management units between 1996 and 2006, there was a general
increase followed by leveling off in siscowet abundance.
Comparative Analysis

Even though we usually found one or more models that were within two AIC
units of the best (lowest AIC) model, we did not resort to model averaging. We did not

use model averaging because the differences among the competitive models in the

Wm -64.

resulting annual estimates for the probability of occurrence for a non-zero catch and the
catch rate for positive catches were slight, and thus differences among the models do not
suggest substantial differences in the trends nor add much uncertainty. We illustrate the
similarities between the best model and its closest competitor by plotting the estimated
probability of occurrence for a non-zero catch and catch rate for positive catches over
time for each management unit (Figures 1.6-1.8).
Discussion

When catch and effort data are used to estimate standardized indices of
abundance, sometimes zero catches are observed. These zeros are often either dropped or
a small constant is added (to zeros or to all observations) to apply normal-based
parametric methods following log-transformation. This approach can be useful when
there is a low proportion of zeros and the assumptions of normality and constant variance
can be approximated. Other approaches commonly used include modeling catches as
count data, or using zero-inﬂated models. These methods also work best when the

proportion of zeros is low because when the proportion of zeros is high, because

31

dispersion tends to be higher than these methods allow for (Maunder and Punt 2004).
Despite the usefulness of the above methods in some situations, alternative approaches
need to be sought given that some catch data include high proportions of zero catches.
An alternative standardization method for catch and effort data, when dealing with such
data, is called the delta approach (Lo et al. 1992; Stefansson 1996; Punt et al. 2000; Ortiz
and Arocha 2004). In the delta approach the probability of non-zero catches and the
catch rate given a positive catch are modeled separately. This methodology is especially
useful for analyzing data from non-target surveys, where a particular ﬁsh of interest is
caught by accident (“by-catch”), and zero catches are common.

In this study we applied delta models to standardized siscowet catch and effort
data from non-target (lean lake trout) surveys in Michigan waters of Lake Superior and
produced a standardized index of abundance for siscowet lake trout. We used both
generalized linear models and generalized linear mixed models to model both the non-
zero catch and the catch rate given a positive catch. This is one of just a few attempts to
apply the delta approach to develop an index of ﬁsh abundance in the Great Lakes (see
Haeseker (2001) for another example) and the ﬁrst applied to a salmonid.

During 1975-1985 in most years no siscowet lake trout were recorded as caught,
and our standardized index was low. More siscowet lake trout were recorded in the catch
during 1986-1995, where our index was higher. Around 1995, there was a substantial
increase in catch and the index, but the period of increase generally ended around 2000.
The analysis strongly suggests that siscowet lake trout were increasing in abundance as

early as 1995 and reached a leveling off period starting in 2000 through 2006. Our

32

annual estimates from the standardized catch rates conﬁrmed concerns about increases in
siscowet catches in lean lake trout habitat.

There is little information documenting trends in abundance for siscowet lake
trout in Lake Superior, and the information that is available is recent. Bronte (2003)
looked at commercial gill-net catch and effort data from both US. and Canadians waters
to evaluate abundance from 1950-1998 and the results indicated that siscowet had
generally increased over that entire period. More recently Bronte and Sitar (2008) used
ﬁshery data to estimate relative abundance during three different ﬁshing periods: early
modern (1929-1939), pre-collapse (1941-1949) and collapse (1953-1961). Their results
indicate that siscowet abundance was declining before the 19405 and that the sea lamprey
likely contributed to the near extirpation of siscowet lake trout.

Our analysis provided limited information on trends prior to the mid-19805, but
suggests a continuing increase in abundance from then until 2006, and in the years that
overlap between our study and that of Bronte et al. (2003), Bronte et al. reported a similar
temporal pattern to what we report (Figure 1.9). Although the temporal patterns turned
out to be similar, we believe our use of survey data and a rigorous statistical approach can
allow managers and biologists to now be more conﬁdent about the patterns. Bronte et al.
(2003) used commercial ﬁshery data to develop a raw index of abundance by using the
ratio of siscowet catch to effort for each year in Lake Superior from 1950 to 1998. Shifts
in who ﬁshes and where they ﬁsh, as well as other factors have been shown in many
circumstances to distort the relationship between the ratio of aggregate catch to effort
(Maunder and Punt 2004; Deroba and Bence 2009). Use of survey data, with more

limited temporal changes in how ﬁsh were collected, and adjustments for what changes

33

 

did occur, provide stronger basis for inferring that CPUE reﬂected abundance changes, at
least in the depth ranges covered by the survey.

We believe that the standardized catch rate for siscowet lake trout, which can be
obtained from the spring lean lake trout survey, is one useful way to monitor trends,
especially in shallower waters of the lake. Although the siscowet morphotype has been
more abundant in waters deeper than those covered by the lean survey, the survey does
overlap with their depth distribution. Furthermore, our analyses (including preliminary
ones not reported here) showed no indication for a shift in siscowet depth distributions
over time. We suspect that this index provides a meaningful measure correlated with
siscowet abundance across their entire depth range. We cannot rule out, however, the
possibility that changes in the relative abundance of siscowet within the lean survey
depths versus deeper waters could make the lean index less reﬂective of total abundance.
Ebener et al. (in preparation), however, did not ﬁnd evidence of such a change between
1996 and 2006 in survey results that covered the entire siscowet depth range.

It is also important to note that we standardized catch and effort data to account
for factors that may affect the assumption that catch rate is proportional to abundance.
We did our best to account for such factors by using general and generalized linear mixed
effect models in developing indices of abundance, however such models are always
subject to reﬁnement or change as additional information becomes available or
conditions change. At this point, given the available data, our analyses indicate that the
delta approach can be used to standardize catch rates of siscowet in lean lake trout

surveys.

34

It appears that siscowet were the most abundant lake trout morphotype in Lake
Superior during the 19905 and early 20005 (Ebener 1995; Kitchell et al. 2000; Bronte et
al. 2003; Sitar et al. 2007), and it is also possible that siscowet were the dominant
morphotype historically (Bronte and Sitar 2008). It has been hypothesized that siscowet
densities are higher than lean densities in the more extensive deep areas of the lake
because siscowet lake trout are better adapted to the deepwater habitat (Sitar et al. 2008).
Sitar et al. (2008) also noted that lean lake trout were primarily caught at depths of 200 m

(~656 ft) or less, whereas siscowets were caught at depths of 40 m (~163 ft) and greater.

 

Thus there is substantial overlap in depth distributions between lean and siscowet
morphotypes, suggesting that an index of siscowet abundance within lean lake trout
habitat (as was developed here) is of interest.

There is interest in developing a commercial ﬁshery for siscowet to extract ﬁsh
oils for dietary-supplement purposes, because of the high amount of lipids in their bodies
(Wang et al. 1990). Development of such a ﬁshery needs to be done cautiously. Both
modeling and empirical studies suggest that siscowet lake trout may only be able to
tolerate relatively low levels of ﬁshing (Kitchell et al. 2000; Bronte et al. 2003; Bence et
al. manuscript). If such a ﬁshery develops it will be important to monitor stock status
using ﬁshery independent data, and the existing lean lake trout survey provides a means

of assessing future changes relative to patterns since the 19805.

35

Acknowledgments

We thank Shawn Sitar (MDNR), Mark Ebener (CORA), Bill Mattes (GLIFWC), Matt
Symbal (Red Cliff Fisheries Department, and all other personnel that collected and
provided data for this project. Mike Jones and Andrew McAdam contributed their
thoughts and guidance during the conduct of this research and on earlier versions of this
paper. In addition, thank you to our colleagues at Quantitative Fisheries Center (QFC),
Michigan State University for technical and modeling advice. This work was funded by
the USFWS Restoration Act program (under cooperative agreement # 301814J260) and
by the Michigan DNR Fisheries Division, and GLIF WC was the agency sponsor for the

Restoration Act Project.

36

 

Table 1.1. Speciﬁc years, number of years, number of grids, and number of gill-net sets
included in this analysis for siscowet lake trout index of abundance for Michigan water of

 

 

Lake Superior.
Management # of # of # of gill-
Unit Years Included years Lﬁds net sets
M13 1975, I987, 1988, 1990-2006 20 2 429
M14 1977, 1987, 1990-2006 19 6 519
M15 1986, 1988, 1990-1995, 1999,2000, 2003-2006 14 5 243
M16 1977, 1980-1985,l988, 1990-1996, 1998-2006 24 9 430
1977, 1985-1988, 1990-1991, I993-I995, 1997-
M17 2005 I9 4 299

 

37

 

Table 1.2. Combinations of random effects considered in models for both the probability
of occurrence for non-zero catch and catch rate (CPUE) for positive catches. The random

terms are deﬁned as follows: 5yg year by grid interaction, 7 yd year by depth
interaction, x1 gd grid by depth interaction and p ygd year by grid by depth interaction.

 

 

 

11:31:21“ Model Structure for random effect
1 No random effects
2 5yg+7yd+4gd+10ygd
3 5yg + y yd + Agd E
4 5yg+ryd+pygd 7
5 6)’8 + ’lgd + Pygd
6 5yg + y yd
7 5yg + ,1 gd
3 5yg + Pygd
9 y yd + ,1 gd
10 7 yd + Pygd
ll ’lrgd + pygd
12 5yg
13 7 yd
14 lgd
15 p ygd
16 7yd+lgd+Pygd

 

38

Table 1.3. Combinations of ﬁxed effects considered in models for both the probability of
occurrence for a non-zero catch and catch rate (CPUE) for positive catches. The ﬁxed

effects are deﬁned as ay is the year effect, ﬁg is the grid effect, and cod is the depth
effect.

 

 

Model Model Structure for fixed effect
Number

1 a y + ﬁg '1' (0d

2 “y + ﬁg

3 ay + cod

4 ay

5 ,u intercept/means model

 

39

 

Table 1.4. Unique candidate models with number of estimated parameters (K), Akaike’s
information criterion differences (AAIC, 0 = best model) and AIC weights for both the
probability of occurrence for a non-zero catch and catch rate for positive catches

 

 

 

 

 

 

 

40

submodels for M13.

Model Structure K AAIC Weights

Probability of occurrence
year + depth 22 0.00 0.730
year + grid + depth 23 2.00 0.370
year + grid x depth 21 14.94 0.000 5
year + grid + gn'd x depth 22 16.88 0.000 5
year + grid + year x depth 22 31.36 0.000 ;
year + year x depth 21 32.07 0.000 I
year + grid + year x depth x grid 22 33.39 0.000
year + grid 21 34.12 0.000
year + year x depth x grid 21 34.82 0.000
year 20 35.87 0.000

Catch rate for positive
catches

year + depth 22 0.00 0.641
year + grid + depth 23 1.17 0.356
year + grid x depth 21 12.54 0.001
year + grid + grid x depth 22 14.49 0.000
year + grid x depth + year x grid x depth 22 14.53 0.000
year + grid + grid x depth + year x grid x depth 23 16.48 0.000
year + year x grid x depth 21 25.60 0.000
year 20 25.97 0.000
year + grid + year x grid x depth 22 26.81 0.000
year + grid 21 27.20 0.000
year + year x depth 21 27.38 0.000
year + grid + year x depth 22 28.89 0.000

Table 1.5. Unique candidate models with number of estimated parameters (K), Akaike’s
information criterion differences (AAIC, 0 = best model) and AIC weights for both the
probability of occurrence for a non-zero catch and catch rate for positive catches
submodels for M14.

 

 

 

 

 

Model Structure K AAIC Weights
Probability of occurrence
year + depth + year x grid x depth 22 0.00 0.603
year + depth + year x grid + year x grid x depth 23 1.41 0.298
year + depth + year x grid 22 4.04 0.080
year + depth 21 8.59 0.008
year + grid + depth + year x grid x depth 27 9.06 0.006
year + grid + depth + year x grid + year x grid x depth 28 10.61 0.003
year + grid + depth + year x grid 27 13.06 0.001
year + grid + depth 26 15.78 0.000
year + grid x depth + year x grid x depth 21 23.85 0.000
year + year x grid + grid x depth + year x grid x depth 22 25.71 0.000
year + year x grid x depth 20 28.28 0.000
year + year x grid + grid x depth 21 29.09 0.000
year + grid x depth _ 20 32.13 0.000
year + grid + grid x depth + year x grid x depth 26 32.89 0.000
year + grid + year x grid + grid x depth + year x grid x
depth 27 34.75 0.000
year + grid + year x gn'd x depth 25 36.61 0.000
year + grid + year x grid + grid x depth 26 38.20 0.000
year + year x grid 20 38.95 0.000
year + year x grid + year x depth 21 40.21 0.000
year + grid + grid x depth 25 41.03 0.000
year 19 43 .05 0.000
year + year x depth 20 45.04 0.000
year + grid + year x grid 25 47.01 0.000
year + grid + year x grid + year x depth 26 48.57 0.000
year + grid 24 48.76 0.000
Catch rate for positive
catches
year + grid + depth 26 0.00 0.694
year + grid + depth + grid x depth 27 1.98 0.258
year + depth + grid x depth 22 5.35 0.048
year + grid x depth 20 19.00 0.000
year + grid + grid x depth 25 25.59 0.000
year + depth + year x grid 22 27.54 0.000
year + depth 21 28.92 0.000

 

41

Table 1.5 (cont’d).

 

 

 

Model Structure K AAIC Weights
Catch rate for positive
catches

year + depth + year x grid x depth 22 29.42 0.000
year + grid + year x depth 25 52.06 0.000
year + grid 24 59.89 0.000
year + grid + year x grid x depth 25 60.17 0.000
year + year x depth + year x grid x depth 21 75.14 0.000
year + year x grid x depth 20 75.98 0.000
year + year x grid + year x depth 21 76.12 0.000
year + year x grid + year x depth + year x grid x

depth 22 77.12 0.000
year + year x depth 20 78.34 0.000
year 19 84.83 0.000
year + year x grid 20 85.41 0.000

 

42

Table 1.6. Unique candidate models with number of estimated parameters (K), Akaike’s
information criterion differences (AAIC, 0 = best model) and AIC weights for both the

probability of occurrence for a non-zero catch and catch rate for positive catches
submodels for M15.

 

 

 

Model Structure K AAIC vLeights
Probability of occurrence
year + depth + year x grid x depth 17 0.00 0.250
year + depth + year x grid 17 0.55 0.190
year + depth + year x grid + year x grid x depth 18 1.67 0.109
year + depth 16 2.41 0.075
year + depth + year x grid + grid x depth 18 2.46 0.073
year + grid + depth 20 2.98 0.056
year + depth + grid x depth 17 3.24 0.049
year + grid + depth + year x grid 21 3.61 0.041
year + grid + depth + year x grid x depth 21 3.77 0.038
year + year x grid _ grid x depth 16 4.18 0.031
year + grid x depth + year x grid x depth 16 4.53 0.026
year + grid x depth 15 4.85 0.022
year + grid + depth + year x grid + year x grid x
depth 22 5.42 0.017
year + year x grid + grid x depth + year x grid x depth 17 5.93 0.013
year + year x grid x depth 15 9.19 0.003
year + grid + year x grid + grid x depth 20 10.28 0.001
year + grid + grid x depth 19 10.47 0.001
year + grid + grid x depth + year x grid x depth 20 10.57 0.001
year + grid + year x grid x depth 19 11.69 0.001
year + grid + year x grid + grid x depth + year x grid
x depth 21 12.09 0.001
year + year x grid 15 13.57 0.000
year + grid 18 14.04 0.000
year + grid + year x grid 19 14.35 0.000
year + grid + year x depth 19 15.45 0.000
year + year x depth 15 17.14 0.000
year 14 17.85 0.000

 

43

Table 1.6 (cont’d).

 

 

 

Model Structure K AAIC Weigﬂ

Catch rate for positive
catches

year + grid + depth 20 0.00 0.851
year + depth 16 4.05 0.112
year 14 8.29 0.013
year + grid x depth 15 8.61 0.011
year + grid 18 9.98 0.006
year + grid + grid x depth 19 10.83 0.004
jear + grid + year x depth 19 1 1.79 0.002

 

44

Table 1.7. Unique candidate models with number of estimated parameters (K), Akaike’s
information criterion differences (AAIC, 0 = best model) and AIC weights for both the

probability of occurrence for a non-zero catch and catch rate for positive catches

 

 

 

 

 

submodels for M16.
Model K AAIC Weights
Probability of occurrence
year + depth 26 0.00 0.513
year + grid + grid x depth 27 1.96 0.192
year + depth + year x grid + grid x depth 27 2.00 0.189
year + depth + year x grid + grid x depth 28 3.34 0.096
year + grid + depth 36 8.50 0.007
year + grid + depth + year x grid 37 10.46 0.003
year + grid x depth 25 26.85 0.000
year + year x grid + grid x depth 26 28.33 0.000
year + year x depth 25 35.20 0.000
year 24 35.60 0.000
year + grid + year x grid + year x depth 26 36.51 0.000
year + year x grid 25 37.26 0.000
year + year x grid x depth 25 37.52 0.000
year + grid + year x grid + grid x depth 36 41.27 0.000
year + grid 34 44.73 0.000
year + grid + year x depth 35 44.92 0.000
year + grid + year x grid x depth 35 46.57 0.000
year + grid + year x grid 35 46.73 0.000
year + grid + year x grid + year x depth 36 46.76 0.000
year + grid + year x depth + year x grid x depth 36 46.92 0.000
Catch rate for positive
catches
year + depth 26 0.00 0.508
' year + grid + depth 36 0.06 0.492
year + grid x depth 25 18.87 0.000
year + grid + grid x depth 35 26.35 0.000
year 24 28.39 0.000
year + year x depth 25 29.82 0.000
year + grid 34 30.28 0.000
year + grid + year x depth 35 31.55 0.000

 

45

Table 1.8. Unique candidate models with number of estimated parameters (K), Akaike’s
information criterion differences (AAIC, 0 = best model) and AIC weights for both the
probability of occurrence for a non-zero catch and catch rate for positive catches
submodels for M17.

 

 

 

Model Structure K AAIC Weights
Probability of occurrence
year + depth 21 0.00 0.929
year + grid + depth 24 5.13 0.071
year + grid x depth 20 22.44 0.000
year + grid + grid x depth 23 27.90 0.000
year + year x depth 20 61.47 0.000
year + grid + year x depth 23 64.29 0.000
year + grid 22 65.03 0.000
year 19 65.47 0.000
year + grid + year x grid x depth 23 66.97 0.000
year + year x grid x depth 20 67.20 0.000
Catch rate for positive
catches
year + grid + depth 24 0.00 0.624
year + depth 21 1.67 0.271
year + depth + grid x depth 22 3.56 0.105
year + grid x depth 20 17.68 0.000
year + grid + grid x depth 23 22.73 0.000
year 19 37.68 0.000
year + year x depth 20 37.94 0.000
year + year x grid x depth 20 38.57 0.000
year + grid 22 39.52 0.000
year + year x depth + year x grid x depth 21 39.75 0.000
year + grid + year x depth 23 40.16 0.000
year + grid + year x grid x depth 23 40.89 0.000
year + grid + year x depth + year x grid x depth 24 42.11 0.000

 

 

 

46

Table 1.9. Unique candidate models with number of estimated parameters (K), Akaike’s
information criterion differences (AAIC, 0 = best model) and AIC weights for both the
probability of occurrence for a non-zero catch and catch rate for positive catches
submodels for M15 for the second data selection procedure.

 

 

 

 

Model Structure K AAIC Weights
Probability of occurrence
year + depth + year x grid x depth 17 0.00 0.195
year + depth + year x grid 17 0.34 0.164
year + grid + depth 19 0.86 0.127
year + grid + depth + year x grid 20 1.45 0.094
year + depth + year x grid + year x grid x depth 18 1.54 0.090
year + grid + depth + year x grid x depth 20 1.66 0.085
year + depth 16 2.33 0.061
year + depth + year x grid + grid x depth 18 2.34 0.060
year + grid + depth + year x grid + year x grid x depth 21 3.26 0.038
year + depth + grid x depth 17 3.66 0.031
year + year x grid + grid x depth 16 5.58 0.012
year + grid + depth + year x depth + grid x depth +
year x grid x depth 22 5.66 0.011
year + grid x depth + year x grid x depth 16 5.89 0.010
year + grid x depth 15 6.1 1 0.009
year + year x grid + grid x depth + year x grid x depth 17 7.33 0.002
year + grid + year x grid + grid x depth 19 9.71 0.001
year + grid + grid x depth 18 9.75 0.001
year + grid + grid x depth + year x grid x depth 19 9.97 0.001
year + year x grid x depth 15 10.38 0.001
year + grid + year x grid x depth 18 11.02 0.001
year + grid + year x grid + grid x depth + year x grid x
depth 20 11.52 0.001
year + grid 17 13.20 0.000
year + grid + year x grid 18 13.60 0.000
year + grid + year x grid + year x depth 19 14.28 0.000
year + grid + year x depth 18 14.39 0.000
year + year x grid 15 14.62 0.000
year + year x depth 15 17.99 0.000
year 14 18.92 0.000
Catch rate for positive
catches
year + depth 16 0.00 0.909
year + grid + depth 19 4.92 0.078
year 14 10.01 0.006

 

47

Table 1.9 (cont’d)

 

 

 

Model Structure K AAIC Weights

Catch rate for positive
catches

year + grid x depth 15 10.71 0.004

year + year x depth 15 11.65 0.003

year + grid 17 15.73 0.000

year + grid + grid x depth 18 16.54 0.000

year + grid + year x depth 18 17.28 0.000

 

48

 

Table 1.10. Unique candidate models with number of estimated parameters (K), Akaike’s
information criterion differences (AAIC, 0 = best model) and AIC weights for both the
probability of occurrence for a non-zero catch and catch rate for positive catches
submodels for M16 for the second data selection procedure.

Model Structure K AAIC Weights

Probability of occurrence

 

 

year + depth 26 0.00 0.599
year + depth + depth + year x grid 27 0.85 0.392
year + grid + depth 34 9.31 0.006
year + grid + depth + year x grid 35 10.61 0.003
year + grid x depth 25 21.58 0.000
year + year x grid + grid x depth 26 22.24 0.000
year 24 25.13 0.000
year + year x grid 25 26.19 0.000
year + year x grid x depth 25 27.05 0.000
year + year x grid + year x depth 26 28.16 0.000
year + grid + grid x depth 33 34.24 0.000
year + grid + year x grid + grid x depth 34 35.03 0.000
year + grid 32 36.75 0.000
year + grid + year x grid 33 38.03 0.000
year + grid + year x grid x depth 33 38.58 0.000
year + grid + year x grid + year x depth 34 40.01 0.000

 

Catch rate for positive

 

catches
year + grid + depth 34 0.00 0.435
year + depth 26 1.16 0.244
year + grid + depth + year x depth 35 2.00 0.160
year + grid + depth + grid x depth 35 2.00 0.160
year + grid x depth 25 16.54 0.000
year + grid + grid x depth 33 23.16 0.000
year 24 25.67 0.000
year + year x depth 25 26.54 0.000
year + grid 32 27.36 0.000
year + grid + year x depth 33 27.94 0.000

 

49

Table 1.11. Unique candidate models with number of estimated parameters (K), Akaike’s
information criterion differences (AAIC, 0 = best model) and AIC weights for both the
probability of occurrence for a non-zero catch and catch rate for positive catches
submodels for M17 for second data selection Eocedure.

 

 

Model Structure K AAIC Wﬂhts
Probability of occurrence
year + depth 21 0.00 0.847
year + grid + depth 23 3.43 0.153
year + grid x depth 20 19.82 0.000
year + grid + grid x depth 22 23.50 0.000
year + year x depth 20 60.59 0.000
year + grid + year x depth 22 62.05 0.000
year + grid 21 62.50 0.000
year 19 64.13 0.000
year + grid + year x grid x depth 22 64.19 0.000
year + year x grid x depth 20 65.49 0.000
Catch rate for positive
catches
year + grid + depth 23 0.00 0.808
year + depth 21 3.53 0.138
year + depth + grid x depth 22 5.43 0.053
year + grid x depth 20 20.36 0.000
year + grid + grid x depth 22 23.57 0.000
year 19 40.66 0.000
year + grid 21 40.77 0.000
year + year x depth 20 40.91 0.000
year + grid + year x depth 22 41.39 0.000
year + year x grid x depth 20 41.46 0.000
year + grid + year x grid x depth 22 42.08 0.000
year + year x depth + year x grid x depth 21 42.66 0.000
year + grid + year x depth + year x grid x depth 23 43.31 0.000

 

 

 

50

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

    

 

   

Wisconsin Michigan

Figure 1.1. Lake trout management units of Lake Superior (Hansen et al. 1995). The
letter abbreviations denote U. S. waters by state MN — Minnesota, MI — Michigan, and
W1 — Wisconsin, and numbers represent Canadian waters. Bolded management units
were the ones that supplied data used in this paper.

51

 

 

L0

013‘

015-

011*

052-

Proportion of siscowet catches

 

 

 

0.0 If I I I I
1975 1980 1985 1990 1995 2000 2005

I I

Year

Figure 1.2. Proportion of gill-net sets that caught at least one siscowet from the
standardized spring lean lake trout survey from 1975-2006.

52

 

 

 

 

  
   
 
 
 

 

 

 

 

 

 

A: _ A: 4
§ "0 M13 233 "0 M14
2 0.8 - 2 0.8 -
a “9’
g 0.6 - § 0.6 -
E a
o 0.4 - “5 0.4 -
.é‘ a»
:g 0.2 - E 0.2 -
.D
g 0_0 4W0 . . E ()_0 «airmnin , ,
1974 1981 1988 1995 2002 1974 1981 1988 1995 2002
Year Year
J: .1:
,5? LI) WMIS g 1.0 )MI6
O O
._ 0.8 - t. 0.8 —
8 “5’ ..
S: 0.6 - § 0.6 ~ _
co «3
‘8 0.4 ~ “5 0.4 -
a- " b
{-3 0.2 - :3 0.2 -
<6 «I
-8 l i 8 i
8: 0-0 5: 0.0 —.——
1974 1981 1988 1995 2002 1974 1981 1988 1995 2002
Year Year
.I':
E 1.0 - M17
0
g 0.8 ‘
§ 0.6 -
to
“a 0.4 -
E
~25 0.2 -
<6
'8
g: 0.0 4
1974 1981 1988 1995 2002
Year

Figure 1.3. Probability of occurrence of a non-zero catch of siscowet from the spring lean
lake trout survey for ﬁve Michigan management units in Lake Superior during 1975-2006
(solid circles joined by dashed line). The open circles show years that did not catch any
siscowet for each unit.

53

 

4.0 7

4.0 -

 

 

 

 

 

 

 

 

 

 

M13 M14
3.0 - 3.0 a
([3 2.0 1 (,3 2.0 a
a a
8 1.0 - 8 1.0 r
5 0.0 i If 5 0.0 — f I
-1.0 - -1.0 a
W O CDCIIImIDG)
-2.0 r v . r -2.0 . ﬂ . I
1974 1981 1988 1995 2002 1974 1981 1988 1995 2002
Year Year
4'0 9 M15 4'0 I M16
3.0 ~ E 3.0 -
a 2.0 - {5 2.0 -
a 54 a
B 1.0 T 8 1.0 T
500- {ﬁg 500-} {
-l.0 ~ -l.0 -
WOO (II) (I) COG) (1)0 O
-2.0 . . . . -2.0 . . - w
1974 1981 1988 1995 2002 1974 1981 1988 1995 2002
Year Year
4.0 4 M17
3.0 -
a 2.0 -
a f
B 1.0 d
5 0.0 -
.0. r
(IIIIIIIII) O O
-21) , 4 . r
1974 1981 1988 1995 2002
Year

Figure 1.4. Estimated log-scale catch per unit effort (CPUE) for siscowet positive catches
from the lean lake trout survey for ﬁve Michigan management units in Lake Superior
during 1975-2006 (solid circles joined by dashed line). The Open circles show years that
did not catch any siscowet lake trout.

54

 

 

 

 

 

 

 

 

 

 

2 4.0 - M13 2 4.0 M14
«.1 N
9‘ 2.0 - 9‘ 2.0 —
.5 .C‘.
3 2
:3 0.0 - m 8 0.0 —
‘O 'U
E -20 l g E -20 -
s :2 '
<6
'2 -4_0 - momma) o g -4_0 —m.qr:cr:o:r:o£r)
S a
-6.0 . . . . -6.0 a . . -
1974 1981 1988 1995 2002 1974 1981 1988 1995 2002
Year Year
2 4.0 “M15 9. 4.0 ]M16
52 20 - g 20
g n g ﬁ ﬁ -
8 00 - i 8 0.0
t I r l
g —20 — '3»: 2.0 Li mi
N EU
E -40 mmmmoo 0:0 00 g -_-|40
a :71
-6.0 . v . v ﬁlo .
1974 1981 1988 1995 2002 1974 1981 1988 1995 2002
Year Year
8 4.0 - M17
CU
C4 2.0 —
.C:
3
6 0.0 — {if
8
g -2.0 ~
Cd
2 -4.0 —
N
:73
-6.0
1974 1981 1988 1995 2002
Year

Figure 1.5. Estimated standardized catch rates (loge scale) of siscowet lake trout from the
spring lean lake trout survey for ﬁve Michigan management units in Lake Superior
during 1975-2006 (solid circles joined by dashed line). The open circles show years that
did not catch any siscowet lake trout.

55

Probability of a non-zero catch Probability of a non-zero catch

Probability of a non-zero catch

1.0 -
0.8 ~
0.6 -
0.4 e

0.2 a

 

0.0

MI-3

l

 

197419

1.0 -

0.8 -

0.6 -

0.4 -

0.2 -

 

0.0

T

M15

81 1988 1995 2002

T

fr

0

 

1.0 -
0.8 -
0.6 -
0.4 -
0.2 *

 

0.0

197419

j

M17

0

 

I

1974 1981 1988 1995 2002

Year

J

r

81 19881995 2002

Year

Probability of a non-zero catch

Probability of a non-zero catch

1.0 7
0.8 l
0.6 —
0.4 «

0.2 4

 

0.0

MI-4

O O

 

1.0 -
0.8 -*
0.6 a
0.4 -
0.2 a
0.0 *

 

I

1974 1981 1988 1995 2002

Year

M16

0 O

 

1974 1981 1988 1995 2002

Year

Figure 1.6. Estimated probability of occurrence of a non-zero catch of siscowet from the
spring lean lake trout survey for ﬁve Michigan management units in Lake Superior
during 1975-2006 for best (ﬁlled circles) and second best (open circles) selected models
using AIC. When only one symbol is visible for a year (open circle) then the two
estimates are identical.

 

 

 

 

 

 

 

 

3 1 -
M13 3 M14

2 a 2 a
63‘ E
:3 1 a D 1 _
a. o.
s; a
c: _ = a
._l 0 0 do .4 0 O O

-1 — _1 a

19741981 198819952002 19741981 198819952002

Year Year
3 ~ 3 a
M15 . M16

2 — O 2 _
63 c- 3933 6.?
E I ~ ‘I’ E 1 d
9, mg 9,
.5 0 ~ 8 oOc> .3 0 4 g

o
-1 _ -1 4
19741981 198819952002 19741981 198819952002
Year Year

Ln(CPUE)

0.1

-l"

 

M17

1’”

 

1974 1981 1988 1995 2002

Year

Figure 1.7. Estimated log-scale catch per unit effort for siscowet from the spring lean
lake trout survey for ﬁve Michigan management units in Lake Superior during 1975-2006
for best (ﬁlled circles) and second best (open circles) selected models using AIC. When
only one symbol is visible for a year (open circle) then the two estimates are identical.

57

 

Standardized Catch Rate Standardized Catch Rate

Standardized Catch Rate

 

 

 

 

 

3 -

2 “M13

1 a

-1 -

-2 -0 QC

-3 -

-4 -

-5 - _,_

1974 1981 1988 1995 2002
Year

3 -

2 AMIS

1 - 63 59°

0 H 8

-1 - a of

-2 - o

-3 -

-4 —

-5 . , . ,

1974 1981 1988 1995 2002
Year

: ]MI7

ﬂ .4 %a F

O .4

-1 _

-2 — o F

-3 —

-4 -

-5 _-_--ﬁﬁ—e

 

1974 1981 1988 1995 2002

Year

Standardized Catch Rate

Standardized Catch Rate

 

-5 ,1-L%*+-

1974 1981 1988 1995 2002

 

 

Year

3 7 M16

2 _-

l _

0 _

-1 —

-2 _

-3 - o 9

-4 —

_5 r r r .

1974 1981 1988 1995 2002
Year

Figure 1.8. Estimated standardized catch rates for siscowet from the spring lean lake
trout survey for ﬁve Michigan management units in Lake Superior during 1975-2006 for
best (ﬁlled circles) and second best (open circles) selected models using AIC. When only
one symbol is visible for a year (open circle) then the two estimates are identical.

 

 

 

 

I IIIIIIIII I lllllllll I lllllllll II'TIITIIITIUIIITTI

1950 1960 1970 1980 1990
Year

Figure 1.9. Relative abundance (CPUE) of siscowet lake trout in commercial ﬁsheries in
all area US. and Canadian waters of Lake Superior during 1950-1989 (from Bronte et a1.
2003)

59

 

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62

CHAPTER 2

ABSTRACT
SISCOWET BIOLOGY ACROSS REGIONS AND OVER TIME IN MICHIGAN
WATERS OF LAKE SUPERIOR
By
Melissa T. Mata

The siscowet form of lake trout (Salvelinus namaycush) is the most abundant of three
lake trout morphotypes found in Lake Superior of the North American Laurentian Great
Lakes, but its biology has been little studied. We investigated spatial and temporal
patterns in life-history attributes of siscowet lake trout across Michigan waters of Lake
Superior from 1990 through 2006. The most striking spatial and temporal patterns we
saw were for length-at-50% maturity and condition (mass-at-length). In the eastern most
spatial zone of Michigan waters of Lake Superior considered in our analysis
(corresponding to lake trout management unit M17) siscowets matured at smaller sizes
and were in better condition than in waters west of that zone. In this eastern zone length-
at-maturity did not show striking changes over time, whereas in Michigan waters west of
M17 ﬁsh matured at greater lengths after 1999. There was a general pattern for condition
to decline over time and for larger sizes of siscowet lake trout to make up a larger
proportion of the populations after 1999. The life history and biological characteristics
found in this study could be used as a basis for calculating per-recruit reference points to
help identify possible levels of sustainable ﬁshing, and also suggest what sort of spatial
variation and changes over time might be expected for the siscowet form of lake trout if

they were introduced in other lakes.

63

Introduction

The siscowet lake trout (Salvelinus namaycush), also known as a “fat”, is one of
three lake trout morphotypes widely distributed in Lake Superior of the North American
Laurentian Great Lakes (hereafter Great Lakes, Khan and Qadri 1970; Lawrie and Rahrer
1973; Pycha and King 1975). They primarily inhabit deep water (~80 m and greater)
(Sweeny 1890; Eschmeyer 1955; Lawrie and Rahrer 1973; Goodier 1981; Bronte et al.
2003) and siscowet densities are higher, or at least the catch rates for them are, in deeper
water (Sitar et al. 2008). However, siscowet lake trout are known to utilize both shallow
and deep waters of the lake throughout their life (Bronte et al. 2003). It is also believed
that they were once abundant in all the other Great Lakes (except Lake Erie), from which
they are now extirpated (Brown et al. 1981).

Siscowet lake trout are the most abundant lake trout morphotype and make up
most of the biomass of lake trout in Lake Superior (Ebener 1995; Bronte et al. 2003;
Bence et al. manuscript). Siscowet lake trout have become increasingly abundant inshore
as a consequence of an increase in overall abundance and possibly also because of a
change in depth distribution (Bronte and Moore 2007; Bronte and Sitar 2008; Chapter 1).
There have been concerns among biologists, anglers, and commercial ﬁsherman that
increased abundance, particularly in shallower depths inhabited by leans, will have
detrimental effects on leans and/or other deepwater species (Bronte and Moore 2007;
Bronte and Sitar 2008). To address such concerns, additional basic information on
siscowet biology, life history, and population dynamics is needed to supplement the

limited information now available. Therefore, during the early 19905 the Lake Superior

64

Technical Committee initiated research and a survey to focus on siscowet lake trout so as
to gain an improved understanding of both their biology and life history.

As part of the initiative, researchers evaluated potential effects siscowet would
have on lean lake trout abundance and diet, by examining the extent of overlap in
distribution and diet. It is well established that lean lake trout have been successfully
rehabilitated in Michigan waters of Lake Superior, and there is evidence that their
abundance has exceeded historic levels in some areas of Lake Superior (Hansen et al.
1995; Bronte et al. 2003; Wilberg et al. 2003; Richards et al. 2004; Sitar et al. 2007). The
increased abundance of siscowet has not obviously affected lean lake trout, as indicated
by similar trends in abundance (rather than a negative correlation), albeit at different
magnitudes, for the two morphotypes (Bronte et al. 2003; Wilberg et al. 2003; Sitar et
al.2007; Chapter 1). Recent studies have also indicated there is very little dietary overlap
between the two lake trout morphotypes (Kitchell et al. 2000; Harvey and Kitchell 2000;
Harvey et al. 2003; Ray et al. 2008), and this may explain why there has not been an
obvious detrimental effect on lean lake trout of the increased abundance of siscowet lake
trout in depths occupied by lean lake trout. Kitchell et al. (2000) also used system
modeling to predict that if a ﬁshery was directed toward siscowet, siscowet abundance
would decline rapidly, but their decline would not lead to an increase in lean lake trout
abundance. Thus far, there are no indications that siscowet lake trout are impeding lean
lake trout populations.

While biologists are still cognizant that there could be as yet undetected
detrimental effects of siscowet on lean lake trout, interest in siscowet recently shifted

more toward two other objectives: 1) in part, because of failure to achieve similar

65

rehabilitation of lean lake trout in the other Great Lakes, managers have become
interested in exploring the possible reestablishment of deepwater morphotypes of lake
trout in those lakes, and 2) there is interest in whether siscowet, which are high in omega-
3 fatty acids (Wang et al. 1990), can be harvested to extract these fatty acids for
pharmaceutical purposes (Bronte and Sitar 2009). An improved basic understanding of
the biology, life history, and population dynamics of the siscowet form will facilitate
addressing these objectives. Some limited basic biology and life history attributes have
been described in previous studies, for example, siscowet lake trout have an estimated
Brody growth coefﬁcients (K) ranging from (0.053-0.080), ﬁrst maturity near age 8, and
mass-speciﬁc fecundity has been estimated at 1025 eggs/kg (Carlander 1970; Peck 1988;
Kitchell et al. 2000; Miller and Schram 2000). However, there is still much more to be
learned about their life history, biology, and population dynamics. Our study is the ﬁrst
to look simultaneously at age and size composition, condition, growth, maturation, and
mortality of siscowet in Lake Superior.

The objective of this study was to examine all these aspects of biology/life history
together, and for each biological measure describe temporal and spatial variation and
assess whether the measures are related to siscowet density. The sources of information
for this study were derived from several ﬁsh surveys, primarily targeting leans or
siscowets that use gill-nets with either ﬁxed or varying mesh sizes. Reliable siscowet
biological data start as early as 1990 and continue through 2006; for most analyses we
created two time periods: period 1 included1990-1999 and period 2 includes 2000
through 2006. The 1990s represent a period of substantial increase in siscowet

abundance, whereas during the 2000s, increases were still occurring but at a declining

66

rate, potentially approaching an asymptote (Chapter 1, Bence et al. manuscript). Our
study sought to identify whether there is evidence that siscowet biology has changed
between these periods when large changes in abundance took place. In addition, we were
interested in identifying whether there were spatial differences in siscowet biology within
the Michigan waters represented in the survey data we used (Management units M12
through M17 (Figure 2.1)). To evaluate this we looked for differences among zones
consisting of one or more management units (described in Methods). Spatial zones will
identify whether geographic areas of Lake Superior contain stocks or populations of
siscowet that differ in biological characteristics that may be used for future management
efforts in potential harvesting siscowet lake trout.
Methods
Assessment ﬁshery data

We analyzed data obtained from samples collected in Michigan waters of Lake
Superior by the Michigan Department of Natural Resources (MDNR), Chippewa Ottawa
Resource Authority (CORA), and Great Lakes Indian Fish and Wildlife Commission
(GLIF WC) (Figure 2.1). These data come from three different bottom-set gill-net
surveys that date back to as early as 1959: a siscowet/deepwater survey, a spring lean
lake trout survey, and a summer recruit survey. Only biological data archived
electronically were used, limiting our analysis to 1990 through 2006. This also
corresponds to the time period when focus shifted to siscowet lake trout so that more
biological data started to be collected on this morphotype. Michigan waters of Lake
Superior are divided into eight management units, and the ending years for available data

were either 2005 or 2006 depending upon management unit and survey.

67

 

The primary purpose for the spring lean lake trout survey was to provide an index
of abundance for lean lake trout. This survey will be referred to as survey 1 throughout
the rest of the paper. Sampling occurred during April through June at ﬁxed stations,
using large mesh gill-nets (4.5 inch stretched mesh), and set across contours targeting
depths from 30 — 250 feet (ft). This survey has been described in detail by Hansen et al.
(1994)

The summer recruit survey used graded mesh to assess the abundance of juvenile

lake trout. This survey will be referred to as survey 2 throughout the rest of the paper.

 

This survey was conducted during July and August. The survey used multiﬁlament nylon l;

gill nets with a net size 6 ft high by 300 ft long per mesh size, with mesh sizes ranging

from 2 inches to 3 inches in 1%: inch increments, with an additional mesh size of 3.5

inches, for a total gang length of 1800 ft. The net was set across depth contours ranging
from 90 ft to 240 ft in depth.

The siscowet/deepwater survey was designed to assess siscowet populations to
gain an understanding of their current abundance and to deﬁne their population dynamics
based on sampling that covers the deeper waters where they are most abundant. This ,
survey will be referred to as survey 3 throughout the rest of the paper. Sampling for this
survey was conducted in June, with the exception of 1997 when sampling was in August.
The survey was initiated in some areas in 1996 and in others in 1997. Starting in 2000
the survey has been done once every three years in each area, with additional sampling in

a number of intervening years in M14. Sampling gear used was a graded mesh (2 to 6 in

mesh by 1/2 in increments) set across contours at six different depth intervals (0-19, 20-

68

39, 40-59, 60-79, 80-99, 100-119 fathoms). The overall survey design has been
described by Sitar et al. (2008).

Data collected for each gill-net set include: date, length of gill-net set, water depth
at start and end of the set, management unit, number by species (or morphotype) of ﬁsh
caught, mass, length, age and maturation status. For analyses that made use of age data
we only used ages based on otoliths, and such ages were ﬁrst recorded in 1994. Otoliths
ages were used rather than scale ages because scale ages tend to be biased low for lake
trout (Schram and F abrizio 1998). Sex and maturity status of a ﬁsh were determined by
internal examination of the gonads.

To evaluate spatial patterns we adopted the idea of zones. Zones were delineated
based on an understanding of similar bathymetry in each management unit area and
observed biological differences of siscowet lake trout in these areas. Agency biologist,
Shawn Sitar, MDNR, has used a similar spatial delineation. There are four different
zones: zone 1 combines management units M12 and M13, zone 2 is management unit
M14, zone 3 combines management units M15 and M16, and zone 4 is management unit
M17 (Figure 2.1). Management units M11 and M18 were not included because there were
insufﬁcient data for analyses. The amount of data available for analyses varied among
zones and surveys for each analysis (age-size composition, condition, length-at-maturity,
mortality and growth) (Table 2.1).

Temporal changes were identiﬁed either through evaluating differences among
years or between the two deﬁned time periods. The data were insufﬁcient to obtain
annual estimates for analyses that depended on age determinations or for length-at-

maturity.

69

 

General Analysis Procedures

Model diagnostics were evaluated to determine whether there were gross
violations of the normality and constant variance assumptions for each analysis, when
applicable. Model diagnostics consisted of evaluating a frequency histogram of the
residuals, a quantile-quantile plot, and plotting residuals against the predicted values.
The maturation analysis was done using R version 2.4.0, the growth analysis using AD
Model builder, other analyses were done using SAS version 9.1 (SAS 2003).

Age and size composition

.“'-; r O "

Age and size composition was estimated with length frequency histograms and

“I

summary statistics of the data for each survey, zone, and temporal period. Length
frequency histograms were constructed using 10 mm increments in length, and age
frequency histograms were constructed reporting the frequency of age in annual
increments. Age and length frequency histograms were constructed from sample data
collected during 1994 through 2006. Sample statistics included sample size, minimum
(length, mm or age, year), maximum, mean, and standard deviation. To determine if both
size and age differed between period and/or zone, we compared length or age between

period and zone using a general linear model:

[1] Yepi=ll+ae+l3p+7ep+ei
where the response variable (Y) is either loge(length) or age, p is the overall mean

(intercept), one is the effect of zone, [3 p is the effect for period, Yep is the interaction

effect of zone and period, and 81', is the unexplained residual error. The error term is

70

assumed to be normally distributed with a mean of zero and variance estimated by the
model. For both size and age, least square means were generated by SAS Proc Mixed to
compare mean size or age by period and zone separately for each survey (SAS Institute
2003). Signiﬁcance tests were done using the Tukey-Kramer procedure for multiple
comparisons for least-square means (Kutner et al. 2005) with results with P < .05
declared statistically signiﬁcant. We excluded survey 1 in zone 3 from analysis of both
age and size because siscowet were not captured in period 1 for that survey and zone,

precluding a comparison between periods.

“—1. ‘.-3 ‘ '0

Mortality

The instantaneous rate of mortality (Z) was estimated for each survey, zone, and
temporal period using age-based catch curves (Ricker, 1975). The basic approach was to
conduct a linear regression of the natural logarithm of number of ﬁsh in an age class
versus age. The slope of the regression provides an estimate of mortality (Z). The ﬁrst
fully recruited age of siscowet caught by each survey, zone, and period was estimated by
visually examining the dome and descending limb of the catch curve (e. g., Ricker 1975).
We assume that siscowets caught from that particular age are fully recruited to the survey
and older ﬁsh are equally likely to be captured. Also based on visual inspection of the
catch curves, we omitted ages above an upper age at which abundance reached low
values and it was judged that log abundance provided little information on mortality.
Mortality estimates were not calculated for survey 1 in zone 3 and period 1, because

siscowets were not captured during this period or zone.

71

Length-at—5 0% maturation

Maturity was based on visual examination of the gonads and classiﬁcations were
placed into two categories: mature and immature. A mature ﬁsh is deﬁned as a ﬁsh that
was going to reproduce or has physical indications that it has reproduced in previous

years. An immature ﬁsh has no physical indication of reproducing in the past or present

(Sitar and He 2006). We use estimated length-at-50% maturity (L50) as our maturation

schedule index, which is deﬁned as the length at which 50% of the ﬁsh population is
mature (Beaucharnp et al. 2004). For each survey, zone, and period, we ﬁtted a logistic
regression model to data with maturity status (l=immature; 0=mature) as a binary
response with length as the response variable. The logistic regression model for the ith

observation is:

[2] 10git(pi) = 10ge(pi/(1- pi» = a + ﬂ X L

where p is the probability of being mature, a is the intercept, and B is the slope for length

(L) the explanatory variable, and L50 was estimated as the negative of the ratio of

estimates intercept/slope.

We calculated 95% conﬁdence intervals (CIs) for the L50 estimates by using a

bias-corrected bootstrap technique using 1000 bootstrap samples (Efron 1987).

Statistical differences for L50 were evaluated by comparing the 95% C13. During

preliminary analysis we determined that both survey 1 and 3 provided inadequate data in

identify length-at-50% maturity (L50) for some zone and period combinations due to low

proportions of mature siscowet or missing information on maturity status. Therefore,

only maturation results for survey 2 are presented in the results section. In cases where

72

 

length-at-50% maturity could be ascertained for the other surveys, qualitative patterns
among zones and between periods were consistent with those for survey 2.
Mass-Length Relationship — Condition Indices

We modiﬁed the usual mass-length power model [3] to be a linear mixed-effects
model so as to evaluate spatial and temporal changes in the mass-length relationship for

siscowet lake trout. As a starting point we linearized the power function:

ﬂ

[3] W =aLb,

by taking logarithms of both sides to obtain

 

[4] loge(W) = loge(a) + b loge(L) = ,u + a * loge(L). Here Wis the observed ﬁsh mass i‘
in grams (g), L is observed ﬁsh length in mm, loge(a) = p. is the intercept, and b = a is the

slope. We then modiﬁed this model so that the slope and intercept could potentially
depend upon year and zone to obtain the fully (saturated) mixed effects model for the

mass-length relationship:

[5] 1086(W)yei = #ﬂgy +06 +10 +¢e +7y +Pyel*108e(L)+/ley +5yei

where ,u is the overall mean (intercept), or is the effect for loge(length), By is the effect for

year, we is the effect for zone, ‘l’e is ﬁxed interaction for loge(length) and zone, Y), is the

random interaction for loge(length) and year, key is the random interaction for zone and

year, Pye is the random interaction for loge(length) by year by zone and aye i is the

73

unexplained residual error. All random effects and error term are assumed to be normally

distributed with a mean of zero and variance estimated by the model.

All main effects were ﬁxed. Loge(length) is a continuous variable, whereas year

and zone were categorical variables. Interactions that involved year were treated as

random effects. Loge(length) is treated as a ﬁxed effect because ﬁsh have a deﬁned

power relationship between weight and length. Our goal here is to estimate mass for each
year and zone so as to identify potential systematic patterns over the study period. Thus,
we treat year as ﬁxed. Zone is treated as a ﬁxed effect, because zones represent a small
number of speciﬁc areas of interest, which cannot be reasonably viewed as a random
sample of a larger population.

Our modeling of the interactions between the ﬁxed year effect and other ﬁxed
effects were random, contrasts with the more usual treatment of these as ﬁxed in the
context of a manipulative experiment. The idea here is that these interactions reﬂect
relatively short-term and/or smaller spatial scale variations about overriding spatial and
temporal patterns that are essentially unpredictable and thus can be viewed as if random.
For example, we are treating the year by zone interactions as reﬂecting chance variations
that are transient and not region-wide and hence not systematic effects of interest.

Our ﬁnal model and associated predicted masses did not include all these
potential ﬁxed and random effects, as we ﬁrst went through a model selection process to
avoid an over-parameterized model. Our approach was to ﬁrst select which random
effects to include based on the model that produced the lowest Akaike’s information

criterion (AIC), by comparing models with all possible random effect combinations in

74

models that contained all ﬁxed effects (Burnham and Anderson 2003). Restricted
maximum likelihood techniques were used for model ﬁtting when comparing random
effect models (N go and Brand 1997; Bolker et al. 2009). Once the best random effects
were selected, the best ﬁxed effects model was also selected based on AIC. Here we

selected from among the ﬁxed-effect models representing all combination of these effects

provided that loge(length) was in each model, plus the model that included no ﬁxed

effects (intercept only). Maximum likelihood techniques were used for model ﬁtting
when making comparisons among ﬁxed effect models (N go and Brand 1997; Bolker et
al. 2009). There were eight different candidate models for random effects (Table 2.2),
and seven different candidate models for ﬁxed effects (Table 2.3). However, many
random effects had variance components that converged on zero, and hence a number of
models were effectively identical to more parsimonious models. We only report results
for those models that are unique and also do not report the intercept model, which was
always the worst based on AIC (see below).

Once the best model was selected, predicted masses for two different size classes,
450 mm and 700 mm, were used to assess ﬁsh condition over time by zone for each
survey. The two size classes were chosen based on a preliminary examination of length
distributions for each survey. These sizes were well within the length distributions but
represented relatively small and large siscowet. We selected a small and large size to
evaluate possible differences in the magnitude of spatial or temporal differences in ﬁsh
condition between ﬁsh of different sizes. In addition to evaluating predicted mass-at-
length from our best model, we also made such predictions for other models with AIC

within 2 of the best model. We only present results for the best model because predicted

75

 

temporal and spatial patterns from these other competitive models were similar to those
from our best model.
Modeling time-vary growth

Growth was evaluated by ﬁtting an incremental version of the von Bertalanffy
growth model to a time-series of length-at-age data. For pragmatic reasons, we used a
Bayesian hierarchical approach implemented in AD Model Builder rather than a
nonlinear mixed-model ﬁt by maximum likelihood to evaluate changes in growth. Given
the complexity of the dynamic model, the analysis was not easily implementable in
standard packages such as R or SAS. Attempts to ﬁt this model using a version of AD
Model Builder designed for nonlinear random effects led to point estimates for
parameters that produced years where growth was negative. Attempts to force positive
growth (see below) led to numerical problems when the software attempted to integrate
out the random effects.

Data used in this analysis were all observed lengths-at-age from 1996-2006 across
zones and surveys. For this analysis we looked at two scenarios: 1) we pooled data over
zones and surveys and 2) we ﬁt models separately by zone (with surveys still pooled).
We pooled surveys given the limited numbers of aged ﬁsh. The full model we
considered was:

La,y = La—l,y—l + (Looy — La—1,y-1)(1— exp(—Ky)
l6] La,y,i = La, y exp(ei)

3i ~ N (0, 01-2)
Where La,y is the median length at age a in year y, Loo and K are the year speciﬁc

asymptotic length and Brody growth coefﬁcients, Lay. ,- is the length of the ith

76

 

observation for a ﬁsh of age a in year y, and 6‘” represents among ﬁsh variation in length

about the year and age speciﬁc median, assumed to be lognorrnally distributed. Initial
median length at age-3 was assumed constant for all years based on an initial examination ,
of observed mean lengths. Median lengths-at-ages over age 3 in the ﬁrst year (1996)

were obtained as:

[7] La,l 996 = La—l,l 996 + (L001996 - La—l,l 996 )(1 — exp(—K1996» ,

which effectively assumes that the initial length-at-ages could have arisen from von
Bertalanffy growth under constant growth conditions. In models that allowed Loo or K to

vary the values were estimated for 1996 as separate parameters, rather than from the
random walk process (see below). When a parameter was assumed to be constant over

time the 1996 value was set to the same value estimated for subsequent years.
We considered alternative models in which both K and L00 varied over years, K only
varied over years, Loo only varied over years, or where both growth parameters were

constant. In our base analysis we modeled temporal variation in growth parameters as

arising from a random walk on a log-scale:

Indy =ln6y_1+77y_1
[81 77 ~ No.03)
6={Lw,K}

using methods similar to those of Szalai et al. (2003) and He and Bence (2007). The

observation error variance was estimated for each modeling scenario prior to model

ﬁtting based on an empirical measure of among ﬁsh variation in loge(1ength) about the

average for that age and year, using only ages and years that contributed ten or more

77

 

observations. The resulting values ranged from 0.013 to 0.019 (Table 2.4), these values
were ﬁxed when other parameters were estimated. The vectors of deviations inﬂuencing
year speciﬁc values through the random walks are random effects, and their variances (on
log scale) were estimated along with other parameters. The random walks are deﬁned by
the initial value of the particular growth parameter in 1996, and the associated variance

parameter for subsequent deviations.

To avoid negative growth when Loo was allowed to vary, any negative increment

was assumed to be zero. Technically, to ensure differentiability required by the model
ﬁtting method, this was done by multiplying all grth increments by the output from a
logistic function that rapidly went from zero to 1.0 as growth increments went from
negative to positive. In additional preliminary analyses we also considered models where
the von Bertalanffy model parameters were estimated as separate parameters for each
year, rather than being modeled as random walks (see results).

When using a Bayesian approach, inferences about parameters (or quantities
calculated from them) are based on the posterior distribution of the parameters. These
posterior distributions depend both on the likelihood of the data given the parameters and
prior distribution assumed for the parameters. We speciﬁed the priors for each parameter
and the likelihood for the data and then we used MCMC simulations to approximate the
posterior distribution. Most parameters were given a diffuse/non-infonnative prior,
which effectively adds a constant to the log posterior density and thus does not need to be
incorporated into the calculations used to generate the posterior distribution. One
exception to the use of diffuse priors was the random deviations (which in a Bayesian

context are considered parameters), which were assumed to be normally and identically

78

 

distributed with mean zero. The standard deviations for these deviations were also
estimated parameters on a log scale, and these were given normal priors, with
distributional parameters (mean= -2.919, sd= 1.04) that allowed a wide range of possible
levels of inter-annual variation. Diagnostics of trace plots for several scenarios and
model combinations determined that the posterior distribution of the standard deviation
for the inter-annual changes in K sometimes did not converge to a stable solution. When
this occurred the value at the peak of the posterior occurred at very small values for the
standard deviation (<.001), and all values in the MCMC chain were also near zero. We
interpret this result as indicating for these cases that temporal variation in K was
negligible and thus dropped those models from consideration. Initially we had assumed
diffuse priors for the log standard deviation parameters also, but had implemented
modestly informative priors in an attempt to address the problem with the MCMC chains
for the standard deviation associated with K. Implementation of these priors did not ﬁrlly
resolve the problem but did help us better determine that the problem was occurring
because of a tendency for the standard deviations to converge toward zero. Reliable
model ﬁts obtained with and without the informative priors for the standard deviations
were similar.

Deviance information criterion (DIC), which for Bayesian modeling is analogous
to AIC, was used separately for each scenario to compare models making different
assumptions about temporal variation in growth (Gelman et al. 2004; He and Bence
2007). We selected the model with the lowest (best) DIC value and report the result for
all models that produced reliable estimates of the posterior distribution. Predicted values

of length-at-age (presented for the best model) are calculated using posterior averages of

79

 

parameters. We present these predictions for ages 6, 12, and 20 to illustrate how changes
in length at age differ among a range of ages. We used MCMC simulations with a
Metropolis-Hastings algorithm to calculate the posterior distribution using AD Model

Builder. The chain length for the MCMC simulations was 100,000 cycles for each

model, where we saved every 100th cycle for analysis. We dropped the ﬁrst 25% of each

chain as a bum-in period, so all analyses and inferences are based on a saved chain of 750
values.
Results
Age and size composition

A total of 13,588 of siscowet lake trout were examined for both age and size for
all surveys combined, where surveys 1-3 contributed 2937, 6183 and 4468 samples,
respectively. The length-frequency distributions were mostly unimodal, regardless of the
survey, zone, and temporal period (Figure 2.2-2.4). There were no clear spatial patterns
in length distributions across all surveys, but for surveys 1 and 2, there was a general
increase in mean length (Table 2.5) and the frequency of larger ﬁsh (Figures 2.2 & 2.3)
from period 1 to period 2. The increase in mean length for survey 2 from period 1 to
period 2 in zones 1, 2, and 4 were the only statistically signiﬁcant (P < .05) changes. In
contrast to those surveys, changes in size distributions from period 1 to period 2 were
inconsistent among the zones for survey 3 (Table 2.5, Figure 2.4). For example, for
survey 3 mean lengths were signiﬁcantly (P < .05) larger in period 2 than in period 1 for
zone 3, whereas in zone 4 there was a signiﬁcant change in the opposite direction. Both

surveys 1 and 3 had the smallest mean lengths in zone 4 in each temporal period (Table

80

 

 

2.5). In contrast, for survey 2 mean lengths were larger in zone 4 than in the other
regions (Table 2.5).

There were more than 20 age groups in each survey, zone and period
combinations, and very few siscowet younger than age 5 or older than age 25 (Figure 2.5-
2.7). The age composition of siscowet lake trout differed substantially among
zone/period combinations and the spatial-temporal pattern for age-compositions was not
obviously related to the pattern seen for length compositions. Overall, the youngest
siscowet captured was an age-3 ﬁsh in survey 2 (pre-recruit survey) and the oldest

siscowet, 43 years of age, was captured by survey 1 (Table 2.6). Average age was

 

signiﬁcantly less (P < .05) in zone 4 than in the other regions, regardless of survey or
temporal period (Table 2.6). In addition, for survey 3 average age increased from period
1 to period 2 for every zone (Table 2.6), and these changes were signiﬁcant except in
zone 4. Even though on average younger ﬁsh were captured in zone 4, 66% of the time
the oldest ﬁsh were also found in this region (Table 2.6).
Mortality

We did not calculate mortality estimates for survey 3 in zone 4 and period 1
because the age composition did not have a range of ages that seemed to be consistent
with an exponential drop off due to mortality (there was essentially no drop off from a
broad dome of the catch curve). The estimates of Z varied between 0.16 in for survey 2
in zone 2 during period 2 to 0.59 for survey 3 in zone 2 during period 1 (Table 2.7).
Estimates of mortality based on survey 1 and 2 were substantially lower than those

estimated using survey 3 data (Table 2.7). Individual mortality estimates were very

81

uncertain and there was no obvious pattern of differences between periods that was
consistent across zones.

The results shown here for mortality should be interpreted with caution; the
different mortality estimates derived from each survey suggest that the catch data are
highly variable. We would have expected that our best mortality estimates would be
based on data from survey 3, given that this survey better covers the depth range of this
form, but we do not have an obvious explanation for why these estimates should be
higher than those of the other surveys. These highly variable results may be an artifact of
the assumption of traditional catch curves being violated. One assumption when
evaluating catch curves is that recruitment is varying without trend. The fact that we
know that siscowet abundance has been increasing through time (Chapter 1) suggests that
this may not be true.

Length-at-5 0% maturity

Length-at-50% maturity (L 50) (in survey 2) varied between zone and temporal

periods. Siscowet L50 increased from period 1 to period 2 in zones 1 through 3, but the

difference was signiﬁcant (P < .05) only zones 1 and 3 based on non-overlapping

conﬁdence intervals between periods for those zones (Table 2.8). In zone 4 the L503

were lower than in all other zones, and the difference with zone 2 during period 1 and
with all zones during period 2 were statistically'signiﬁcant (P < .05) (Table 2.8).
Model Selection for the mass-length relationship

The best random effects were selected prior to selecting the best ﬁxed effects

portion of the model to combine with them. This was done by evaluating alternative

82

 

random effect models with all ﬁxed effects included in the model (Table 2.9). This
analysis identiﬁed, in addition to the best random effects model, a plausible alternative
for both surveys 1 and 3 (AAIC < 4, Table 2.9). We then considered unique combination
of ﬁxed effects in association with the best random effects (AAIC = 0) model from Table
2.9 (Table 2.10), as well as for the plausible alternative random effects models for
surveys l and 3 (results not shown).

The ﬁnal models that best explained the mass-length relationship for siscowet
lake trout were different for each survey (Table 2.10). For both survey 1 and 3, a ﬁnal
model that included all four ﬁxed effects was far superior to any other ﬁxed effect

options. For survey 2, the ﬁnal model included the main ﬁxed effects but did not include

the ﬁxed interaction of loge(length) with zone, but a model that added this effect was

somewhat plausible (AAIC < 4) (Table 2.10). Thus, there is compelling evidence that

loge(length), year, and zone are useful for predicting mass.

Predicted Mass at 450 mm and 700 mm as condition indices

Predicted masses are shown only for the best model because predictions from
plausible alternative models (based on the best or alternative random effect portions of
the model) yielded similar qualitative patterns (see Methods). Siscowet lake trout
predicted mass at 450 mm TL for survey 1 was highest in zone 4 and lowest in zone 1.
Most annual predicted masses at 450 mm were below the lake-wide predicted average of
6.60 g, starting from 1997 through 2006 for zones 1 and 3. In contrast, in zone 4 annual
predictions were above the predicted average from 1990-2006, except for 2002 (Figure

2.8). The average predicted masses for zone 2 fell below the lake-wide predicted average

83

 

in 2000 through 2005. Siscowet predicted mass at 700 mm TL was also highest in zone 4
and lowest in zone 1. Temporal and spatial patterns in annual predicted masses for
siscowet at 700 mm were similar to patterns for siscowet at 450 mm (Figure 2.8).

Siscowet lake trout predicted mass at 450 mm TL for survey 2 were also highest
in zone 4 of Lake Superior and the ranking of predicted masses in the other zones varied
over time. Most annual predicted masses from 1999 to 2005 were below the lake-wide
predicted average (6.60 g) for zones 1-3, whereas predicted values for zone 4 fell below
the average once in 2002 (Figure 2.8). Qualitative spatial and temporal patterns for
predicted masses at 700 mm TL for survey 2 were the same as was observed for 450 mm
TL in that survey (Figure 2.8). On average, zone 3 predicted masses were greater than
predicted masses in zone 1 and 2, except in 2002-2004, when predicted masses for zone 3
fell below those of zones 1 and 2 (Figure 2.8).

There were some modest differences in patterns observed for siscowet lake trout
predicted mass at 450 mm TL for survey 3 in comparison with surveys 1 and 2. In this
survey predicted masses at 450 mm TL were also highest in zone 4, but the lowest
predicted masses were in zone 3. Most annual predicted masses from 1999 to 2005 were
below the lake-wide predicted average (6.60) for zones 1-3, whereas predicted values for
zone 4 fell below the average once in 2002 (Figure 2.8). Spatial and temporal patterns
for predicted masses at 700 mm TL for survey 3 were generally qualitatively the same as
was observed for 450 mm TL ﬁsh in that survey (Figure 2.8). An exception to the above
generalization was that the lowest predicted masses at 700 mm were found in zone 1
versus the lowest being found in zone 3 at 450 mm. The temporal pattern of variation was

similar for these larger ﬁsh in‘zones 1-3, with predictions below the lake-wide predicted

84

 

average from 2000 through 2006 (Figure 2.8) and zone 4 predictions never fell below the
lake-wide predicted average.

Despite the differences in predicted mass among the surveys, likely caused by
gear selection, there was an overall pattern of predicted masses for a given length
declining over time. In our analysis the pattern was similar across zones but this may be
a result of our treatment of interactions involving year and zone as being random. For
each survey, predicted masses at 450 mm TL suggested a declining temporal trend and a
linear trend was statistically signiﬁcant (P < .05), except in the cases of zones 1 and 2 for
survey 1. The pattern for predicted mass at 700 mm also suggested a decline over time,
and the linear trend was signiﬁcant (P < .05) for all zones and surveys.

Growth and length-at-age

In our combined zone analyses, the model that allowed both Loo and K to vary

over time according to random walks was superior (lower DIC) to the alternatives, and all
the models that allowed temporal changes in growth were superior to a constant growth
model (Table 2.11). These results run counter to preliminary comparisons among
alternative models in which growth parameters were estimated separately by year. In this
case, given that there were no random effects, we were able to ﬁt the models by
maximum likelihood and compare models by AIC. The constant growth model produced
the lowest AIC. While it is not legitimate to directly compare a model in which an effect
is modeled as random versus as ﬁxed, our results suggest there is some evidence for
growth parameters changing with some inertia, but the data do not provide enough
information to freely estimate year speciﬁc growth parameters without such an

assumption. Results from our best model, with time varying parameters, suggest modest

85

~---—-- a...”

 

changes in growth over time, most notably declines in length-at-age after 2001, with

some increases in 2006 for younger ages (Figure 2.9).

When analyzing growth by zone the model allowing only 1.00 to vary through
time was far superior to any other model for zones 1, 3, and 4 (Table 2.10). For zone 2,
although the model with only [.00 varying had the lowest DIC, the model that allowed
both £00 and K to vary over time had nearly as low a DIC (Table 2.10). Results from
our best model for each zone (with only L00 varying); suggest that in general there have

been modest changes in growth over time. Most notable changes are declines in length-

 

Hnwnu ab"- .
‘

at-age in zones 1 and 3 after 2001, for younger ﬁsh with a less notable change in zone 4
(Figure 2.10). Changes in growth for older aged siscowet (20 years of age) the declines
are very modest compared to those observed for 6 year old siscowets (Figure 2.10).
Similar to age 6 growth trends, these declines in length-at-age are only observed in zones
1, 3, and 4 after 2001 (Figure 2.10). For both younger and older ﬁsh length-at—age in
zone 2 did not change as much through time as was the case in the other zones (Figure
2.10). Siscowet lake trout found in zone 4 are larger in size at younger ages and smaller
at older ages compared to other zones (Figure 2.10).
Discussion

Our analysis of age and size composition, mortality, maturation, and condition
demonstrated that the survey used to sample siscowet could inﬂuence the overall
representation of siscowet biology. Even though results across surveys were not
completely congruent, there were some important temporal and spatial patterns that were
consistent. The unexplained differences among surveys may reﬂect differences in gear

selectivity and sampling design (particular depth at which gill-nets were set). Gear

86

selectivity can be a problem when describing biological attributes of a population because
different gears could exclude speciﬁc size classes that could be used in analysis (Potts
and Manooch III 2002; Jones et a1 2008; Colombo et al. 2008). For two of the three
surveys, siscowets were collected by gill-nets set in shallow water depths, which is not
their primary habitat. The siscowet survey was designed to include sampling at deeper
depths. Therefore, when interpreting results from a speciﬁc survey, care should be taken
to consider the potential sampling biases, in particular those associated with habitat
preferences and behavior of organisms.

The general patterns in our results show that siscowet lake trout in zone 4, which
is the eastern part of the lake, have different characteristics than those found elsewhere.
In zone 4 siscowet were on average smaller, younger, in better condition, and matured at
lower lengths compared to other zones. It has been suggested that regional differences in
siscowet characteristics is associated with availability of bathymetric habitat. Bronte and
Moore (2007) suggest that there may be smaller local stocks located in the eastern region
of the lake, where the bathymetry is highly variable compared to other parts of the lake
and this may contribute to difference seen in siscowet morphology. Bathymetry is likely
to be important in contributing to the differences between siscowet in zone 4 and other
zones, but we cannot rule out the importance of other habitat and environmental factors,
and relatively little is known about how these other factors inﬂuence siscowet.

Our analysis demonstrates that biological characteristics of siscowet lake trout
were changing through the 19905 and 20008. These changes may be related to changes in
siscowet densities from the 19908 to the 20005 (Figure 2.11; Chapter 1). Across all

surveys, the frequency of older and larger siscowet increased between periods 1 and 2. In

87

 

addition, siscowets were maturing at smaller sizes compared to those observed in the

19905. Siscowet condition and length-at-age declined over time, with the largest rate of
decrease during the 2000s. Declines in length-at-age were modest compared to changes
in condition. Similar declines for lean lake trout in Lake Huron were associated with

changes in prey availability (He et. a1 2008). Decreases in prey biomass (rainbow smelt
Osmerus mordax and cisco Coregonus artedi artedi) may also be the reason for declines '5‘-
in growth rates of lean lake trout in Lake Superior during the 1970 through 2003 period

(Bronte et al. 2003; Sitar and He 2006). In addition, lean lake trout length-at-50%

 

maturity (L 50 ) declined during a period when lean lake trout abundance was increasing F

and prey ﬁsh abundance was low (Sitar and He 2006). Our result for maturation indicate

a general increase in siscowet L50 over time, which can possibly be explained by the

same reasons Sitar and He (2006) proposed for lean lake trout. Siscowets were
increasing in abundance during the 19905 and the rate of increase decreased in the early
20005 moving towards an asymptote (Figure 2.1]; Chapter 1). Siscowet lake trout feed
primarily upon coregonines (cisco, bloater Coregonus hoyi, kiyi Coregonus kiyi kiyi),
sculpins, burbot Lota Iota and rainbow smelt (Conner et al. 1993; Kitchell et al. 2000;
Bronte et al. 2003; Ray et a1. 2007). Rainbow smelt abundance has been decreasing since
the 19703 and coregonine abundance began decreasing in the 19905 (Bronte et al. 2003;
Eby et al. 1995). Therefore, both changes in abundance of siscowet and several of their
principal prey suggest that food limitation and intraspeciﬁc competition may be playing
an important role in causing the changes we observed in maturation and condition.

Our mortality estimates varied greatly among surveys, zones, and temporal

periods, and no obvious general spatial or temporal patterns were evident. The most

88

obvious pattern was that mortality estimates from the siscowet survey were higher than
for the other surveys, and this clearly must be a consequence of differences in survey
designs as the mortality estimates differed for the same zone and periods, although we
have not been able to formulate a more speciﬁc hypothesis that can explain the
difference.

Overall our results support speculations that siscowet are experiencing density
dependent life history responses similar to what has been found with lean lake trout
(Bronte et al. 2003; Sitar and He 2006). While different data sources suggest some
different responses in the details, we saw pervasive patterns across three different surveys
differing in mesh size conﬁgurations, sampling locations, depths, and time of year of
sampling. Therefore, we believe these results provide important information on real
changes that are occurring and actual zone differences in siscowet populations, and
provide an important baseline about siscowet biology. This information provides a basis
for better understanding possible interactions between leans and siscowet, as well as the
critical information needed to make informed judgments about the per recruit
contributions of siscowet both in response to changes in mortality in Lake Superior (e. g.,
due to changes in a sea lamprey control or ﬁshery harvest) and under conditions that
might exist if siscowet are reintroduced to the lower Great Lakes (Eshenroder et al. 1999;
Janssen et al. 2007). The manner in which these life-history characteristics vary spatially
and over time might provide clues to whether stocks in Lake Superior are approaching
biological limits or whether if the siscowet form were introduced into other lakes its
biology might differ from what has been seen in particular areas of Lake Superior.

Further studies that provide detailed understanding of intraspeciﬁc variation in siscowet

89

 

biology through time and space, and connecting these observed changes to either
environmental changes or behavior would improve our ecological understanding of

siscowet lake trout in Lake Superior.

 

90

 

Acknowledgments

We thank Shawn Sitar, Michigan (MDNR), Mark Ebener (CORA), Bill Mattes
(GLIFWC), and Matt Symbal, Red Cliff Fisheries Department for their advice and
assistance in assembling and interpreting their agency data, and all personnel that
collected and provided data for this project. We also thank Mike Jones and Andrew
McAdam for their thoughts and guidance during the course of this research and on earlier
drafts of this manuscript. In addition, we thank our colleagues at the Quantitative
Fisheries Center (QFC) at Michigan State University for technical and modeling advice.

Funding was provided by the US. Fish and Wildlife Service Restoration Act Program

 

under cooperative agreement #301 8 14J 260 and by the Michigan Department of Natural
Resources. We are grateful to the GLIFWC who acted as the agency sponsor for this

Restoration Act project.

91

Table 2.1. Number of observations (N) on individual siscowet included for each analysis
by survey and zone for Michigan waters of Lake Superior.

 

 

 

Zone
Analysis Survey N l 2 3 4
Age and Size Composition, Mortality,
Growth 1 2937 379 61 1 694 1253
Age and Size Composition, Mortality,
Growth 2 6183 1916 1509 2197 561
Age and Size Composition, Mortality,
Growth 3 4468 1212 1042 1554 660
Condition 1 4983 418 988 1369 2208
Condition 2 9467 2792 2560 3266 849
Condition 3 5952 1552 1207 1984 1209
Maturation 1 7481 1226 2317 1642 2296
Maturation 2 11251 3567 3153 3617 914
Maturation 3 6714 2159 1290 2055 1210

 

92

 

 

Table 2.2. All possible combinations of random effects considered in models for mass-
length relationship that included all ﬁxed effects. Model shorthand notation is used to
indicate which random effects are included in the model (e. g., length*year indicates that a
random interaction of length and year was included). For the actual model see equation 3.

 

 

Model All Possible Random-Effect Models for Mass-Length Relationship
Number

1 loge(length)*year zone"‘year loge(length)*year*eco*region

2 loge(length)*year zone*year

3 loge(length)*year loge(length)*year*zone

4 zone*year loge(length)*year*zone

5 loge(length)*year

6 zone*year

7 loge(length)*year*zone

3 No effects (intercept only)

 

93

 

Table 2.3. All possible combinations of ﬁxed effects for mass-length relationship that
were considered and used with best random effects model. Model shorthand notation is
used to indicate which effects are included in the model (e.g., year indicates an effect of

year was included, and length*zone that an interaction of length and zone was included).

For the actual model see equation 3.

Model
Number

All Possible Random-Effect Models for Mass-Length
Relationship

 

1

2
3
4
5
6
7

loge(length) year zone loge(length)*zone
loge(length) zone year

loge(length) zone loge(length)*zone
loge(length) year

loge(length) zone

loge(length)
No effects (intercept only)

94

 

Table 2.4. Estimated observation error (among individual variation not explained by age
or year) used for each analysis for modeling time varying von Bertalanffy growth model.
Zones are deﬁned as combination of management units: zone 1 is M12 and M13, zone 2
is M14, zone 3 is M15 and M16 and zone 4 is M17.

 

 

Model Scenario Observation error
Combined zones 0.019
Zone 1 0.015
Zone 2 0.019
Zone 3 0.018
Zone 4 0.013

 

95

 

Table 2.5. Length distribution (mm) summary statistics for siscowet lake trout for each
survey, time period, and zone from samples collected during 1996-2006. Statistics are
denoted by: sample size (N), minimum (min), maximum (max), mean, and standard
deviations (std).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Period 1
Survey Zone
N min max mean std

1 l 169 341 815 594.94 76.47

1 2 175 317 798 569.53 86.40

1 4 819 334 755 524.92 53.33
Period 2

1 1 210 140 834 576.86 99.22

1 2 436 327 949 578.12 91.48

1 3 694 388 938 561.27 74.56

1 4 434 406 775 534.64 56.26
Period 1

2 1 677 234 772 442.82 88.14

2 2 631 231 805 425.89 97.68

2 3 891 221 778 457.43 98.56

2 4 306 261 730 462.73 70.74
Period 2

2 1 1239 160 803 480.14 108.81

2 2 878 251 815 461.28 106.93

2 3 1306 215 829 463.25 94.53

2 4 255 339 675 489.24 63.28
Period 1

3 l 895 203 853 536.75 101.19

3 2 400 260 831 517.04 111.67

3 3 1078 236 922 521.96 105.08

3 4 401 302 770 508.60 105.21
Period 2

3 1 317 287 787 535.65 97.22

3 2 642 178 859 509.58 129.80

3 3 476 250 943 542.72 1 18.62

3 4 259 248 715 475.64 94.70

 

 

 

96

 

 

 

Table 2.6. Age (years) distribution summary statistics for siscowet lake trout for each
survey, time period, and zone from samples collected during 1996-2006. Statistics are
denoted by: sample size (N), minimum (min), maximum (max), mean, and standard
deviations (std).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

. Period 1
Survey Zone
N min Max mean std
1 1 169 5 26 16.56 3.48
1 2 175 5 23 14.63 3.58
4 819 5 43 10.75 3.49
Period 2
1 1 210 4 32 15.54 4.66
1 2 436 5 27 14.16 4.77
1 3 694 5 36 13.53 4.30
1 4 434 5 37 11.00 3.74
Period 1
2 1 677 3 26 11.57 3.67
2 2 631 3 24 10.67 3.99
2 3 891 3 28 11.49 4.40
2 4 306 4 31 9.51 3.58
Period 2
2 1 1239 3 31 12.79 5.13
2 2 878 3 33 11.27 4.78
2 3 1306 3 26 10.87 4.19
2 4 255 4 26 9.50 2.94
Period 1
3 1 895 4 27 14.18 3.75
3 2 400 5 28 13.77 4.02
3 3 1078 3 30 13.41 3.72
3 4 401 4 32 12.63 4.69
Period 2
3 1 317 6 37 15.45 4.24
3 2 642 5 29 15.57 4.92
3 3 476 4 31 15.89 5.10
3 4 259 4 29 12.82 5.24

 

 

 

 

97

 

Table 2.7. Estimates of instantaneous rates of total mortality (Z) for each survey by zone
and period and 95% conﬁdence intervals (denoted by lower and upper bounds for

 

 

 

 

 

 

 

 

 

 

 

intervals).
Period 1
Survey Zone
Ages Estimated Z lower bound rmper bound
1 1 >=19 0.324 0.046 0.602
1 2 >=19 0.450 0.124 1.022
1 4 1420 0.463 0.357 0.569
Period 2
1 1 18-26 0.360 0.126 0.487
1 2 >=12 0.210 0.132 0.289
1 3 >=13 0.199 0.156 0.242
1 4 1221 0.383 0.242 0.523
Period 1
2 1 12-22 0.297 0.202 0.392
2 2 10-21 0270 0.158 0.381
2 3 13-24 0.294 0.189 0.398
2 4 11-20 0294 0.127 0.371
Period 2
2 1 15-27 0.323 0.221 0.424
2 2 12-25 0.156 0.120 0.193
2 3 13-35 0.307 0.199 0.416
2 4 1 1-20 0.270 0.225 0.514
Period 1
3 1 18-24 0.584 0.356 0.811
3 2 17-21 0.592 0.139 1.049
3 3 17-25 0.506 0.321 0.690
3 4
Period 2
3 1 18-27 0.330 0.244 0.416
3 2 21-28 0.547 0.429 0.665
3 3 21-28 0.552 0.412 0.692
3 4 14-25 0.183 0.087 0.278

 

 

 

 

 

98

 

 

 

Table 2.8. The number of siscowet sampled (N) and length-at-50% maturity (L50, mm)
with 95 % conﬁdence intervals in parentheses for each zone and temporal period for
survey 2. Zones are deﬁned as combination of management units: zone 1 is M12 and

M13, zone 2 is M14, zone 3 is M15 and M16 and zone 4 is M17. Period 1 includes years <
2000 and period 2 includes years > 1999.

 

 

 

 

Period 1 Period 2
Zone N L50 N L50
1 1667 571 (563, 579) 1900 594 (586, 602)
2 1305 579 (571, 590) 1848 589 (578, 601)
3 1466 569 (561, 577) 2150 600 (590, 615) I“
4 464 544 (527, 565) 450 524 (512, 542) l

 

 

99

 

Table 2.9. Unique candidate models for random effects in mass-length models with

number of estimated parameters (Np), AIC differences (AAIC, 0 = best model), and AIC

weights for the mass-length relationship model for each survey. All ﬁxed effects were
included in all models.

 

 

 

 

 

 

Survey 1
Model Structure Np AAIC Weights
logeﬂength) ”Wear *zone 2.0 0.0 0.562
zone *year 2.0 0.5 0.438
No random effects 1.0 51.4 0.000

Survey 2
logeﬂength) *year + zone *year 3.0 0.0 0.948
logeﬂength) *year + logeﬂength) *year*zone 3,0 5.8 0,052
zone *year 2.0 25.1 0.000
logeﬂength) Weaﬂzone 2.0 28.9 0.000
logeﬂength) *year 2.0 148.4 0.000
No random effects 1.0 167.2 0.000

Survey 3
logeﬂength) *year + zone Wear 3.0 0.0 0.760
logeﬂength) *year + logeﬂength) “year *zone 3,0 2,3 0,240
zone *year 2.0 38.7 0.000
logetlength) *year*zone 2.0 39.4 0.000
logetlength) *year 2.0 72.8 0.000
No random effects 1.0 94.9 0.000

 

100

 

 

 

 

 

 

 

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102

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32.3 o; OBS

 

Table 2.11. List of alternative growth models for model comparison based on deviance

information criteria (DIC), number of estimated parameters ne, and ADIC is the
differences between DICs with the best model (lowest DIC). When parameters were
allowed to vary over time they followed a random walk model (see text).

 

 

 

 

 

 

 

 

Model (Time varying parameters) DIC ne ADIC
Zones Combined
Loo and K 12378.38 14.14 0.00
K* - - -
Loo 12409.10 14.07 30.73 E
Constant 12896.97 2.98 518.59 1
Zone 1 :5
L00 and K* - - -
K 2337.94 3.39 16.09
LoO 2321.85 0.73 0.00 ..
Constant 2439.23 3.07 1 17.39 '
Zone 2
L00 and K 2250.76 8.69 0.24
K 2258.63 5.00 8.10
Loo 2250.53 7.84 0.00
Constant 2403.53 2.95 153.01
Zone 3
L00 and K* - - -
K* - - -
Loo 3208.83 8.74 0.00
Constant 3551.62 2.99 342.80
Zone 4
LOD and K* - - -
K“ - - -
Loo 510.29 11.08 0.00
Constant 851.41 2.93 341.12

 

* indicates that the variance component of K converged toward zero and

is a more parsimonious model

103

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

‘ 1 g 13 I 17 20 Ontario
5 4 15 21 23
I 16
. 22 24 28
Minnesota MB 25 0E) 29
MN3 M4 \
MI3 27 .
/¢N2 ' o 30 31, >
wu2 MD MI6 32 33
N <1 soquoD / 7
W y" “ MIS MI
’ \
Wisconsin Michigan 1mg,

 

Figure 2.]. Lake trout management units of Lake Superior (Hansen et al. 1995). The
letter abbreviations denote U. S. waters by state MN — Minnesota, MI — Michigan, and
W1 — Wisconsin, and numbers represent Canadian waters. Bolded management units
were the ones that supplied data used in this paper.

104

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

§ 0'12 Zone] ‘2’ 0'12 Zonel
g 0.10 J 2 0.10 -
3
o .1 U _.
5 0.08 5 0.08
“a 0.06 5 “a 0.06 -
>5 >\
g 0.04 a g 0.04 «
5.; 0.02 - :3 0.02 —
u. 0.00 - “-1 0.00 _
0 200 400 600 8001000 0 200 400 600 8001000
Length (mm) Length (mm)
“é 0'12 Zone2 8 0'12 Zone2
2 0.10 - § 0.10 ..
8 008 — 8 008
O . 8 .
“a 0.06 - “5 0.06 -
g 0.04 - g 0.04 5
§ 0.02 ~ § 0.02 —
L“ 0. 00 - L“ 0.00 -
0 200 400 600 8001000 0 200 400 600 8001000
Length (mm) Length (mm)
§ 0.12 Zone 3
g 0.10 -
8 008
8 - '
“5 0.06 —
5‘ 0 04 -
§ .
3' 0.02 4
m 0.00—
0 200 400 600 8001000
Length (mm)
8 0.12 20““ “:2 0.12 Zen“
g, 0.10 — g 0-10 ‘
g 0.08 - g 0.08 .
«5 0.06 - “5 0.06 .
E‘ 0.04 - g 0.04 ~
0
E 0.02 - Eu; 0.02 -
La 0.00 - ‘“ 000 A
0 200 400 600 8001000 0 200 400 600 8001000
Length (mm) Length (mm)

Figure 2.2. Length-frequency distributions for siscowet lake trout sampled in survey 1
for each period and zone. Left panels are for period 1 and right panels are for period 2.
Zones are deﬁned as combination of management units: zone 1 is M12 and M13, zone 2
is MI4, zone 3 is M15 and M16, and zone 4 is M17. Period 1 includes years < 2000 and
period 2 includes years > 1999.

105

 

 

   
        

 

 

 

 

 

 

 

   

 

 

 

 

   

 

 

 

 

 

 

   

 

 

 

 

 

 

 

   

8 Zone 1 8 Zone 1
C C."
35 0.08 — 25’
8 8
O 0.06 - O
‘o-a 1 C1—-
0 g. o
5 0.04 ~ .11 5‘
E 15"” 5
a 0.02 — 1;}! l» a
2 Iliii'iilllml 2
“- 0.00 — - “ L“
O 200 400 600 8001000 0 200 400 600 8001000
Length (mm) Length (mm)
10 .
g 0 Zone 2 g 0 10 Zone 2
g 95’ 0.08 —
U U
8 5 0.06 —
Q— Q—
o o
5‘ g» 0.04 — y
5 5 111‘?
3- g. 0.02 - . H
E 8 1111 111.1... N
1 0.00 - ' ‘ 1
O 200 400 600 800100 0 200 400 600 800100
Length (mm)
0 Length (mm)
0
§ 0'10 Zone 3 “g 0'10 Zone 3
:3
g g 0.08 -
O 8
“5 O 0.06 ~
g; “5
5 (>3 0.04 —
:3 C.‘
1.7 g 002 -
u. g '
L“ 0.00 —
0 200 400 600 8001000 0 200 400 600 8001000
Length (mm) Length (mm)
0.10 0.10
“3’ Zone 4 § Zone 4
D O
S 5
° 8
55 o
l~0-1 “-1
o o
8‘ b
8 5
.‘3 :3
8' 8'
a . a
0 200 400 600 8001000 0 200 400 600 8001000
Length (mm) Length (mm)

Figure 2.3. Length-frequency distributions for siscowet lake trout sampled in survey 2
for each period and zone. Left panels are for period 1 and right panels are for period 2.
Zones are deﬁned as combination of management units: zone 1 is M12 and M13, zone 2
is MI4, zone 3 is M15 and M16, and zone 4 is M17. Period 1 includes years < 2000 and
period 2 includes years > 1999.

106

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

“g 0"0 Zonel “g 0'10 Zone]
g 0-03 ‘ g 0.08 —
Q
g 0.06 ~ 5 0.06 «
Q— Q—
0 O
5 0.04 a 3 0.04 a
G G
3 002 4 g 002 i
a ' a '
L“ 0.00 - L“ 0.00 -
0 200 400 600 8001000 0 200 400 600 8001000
Lenght (mm) Length (mm)
a 0.10 Zone2 E 0.10 Zone2
E 0.08 ~ g 0.03 1
§ 0.06 4 g 0.06 4
o ‘8
a 0.04 ~ 5» 0.04 —
5 5
:3
g 0.02 - g 0.02 a
u‘ 0-00 " ”‘ 0.00 —
0 200 400 600 8001000 0 200 400 600 8001000
0 Length (mm) Length (mm)
0
{3. 0'10 Zone3 3); 0'10 Zone3
g 0.03 « “g 0.08 —
8
“5 0.06 ~ 0 0.06 -
a “5
5 004 -1 5‘ 0.04 “
:3 C
O' O
2 0.02 - = 0.02 -
.. a
o 00 — “- 0.00 -
0 200 400 600 8001000 0 200 400 600 8001000
Length (mm) Length (mm)
8 0'10 Zone4 8 0.10 Zone4
= § 0 08 -
g 0.08 ‘ 3 '
O
5" 0.06 . 8 0.06 i
O O
9 0.04 - E 0.04 ~
C
“5. 0.02 - :3;- 0-02 ‘
2 u...
“- 0.00 . , u. 0.00 ‘

 

 

 

 

 

o 200 400 600 8001000 0 200 400 600 8001000

Length (mm) Length (mm)
Figure 2.4. Length-frequency distributions for siscowet lake trout sampled in survey 3
for each period and zone. Left panels are for period 1 and right panels are for period 2.
Zones are deﬁned as combination of management units: zone 1 is M12 and M13, zone 2
is MI4, zone 3 is M15 and M16, and zone 4 is M17. Period 1 includes years < 2000 and
period 2 includes years > 1999.

107

 

 

0.25

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

g Zone 1 “g Zone 1
g 0.20 4 15’ 0.2 —
U Q
5 0.15 4 5
kn B—
O O
5‘ 0.10 '1 5. (H q
5 5
§ 0.05 - g.
“‘ 0.00 .. . . n . u- QO ..
0 10 20 30 4O 0 5 1015 2025303540
Age (years) Age (years)
“8’ 0'25 Zone2 g 0'25 Zone2
g 0.20 4 g 0.20 ~
0 O
8 0.154 8 0.15 -
k— “-1
o o
5‘ 0.10 1 3. 0.10 _
8 8
a. 0.05 - 3- 0.05 -‘
2 e
L“ 0.00 - L" 0.00 4
0 10 20 30 40 0 10 20 30 40
Age (years) Age 06%)
g 0.25 Zone3
95’ 0.20 4
g 0.15 4
Q—
o
5 0.10 -
5
3- 0.05 -4
“.3.
L“ 0.00 4
O 10 20 30 40
3 025 025 Agwem)
g ' Zone4 3g ' Zone4
3 0.20 - j g 0.20 4
o 8 1
“a 0.l5 - O 0.15 e
3 “5
5 0.10 ~ 3 0.10 -
3 C
3 005 a g 005 .
L: a g o
0.00 ” 1‘ I ”I. 0.00 9‘ r___
0 10 20 30 40 0 10 20 30 40
Age (years) Age (years)

 

Figure 2.5. Age-frequency distributions for siscowet lake trout sampled in survey 1 for
each period and zone. Leﬁ panels are for period 1 and right panels are for period 2.
Zones are deﬁned as combination of management units: zone 1 is M12 and M13, zone 2
is M14, zone 3 is M15 and M16, and zone 4 is M17. Period 1 includes years < 2000 and
period 2 includes years > 1999.

108

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

g 0.25 Zone I E; 0.25 Zone I
E g
0 0
<3 5
“-1 “-0
O O
:2" §
3 a
5 E
1.1.. u.
0 10 20 3O 40
Age (years)
0 —l
13- 0.20 g
8 0.15 4 <8
«— a...
O 3; O
5 0.10 - “- g.
a a
g 0.05 — 4| "l g,
L: 0.00 _ : l1 all' - L:
0 10 20 30 40
Age (years)
3 0'25 Zone3 8
g 0.20 4 g
3 8
8 $3 .
“5 °
a E
g a
8 g .'.=|
E 1 LL '
0 10 20 30 40 0 10 20 30 40
Age (years) Age (years)
.2 .
£31 0 5 Zone4 g 025 Zone4
O 0
a 0.20 . g 0.20 - l-
5 0.15 4 '5 0.15 ~
“5 “a
3 0.10 . 3 0.10 -
c: 1:
3 005 4 3 005 -
E ' a? '
L“ 0.00 - . L“ 0.00 . *
0 10 20 3O 40 O 10 20 3O 40

Age (years)

Age (years)

Figure 2.6. Age-frequency distributions for siscowet lake trout sampled in survey 2 for
each period and zone. Left panels are for period 1 and right panels are for period 2.
Zones are deﬁned as combination of management units: zone 1 is M12 and M13, zone 2
is M14, zone 3 is M15 and M16, and zone 4 is M17. Period 1 includes years < 2000 and
period 2 includes years > 1999.

109

Frequency of Occurence Frequency of Occurenc Frequency of Occurence

Frequency of Occurence

 

Zone 1

 

 

Age (years)

 

Zone 2

a

 

 

Age (years)

 

 

 

 

0 10 20 30 40

 

Zone 4

 

 

 

 

 

Frequency of Occurence Frequency of Occurence

Frequency of Occurence

Frequency of Occurence

 

 

Zone 1

 

 

 

 

_ I
1
5 i

10 20 30
Age (years)

 

40

 

 

  

Zone 3

   
  

   
   

    

 

lllllilm
10 - 20 30
Age (years)

  

  

 

40

 

 

   

Zone 4

1;
4

i
E

Ill

 

Figure 2.7. Age-frequency distributions for siscowet lake trout sampled in survey 3 for
each period and zone. Left panels are for period 1 and right panels are for period 2.
Zones are deﬁned as combination of management units: zone 1 is M12 and M13, zone 2
is MI4, zone 3 is M15 and M16, and zone 4 is M17. Period 1 includes years < 2000 and
period 2 includes years > 1999.

 

 

Predicted Loge(Mass)

Predicted Loge(Mass)

Predicted Loge(Mass)

6.85
6.80
6.75
6.70
6.65
6.60

6.55 -

6.50
6.45

6.85
6.80
6.75
6.70
6.65
6.60
6.55
6.50
6.45

6.85
6.80
6.75
6.70
6.65
6.60
6.55
6.50
6.45

 

 

 

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Predicted Loge(Mass)

Predicted Loge(Mass)

Predicted Loge(Mass)

 

 

 

 

 

 

700 mm
:32 A Survey 1
8:20--9 80
8.15 - v V :Ae A
8.10 ‘ . .. '09009 g
8.05 - :vv'v'oﬂéﬂ
a00 4 -"- 9 VV'
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7.90
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8.25 urvey2
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8.05 “—335“ AAAL“ 5'

 

 

 

 

 

 

8.00 — O
795 - ; °§6§905
7.90
{#0“#*1§9% 09 090005
Year
2:? _ Survey 3
8.20 " AAAA
8.15 ‘ o A
810-4 93 AA A AA
0054 ;.'9 oerO
Ova V
8.00 " : ..O.x
7.95 — z
7.90

 

 

 

(955c95059M4094§®.g§9

Year

Figure 2.8. Predicted logarithm of masses at 450 (on left) and 700 mm (on right) total
length for siscowet lake trout in three different surveys for each zone from 1990 to 2006.
The zones are denoted by: solid circle zone 1; open circles zone 2; solid upside-down

triangle zone 3; open triangle zone 4. The vertical line represents the lake-wide average

of loge(mass) within each survey and length class.

111

 

 

700

 

 

 

 

 

600 ‘ r—““'—_"‘Y/"~~v“v“"“v—"'
500 - o°o ------- 00° """" °~---~o ....... 0......) ........ o
E 400 ~
5 W
E0 300 a
a)
.—1
200
—0—— Age6
100 _ ..... o ..... Age 12
—-v-- Age 20
O I I

 

 

 

1996 1998 2000 2002 2004 ‘ 2006

Year

Figure 2.9. Length at age (mm) estimated by (mean of posterior distribution) nonlinear
von Bertalanffy model that allowed parametersto vary over time (see text) for three
selected ages.

112

 

 

 

 

 

700 -
600 a
500 ~
5 400 d A, A- A/ /'_“V'~ A‘ ‘A‘..—A
.1: . '~ A
g ‘ ....__. ‘
200 - .
——-O— Eco-Region l
........ 0... Eco-Region 2
100 ~ -—-v—-- Eco-Region 3
—~-A-—~ Eco-Region 4
0 I I I I I I
I 996 1998 2000 2002 2004 2006

Year
Figure 2.10. Length at age (mm) estimated (mean of posterior distribution) by nonlinear
von Bertalanffy model that allowed parameters to vary over time (see text) for age 6 and
age 20. The ﬁrst four lower lines are predicted values for age 6 and top four lines
correspond to age 20 siscowet.

 

113

4.0 v 4.0 -

 

 

 

 

 

 

 

 

 

 

3 M13 3 M14
(3 (U
a: 2.0 4 °‘ 2-0 i
.1: .=
8 3
8 0.0 . m 63 0.0 «
"O "U
3 20 i g 3 20 ~
g ' . g ' . f
E 4.0 ~ mm o '2 .40 «common
m 3
-6.0 v ' v r -6.0 . . . r
1974 1981 1988 1995 2002 1974 1981 1988 1995 2002
Year Year
a 4.0 "M15 3 4.0 'M16
g 20 . g 20 -
g I I E 5 I
{3 0.0 — i 33 0.0 1
'U '0
3:3 -20 ~ 1 3 20 ~
_° . :6 ' .
a a .1. .1.
a -4,0 ~<ImImII>00 (1:0 (:0 g -4.0 q
5 :7)
-6.0 . . . . 45,0 . . . .
1974 1981 I988 1995 2002 1974 1981 1988 1995 2002
Year Year
2 4.0 — M"
(U
m 2.0 r
u:
3
63 0.0 - 95
'O
.3 -20 4 E
U .
{a
E -4.0 ~00 o 0
CD
-6.0 . . v .
1974 1981 1988 1995 2002

Year

Figure 2.11. Estimated standardized catch rates (loge scale) of siscowet lake trout from

the spring lean lake trout survey for ﬁve Michigan management units in Lake Superior
during 1975-2006 (solid circles joined by dashed line). The open circles show years that
did not catch any siscowet lake trout (reproduced from Chapter 1).

114

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119

 

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