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DEVELOPING DECISION TOOLS FOR INLAND LAKE
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DEVELOPING DECISION TOOLS FOR INLAND LAKE MANAGEMENT
THROUGH FIELD SAMPLING AND STATISTICAL MODELS

BY

TYLER WAGNER

A DISSERTATION

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

DOCTOR OF PHILOSOPHY
Department of Fisheries and Wildlife

2006

ABSTRACT

DEVELOPING DECISION TOOLS FOR INLAND LAKE MANAGEMENT
THROUGH FIELD SAMPLING AND STATISTICAL MODELS

BY

Tyler Wagner
My research encompasses several aspects of ﬁsheries management, ranging from the use
of historical databases to help guide monitoring programs to a ﬁeld study examining the
effects of natural and anthropogenic factors on largemouth bass nest success. A common
feature of my research is the use of mixed models and generalized linear mixed models to
partition variance in ecological response variables and to account for hierarchical data
structures. Because the use of mixed models is not commonly employed in ﬁsheries
research, where hierarchical data structures are common, my ﬁrst chapter is an
instructional paper on the advantages of using mixed models versus general linear models
and how to implement mixed model analyses in a common statistical package, SAS. My
other chapters use mixed models to address speciﬁc questions and hypotheses. For my
second chapter, the speciﬁc research question was: are the ecoregion and watershed
frameworks for lake classiﬁcation useful approaches for grouping lakes with regards to
ﬁsh growth rates (i.e., can mean ﬁsh length at age be partitioned by ecoregions and
watersheds)? For the ecoregions analysis, I also examined if within-ecoregion variability
could be explained by local water quality and lake morphometry characteristics. Variance
in mean length at age between ecoregions for all species was not signiﬁcant, and
between-watershed variance estimates were only signiﬁcant in 3 out of 14 analyses,
indicating that ecoregions and watersheds were ineffective in partitioning variability in

mean length at age. The results suggest that managers should not rely solely on

ecoregions or watersheds for grouping lakes with similar growth rates. For my third
chapter, I examined if habitat alteration and spring angling could explain variability in
largemouth bass nest success. In 2004, we monitored nest distribution and success and
quantiﬁed local nest habitat features, lakewide angler effort, and lakeshore development
in ﬁve Michigan lakes to determine the extent to which habitat alteration and/or ﬁshing
limit the number of successful nests. Surprisingly, local habitat characteristics were not
important determinants of the probability of a nest producing swim-up fry (P > 0.05). At
the whole-lake scale, however, nest success was negatively related to dwelling density,
with the probability of a nest producing swim-up ﬁ'y declining from 0.77 in the lowest
dwelling density lake to 0.45 in the highest dwelling density lake (P = 0.018). These
results demonstrate that knowledge of the magnitude of anthropogenic effects and the
spatial scale at which they operate is integral for black bass management. For my fourth
chapter I examined statewide trends, and the statistical power to detect trends, in mean
length at age for seven ﬁsh species in Michigan and Wisconsin inland lakes. Of the 42
datasets examined, only four demonstrated signiﬁcant regional trends. The structure of
variation differed substantially among datasets and these differences had a strong effect
on the power to detect trends. To maximize trend detection capabilities, ﬁsheries
management agencies should consider variance structures prior to choosing indices for
monitoring and realize that trend detection capabilities are species-speciﬁc. Through the
use of historical data analysis, ﬁeld sampling, statistical modeling, my research informs
monitoring efforts, quantiﬁes anthropogenic effects on an important demographic
parameter for largemouth bass, and helps understand the underlying variation among

lakes.

DEDICATION

I dedicate this dissertation to my parents, Gordon and Sandy Wagner.

iv

ACKNOWLEDGMENTS
This project was funded by a grant from the Michigan Department of Natural Resources,
Fisheries Division. I would like to thank my major professor Mary Bremigan for all her
support and guidance over the past several years. I thank my committee members Mike
Jones, Pat Soranno, and Jan Stevenson for their helpful advice throughout the research
and writing process. I also thank my many coauthors on manuscripts from my
dissertation research including Dan Hayes, Jim Bence, Mike Wilberg, Nancy Nate, Aaron
J ubar, Kendra Spence Cheruvelil, and Jim Breck. Thanks to the many individuals who
helped with data collection, especially with the historical data used in my research,
including Abby Mahan, Cassandra Meier, David Myers, Lidia Szabo Kraﬁ, Mike
Belligan, and all the individuals who worked for Fisheries Division and the Wisconsin
Department of Natural Resources who collected ﬁsh growth data over the past several
decades. I would also like to thank Chris Carman, Nick Longbucco, and Aaron Schultz
for assistance in the ﬁeld and Kimberly Maier for statistical advice. Finally, I would like

to thank Rebecca Kolar for her support, sense of humor, and encouragement.

PREFACE

Chapter 1 is in press in the American Fisheries Society journal Fisheries as:

Wagner, T., Hayes, D. B., and Bremigan, M. T. In Press. Accounting for multilevel data '

structures in ﬁsheries data using mixed models.

Chapter 2 has been submitted for publication in the journal Environmental Monitoring

and Assessment and is currently under review as:

Wagner, T., Bremigan, M. T., Spence Cheruvelil, K., Soranno, P. A., Nate, N. A., and
Breck, J. E. A multilevel modeling approach to assessing regional and local
landscape features for lake classiﬁcation and assessment of ﬁsh growth rates.

Chapter 3 is in press in the journal Transactions of the American Fisheries Society as:

Wagner, T. J ubar, A. K., and Bremigan, M. T. Can habitat alteration and spring angling
explain largemouth bass nest success?

Chapter 4 will be submitted for publication to the Canadian Journal of Fisheries and

Aquatic Sciences as:

Wagner, T., Bence, J. R., Bremigan, M. T., Hayes, D. B., and Wilberg, M. J. Regional
trends in ﬁsh mean length at age: components of variance and the power to detect

trends.

vi

TABLE OF CONTENTS

LIST OF TABLES ........................................................................................................... viii
LIST OF FIGURES ......................................................................................................... xi
INTRODUCTION ........................................................................................................... 1
CHAPTER 1: ACCOUNTING FOR MULTILEVEL DATA STRUCTURES IN
FISHERIES DATA USING MIXED MODELS ............................................................. 10
Abstract ..................................................................................................................... 10
Introduction ............................................................................................................... 1 1
Example 1: Examining the effects of in-stream barriers on ﬁsh density .................. 12
Example 2: Examining the relationship between aquatic macrophyte percent cover
and stomach fullness of yellow perch (Percaﬂavescens) in inland lakes ................ 21
Conclusion ................................................................................................................ 28
References ................................................................................................................. 29

CHAPTER 2: A MULTILEVEL MODELING APPROACH TO ASSESSING
REGIONAL AND LOCAL LANDSCAPE FEATURES FOR LAKE

CLASSIFICATION AND ASSESSMENT OF FISH GROWTH RATES ..................... 37
Abstract ..................................................................................................................... 37
Introduction ............................................................................................................... 38
Methods .................................................................................................................... 45
Results ....................................................................................................................... 51
Discussion ................................................................................................................. 53
References ................................................................................................................. 62

CHAPTER 3: CAN HABITAT ALTERATION AND SPRING AN GLING EXPLAIN

LARGEMOUTH BASS NEST SUCCESS? ................................................................... 81
Abstract ..................................................................................................................... 81
Introduction ............................................................................................................... 82
Methods .................................................................................................................... 84
Results ....................................................................................................................... 91
Discussion ................................................................................................................. 94
References ................................................................................................................. 101

CHAPTER 4: REGIONAL TRENDS IN FISH MEAN LENGTH AT AGE:

COMPONENTS OF VARIANCE AND THE POWER TO DETECT TRENDS .......... 110
Abstract ..................................................................................................................... 110
Introduction ............................................................................................................... 1 1 1
Methods .................................................................................................................... 1 13
Results ....................................................................................................................... 118
Discussion ................................................................................................................. 121
References ................................................................................................................. 1 30

vii

LIST OF TABLES
Chapter 1:

Table 1. Simulated dataset used for example 1. Numbers represent simulated ﬁsh
densities (ﬁsh/m2) for sites nested within treatment (barrier) and control (no barrier)
streams and for sample sites above or below the barrier or reference line. Values used to
calculate within group means are shown outlined in a dashed line. ................................ 31

Table 2. Least-squares means (LSM) and standard error (SE) estimates for example 1
analyzed in SAS using a general linear model (PROC GLM) and a multilevel model
(PROC MIXED). For each analysis (column) least-squares means with different
superscripted letters are signiﬁcantly different (P < 0.05 using Tukey-Kramer multiple
comparison test). Least-squares means correspond to the arithmetic within group means
which can be calculated using the values in Table 1. ...................................................... 32

Table 3. Final parameter and variance estimates, standard errors (SE) and P -— values for
example 2. ....................................................................................................................... 33

Appendix I. An example of the data structure required to analyze the stream barrier
dataset (example 1) using SAS. The DATA statement speciﬁes the name of the dataset
that is generated. The INPUT statement speciﬁes the variables that are read from the
program editor window and the “S” designates variables as character variables. The data
corresponding to the variables listed in the INPUT statement are entered aﬁer the
DATALINES statement. .................................................................................................. 36

Chapter 2:

Table 1. Sample size ranges (number of lakes per ecoregion or 8 digit hydrologic unit
(HU)) and the number of HUS used in the analysis of each species and age combination.
The number of ecoregions used in the analyses was always four .................................... 67

Table 2. List of water quality and landscape covariates used in the analyses. Means for
each species/age combination are followed by ranges in parentheses. SDF = shoreline
development factor, GDD = growing degree days (see Methods for description). ......... 68

Table 3. Fixed effects and variance estimates for ecoregion unconditional models.
)700 =grand mean of mean length at age for all ecoregions (mm), 6'2 represents the
within-ecoregion variability in mean length at age, {'00 represents the between-ecoregion

variability in mean length at age, and ,5 is the intraclass correlation coefﬁcient

(%,,b=f00/(2100+6'2). ................................................................................................. 70

Table 4. Fixed effects and variance estimates for watershed unconditional models.
7700 =grand mean of mean length at age for all watersheds (mm), 6'2 represents the
within-watershed variability in mean length at age, €00 represents the between-watershed

viii

variability in mean length at age, and f) is the intraclass correlation coefﬁcient

(%, a = £00 «£00 + a2) .................................................................................................... 72

Table 5. Final multilevel mixed model parameter estimates for the watershed analysis.
Summer, fall, and winter are dummy variables for sampling season (reference category is
spring). No signiﬁcant between-watershed variance remained in either northern pike
models aﬁer watershed average chlorophyll a was included in the models. ................... 74

Table 6. Final multilevel mixed model parameter estimates for the ecoregion analysis.
Summer, fall, and winter are dummy variables for sampling season (reference category is
spring), TN = total nitrogen, TP = total phosphorus, Chla = chlorophyll a, GDD =
growing degree days, SDF = shoreline development factor, NS = no signiﬁcant
covariates. ........................................................................................................................ 75

Chapter 3:

Table 1. Lake morphometry and water quality characteristics for the six study lakes
surveyed for black bass reproductive success. Shoreline complexity is deﬁned as the ratio
of the length of the shoreline to the circumference of a circle of area equal to that of the
lake. .................................................................................................................................. 104

Table 2. List of covariates used in the analysis of largemouth bass nest success using a
generalized linear mixed model. Level 1 covariates are those measured at the nest-scale;
level 2 covariates are those measured at the lake scale. .................................................. 105

Table 3. The total number of largemouth bass nests and the number of successful and
failed nests located at each study lake. The sum of the numbers of successful and failed
nests is less than the total number of nests because the total number of nests includes
those nests for which the fate could not be determined. Lakes are ordered according to
increasing dwelling density .............................................................................................. 106

Chapter 4:

Table 1. Fish species, age, sample size (N, number of observations used in the analyses),
gear type used to collect ﬁsh, and sampling years used in the trend analysis for Michigan
and Wisconsin inland lakes. M1 = Michigan, WI = Wisconsin, BLG = bluegill, PSF =
pumpkinseed sunﬁsh, LMB = largemouth bass, SMB = smallmouth bass, YEP = yellow
perch, NOP = northern pike, WAE = walleye, EF = electroﬁshing, TN = trap net, FN =
fyke net ............................................................................................................................. 133

Table 2. Parameter estimates for the ﬁxed effect of sampling year (ﬁxed regional trend

(mm-year"),/f ) followed by standard error (s.e.) in parentheses, F -value, and P—value for
mean length at age of seven warm and coolwater ﬁsh species in Michigan and Wisconsin
inland lakes. Signiﬁcant regional trends are shown in bold (or =0.05). MI = Michigan, WI
= Wisconsin, BLG = bluegill, PSF = pumpkinseed sunﬁsh, LMB = largemouth bass,

ix

SMB = smallmouth bass, YEP = yellow perch, NOP = northern pike, WAE = walleye,
n.e. = not estimable .......................................................................................................... 135

Table 3. Estimated variance components followed by standard error in parentheses from a
weighted mixed model examining mean length at age over time for Michigan and

Wisconsin inland lakes. Variance components signiﬁcantly different from zero are shown
in bold (a =0.05). YEP = yellow perch, LMB = largemouth bass, WAE = walleye ...... 138

Table 4. Mean percent increase in statistical power due to setting the estimated residual
and coherent yearly variance to 50 and 25% of estimated values. The power estimates
correspond to a temporal trend of -1.0 mm-year'l in mean length at age for age 4 walleye
sampled in Wisconsin inland lakes. The mean percent increase reported is the average
percent increase in power over the sampling period (5 — 25 years) compared to a situation
using the estimated variance components from historical data (see Table 3 for variance
estimates; population of lakes = 50, 30 lakes sampled each year for 25 years, 10 ﬁsh
sampled per lake) ............................................................................................................. 139

LIST OF FIGURES
Chapter 1:

Figure 1. An illustration of the study-design used for the stream barrier example. Each
stream type was replicated four times (treatment streams A - D and control streams E -
H). ................................................................................................................................... 34

Figure 2. An illustration of the study-design used for the yellow perch stomach fullness
example. Yellow perch (level 1 of the hierarchy) were sampled from eight sample sites
(level 2 of the hierarchy) within four lakes (level 3 of the hierarchy; lakes A - D).
Stomach fullness (dependent variable) and weight (level 1 predictor variable) were
determined for each ﬁsh and percent macrophyte cover (level 2 predictor variable) was
determined for each sample site ....................................................................................... 35

Chapter 2:

Figure 1. Map illustrating the four ecoregion sections and 8-digit hydrologic units
(Seaber et al. 1987) in Michigan. Ecoregion sections deﬁned by Albert (1995) are
numbered six through nine. Black circles represent lakes used in the analyses. ............. 79

Figure 2. Mean length at age box and whisker plots for ages 2 and 3 of three warmwater
species: bluegill (BLG), pumpkinseed (PSF), largemouth bass (LMB), and four coolwater
species: smallmouth bass (SMB), yellow perch (YEP), walleye (WAE), and northern pike
(NOP) for all seasons combined. The lowest, second lowest, middle, second highest, and
highest box points represent the 10th, 25‘“, median, 75th, and 90th percentiles, respectively.
The mean is shown as a circle .......................................................................................... 80

Chapter 3:

Figure l.——Location of the six study lakes surveyed to assess largemouth bass
reproductive success. ....................................................................................................... 107

Figure 2.—Predicted probability of success (solid line) and 95% conﬁdence intervals
(dashed line) for largemouth bass nests in relation to residential lakeshore development.
.......................................................................................................................................... 108

Figure 3.—Observed proportions of habitat types used by spawning largemouth bass to
construct nests (black bars) and proportions of total available habitat types (grey bars) in
each study lake. P-values are for Chi-square goodness-of-ﬁt test. Lakes are ordered from
low to high lakeshore dwelling density. UD = undeveloped, DM = developed maintained,
DR = developed with retaining wall, Low = low wind exposure, High = high wind
exposure. .......................................................................................................................... 1 09

Chapter 4:

xi

Figure 1. Estimated percent of total variation attributed to lake, coherent temporal,
ephemeral temporal, trend variation, and residual variance. Estimates are from a mixed
model for mean length at age versus time for six species/age combinations of ﬁsh ﬁ'om
Michigan (MI) and Wisconsin (WI) inland lakes. YEP = yellow perch, LMB =
largemouth bass, WAE = walleye .................................................................................... 140

Figure 2. Power curves for detecting temporal trends in mean length at age with
increasing trend magnitude (1» = mm-year") for age 4 walleye in Michigan and Wisconsin
inland lakes (30 lakes sampled each year, 10 ﬁsh sampled per lake). ............................. 141

Figure 3. Power curves for detecting temporal trends in mean length at age for age 4
walleye in Michigan and Wisconsin inland lakes as a function of the number of lakes
sampled each year and the number of ﬁsh sampled from each lake (1 = -1.0 mm'yr'l) for
a 10 (bottom set of curves) and 25 (top set of curves) year sampling duration ............... 142

Figure 4. Power curves for detecting temporal trends in mean length at age for age 4
walleye in Michigan and Wisconsin inland lakes. Lake-to-lake variance is shown at the
estimated value from historical data, decreased by 50%, and set to zero (1» = -l .0
mm°year'l, 30 lakes sampled each year, 10 ﬁsh sampled per lake). Power curves on left
panels represent a scenario when 60% of the population of lakes is sampled each year.
Power curves on the right panels represent a scenario when 3% of the population of lakes
is sampled each year ........................................................................................................ 143

xii

INTRODUCTION

Freshwater ecosystems and inland lake ecosystems in particular, are important and
valued resources, providing services that are essential for the sustainability of both
aquatic and terrestrial life. These services include the direct use of water and aquatic
organisms by humans and other ecosystem services, including nutrient cycling and
enhanced biological production (Lubchenco 1998). Over the foreseeable future there will
be an increasing demand on this ﬁnite resource due to increasing global population
growth. For example, the global human population is estimated to be growing at a rate of
1.2% per year, resulting in an increase of 80 million people annually (PRB 2005). Also,
the uncertain effects of global climate change and its interactions with human population
growth on aquatic ecosystems (Verbsmarty et a1. 2000), further demonstrate the need for
sustainable management of freshwater ecosystems. The sustainable management of
freshwater ecosystems includes ensuring that they are functionally intact and biologically
diverse. Maintenance of the structure and function of aquatic ecosystems is necessary not
only to retain the integrity and diversity of natural ecosystems, but also to ensure that
humans beneﬁt from these systems well into the future (Baron et a1. 2002).

Sustainable management of inland lake ecosystems requires an understanding of how
factors, both natural and anthropogenic, affect the structure and/or function of these
ecosystems. Implicit in this understanding is the need to identify the role of scale, both
spatial and temporal, in identifying the most important controlling factors of variables
and processes of interest, such as water clarity and ﬁsh production. Because lakes are

strongly linked to terrestrial environments, this also means that studying lakes within a

landscape context is critical to identifying factors that affect lake structure and function.
Therefore, in my research I use a multiple spatial scale approach to identifying important
drivers of in-lake processes and I examine the temporal dynamics of lake systems while
estimating the magnitude of several spatial and temporal sources of variation.
Collectively, this research provides insight into the sustainable management of inland
lake ecosystems, with an emphasis on the design of monitoring programs, which is an
essential component of aquatic resource management.

Research questions.-Through the use of historical data, statistical and simulation
_ modeling, and ﬁeld sampling, my research addresses the following questions and
challenges faced by ecologists. (1) How do we account for the spatial structure/hierarchy
inherent in ecological data? (2) How do we monitor and manage many aquatic systems
over large geographic regions? (3) How can we quantify the effects of anthropogenic and
natural features, at multiple spatial scales, that affect within-lake processes?
Synthesis and applications

The hierarchical structure of ecological data (e. g., a hierarchical data structure may
consist of measurements taken on individual ﬁsh (lower level) that are nested within
lakes or streams (higher level)) along with inherently high variability makes studying and
managing aquatic ecosystems difﬁcult. With methodological advancements and advances
in computing over the past several decades, we are better able to meet these analytical
challenges. For example, statistical methods (e.g., mixed effect models) can assist with
the management of aquatic systems by allowing for the analysis of patterns across spatial

and temporal scales. Thus I use mixed models extensively in my dissertation research.

To address question 1, I explain how multilevel models (i.e., mixed models), that
account for multilevel (hierarchical) data structures in ﬁsheries data, can be used to test
hypotheses, and discuss how the analytical approach (accounting for versus ignoring
multilevel data structures) affects hypothesis testing and inferences. To accomplish these
goals I provide two examples using simulated data similar in structure to published
studies and contrast the ﬁndings obtained using mixed models with those obtained using
traditional ordinary least squares methods. This paper also provides examples of how to
implement the analyses in a commonly used statistical software package. This research
will provide ﬁsheries scientists and professionals with an accessible example of how to
analyze data using mixed models.

Because environmental policy is developed over broad spatial scales, regional (e.g.,
statewide) management of aquatic systems is a necessity. A common ﬁrst step in the
development of regional management plans involves dividing the landscape into
management units that, ideally, group waterbodies that are ecologically similar. In my
second chapter, through the use of historical datasets, I address question 2 by examining
how variability in inland lake ﬁsh growth rates is partitioned within and between
ecoregions and major river watersheds in Michigan. In the United States, these two
approaches (ecoregions and watersheds) to regional management dominate how agencies
divide land into management units (Brown and Marshall 1996); however, they have yet
to be evaluated for ﬁsh growth. The goal of this research was to determine if commonly
used classiﬁcation frameworks, ecoregions and major river watersheds, are useful for
grouping lakes based on ﬁsh growth. The results of this analysis indicate that both

ecoregions and watersheds are ineffective at partitioning variability in ﬁsh mean length at

age and therefore are not useful regionalization frameworks for this metric. Thus,
although ecoregions and watersheds have partitioned variability in some stream and lake
water quality and aquatic invertebrate diversity metrics, these frameworks need to be
further evaluated prior to wide-scale implementation for multiple metrics, especially in
lakes.

Also during this analysis, I determined what lake morphometric and water quality
characteristics can predict within-ecoregion variability in ﬁsh growth rates. The results of
this study indicate that relatively little of the total variance in ﬁsh mean length at age can
be accounted for by lake morphometry and water quality characteristics (accounting for 2
— 23% of the total variance). However, this study provides insight into what variables
might be useful in future efforts to develop a lake classiﬁcation scheme that facilitates
monitoring of mean length at age as a monitoring metric.

To further explore issues related to regional lake management, in my fourth chapter,
I used historical time series data on ﬁsh growth (mean size at age), mixed models, and
simulations, to examine regional (statewide) temporal trends of growth for seven ﬁsh
species in Michigan and Wisconsin inland lakes, quantify the structure of the total
variation in the time series, and explore how the variance structure affects the statistical
power to detect temporal trends (question 2). This research, along with the research
examining the ability of ecoregions and watersheds to partition variability in mean length
at age, has implications for the design and implementation of regional ecological
monitoring programs for inland lake ﬁsheries. For example, the ability to detect regional
(e. g., statewide) temporal trends is crucial for the evaluation of many management

actions and to examine responses to natural or anthropogenic perturbations. Furthermore,

the early detection of regional changes is important in many cases to allow time for
managers and policy-makers to respond and take appropriate action (Vaughan et al.
2001). Through the use of a components of variance analysis (decomposing the total
variance into several spatial and temporal components, including (1) lake-to-lake (spatial)
variation, (2) coherent (year-to-year) variation affecting all lakes in a similar manner, (3)
ephemeral temporal variation (e.g., lake-by-year interaction) corresponding to
independent yearly variation at each lake, (4) trend variation where each lake is allowed
to have its own trend, and (5) residual variation (variation due to sampling error)), I
demonstrate that the partitioning of variance differed substantially among species, ages,
and states and that the variance structure greatly inﬂuences the power to detect regional
temporal trends in mean length at age. For example, the power to detect a trend in age 4
walleye size at age was greatly reduced compared to Michigan age 4 walleye due to the
inﬂuence of a signiﬁcant coherent temporal variation component for the Wisconsin data.
This illustrates the importance of evaluating metrics for monitoring prior to
implementation of the monitoring program.

Both studies examining the regional management of ﬁsh mean length at age
(dissertation chapters 2 and 4) pose the question of whether or not ﬁsh mean length at age
is a “good” metric to monitor from a ﬁsheries management perspective. I show that it will
likely be difﬁcult to partition variability in mean length at age, especially at the state
level, and that the power to detect trends is greatly reduced if coherent temporal variation
is present. Fisheries management agencies measure and monitor mean length at age
because it is understood that it is important both ecologically and from a management

perspective (e. g., Shuter et al. 1998). However, if regional management is the goal, then

other potential metrics should be evaluated to determine if a different metric is more
informative for ﬁsheries monitoring and management. So, if ﬁsh size at age is not a very
informative metric, then other aspects of ﬁsh population size structures should be
considered and evaluated.

How “useful” a metric is, however, depends on the speciﬁc management and
monitoring objectives. Furthermore, metrics should meet the following requirements
(Graedel and Allenby 2002):

1. They must be related to underlying causal relationships within the systems being
monitored, and must aggregate as much information as possible into a meaningful
composite measure. Metrics should also be easy to understand.

2. They must accurately reﬂect a trend within an appropriate timescale.

3. They must link to existing management objectives.

4. They must be clear and understandable to the public.

Other metrics, besides ﬁsh mean length at age, have been identiﬁed for marine
ﬁsheries that are simple and easy to understand. These metrics also give insight into
population dynamics as well as to the effects of the ﬁshery on the ﬁsh population(s).
Some of these metrics include, (1) the percentage of mature ﬁsh in catch, (2) percent of
ﬁsh with optimum length in catch (optimum length is often larger than length at ﬁrst
maturity), and (3) percentage of “mega-spawners” in catch (i.e., the percentage of old,
large ﬁsh in the catch; Froese 2004). Indicator 1 can be described as “let them spawn”,
indicator 2 as “let them grow”, and indicator 3 as “let mega-spawners live” (Froese
2004). These metrics, if they help meet the objectives of an inland lake ﬁsheries

management agency, might represent more reliable, useful metrics to monitor over time

compared to ﬁsh mean length at age. However, because ﬁsh grth data can be useful
(e. g., Shuter et al. 1998), new metrics could be monitored in conjunction with ﬁsh length
at age to better inform regional management of inland lake ﬁsheries. I would recommend
that alternative metrics, such as those identiﬁed by F roese (2004) be evaluated for inland
lake monitoring and assessment.

Finally, in my third chapter I examine the importance identifying controlling factors
of within lake processes. It is well established that both natural and anthropogenic
factors, acting at different spatial scales, can be important in driving lake processes. So,
through the use of a multi-lake ﬁeld study and the application of a generalized linear
mixed model, I examine the importance of local nest habitat features and lake—wide
features, such as dwelling density and angling effort, in determining largemouth bass nest
success (question 3). This research also provides another demonstration of the
hierarchical nature of ecological data. In this case, bass nests (lower level) are nested
within lakes (higher level), and there are covariates measured at each level.

Largemouth bass are keystone predators and a valued sport ﬁsh in North American
lakes. They also possess life history characteristics that make them vulnerable to within-
lake habitat conditions and perturbations associated with human development of lake
shorelines. Because of their ecological and socioeconomic importance and life history
characteristics, largemouth bass populations represent an opportunity to quantify the
effects of habitat conditions and anthropogenic activities, at multiple spatial scales, on
important demographic properties of ﬁshes. Our results indicated that nest success was
negatively related to lakeshore dwelling density, with the probability of a nest producing

swim-up ﬁ'y declining from 0.7 7 in the lowest dwelling density lake to 0.45 in the highest

dwelling density lake. Examining covariates at multiple spatial scales (e.g., local nest-
level and lake-wide) allowed for the identiﬁcation of a covariate (i.e., dwelling density)
important to nest success that would have been overlooked if a multiple spatial scale
approach had not been used. Furthermore, this research is rather new, as most studies
examining factors affecting nest success focus on single lakes and ignore the hierarchical
nature of the data. This study helps illustrate that knowledge of the magnitude of
anthropogenic effects and the spatial scale at which they operate is integral for black bass
management.

My dissertation research is an example of combining multiple approaches to address
ecological and lake management issues. The use of historical data can provide valuable
information to address research questions and to provide information to help guide future
management decisions and design statistically powerful monitoring programs. The use of
multilevel models provides a useful framework to not only account for hierarchical data
structures often encountered in ecology, but also to examine questions that span multiple
spatial and temporal scales. The design of statistically powerful monitoring programs, as
well as implicitly accounting for the spatial and temporal variation in ecological data,
provides researchers and managers with some of the necessary information for the

sustainable management of aquatic ecosystems.

References

Baron, J., S. LeRoy, N. P., Angermeir, P. L., Dahm, C. N., Gleick, P. H., Hairston, N. G.,
Jackson, R. B., Johnston, C. A., Richter, B. D., and Steinman, A. D. 2002. Meeting
ecological and societal needs for freshwater. Ecological Applications 12:1247-1260.

Brown, R. S. and Marshall, K. 1996, Ecosystem management in state governments.
Ecological Applications 6: 721-723.

Froese, R. 2004. Keep it simple: three indicators to deal with overﬁshing. Fish and
Fisheries 5:86-91.

Graedel, T. E., and Allenby, B. R. 2002. Hierarchical metrics for sustainability.
Environmental Management 21 -30.

Lubchenco, J. Entering the century of the environment: a new social contract for science.
1998. Science 279:491-497.

PRB. 2005. World Population Data Sheet. Washington, DC: Population Reference
Bureau.

Shuter, B. J ., Jones, M. L., Korver, R. M. and Lester, N. P. 1998. A general, life history
based model for regional management of ﬁsh stocks: the inland lake trout
(Salvelinus namaycush) ﬁsheries in Ontario. Canadian Journal of Fisheries and
Aquatic Sciences. 55:2161-2177.

Vaughan, H., Brydges, T., F enech, A., and Lumb, A. 2001. Monitoring long-term
ecological changes through the ecological monitoring and assessment network:
science-based and policy relevant. Environ. Monit. Assess. 67:3-28.

Vdrosmarty, C. J ., Green, P., Salisbury, J ., and Lammers, R. B. 2000. Global water
resources: vulnerability from climate change and population growth. Science
289:284-288.

CHAPTER 1: ACCOUNTING FOR MULTILEVEL DATA STRUCTURES IN

FISHERIES DATA USING MIXED MODELS

Abstract

Multilevel data structures are those that have a hierarchical structure, in which
response variables are measured at the lowest level of the hierarchy and modeled as a
function of predictor variables measured at that level and higher levels of the hierarchy.
For example, a multilevel data structure may consist of measurements taken on individual
ﬁsh (lower level) that are nested within lakes or streams (higher level). Multilevel data
structures are a common feature in ﬁsheries research. We provide simulated ﬁsheries data
examples, similar in structure to other published studies, to illustrate the application of
multilevel models and discuss how hypothesis testing and inferences can be incorrect if
multilevel data structures are ignored. Ignoring multilevel data structures has implications
for the use of commonly-used ordinary least squares (OLS) approaches to test hypotheses
and to make inferences. Multilevel models are an alternate approach that circumvents
problems associated with traditional OLS methods and allows valid inferences to be

made.

10

Introduction

Aquatic systems are often viewed as being hierarchically organized, with lower
levels of organization nested within higher levels (e.g., F rissell et al. 1986; Irnhof et al.
1996). For example, a hierarchy may consist of headwater streams nested within
subwatersheds that are nested within larger watersheds, or lakes nested within
ecoregions. This hierarchical organization provides a conceptual basis for testing
hypotheses, often leading to sampling designs that are also hierarchically organized. A
common feature of such sampling designs is that the response variable is measured at the
lowest level (i.e., ﬁnest scale) of the hierarchy and is modeled as a function of predictors
measured at that level as well as one or more higher levels. This hierarchical organization
leads to multilevel data structures for which traditional methods of statistical inference
are often inappropriate (Raudenbush and Bryk 2002).

The ﬁsheries literature is replete with examples of studies that have collected data
with a multilevel structure. Despite this prevalence, the hierarchical structure of the data
is often ignored during statistical analysis. A fundamental problem with ignoring the
multilevel structure during analyses is that observations measured within a higher level
(e. g., measurements made within the same stream) are likely to be more similar to each
other compared to observations between levels (e. g., measurements made in different
streams). Therefore, analyses that ignore the multilevel structure of the data violate a
critical assumption to commonly-used analyses, namely the assumption of independence.
Although the importance of accounting for the correlation structure of repeated
measurements on individuals has received attention in the ﬁsheries literature, especially

with respect to laboratory studies and analyzing size-at-age data obtained from scales and

11

otoliths of ﬁshes (e. g., Jones 2000; Schaalje et al. 2002; Pedersen and Malte 2004),
multilevel data structures in ﬁeld settings have been largely ignored.

The goals of this article are (l) to explain how to use multilevel models that account
for multilevel data structures in ﬁsheries data to test hypotheses and (2) to discuss how
the analytical approach affects hypothesis testing and inferences. To accomplish these
goals we provide two examples using simulated data similar in structure to published
studies. We illustrate the analysis of these data with a commonly used statistical package,
SAS®. The ﬁrst example uses data with a two-level data structure to emphasize how
hypothesis testing and inferences are affected depending on the statistical approach used,
while the second example provides a detailed example of how to model data with a three-
level data structure.

Example 1: Examining the effects of in-stream barriers on fish density

To introduce a simple multilevel data structure we present the following example.
Data were generated to emulate a commonly-used ﬁeld study design to examine the
effects of instream barriers on ﬁsh density. The simulated dataset contains sample sites
(level 1) nested within streams (level 2; Figure 1). We used these data to test the null
hypothesis that ﬁsh densities do not differ between sites above and below barriers or
between streams with or without barriers. The dataset contains measurements for eight
streams: four ”treatment” streams that contain instream barriers and four ”control”
streams that lack instream barriers. For each treatment stream, ﬁsh density measurements
were generated for three sites below the barrier and three sites above the barrier (or
”reference line” for control streams; Figure 1; Table 1). The data were then analyzed two

ways—using a general linear model (GLM) and a multilevel model (MIXED) in

12

Statistical Analysis System (SAS), and using the GLM and MIXED procedures,
respectively (Littell et al. 1996; SAS Institute Inc. 2000; Littell et al. 2002). The data
were generated to represent a case where mean ﬁsh densities were reduced in treatment
streams as a whole relative to control streams, and with a greater reduction in sites above
the barriers in the treatment streams. In the control streams, mean ﬁsh density was similar
in sites above and below the reference line.
Contrasting traditional and multilevel models

Traditional approaches - Two ordinary least squares (OLS) approaches are
commonly used to analyze multilevel data: an aggregating and a disaggregating
approach. For the aggregated approach, observations within each higher level group are
combined (analysis is performed at the higher level). For our stream barrier example,
aggregation would occur if mean densities were calculated for each stream based on the
six sample sites within each stream (Figure 1). When this approach is used, within-group
variation is ignored (e.g., within stream), which may be a large proportion of the total
variance, resulting in a loss of information and statistical power. For the disaggregated
approach, all observations are used, but the higher level grouping factor (e.g., stream) is
not factored into the analysis. For our stream barrier example, disaggregation would
occur if each measurement of ﬁsh density was treated as an independent replicate sample
from each stream. This approach is inappropriate however, because the experimental unit
is actually the stream, not individual sites, and because the between-group variation is
ignored (analysis is performed at the lower level). When this occurs “replicate” samples
from a higher level grouping factor are assumed to be independent, which is often an

invalid assumption and results in pseudoreplication (Hurlbert 1984). This approach can

13

underestimate standard errors and thus increase the probability of type I errors, i.e.,
ﬁnding a signiﬁcant difference when one does not actually exist. Furthermore, groups
with the largest sample size may dominate the coefﬁcient estimates.

Multilevel models - Multilevel models have received much attention in the past
several years, especially in the social and behavioral sciences. Their increase in
popularity is partly due to methodological advances and advances in statistical computing
over the past several decades. As a result, several excellent references on the theory and
application of multilevel models in the social and behavioral sciences are available; we
refer readers to these references for more detailed information (e. g., Hox 2002;
Raudenbush and Bryk 2002; Duan and Reise 2003).

Multilevel models are represented in the literature under a variety of names including
mixed-effects models, hierarchical linear models, random-effects models, and random
coefﬁcient regression models. Multilevel models circumvent the problems described
above associated with using OLS approaches. For example, multilevel models estimate
standard errors correctly and result in improved estimation of ﬁxed effects when
multilevel data structures exist. Furthermore, both continuous and categorical variables
can be speciﬁed to have ﬁxed or random effects. A factor is ﬁxed if it represents all
possible levels of a factor for which inferences are to be made. For the instream barrier
example, if the streams used in the analysis were the only streams for which inferences
were to be made (e.g., if the researchers did not want to generalize their results to other
streams) then stream would be speciﬁed as a ﬁxed effect. A factor is random if it
represents a random sample of a larger set of potential factors. For the instream barrier

example, if the study streams represented a sample of streams from a larger population of

14

streams with and without barriers, stream would be speciﬁed as a random effect. Another
way to illustrate the difference between ﬁxed and random effects was presented by
Bennington and Thayne (1994). Their deﬁnition is presented in terms of the null
hypothesis being tested for each effect. “Consider two effects, A and B, where A is ﬁxed,
B is random, and there is an interaction (A x B) possible between them. For a given
dependent variable, the null hypothesis concerning A is that there is no difference in
means among the levels of A in the experiment. For B, the null hypothesis is that there is
no variability among all possible levels of B (including those not sampled), not that there
are no differences among levels of that effect included in the experiment. For the
interaction term (A x B), the null hypothesis is that variability among levels of B is the
same for all levels of A. This differs from the case for ﬁxed effects in that the null
hypothesis for an interaction between two ﬁxed effects (A and C) is that the response of
the dependent variable is not different among speciﬁc levels of A depending upon the
particular level of C.”
Analysis of Example 1

Ordinary least squares - We ﬁrst analyzed the simulated stream data assuming all
factors are ﬁxed effects (we assumed streams were not randomly selected from a larger
population of streams) while ignoring the fact that sites are nested within streams. This is
equivalent to using a disaggregated OLS approach, and was performed using the GLM
procedure in SAS. An aggregated approach could also be implemented with these data,
but for illustration purposes we restrict our analysis and discussion to the disaggregated

approach, which is a common approach used in the analysis of ﬁsheries data. Fish density

15

was the response variable and site position (above or below a barrier) and stream type

(barrier or no barrier) were ﬁxed effects. The general form of this model is as follows:

Yijk = u + Position,- + Stream _ Type j + (Position x Stream _Type)l-j + eijk (1)

Where Yijk is the kth measurement on the ith position, in the jth stream, u is the overall

mean, (Position x Stream _ Type),-j is the interaction effect, and errors (eijk ) are assumed

independent and eijk ~ N (O, 0'2 ). An example of the data structure needed for analyzing

the dataset in SAS is given in Appendix I. The SAS code for performing the GLM
analysis is as follows.

PROC GLM DATA = barrier_data;

CLASS stream stream_type position;

MODEL density = stream_type position stream_type*position / SOLUTION;
LSMEANS stream_type position stream_type*position / STDERR PDIFF ADJUST =
tukey;

RUN;

For a detailed description of the SAS syntax, see Littell et al. (2002). Brieﬂy, the
CLASS statement contains the classiﬁcation variables (categorical independent
variables), the MODEL statement deﬁnes the model to be ﬁt, and the SOLUTION Option
requests the parameter estimates. The LSMEANS statement requests that the least-
squares (LS) means be calculated for each classiﬁcation variable listed in the statement.
Least-squares means are within-group means adjusted for other effects in the model and
are also known as the population marginal means (Searle 1987). The PDIFF option

reports the results of the hypothesis test of the differences between LS means (Ho: LS

l6

mean; = LS mean,). The ADJUST = tukey statement requests a multiple comparison test
with adjusted P-values and conﬁdence limits for the LS means using the Tukey-Kramer
method. This adjustment controls for the overall experiment-wise error rate (e.g., controls
for type I error rate). Note that PROC GLM allows for random terms; however, the
standard errors from the LSMEANS statement are usually not computed correctly (Littell
et al. 1998). The GLM procedure in this example was run with only ﬁxed effects.

The Type III sums of squares tests for the signiﬁcance of the ﬁxed effects, which
account for the other effects in the model, are as follows, stream type F = 58.31, P =
<0.0001, position F = 1.01, P = 0.319, stream typeXposition interaction F = 1.71, P =
0.197. The analysis indicates there is a signiﬁcant difference in mean ﬁsh density

between stream types, with barrier streams having signiﬁcantly lower mean density levels
compared to control streams (barrier stream 2? = 26.8 ﬁsh/m2, standard error (SE) = 2.92;

control stream f = 58.4 ﬁsh/m2, SE = 2.92). Table 2 contains the LS means and standard
error estimates for each stream type and site position. The analysis did not detect any
interaction between site position and stream type, although we had simulated an
interaction effect in the dataset.

Multilevel model - Because multilevel models have received more attention in the
social and behavioral sciences and thus references are not available speciﬁcally for the
natural sciences, we use symbols consistent with Raudenbush and Bryk (2002) in our
description of multilevel models. For this analysis, the dependent variable was the same
as in the GLM analysis; however, we took into account the nested structure of the data
(sites nested within streams) and analyzed the data using the MIXED procedure in SAS

with random effects. Position, above or below the barrier, was the site-level (level 1)

17

predictor and stream type (with or without a barrier) was the stream-level predictor (level
2). Stream was regarded as a random effect. Typically, it is likely that measurements of
ﬁsh density from the same stream are correlated (i.e., lack statistical independence); one
way to model this correlation is by treating each stream as having a random effect.

F urtherrnore, we assumed that streams used in the study represented a random sample of

a larger population of streams; therefore, we can generalize our results to other similar

systems.

The model can also be viewed in two levels and in a combined form as follows:
Level 1 model: Yij = ,BOj + ,8” (Position) + ry- (2)
where Yij is the density of ﬁsh in site i in stream j, ,Boj is the mean outcome for stream

j, ,8”- is the coefﬁcient for the ﬁxed effect of site position on ﬁsh density, rij is the level-1

error, where ry- ~ N (0,02) , and 0'2 is the variance at level 1 after controlling for the

effects of position.

Level 2 model: 1601’ == 700 + 701(Stream_ Type) + u0 j , and

1311' = 710 (3)
where 700 is the grand mean density, 701 is the estimated coefﬁcient for the ﬁxed effect
of stream type (i.e., barrier or control) on stream mean ﬁsh density, 710 is a ﬁxed effect
representing the coefﬁcient for the effect of position on ﬁsh density, and uo j is the
residual, where uoj ~ N (0, too) and too is the conditional variance (the stream-level

Variance after controlling for stream type). The combined model can then be written to

contain the site positionxstream type interaction as follows:

18

Yij = 700 + 710(Position) + y01(Stream_Type) + 711(Position >< Stream _Type) + “Oj + ’i‘j

(4)
where 711 is the estimated coefﬁcient for the interaction term and all other variables are
deﬁned as above. The model can be implemented using the following code:

PROC MIXED COVTEST DATA= barrier_data;

CLASS stream stream_type position;

MODEL density = stream_type position stream_type*position / SOLUTION;
RANDOM intercept / SUBJECT = stream;

LSMEANS stream_type position stream_type*position / PDIFF ADJUST = tukey;
RUN;

For an extensive explanation of the PROC MIXED syntax, see Littell et al. (1996). The
syntax is similar to that used in the GLM procedure; however, important differences

exist. The COVTEST statement produces asymptotic standard errors and Wald Z-tests for

the covariance parameter estimates, 6'2 and foo. The CLASS statement is the same as

described for the GLM procedure, while the MODEL statement lists the dependent
variable and only the ﬁxed effects. The SOLUTION option after the MODEL statement
requests the parameter estimates and their standard errors for the ﬁxed effects. The
RANDOM statement speciﬁes the random effects in the model. The intercept is
designated as random in this model because it is assumed that the stream—level intercepts
are from a larger population of stream-level intercepts. The SUBJECT option identiﬁes
the subject(s) in the multilevel model. Specifying a subject is equivalent to nesting all
effects in the RANDOM statement within the subject effect (Littell et al. 1996).

Therefore, the above syntax is modeling ﬁsh density while accounting for the data being

19

clustered (grouped) by streams. As in the GLM procedure, the LSMEANS statement
requests the LS means estimates for the speciﬁed ﬁxed effects and the PDIFF option for
the LSMEANS statement requests the differences between the LS means.

The analysis indicated that there was a signiﬁcant position X stream type interaction.
The overall Type 111 tests for the ﬁxed effects are as follows: stream type, F = 9.44, P =
0.0039; position, F = 5.56, P = 0.024; and position X stream type interaction, F = 9.39, P
= 0.004. Note that because PROC MIXED uses a likelihood—based approach to
estimation it does not directly compute or display the sums of squares; however, the Type
III tests are equivalent to those produced by PROC GLM. Table 2 contains the LS means
estimates and standard errors for each stream type and site position. In treatment streams,
sites located above the barrier had signiﬁcantly lower mean ﬁsh density estimates
compared to sites below the barrier; whereas, in control streams mean ﬁsh density did not
differ between sites located above or below the barrier reference line. Treatment streams
had lower ﬁsh density estimates compared to control streams, regardless of position, but
considering only sites below the barriers, treatment and control streams did not differ
signiﬁcantly in mean ﬁsh density estimates.

Both the traditional (OLS) and multilevel analyses resulted in the same LS means
point estimates and they were equal to the arithmetic means of the values outlined in
Table 1. Least-squares means will be equivalent to arithmetic means for cases with
balanced designs, as in this example. However, for unbalanced designs, which are
common in ecological studies, the LS means estimates will typically not equal the

arithmetic means.

20

There are two major differences between the traditional and multilevel analyses that
have implications for hypothesis testing and inferences: (1) the difference in standard
error estimates and (2) the speciﬁcation of random versus ﬁxed effects. In the multilevel
analysis, the standard error estimates of the means are about two times larger compared
to the OLS estimates. This difference is due to the fact that the standard error in the
traditional analysis is calculated using only the residual variance (the residual variance is
the only variance component in ﬁxed effects models); whereas, the standard error in the
multilevel analysis is calculated using two variance components: the residual variance
and a between-stream variance. The smaller standard errors estimated using the
traditional approach can lead to increased probabilities of type I error rates, i.e., ﬁnding a
signiﬁcant difference when one does not actually exist.

The second major difference between our two analyses is the speciﬁcation of stream
as a random effect in the multilevel analysis. The speciﬁcation of random effects has
implications for what inferences can be made based on the results of the analyses. For the
traditional approach, with stream as a ﬁxed effect, results can not be generalized to
streams that were not used in the analysis and must be restricted to the eight streams used
in the study. For the multilevel analysis, where stream was speciﬁed as a random effect,
inferences can be generalized to a larger population of barrier and no-barrier streams.
Often a goal of a study is the ability to generalize results found from a subset of study
streams or lakes to a larger population of streams or lakes of interest. The use of random
effects allows for such inference whereas purely ﬁxed effects models do not.

Example 2: Examining the relationship between aquatic macrophyte percent cover

and stomach fullness of yellow perch (Percaﬂavescens) in inland lakes

21

For this example, we focus our analysis on the multilevel modeling approach to
demonstrate how to analyze and interpret datasets with three levels. As a result, we do
not compare this multilevel analysis with a traditional OLS analysis. The limitations of
using traditional OLS approaches as discussed previously, however, do exist for
analyzing these data. We realize that some of the following model details are fairly
dense; however, it is our goal that these details will aid in the understanding and
interpretation of the model. ,

Data were generated to emulate a ﬁeld study designed to examine the effects of
macrophyte cover on percent stomach fullness of yellow perch in inland lakes. The
dataset contains individual ﬁsh (level 1), nested within sampling sites (level 2), nested
within lakes (level 3). In this example, sample sites were assumed to be randomly chosen
within lakes and lakes were randomly selected from a larger population of lakes. The data
were used to test the null hypothesis that percent stomach fullness is not related to
percent macrophyte cover while controlling for the effect of individual ﬁsh weight on
stomach fullness. The dataset contains measurements of percent stomach fullness and
weight (g) for individual ﬁsh sampled from eight sample sites within each of four lakes.
Sample sizes of individual ﬁsh varied among sites and lakes, ranging from 0 — 46 ﬁsh per
site and from 160 — 245 ﬁsh per lake for a total of 751 observations. Weight and percent
stomach fullness of individual ﬁsh ranged between 110 — 293 g and 14.4 — 42.2%,
respectively. Percent macrophyte cover was generated for each sample site and ranged
from 2 — 97%.

We introduced complexity to this dataset by not only introducing a third level to the

hierarchy, but by also including predictors at multiple levels: the predictor at level 1 (the

22

individual ﬁsh level) is ﬁsh weight and the predictor at level 2 (the site level) is percent
macrophyte cover. Because of this complexity, we are going to view this analysis as a
two-stage process.

Stage 1 - The ﬁrst stage involves obtaining initial estimates of the total variance,
how the variation is partitioned (i.e., obtain variance estimates that describe how much
variation in stomach fullness there is due to individual differences of ﬁsh within sites
nested within lakes, among sites nested within lakes, and among lakes). These variance
estimates are also used, along with variance estimates obtained in stage 2, to determine
the percent variation explained at each level of the model by the predictor variables. The
model that produces these estimates is a one-way ANOVA with random effects and is
also referred to as an unconditional model because it does not contain any predictor
variables. This one-way ANOVA with random effects can be viewed as a three-level
model as follows:

LCVCI 1 mOdel: Yljk -——’ ”Ojk + el'jk (5)
where Yijk is the percent stomach fullness of ﬁsh i in site j and lake k, ﬂojk is the mean

stomach fullness of site j in lake k, and eijk is the random “ﬁsh effect”, and

eijk ~ N (0, 0'2 ), where 0'2 is the residual variance component due to individual

differences of ﬁsh within sites nested within lakes.

Level 2 model: ”Ojk = 500k +r0jk (6)
where 500k is the mean fullness in lake k, r0jk is the random “site effect”, and
rOjk ~ N (0,23,), where r” is the variance between sites nested within lakes.

Level 3 model: 500k = 7000 + “00k (7)

23

where 7000 is the overall grand mean fullness, “00k is the random “lake effect”, and

“00k ~ N (0, rﬂ), where rﬂ is the variance between lakes. The combined unconditional
model, therefore, has a ﬁxed effect (7000) and three random effects (“00k , rOJ-k , and

eijk ) and is as follows:

Yijk = 7000 + “00k + rOjk + eijk (8)
Examining the initial variance estimates provides information regarding how much total
variation there is at each level that can subsequently be modeled with predictor variables.
The code required for performing the one-way ANOVA with random effects for this
example is:
PROC MIXED COVTEST DATA = lake_data;
CLASS lake site;
MODEL fullness =/ SOLUTION;
RANDOM intercept / SUBJECT = lake;
RANDOM intercept / SUBJECT = site(lake);
RUN;
The syntax for this unconditional model is similar to that described in example 1;
however, there is an additional RANDOM statement which speciﬁes that sites are nested
within lakes.

Results from the one-way AN OVA with random effects show that the grand

mean ()7000) stomach fullness over all lakes is 24% and the estimates of variance among-

ﬁsh-within-sites-nested-within-lakes (6' 2 ), among-sites-within-lakes ( f7; ), and among-

lakes (fﬂ) are 8.67 (SE = 0.46, P < 0.0001), 7.44 (SE = 2.18, P = 0.0003), and 2.18 (SE

24

= 2.6, P = 0.202), respectively. The percent variance among ﬁsh within sites nested
within lakes, among sites within lakes, and among lakes is 47%, 41%, and 12%,
respectively. We now have information on how the variance is partitioned in our dataset
and a conditional model can be speciﬁed in stage 2.

Stage 2 - The predictor of interest in this study is percent macrophyte cover.
However, we also need to account for the effect of individual ﬁsh weight on stomach
fullness in the model. Therefore, our two predictors are ﬁsh weight, modeled at level 1,
and percent macrophyte cover, modeled at level 2. Level 3 (the lake level) is left
unconditional, with no predictor variables (covariates). Again, the model can be viewed
as three levels and in a combined form as follows:

Level 1 model: Yijk = Irojk + ”ljk(Weight)1jk + er'jk (9)
where Yijk is the stomach fullness for ﬁsh i in site j in lake k, ”Ojk is the intercept for site
j in lake k, rrljk is the estimated coefﬁcient for the ﬁxed effect of ﬁsh weight on stomach
fullness, and ey-k is the level—l random effect.
Level 2 model: ﬂojk = 600k + ,601 k (Percent_Cover) jk + "0jk

mﬁ=aa am
where ﬂOOk is the intercept for lake k, 16011: is the estimated coefﬁcient for the ﬁxed

effect of percent macrophyte cover, [310k is a ﬁxed effect representing the coefﬁcient for

the effect of ﬁsh weight on stomach fullness, and "Ojk is the level-2 random effect.

Lével 3 model: ﬂoor = 700013101. = rrooaﬂmk = 7010 (11)

25

where 7000 represents the coefﬁcient for the level 2 intercept, 7100 represents the
coefﬁcient for the ﬁxed effect of ﬁsh weight on stomach fullness, and 7010 represents the

coefﬁcient for the ﬁxed effect of percent macrophyte cover on stomach fullness. The

combined model is as follows:

Yijk = 7000 + 7100(Weight) + 7010(Percent _ Cover) + 7110(Weightx Percent _ Cover) +

“00k + rOjk + 80k
(12)

where y] 10 is the estimated coefﬁcient for the interaction term and all other variables are

deﬁned as above. The model can be speciﬁed using the following code:

PROC MIXED COVTEST DATA = lake_data;

CLASS lake site;

MODEL fullness = weight cover weight*cover/ SOLUTION;

RANDOM intercept / SUBJECT = lake;

RANDOM intercept / SUBJECT = site(lake);

RUN;

The syntax is similar to that described in the unconditional model; however, we now have
speciﬁed the full model in the MODEL statement.

The analysis indicated that both ﬁsh weight and percent macrophyte cover were
signiﬁcantly and positively associated with percent stomach fullness and that there was
not a signiﬁcant interaction effect (Table 3). Variance estimates obtained from the ﬁnal
model (full model) can be used along with the variance estimates from the unconditional

model to determine how much variation was explained at each level as follows:

26

Varianceunconditional — Variance fu 1,

(13)

 

Percent variance explained = _
V ar lanceunconditional

, o . A 2 A A o u
where Varzanceuncondmonal rs an estrmate of o: , r”, or 7'3 from the unconditional

model and Variance full is an estimate of 6'2 , f” , or {'5 from the full model. For

example, to determine how much of the variation in stomach fullness among ﬁsh within
sites nested within lakes was explained by ﬁsh weight we perform the following

calculation:

8.67(6'2unconditional)‘1-O7(&2full) ___

.2 0.88 (14)
8.67(0' unconditional)

 

thus, ﬁsh weight explained 88% of the among-ﬁsh-within-site-nested-within-lake (level
1) variation in stomach fullness. Using equation 13, we can determine that percent
macrophyte cover explained 31% of the variation in ﬁsh stomach fullness among sites
within lakes (level 2). Because we did not have predictors at the lake-level (level 3), we
do not need to calculate percent variation explained at this level. However, if predictors
were included at level 3, the same calculation could be performed to determine percent
variation explained.

In this example, the multilevel model accounted for the fact that ﬁsh were nested
within sample sites within lakes and sample sites were nested within lakes. As in example
1, the speciﬁcation of random effects allowed us to account for the lack of independence
of observations within sites and lakes with similar implications for inferring (e. g., the
ability to generalize to a larger population of lakes). The analysis also allowed for the
partitioning of variance among the three levels. Variance partitioning provides valuable

information on how much variation is contained at each level. Knowledge of how much

27

variation exists at each level can also help guide future data collection efforts by allowing
researchers to focus data collection at the level (e.g., spatial scale) that contains much of
the variability that needs to be explained.
Conclusion

Multilevel models provide several advantages over the more commonly-used OLS
approaches when analyzing data with a hierarchical structure. Because hierarchical
structures are common to both experimental and ﬁeld (observational) studies in ﬁsheries
research, we encourage the use of multilevel models where appropriate. Some other
examples of where hierarchical data structures may arise in ﬁsheries research, where
multilevel models would be applicable, include investigations of ﬁshing tournament
related mortality, where ﬁsh are nested within tournaments and tournaments are nested
within lakes, and investigations of landscape features on lake or stream attributes, where
waterbodies are nested within watersheds and watersheds are nested within ecoregions.
Furthermore, due to statistical computing advances, multilevel models can be
implemented in widely available statistical software packages. These approaches provide
better estimation of ﬁxed effects, allow for the partitioning of variance components
across levels, and allow for generalizations beyond the particular groups (e.g., streams or

lakes) used in the study.

28

References

Bennington, C. C., and Thayne, W. V. 1994. Use and misuse of mixed model analysis of
variance in ecological studies. Ecology 75:717-722.

Duan, N., and S. P. Reise (Eds). 2003. Multilevel modeling. Methodological advances,
issues, and applications. Lawrence Erlbaum Associates, Mahwah, NJ.

Frissell, C.A., W.J. Liss, C.E. Warren, and MD. Hurley. 1986. A hierarchical framework
for stream habitat classiﬁcation: viewing streams in a watershed context.
Environmental Management 10:199-214.

Hox, J. J. 2002. Multilevel analysis: techniques and applications. Lawrence Erlbaum
Associates, Mahwah, NJ.

Hurlbert, S. H. 1984. Pseudoreplication and the design of ecological ﬁeld experiments.
Ecological Applications 54: 1 87-21 1.

Jones, C. M. 2000. Fitting growth curves to retrospective size-at-age data. Fisheries
Research 46:123-129.

Imhof, J. G., J. Fitzgibbon, and W. K. Annable. 1996. A hierarchical evaluation for
characterizing watershed ecosystems for ﬁsh habitat. Canadian Journal of
Fisheries and Aquatic Sciences 53:312-326.

Littell, R. C., G. A. Milliken, W. W. Stroup, and R. S. Wolﬁnger. 1996. SAS System for
Mixed Models. SAS Institute Inc., Cary, North Carolina.

Littell, R. C., P. R. Henry, and C. B. Ammerman. 1998. Statistical analysis or repeated
measures data using SAS procedures. Journal of Animal Science 76:1216-1231.

Littell, R. C., W. W. Stroup, and R. J. Freund. 2002. SAS® for linear models. SAS
Institute Inc., Cary, North Carolina.

Pedersen, L. F., and H. Malte. 2004. Repetitive acceleration swimming performance of
brown trout in fresh water and after acute seawater exposure. Journal of Fish
Biology 64:273-278.

Raudenbush, S. W., and A. S. Bryk. 2002. Hierarchical linear models (2nd ed.). Sage
Publications, Thousand Oaks, CA.

SAS Institute Inc. 2000. SAS/STAT user’s guide. SAS Institute Inc., Cary, NC.
Schaalje, G. B., J .L. Shaw, and M. C. Belk. 2002. Using nonlinear hierarchical models

for analyzing annulus-based size-at-age data. Canadian Journal of Fisheries and
Aquatic Sciences 59: 1524-1532.

29

Searle, S. R. 1987. Linear models for unbalanced data. John Wiley & Sons, Inc., New
York.

30

Table 1. Simulated dataset used for example 1. Numbers represent simulated ﬁsh
densities (ﬁsh/m2) for sites nested within treatment (banier) and control (no barrier)
streams and for sample sites above or below the barrier or reference line. Values used to

calculate within group means are shown outlined in a dashed line.

 

 

 

 

 

Barrier Control
Stream A B C D E F G H

Site Position

1 Above """ 1'5""W49WW'1'4 """" i '2’"? "'"4'6 """" 07' """ 4'5"m"7'4""
2 Above 14 47 15 9 41 70 45 67
3 Above 7 39 25 18 42 82 57 72
4 Below §""3’8""""4'5 """" 2120 {"49 """" 7.6- """ 3'9'"""'6"6""
5 Below 13 50 31 24 50 76 37 64
6 Below 24 50 33 30 55 74 35 72

.-------_-------_-__----------------_--_--- >-------- ------------------------------

 

31

Table 2. Least-squares means (LSM) and standard error (SE) estimates for example 1

analyzed in SAS using a general linear model (PROC GLM) and a multilevel model

(PROC MIXED). For each analysis (column) least-squares means with different

superscripted letters are signiﬁcantly different (P < 0.05 using Tukey-Kramer multiple

comparison test). Least-squares means correspond to the arithmetic within group means

which can be calculated using the values in Table l.

 

General linear model

Multilevel model

 

 

Stream type Position LSM SE LSM SE
Barrier Above 22.0a 4.14 22.0“‘ 7.38
Barrier Below 31.6: 4.14 31.61) 7.38
Control Above 59.0b 4.14 59.0b 7.38
Control Below 57.8b 4.14 57.8b 7.38

 

32

Table 3. Final parameter and variance estimates, standard errors (SE) and P -— values for

 

 

 

example 2.
Parameter Estimate SE P — value

Intercept ()3000) 5.92 1.31 0.02

Weight ()9100) 0.10 0.003 <0.0001

Percent cover (£010) 5.02 1.26 <0.0001

Weight X percent cover ()7110) -0.005 0.004 0.24

Variance components

Among ﬁsh within sites nested within lakes (6'2) 1'07 0'05 <0'0001

Among sites within lakes (in) 5.15 1.48 0.0002
1.71 1.95 0.19

Among lakes (f5)

 

33

Figure 1

Treatment streams Control streams
A - D E - H

In-stream barrier

 

Sample sites

 

34

Figure 2

 

 

35

Appendix I. An example of the data structure required to analyze the stream barrier
dataset (example 1) using SAS. The DATA statement speciﬁes the name of the dataset
that is generated. The INPUT statement speciﬁes the variables that are read from the
program editor window and the “$” designates variables as character variables. The data
corresponding to the variables listed in the INPUT statement are entered after the
DATALINES statement.

DATA barrier_data;

INPUT density stream $ site stream_type $ position S;

DATALINES;

15 A 1 Barrier Above

14 A 2 Barrier Above

7 A 3 Barrier Above

49 B 1 Barrier Above

47 B 2 Barrier Above

39 B 3 Barrier Above
14 C 1 Barrier Above
15 C 2 Barrier Above
25 C 3 Barrier Above

72 E 6 Control Below

36

CHAPTER 2: A MULTILEVEL MODELING APPROACH TO ASSESSING
REGIONAL AND LOCAL LANDSCAPE FEATURES FOR LAKE
CLASSIFICATION AND ASSESSMENT OF FISH GROWTH RATES
Abstract

The ecoregion and watershed frameworks are landscape-based classiﬁcations that
have been used to group waterbodies with respect to measures of community structure;
however, they have yet to be evaluated for grouping lakes for demographic
characteristics of ﬁsh populations. We used a multilevel modeling approach to determine
if variability in mean ﬁsh length at age could be partitioned by ecoregions and
watersheds. For the ecoregions analysis, we then examined if within-ecoregion variability
could be explained by local water quality and lake morphometry characteristics. We used
data from agency surveys conducted during 1974 — 1984 for age 2 and 3 ﬁsh of seven
common warm and coolwater ﬁsh species. Variance in mean length at age between
ecoregions for all species was not signiﬁcant, and between-watershed variance estimates
were only signiﬁcant in 3 out of 14 analyses; however, the total amount of variation
between watersheds was very small (ranging from 1.8 to 3.7% of the total variance),
indicating that ecoregions and watersheds were ineffective in partitioning variability in
mean length at age. Within ecoregions, water quality and lake morphometric
characteristics accounted for 2 — 23% of the variation in mean length at age. Measures of
lake productivity were the most common signiﬁcant covariates, with mean length at age
increasing with increasing lake productivity. Much of the variability in mean length at
age was not accounted for, suggesting that other local factors such as biotic interactions,
ﬁsh density, and exploitation are important. The results indicate that the development of

an effective regional framework for managing inland lakes will require a substantial

37

effort to understand sources of demographic variability and that managers should not rely

solely on ecoregions or watersheds for grouping lakes with similar growth rates.

1. Introduction

Over past decades, many state and federal agencies have moved toward a regional
approach for biological assessment and monitoring. This approach often entails
delineating an area of land into discrete management units, which are based on physical
geographical features. In the United States, two approaches dominate how agencies
divide land into management units: basinwide or watershed approaches and ecoregion
classiﬁcation (Brown and Marshall, 1996). An ecoregion is deﬁned as a unit of land that
is homogenous with respect to multiple landscape characteristics such as geology, soil
characteristics, natural vegetation, and climate. A watershed is deﬁned as the
topographical area which drains water into a waterbody (Omemik and Bailey, 1997). In
the United States, however, the use of hydrologic units (HUS) as proxies for watersheds
has increased since the development of digital HU maps by the United States Geological
Survey (Seaber et al., 1987). Hydrological units may or may not overlap with a
waterbody’s topographical watershed (Omemik, 2003); however, they represent a
valuable and accessible framework for classifying waterbodies. Hydrologic units are
classiﬁed into several levels and are identiﬁed based on a unique hydrological unit code
(HUC). Spatial scales of HUCs range from “regions” (2-digit HUC) to “subwatersheds”
(l4-digit HUC).

Although watershed-based approaches are still used in many states, the ecoregion

framework is becoming increasingly popular as ecoregion delineations are becoming

38

available for most states and from multiple sources, including the US. Environmental
Protection Agency (e. g., Bailey, 1983; Omemick, 1987; Albert, 1995). The use of
watershed and ecoregion frameworks is not limited to the United States, as several
European countries have also adopted these approaches for regional environmental
management (Sandin and Johnson, 2000; Santoul et al., 2004). The underlying
assumption behind the use of ecoregions and watersheds is that classiﬁcation of surface
waters will reduce natural within-class variation of ecological data (Genitsen et al.,
2000). If so, then the grouping of lakes that are ecologically similar will facilitate the
identiﬁcation of reference conditions, allow for more precise assessment of aquatic
communities, and provide the opportunity to extrapolate biological information to other
lakes within a relatively homogenous landscape (Gerlitsen et al., 2000).

Although ecoregions or watersheds are often adopted as a framework for classifying
aquatic systems, several limitations exist regarding their ability to group waterbodies
(Johnson, 2000; Van Sickle and Hughes, 2000). First, the delineation of ecoregion
boundaries is subjective at some level. Second, as mentioned above, the delineation of
HUS does not always overlap with topographical watersheds and thus deﬁning a HU is
not Simple (Omemik, 2003). Third, one of the primary assumptions of the ecoregion and
watershed approaches to classifying aquatic systems is that the Spatial variability of the
abiotic features constrains important properties of aquatic ecosystems. If the properties of
aquatic systems that are being measured are not constrained spatially, for example, if
properties vary independently over the landscape, then these frameworks will be
ineffective at partitioning variance (Hawkins and Vinson, 2000). This highlights the need

to determine how well ecoregions and watersheds (i.e., HUS) actually partition variability

39

prior to their implementation for ecosystem management (Johnson, 2000; Omemik,
2003)

To date, most investigations into the effectiveness of ecoregions and watersheds as
frameworks for ecosystem management have focused on streams (N ewall and Magnuson,
1999; Pan et al., 2000), with fewer studies examining lakes (but see Johnson, 2000 and
J enerette et al., 2002). Furthermore, the emphasis of these investigations has often
focused on measures of community structure, such as species richness or diversity and
results from these studies often conﬂict. For example, Newall and Magnuson (1999)
demonstrated ﬁsh community structure was not related to ecoregions in Wisconsin
streams. Conversely, Van Sickle and Hughes (2000) found that stream ﬁsh and
amphibian assemblages were more similar within ecoregions than between ecoregions in
Oregon streams and that ecoregions performed better in grouping Similar stream
vertebrate assemblages as compared to watersheds. Studies have yet to investigate if
ecoregions or watersheds are effective at partitioning variability in demographic
characteristics of aquatic organisms. An understanding of both the spatial patterns of
species assemblages and the Spatial variability in demographic characteristics is
necessary for the conservation and management of aquatic populations.

Although many demographic characteristics are difﬁcult to measure, growth rates of
ﬁshes are relatively easy to determine and often readily available from state and federal
management agencies. Fish growth rates are of great importance to ecological
interactions in aquatic systems (Weatherley, 1972) and of particular interest to ﬁsheries
management agencies because they can be used to assist management decisions regarding

stocking programs and size and bag limits for sport ﬁshes (e. g., Shuter et al., 1998).

40

Furthermore, ﬁsh growth rates are inherently variable among lakes, making regional
management difﬁcult (Shuter et al., 1998). Therefore, ﬁsh growth data represent an
opportunity to assess the ability of the ecoregion and watershed frameworks to partition
variance of demographic data.

Many studies evaluating the ecoregion and watershed approaches have focused
primarily on how well the framework maximizes between-class variability, without
exploring factors that explain within-class variability. However, factors that regulate the
structure and function of aquatic communities operate at multiple Spatial scales (Roth et
al., 1996; Jackson et al., 2001). Identifying whether local or regional controlling factors
explain the most variability among waterbodies will greatly assist the development of
regional management plans. For instance, there is a paucity of information on the relative
importance of local factors such as lake morphometry and water quality versus regional
factors in explaining variability in ﬁsh grth rates and whether potential relationships
vary among ecoregions (or watersheds). The use of multilevel mixed models, as
employed in this study, is a novel approach for the evaluation of the ecoregion and
watershed frameworks that allows for the investigation of factors (covariates) that operate
at multiple Spatial scales in a Single statistical model.

Elucidation of relationships between physical and chemical lake properties and
growth of ﬁshes can lead to the development and/or reﬁnement of lake classiﬁcation
tools to be used independently or conjointly with existing frameworks. Therefore, the
objectives of this study were to: (1) examine how variability in inland lake ﬁsh growth
rates is partitioned within and between ecoregions and major river watersheds in

Michigan, (2) determine what aspects of ecoregions or watersheds can explain between-

41

class variation, if it does exist, and (3) determine what lake morphometric and water
quality characteristics can predict within-class variability in ﬁsh growth rates. Due to data
restrictions, we limited our analysis of factors explaining within-class variation to the
ecoregion analysis (see Methods). We analyzed data for seven ﬁsh species including the
warmwater species bluegill Lepomis macrochirus, pumpkinseed L. gibbosus, largemouth
bass Micropterus salmoides, and the coolwater species smallmouth bass M. dolomieu,
yellow perch Percaﬂavescens, walleye Sander vitreus, and northern pike Esox lucius.
1.1 Hypotheses

Our model-building process was driven by a priori hypotheses, in that covariates
were selected for inclusion in the model-building process based on hypothesized
relationships between the covariate and the growth of ﬁshes. As a framework for
selecting potential covariates, we considered ﬁsh growth to be a function of consumption
and metabolic costs, which is Similar to many bioenergetics models (Hansen et al., 1993).
We restricted our analysis of within-class variation to ecoregions, because sample sizes
were larger than those associated with watersheds. Within this bioenergetics framework,
we hypothesized the following water quality and landscape characteristics to be
important factors inﬂuencing the growth of ﬁshes within and between ecoregions and
between watersheds.
1.1.1 Consumption

We hypothesized that water quality and landscape characteristics would inﬂuence
ﬁsh consumption through three mechanisms, and that these characteristics would show
Similar effects at the local lake scale and the regional watershed/ecoregion scale. The

three mechanisms are: (1) prey availability, (2) prey diversity, and (3) predator-prey

42

overlap. Because species density and diversity (richness) tend to increase with increasing
productivity (Waide et al., 1999), we hypothesized that measures of productivity (e.g.,
chlorophyll a and total phosphorus) would be positively associated with ﬁsh growth
rates. The diversity-productivity relationship in lakes is often considered unimodal, with
diversity decreasing under hypereutrophic conditions. However, given the relatively low
nutrient status of our study lakes, we expected a positive linear relationship.

Species diversity of both ﬁshes and zooplankton is related to local landscape
characteristics (e.g., basin morphology), with diversity increasing with increasing lake
size and depth (Barbour and Brown, 1974; Dodson, 1992). We did not expect, however,
that larger and deeper lakes would necessarily be associated with faster ﬁsh growth rates
because shallower lakes may increase the amount of foraging habitat for Species that
depend primarily on littoral prey (but see Mittelbach and Chesson, 1987 ; Mittelbach and
Osenberg, 1992). Therefore, because the species we included in our analyses all utilize
the littoral regions of lakes for foraging (see below), we hypothesized that large shallow
lakes with extensive littoral areas would be associated with faster growth. Accordingly,
we also hypothesized that lakes with a high shoreline development factor (SDF), which is
a measure of Shoreline complexity, would be positively associated with fast ﬁsh growth.
A lake’s hydrologic position in the landscape is also related to ﬁsh Species richness
(Kratz et al., 1997). For example, lakes that are isolated from other sources of surface
waters (e. g., seepage lakes) have lower species richness as compared to lakes that are
connected to other lakes and streams (Riera et al., 2000). The isolation of seepage lakes

may result in lower richness due to lower invasion probabilities. Therefore, we

43

hypothesized that isolated lakes would have ﬁsh with Slower growth rates compared to
lakes connected to streams and other lakes.
1.1.2 Metabolic costs

Temperature inﬂuences rates of ﬁsh metabolism, consumption, and growth (Power
and van den Heuvel, 1999; Zweifel et al., 1999). Growth increases as temperature
increases to a maximum point (i.e., grth plateaus), beyond which growth decreases as
metabolic costs exceed energy intake at higher temperatures (Kitchell et al., 1977).
Because Michigan is located in the northern portion of the country and therefore has
relatively mild summers, and because we examined data for warm and coolwater ﬁsh
species, we predicted the growth-temperature relationship to be linear and not parabolic,
as temperatures exceeding the thermal optimum for an extended length of time are
unlikely.

We also hypothesized that a lake’s morphometry would indirectly inﬂuence ﬁsh
metabolic rates by affecting the amount of thermally optimal habitat by inﬂuencing
thermal stratiﬁcation and growing season length. Because warm and coolwater species
are included in our analysis, we predicted that deep lakes would have slower growth rates
compared to shallower lakes. Furthermore, large, shallow lakes are predicted to have
highest growth rates due to potentially higher prey diversity and warmer temperatures.
For all species, we also predicted that a large amount of variability in ﬁsh growth rates
would remain unexplained, as biotic interactions and ﬁsh density can substantially
inﬂuence ﬁsh growth rates (Werner and Hall, 1977; Mittelbach, 1988; Pazzia et al.,
2002). The speciﬁc covariates we included in the analyses and their sources are described

in detail below.

44

2. Methods

2.1 Datasets

Growth data (mean length at age) for seven warm and coolwater ﬁsh Species (Table
I) were obtained from historical ﬁsh growth surveys conducted by the Fisheries Division
of the Michigan Department of Natural Resources. Species used in analyses included the
warmwater Species bluegill Lepomis macrochirus, pumpkinseed L. gibbosus, largemouth
bass Micropterus salmoides, and the coolwater Species smallmouth bass M. dolomieu,
yellow perch Percaﬂavescens, walleye Sander vitreus, and northern pike Esox lucius.
Mean length at age data from surveys conducted during 1974 — 1984 were used in the
analyses because they coincide with years during which water quality was also sampled
(see below). In each survey, ﬁsh growth was recorded as the mean length at age for a
given species and age. The corresponding number of ﬁsh that contributed to the mean
was also reported; however, data for individual ﬁsh were not reported. Other data
contained in the surveys included the season of sampling (categorized as spring, summer,
fall, or winter) and the sampling year. The gear type used to collect the ﬁsh was
sometimes reported; however, often multiple gear types were used or no gear type was
reported. Due to the inconsistencies in reporting gear types and the fact that multiple gear
types were often used, we were unable to control for this potentially important covariate.
Historically, the Fisheries Division did not randomly sample lakes. However, the ﬁsh
growth surveys used in this analysis represent a large sample of public lakes (surface area
> 20 ha) distributed across the entire state (Figure 1). We restricted our analyses to mean
length at age 2 and 3 for each species because the reliability of ﬁsh aging decreases with

increasing age (Ricker, 1975) and because the growth of early age classes of ﬁshes is an

45

important factor in determining predator-prey and competitive interactions, which can
affect species distributions, Size-structure, and population dynamics (Ekliiv and Hamrin,
1989; Diehl and Eklév, 1995; Persson et al., 1996).

Water quality data were obtained from the US. Environmental Protection Agency’s
data storage and retrieval system (STORET). All data were collected by the Michigan
Department of Environmental Quality from public lakes greater than 20 ha during 1974 -
1984. We extracted from the database those variables we hypothesized would affect ﬁsh
growth rates, including Secchi depth, water color, total phosphorus, total nitrogen,
chlorophyll a, and alkalinity (Table II). All data are summer (July, August, and
September) values collected from the epilimnion. Growing degree days (GDD) were also
calculated for each lake as the sum of the amounts that daily average air temperature
exceeded a base of 10°C (MDNR 2003). Growing degree days are based on 30 yr average
(1951 — 1980) air temperature records (http://www.climatesource.com) and calculated as
an area-weighted average for each lake to represent a proxy for the thermal conditions
experienced by aquatic organisms throughout the state. Air temperature was used instead
of water temperature because it was more readily available and is correlated with ﬁsh
growth (McCauley and Kilgour, 1990).

Landscape data consisted of measures of lake morphometry and lake connectedness
(i.e., landscape position, Riera et al., 2000). Lake morphometry data were obtained from
a lake polygon coverage for the state of Michigan (MDNR 2003) and include lake area,
perimeter and SDF, which is deﬁned as the ratio of the length of the Shoreline to the
circumference of a circle of area equal to that of the lake (Wetzel, 2001) and is an

indicator of lake shoreline complexity (Table 11). Lake mean depth was calculated by

46

overlaying a grid of points on bathymetric lake maps and calculating the average depth as
the average depth value of all points (Omemik and Kinney, 1983). This approach was
veriﬁed by comparing values to those calculated by measuring the volume of each depth
contour for a sub-sample of lakes (Spence Cheruvelil, unpublished data). Each lake was
classiﬁed according to its hydrologic connectivity as visible on 1:100,000 scale maps as
(1) a seepage lake, with no connections to other surface waters, (2) a lake connected only
to streams, or (3) a lake connected to lakes and streams. We calculated ecoregion and
watershed averages of the covariates listed in Table II, which were measured at the local
lake scale. These averages were then used as covariates to explain any Si gniﬁcant
between-class variance in ﬁsh growth. Therefore, we had water quality and
morphometric covariates representative of both local and regional scales. We used
ecoregion sections in the analysis as deﬁned by Albert (1995) which are primarily based
on long-term climate records. We used 8-digit HUS for our major river watershed
delineation (Seaber et al., 1987; Figure l).
2.2 Statistical analysis

In our analyses, lakes comprised the units of analysis and each lake was represented
once within the 10 yr period. If a lake was sampled in multiple years, the sampling year
with the most data was retained in the analysis. If a lake was sampled more than once in a
season within a year (e. g., sampled twice in the spring), the average of the mean length at
age was calculated and the total number of ﬁsh contributing to the mean was recorded.
However this rarely occurred; less than 5% of the lakes in each dataset were sampled

more than once per year.

47

To accommodate possible dependency among lakes within ecoregions and
watersheds, we employed a multilevel mixed modeling approach which enabled us to
partition the variance in mean length at age within and between ecoregion sections and
watersheds and to examine the importance of water quality and landscape features in
predicting mean length at age within ecoregion sections (Raudenbush and Bryk, 2002). A
separate analysis was performed for each species/age combination. For each analysis,
mean length at age was the dependent variable and the number of ﬁsh contributing to the
mean was used as the weighting factor.

2.2.1 Model building

Because each dataset consisted of a somewhat different suite of lakes (and
watersheds for the watershed analyses; Table I), a general model building strategy was
followed for each species/age dataset. First, descriptive statistics were generated to
examine each dataset for outliers and for collinearity among covariates. The assumption
of normality was assessed for each covariate by examining normal probability plots.
Non-normally distributed covariates were log-transformed to accommodate the
assumptions of normality and homogeneity of variance. Second, an unconditional means
model was ﬁtted to provide baseline variance estimates which were used to calculate an
intraclass correlation coefﬁcient, which measures the proportion of variance in mean
length at age that is between ecoregion sections and watersheds (the level-2 units). The
unconditional means model can be viewed as a two-level model as follows, using
ecoregions as the level-2 unit:

(1) Level-l model: Yij -_- 1601' + rij

48

where Yij is the mean length at age for a Species in lake i in ecoregion j, ﬂoj is the mean

outcome for the jth ecoregion, ’1] is the level-l error, where "ij ~ N (0,0'2) ,

andO'2 represents the within-ecoregion variability in mean length at age.

(2) Level-2 model: ﬂoj = 700 + uoj
Where 700 represents the grand mean of mean length at age for all ecoregions, uo j is the
random effect associated with ecoregion j, and uoj ~ N (0, 100 ) , and too represents the

between-ecoregion variability in mean length at age. The combined unconditional model

is therefore:
(3) Yij =700 +“0j +6]

The intraclass correlation coefﬁcient can then be calculated as follows:

(4) t3: 2°00 /(f00 +52)

As a third step, because the sampling season will affect mean length at age estimates, we
controlled for season by including dummy variables for ﬁsh collected in the spring,
summer, fall, and winter. Each level-1 covariate was then added separately as a ﬁxed
effect (covariates were added as ﬁxed effects because of small sample sizes within
ecoregions) to the model that controlled for the season to identify Signiﬁcant covariates
(or—level = 0.05). After Signiﬁcant, non-correlated level-1 covariates were identiﬁed,
those covariates were included in a single model. With the addition of each covariate, the
more complex model was compared to the simpler model using a likelihood ratio test.
Furthermore, all continuous covariates were grand-mean centered to aid in model
interpretability. The general form of the ﬁnal models is as follows, using ecoregions as

the level-2 unit:

49

Q
(5) Level-l: Yij =30]: +ﬂ1j(summer)+ﬂ2j(fall)+ﬂ3j(winter)+Z] ﬂququ +ry'
q:

where summer, fall, and winter are dummy variables for sampling season (spring is the

reference category) and Q is the number of level 1 covariates. If X qij was a continuous

variable, it was grand mean centered by subtracting it from the grand mean of all
observations (X (”j — X Q“) .

s
(6) Lem-2150; : 700 +220ng +u0j-ﬂ1j = how-ﬁg =7q0

s=l

where 705 is the effect of ecoregion-level covariates (W Sj ) on the adjusted mean
(ﬂoj ) after controlling for season of sampling and any differences among lakes due
to X1...XQ . Thus, the level-1 model models mean length at age as a function of lake-

level covariates and the level-2 model models the average mean length at age of each
ecoregion as a function of ecoregion-level covariates. For example, if the Signiﬁcant
variation in mean length at age occurred among ecoregions, then ecoregion attributes
(e.g., ecoregion average lake total phosphorus) were used to try to explain that variation.
The unconditional model (equations 1 and 2) and the two-level model described above
(equations 5 and 6) were also used for the watershed analyses. However, because the
analysis of within-class variation was restricted to ecoregion analyses, equation 5 only
included the covariates to control for season of sampling (i.e., we were interested in
determining which watershed-level covariates could explain between-watershed
variability in mean length at age after controlling for season of sampling at level-1). After

the ﬁnal model was selected, homogeneity of variance was assessed by examining scatter

50

plots of the residuals against predicted values and histograms of the residuals. All

analyses were performed using the SAS MIXED procedure (SAS Institute Inc., 2000).
3. Results

3.1 Explaining between-ecoregion/watershed variation

Mean length at age for all species varied considerably (Figure 2). For all ecoregion
analyses, between-ecoregion variance estimates in mean length at age were not
signiﬁcant (Table III). For those analyses where the between-ecoregion variability was
not estimated as zero, the intraclass correlation coefﬁcients ranged from 0.04 — 8.4%,
with most < 2% (Table 111). Because the between-ecoregion variance estimates were
nonsigniﬁcant, all models were unconditional at level-2. For the watershed analyses,
there were signiﬁcant between-watershed variance estimates for ages 2 and 3 northern
pike and age-2 yellow perch; however, the total variation between watersheds was small,
ranging from 1.8 ~ 3.7% of the total variance (Table IV). Therefore, conditional level-2
models were constructed for these three datasets to determine which watershed-level
attributes could explain between-watershed variance in mean length at age. All other
between—watershed variance estimates were nonsigniﬁcant (Table IV).

Watershed average chlorophyll a explained all of the variance between watersheds
for ages 2 and 3 northern pike (Table V). Contrary to our predictions, for age-2 and age-3
northern pike, as watershed average lake chlorophyll a increased, watershed average
mean length at age decreased. No watershed-level covariates were signiﬁcant for
predicting between-watershed variance in age-2 yellow perch mean length at age.

3.2 Explaining within-ecoregion variation

51

After controlling for the effects of sampling season, water quality and landscape
covariates explained between 2 — 23% of the variability in mean length at age within
ecoregions (Table VI). However, we were unable to explain any variation in mean length
at age for age-2 largemouth and smallmouth bass and age-3 walleye. The estimated
intercepts can be interpreted as the mean length at age for ﬁsh sampled in the spring from
a lake with characteristics equal to the grand mean of the Signiﬁcant covariates. For

example, the )700 estimate for age-2 northern pike is 466 mm. This is the estimated mean

length at age-2 for northern pike sampled in the spring from a lake with total nitrogen
equal to 577 ug°L", water color of 13.7 platinum-cobalt units, and a mean depth and lake
area of 4.6 m and 404.6 ha, respectively (values from Table II).

3.3 Consumption

We hypothesized that ﬁsh mean length at age would increase with measures of lake
productivity and Shoreline complexity, and would be highest in large, Shallow lakes, and
lowest in isolated seepage lakes. Consistent with our initial hypothesis, mean length at
age increased with increasing lake productivity (e.g., total nitrogen, total phosphorus,
Chla); Signiﬁcant, positive relationships existed for age-2 and 3 bluegill, age-3
smallmouth bass, age-2 yellow perch, and ages-2 and 3 northern pike (Table VI).

Lake area and mean depth were signiﬁcant for several species; however, the Sign of
the coefﬁcient varied among analyses. When lake area was signiﬁcant, mean length at
age generally increased with increasing lake area (e. g., for age-2 pumpkinseed, ages-2
and 3 northern pike). However, mean length at age decreased with increasing lake area
for age-2 bluegill. Also consistent with our hypotheses, mean length at age for ages-2 and

3 pumpkinseed decreased with increasing mean depth. However, mean length at age for

52

age-2 northern pike increased with increasing mean depth. Shoreline development factor
was only signiﬁcant in one analysis (age-2 yellow perch), with mean length at age
decreasing with increasing Shoreline complexity. A lake’s hydrologic position was not
signiﬁcant in predicting mean length at age for any analysis.
3.4 Metabolic costs

We hypothesized that direct and indirect effects of temperature would be a primary
inﬂuence on metabolic processes and subsequently on growth. We speciﬁcally
hypothesized that mean length at age would be positively correlated with GDD and
negatively correlated with mean depth due to a larger volume of cooler water and a
potentially shorter growing season in deep lakes. Contrary to our predictions, GDD was
negatively correlated with mean length at age for age-2 bluegill and age-3 pumpkinseed.
However, mean length at age for age-3 yellow perch was positively correlated with GDD.
Our hypothesis with regards to mean depth was supported in two of the three analyses
(age-2 and 3 pumpkinseed) in which mean depth was a Si gniﬁcant covariate (see above,
Table VI).

4. Discussion

4.1 Explaining between-ecoregion/watershed variation

Variance in mean length at age between ecoregion sections for all species was not
Signiﬁcant, while between-watershed variance estimates were only signiﬁcant in three
analyses. These results indicate that ecoregions and HUC8 watersheds were ineffective in
partitioning variability in mean length at age. Other geographic grouping factors should
be investigated to determine their effectiveness in classifying lakes based on

demographic data.

53

Although it is difﬁcult to hypothesize causal mechanisms for the unexpected
signiﬁcant negative relationship between watershed average chlorophyll a and watershed
average age-2 and age-3 northern pike mean length at age, it is likely due to the spatial
distribution of this covariate in the landscape (i.e., Spatial autocorrelation). For example,
watersheds with higher average lake chlorophyll a levels are located in the southern
portion of the Lower Peninsula of Michigan, while watershed averages for chlorophyll a
are lower in the northern Lower and Upper Peninsulas. This suggests that on average,
watersheds in the northern Lower Peninsula and Upper Peninsula of Michigan have
larger mean length at age-2 and 3 northern pike as compared to the southern part of the
state. Therefore, the watershed groupings may be identifying a latitudinal gradient in pike
mean length at age. The actual mechanism behind this relationship cannot be determined;
however, other unmeasured variables that potentially vary from south to north could be
responsible, such as ﬁsh density. Nonsigniﬁcant between-watershed variance estimates
for other species-age combinations are likely partly due to small sample sizes. For
example, once all watersheds with less than three lakes were excluded from analysis the
sample sizes were often reduced substantially.

The ecoregion analyses suggest that the use of ecoregions as a framework to manage
ﬁsh populations, especially with respect to mean length at age, is not appropriate. Our
watershed analyses also suggest that HUC8 watersheds are of limited use as a spatial
framework for classifying lakes based on mean length at age. Although signiﬁcant
between-watershed variance estimates were obtained for 3 analyses, the proportion of the
total variance that was between watersheds was less than 4% in all cases. Van Sickle and

Hughes (2000) examined the ability of watersheds to group aquatic vertebrate

54

assemblages in western Oregon streams and concluded that watersheds did have utility
for classifying stream vertebrates; however, their ability to classify assemblages was
likely due to spatial autocorrelation effects, as was evident in our watershed analysis. Van
Sickle and Hughes (2000) also concluded that geographic classiﬁcations can be expected
to account for only a small portion of the total variance in stream vertebrate communities,
which is in agreement with our results regarding ﬁsh mean length at age data.

Studies that have evaluated the ecoregion framework using lake ecosystems have
been equivocal to date. J enerette et al. (2002) concluded that ecoregions were relatively
ineffective at minimizing variability in lake water quality in the northeast United States.
In contrast, Johnson (2000) found that ecoregions performed relatively well when
discriminating between measures of species richness and diversity in littoral
macroinvertebrate assemblages in Swedish lakes. The ecoregions used in the study by
Johnson (2000) spanned a larger geographic region, from arctic-alpine to nemoral regions
characterized by deciduous forests, compared to those used by J ennerette et al. (2002)
and those used in our study. This broad geographic range likely contributed to the
differences found in invertebrate assemblages. In fact, most differences occurred between
the ecotone that delineated northern and southern forests types (Johnson 2000). It could
be argued that if our analysis were performed using a landmass equal in size and
geographic diversity to that used by Johnson (2000), we would detect signiﬁcant
between-ecoregion and between-watershed variability due to large differences in growing
conditions over such a broad geographical area. At smaller scales, however, such as the
state-level, ecoregions and HUC8 watersheds are of limited use in partitioning variance

in ﬁsh mean length at age.

55

The poor performance of ecoregions in our study is partly due to the fact that each
ecoregion is composed of a relatively large land area relative to the entire study area of
Michigan. Therefore, even though an ecoregion is deﬁned as a relatively homogenous
landscape, in our case there was still substantial variability in growing degree days,
geology, soils, etc. within ecoregions, which may have contributed to the relatively large
amount of variability within ecoregions in ﬁsh mean length at age. Watersheds were of a
smaller area as compared to ecoregions; however, they were also relatively ineffective at
grouping similar lakes, ﬁrrther demonstrating the need to better understand sources of
variability in ﬁsh growth. Another contributing factor to large within-ecoregion and
within-watershed variability is the alteration of these lake ecosystems by anthropogenic
disturbances and activities that may have removed any or a substantial amount of Spatial
patterns in ﬁsh growth rates that may have previously existed (McCormick et al., 2000).
Given this large amount of variability within these classiﬁcation systems, future research
should focus on alternative ways to classify lakes, perhaps at a smaller spatial scale or by
using different grouping criteria, in order to group ecologically similar lakes for
management and conservation purposes.

4.2 Explaining within-ecoregion variability

We explained 2 — 23 % of the variability in mean length at age within ecoregions
using lake morphometry and water quality variables. This amount of variation lies within
the range found in other studies. For example, Tomcko and Pierce (2001) were able to
explain 16 — 33% of the variation in bluegill growth using lake morphometry and water
quality variables in Minnesota lakes.

4.3 Consumption

56

In 6 of 14 analyses, mean length at age was positively associated with measures of
lake nutrient status. Tomcko and Pierce (2001) also found bluegill length at ages 1 — 6 to
be positively correlated with lake productivity. Greene and Maceina (2000) found the
grth of age-0 largemouth bass was faster in eutrophic as compared to less productive
reservoirs in Alabama. Although causal mechanisms cannot be identiﬁed from these
studies, these patterns are likely due to higher prey abundance or production in more
productive systems.

Morphometric characteristics were important for predicting mean length at age for
several species. The relationship between mean length at age and lake area and depth for
age-2 pumpkinseed was consistent with our hypothesis that mean length at age would be
highest in large, Shallow lakes. This Species Spends a majority of its time in nearshore
waters, using these areas for foraging on littoral prey such as gastropods (Huckins, 1997).
Therefore, a potential mechanism for this relationship is with increasing mean depth,
pumpkinseeds experience a decrease in the amount of foraging habitat, resulting in
slower growth rates in deeper lakes. Also, deeper lakes warm up at a slower rate as
compared to shallower lakes; thus pumpkinseed in deeper lakes may experience a shorter
growing season as compared to shallower lakes that warm up more rapidly in the spring.
Mean length at age for age-3 pumpkinseed also showed a negative relationship with
mean depth; however, lake area was not a Signiﬁcant covariate. Contrary to our
predictions, mean length at age for age-2 yellow perch was negatively associated with
SDF. It is unclear what mechanism is responsible for this relationship. One possibility is
that SDF covaries with another controlling factor. However, in this analysis SDF was not

signiﬁcantly correlated with any other lake morphometry or water quality covariate,

57

suggesting that SDF may be correlated with a covariate that was not used in this study.
Alternatively, because this study relies on variables that are surrogates for hypothesized
mechanisms, there is an increased probability of chance correlations a’eters et al., 1991),
which may explain the Signiﬁcance of SDF in this analysis.

Northern pike length at ages-2 and 3 was positively related to lake area. Contrary to
our initial hypothesis, mean length at age for age-2 northern pike also was positively
related to mean depth. As northern pike grow, their depth preference changes, with older
ﬁsh utilizing deeper water and larger individuals using a wider range of depths compared
to smaller individuals (Casselman and Lewis, 1996). Therefore, large lakes and lakes
with a variety of depth habitats may provide conditions conducive to faster growth. Also,
prey diversity and abundance may be higher in these larger, more productive lakes
providing a wider forage base for northern pike.

4.4 Metabolic costs

Contrary to our predictions, mean length at age was negatively related to GDD for
age-2 bluegill and age-3 pumpkinseed. The reasons for these negative relationships are
unknown. However, because GDD was only Signiﬁcant in three models (positively
associated with mean length at age-3 yellow perch) it may indicate that the GDD data did
not accurately represent the thermal conditions experienced by the ﬁsh populations. The
GDD data used in these analyses were a 30-yr average and because annual temperature
variability can be high, this long-term average may have attenuated any affect of
temperature on ﬁsh growth rates. Alternatively, lakes with high GDD may differ in
angling pressure or other biotic or abiotic factors we were unable to measure as compared

to lakes with lower GDD.

58

Also consistent with our initial hypothesis, a large amount of within-ecoregion
variability in mean length at age was unaccounted for by water quality and morphometric
characteristics. Other factors such as ﬁsh density and exploitation, which can greatly
inﬂuence growth of ﬁshes, were unaccounted for in this analysis and may prove useful in
predicting ﬁsh growth rates in future studies. For example, Drake et al. (1997) found
higher growth of brood-guarding bluegill in lakes with low angling effort as compared to
lakes with higher angling effort. Pierce et al. (2003) found that northern pike density
explained 36 — 57% of the variation in mean back-calculated lengths at ages 2 — 5 for
northern pike populations in north-central Minnesota lakes. This suggests that classifying
lakes based on demographic characteristics may be more difﬁcult compared to
classifying lakes based on species assemblages or water quality variables, especially
when using landscape characteristics to build the classiﬁcation scheme. For example,
variance in lake water chemistry variables was partitioned for Michigan inland lakes
using HUC8 watersheds, with Signiﬁcant among-watershed variance estimates ranging
from 6 to 67% of the total variance. Landscape features were then able to explain
signiﬁcant variation in water quality variables at both the local and watershed scales
(Spence Cheruvelil, 2004). Furthermore, the classiﬁcation of waterbodies should be
based on multiple demographic characteristics; however, this will not be possible until
such data are routinely collected and become widely available. The identiﬁcation of lakes
with Similar demographic properties would facilitate regional management of aquatic
populations.

4.5 Study limitations

59

Although we can learn much from the results in our study, there are some limitations
due to the use of existing historic data. For example, the lack of standardized sampling
protocols and often incomplete or summary records limited the scope of our analyses and
clouded the interpretation of our results. The mean length at age data were collected over
a ten year period, which allowed us to expand the spatial scale of our analyses, but also
added temporal variability to our analyses. To determine if temporal trends inﬂuenced
our ﬁndings, we ran the models with sampling year as a covariate. The parameter
estimates for sampling year were rarely signiﬁcant and when they were, they did not
account for much additional variability, nor did they change the results presented here.
Also, the clear identiﬁcation of mechanisms and processes responsible for the observed
patterns is not possible in our study (Peters et al., 1991). Given these limitations,
however, we were still able to account for Si gniﬁcant within-ecoregion variation in mean
length at age using lake morphometry and water quality characteristics in 11 out of 14
analyses, suggesting that the use of data collected from a statistically valid sampling
program (Hayes et al., 2003) will likely provide further insight into the effects of lake
morphometry and water quality on ﬁsh growth. Although there are limitations to the use
of historic data, this approach also has advantages. For example, the ability to examine
patterns at such a large spatial scale would likely not be possible otherwise. This
approach is also useful in generating new hypotheses and prioritizing research questions
to address in future research (Peters et al., 1991).

4.6 Conclusions
We determined that local lake characteristics can explain a signiﬁcant amount of

variation in mean length at age; however, the relative importance of abiotic factors versus

60

biotic interactions remains unclear. A better understanding of the importance of abiotic
and biotic factors and how they affect ﬁsh populations is needed if the classiﬁcation of
lakes based on demographic properties is going to be successfully implemented for
regional aquatic conservation and management. The relative importance of these factors
in affecting demographic properties of aquatic communities is species- and scale-
dependent. Therefore, it will be necessary for management agencies to have well deﬁned
goals with respect to the target Species and the Spatial scale of management prior to the
development of a classiﬁcation system. F urtherrnore, for regional management to be
effective, agencies must design and implement statistically valid sampling programs with
standardized sampling protocols (Hayes et al., 2003). Our analysis also demonstrates that
ecoregions or watersheds (i.e., HUS), are not effective in grouping lakes with similar ﬁsh

growth rates.

61

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between hydroecoregions in south-westem France’, Internat. Rev. Hydrobiol. 89, 79-
87.

SAS Institute Inc.: 2000, SAS/STAT user '5 guide, SAS Institute Inc., Cary, NC.

Seaber, P. R., Kapinos, F. P. and Knapp, G. L.: 1987, Hydrologic Unit Map, USGS
Water-Supply Paper 2294.

Shuter, B. J ., Jones, M. L., Korver, R. M. and Lester, N. P.: 1998, ‘A general, life history
based model for regional management of ﬁsh stocks: the inland lake trout (Salvelinus
namaycush) ﬁsheries in Ontario’, Can. J. Fish. Aquat. Sci. 55, 2161-2177.

Spence Cheruvelil, K.: 2004, Examining lakes at multiple spatial scales: predicting fish
growth, macrophyte cover and lake physio-chemical variables, PhD thesis, Michigan
State University.

Tomcko, C. M. and Pierce, R. B.: 2001, ‘The relationship of bluegill growth, lake
morphometry, and water quality in Minnesota,’ Trans. Am. Fish. Soc. 130, 317-321.

Van Sickle, J. and Hughes, R. M.: 2000, ‘Classiﬁcation strengths of ecoregions,
catchments, and geographic clusters for aquatic vertebrates in Oregon’, J. N. Am.
Benthol. Soc. 19, 370-384.

Waide, R. B., Willig, M. R., Steiner, C. F., Mittelbach, G., Gough, L., Dodson, S. I.,

Juday, G. P. and Parrnenter, R.: 1999, The relationship between productivity and
species richness’, Annu. Rev. Ecol. Syst. 30, 257-300.

Weatherley, A. H.: 1972, Growth and ecology of fish populations, Academic Press Inc.,
London.

Werner, E. E. and Hall, D. J .: 1977, ‘Competition and habitat Shift in two sunﬁshes
(Centrarchidae)’, Ecology 58, 869-876.

65

Wetzel, R.G.: 2001 , Limnology lake and river ecosystems 3rd edition, Academic Press,
San Diego, CA 92101.

Zweifel, R. D., Hayward, R. S. and Rabeni, C. F.: 1999, ‘Bioenergetics insight into black

bass distribution Shifts in Ozark border region streams’, N. Am. J. Fish. Manage. 19,
192-197.

66

TABLE I
Sample Size ranges (number of lakes per ecoregion or 8 digit hydrologic unit (HU)) and
the number of HUS used in the analysis of each species and age combination. The number

of ecoregions used in the analyses was always four

 

 

Ecoregion section 8-digit HUS Number of HUS
Species (age)
Bluegill (2) 10 - 90 3 - 21 21
Bluegill (3) l3 - 102 3 - 26 24
Pumpkinseed (2) 10 - 35 3 - 8 l3
Pumpkinseed (3) 13 - 49 3 - 10 16
Largemouth bass (2) 3 - 49 3 - 23 21
Largemouth bass (3) 4 - 96 3 - 23 22
Smallmouth bass (2) 9 - 35 3 - 7 10
Smallmouth bass (3) 9 - 33 3 - 7 9
Yellow perch (2) 22 - 74 3 - 19 22
Yellow perch (3) 22 - 69 3 - 19 23
Walleye (2) 6 - 28 3 - 6 7
Walleye (3) 4 - 24 3 - 8 8
Northern pike (2) ll - 65 3 - 15 19
Northern pike (3) 9 - 69 3 - 16 19

 

67

TABLE 11

List of water quality and landscape covariates used in the analyses. Means for each

species/age combination are followed by ranges in parentheses. SDF = shoreline

development factor, GDD = growing degree days (see Methods for description)

 

 

Species (age) Secchi depth Color 1 Total Total Chlorophyll
(m) (platinum- nitrogenl phosphorus1 al (ug0L'1)
cobalt units) (pg-L”) (ug°L'l)
Bluegill (2) 2.9 12.0 644.7 20.1 6.3
(0.5-7.3) (LO-54.0) (112.0-2756) (l .0-155.0) (0.5-66.0)
Bluegill (3) 3.0 11.8 640.3 21.1 6.4
(0.5-7.3) ( l .0-54.0) (112.0-2756) (1 .0-155.0) (0.2-66.0)
Pumpkinseed 2.8 13.8 61 1.4 21.2 6.5
(2) (O.5-7.3) (2.0-61 .0) (112.0-2756) (l .0-155.0) (0.7-35.0)
Pumpkinseed 2.9 13.2 592.3 19.9 5.8
(3) (05-73) (1 .0-61 .0) (112.0-2756) (1 .0-155.0) (0.2-35.0)
Largemouth 3 .0 1 1.5 645 .3 19.7 6.4
bass (2) (05-78) (1 .0-75.0) (112.0-1717) (LO-155.0) (0.5-66.0)
Largemouth 3.0 1 1.7 650.0 21.0 6.6
bass (3) (0.5-7.0) (l .0-75.0) (130.0-2756) (l .0-155.0) (0.5-66.0)
Smallmouth 3.4 1 1.4 439.2 14.1 4.3
bass (2) (0.9-7.3) (1 .0-80.0) (92.0-850) (IO-73.0) (0.2-32.0)
Smallmouth 3.5 13.0 454.8 17.0 5.3
bass (3) (0.6-7.3) (1 .0-80.0) (92.0-1130) (1 .0-1 18.0) (0.2-60.0)
Yellow 3.1 12.7 572.0 18.5 6.3
perch (2) (06-78) (LO-80.0) (112.0-1430) (1 0127.0) (0.5-66.0)
Yellow 3.1 12.6 579.1 19.4 6.1
perch (3) (05-78) (1 080.0) (111.0-2756) (l .0-155.0) (0.5-66.0)
Walleye (2) 3.1 14.3 484.5 21.0 7.3
(06-73) (1 .0-80.0) (112.0-1406) (2.0-118.0) (0.2-60.0)
Walleye (3) 2.9 15.3 515.7 22.0 8.2
(O.6-7.3) (LO-80.0) (l 12.0-1406) (2.0-118.0) (0.2-60.0)
Northern 2.8 13.7 577.1 21.1 7.4
pike (2) (05-58) (1.7-80.0) (130.0-2756) (1 .0-127.0) (0.5-66.0)
Northern 2.9 12.9 570.6 21.0 6.6
pike (3) (05-70) (1 .0-80.0) (130.0-2756) (l .0-127.0) (0.5-60.0)

 

1Variables were log-transforrned prior to analyses to accommodate the assumptions of
normality and homogeneity of variance.

68

TABLE II CONTINUED
List of water quality and landscape covariates used in the analyses. Means for each
Species/age combination are followed by ranges in parentheses. SDF = shoreline

development factor, GDD = growing degree days (see Methods for description)

 

 

Species (age) Alkalinity GDDI SDFI Mean Lake area
(mg-L'l as depth1 (m) (ha)
CaCO3)
Bluegill (2) 105.9 2344 2.2 4.8 210.7
(4.0-197.0) (1451-3121) (1 .0-6.3) (1.2-18.0) (20.9-6988)
Bluegill (3) 103.5 2354 2.2 4.7 243.4
(2.0-66.0) (1451-3121) (LO-6.3) (0.9-18.0) (20.8-6988)
Pumpkinseed 89.6 2105 2.2 4.4 270.6
(2) (4.0-190.0) (1416-2891) (1.1-4.7) (1.2-18.0) (20.8-6988)
Pumpkinseed 88.5 2122 2.2 4.4 321.6
(3) (LO-190.0) (1416-2902) (1.1-6.5) (l.2-18.0) (20.8-1988)
Largemouth 109.8 2413 2.2 4.7 188.2
bass (2) (1 .0-197.0) (1539-3121) (1.1-6.3) (1 .2-1 1.6) (20.8-3545)
Largemouth 107.5 2390 2.2 4.6 183.4
bass (3) (LO-197.0) (1539-3121) (1.1-6.3) (1 .2-1 1.6) (20.8-1848)
Smallmouth 86.3 1919 2.1 5.7 619.6
bass (2) (2.0-166.0) (1488-2747) (1.1-5.4) (1.5-20.4) (31.7-7039)
Smallmouth 85.3 1971 2.2 6.4 668.6
bass (3) (2.0-166.0) (1500-2747) (1.1-5.4) (1.5-42.4) (31 .7-7576)
Yellow 97.9 2197 2.1 5.3 373.9
perch (2) (2.0-186.0) (1416-3121) (l.0-6.5) (1.2-42.4) (20.8-7576)
Yellow 98.1 2184 2.2 5.3 370.0
perch (3) (l .0-190.0) (1451-3121) (1.0- (l.2-42.4) (20.8-7576)
6.45)
Walleye (2) 93.2 1937 2.2 5.3 786.8
(2.0-197.0) (1451-2820) (1 .2-4.7) (1.5-18.0) (30.0-7039)
Walleye (3) 83.2 1897 2.1 4.7 662.5
(2.0-197.0) (1451-2670) (1.1-5.4) (1.5-12.8) (31.7-7039)
Northern 94.7 2123 2.1 4.6 404.6
pike (2) (l .0-197.0) (1416-3121) (1.1-6.5) (1.5-18.0) (20.8-7039)
Northern 96.1 2139 2.2 4.8 396.4
J1k€(3) (l .0-197.0) (1451-3121) (1.1-6.5) (1.2-18.0) (20.9-7039L

 

1Variables were log-transformed prior to analyses to accommodate the assumptions of
normality and homogeneity of variance.

69

TABLE III

Fixed effects and variance estimates for ecoregion unconditional models. )700 =grand

mean of mean length at age for all ecoregions (mm), 6'2 represents the within-ecoregion

variability in mean length at age, TAOO represents the between-ecoregion variability in

mean length at age, and f) is the intraclass correlation coefﬁcient

(%,,D = {:00 «2100 + 6'2)

 

 

Species (age) )700 (95% conﬁdence interval) 5.2 {00a ‘ b
Bluegill (2) 108.7(105.7, 111.7)' 5820' 0.0 na
Bluegill (3) 136.0 (132.5, 139.5)’ 6596‘ 2.3 0.04

Pumpkinseed (2) 111.6 (107.2, 116.0)‘ 2748' 3.4 0.12
Pumpkinseed (3) 135.6 (130.0, 141.2)‘ 2947‘ 19.4 0.65

Largemouthbass 214.1(208.9,219.3)‘ 12014‘ 0.0 na

(2)

Largemouth bass 260.1 (242.3, 277.9)‘ 9939‘ 204.6 2.02
(3)

Smallmouth bass 203.8 (190.9, 216.7)‘ 9898‘ 89.1 0.89
(2)

Smallmouth bass 245.4 (218.7, 272.1)‘ 7175‘ 659.5 8.42
(3)

Yellow perch (2) 154.0 (145.1, 162.9). 7108' 64.1 0.89

Yellow perch (3) 171.4 (162.2, 180.6)‘ 5182‘ 72.5 1.38

Walleye (2) 330.3 (318.9, 341.6)‘ 22765‘ 0.0 na

 

70

 

Walleye (3) 379.9 (354.4, 405.4)‘ 32326' 402.3 1.23
Northernpike(2) 480.9 (455.2, 506.6)’ 37108‘ 483.3 1.28

Northempike(3) 545.3 (505.8, 584.8)‘ 34098‘ 1377 3.88

 

‘ n o a
Variance estimate Slgnlﬁcantly dlfferent from zero (P < 0.05).
a 700 of zero represents variance estimates of near zero.

bIntraclass correlation coefﬁcient was not calculated when 1:00 was estimated near zero.

71

TABLE IV

Fixed effects and variance estimates for watershed unconditional models. 700 =grand

mean of mean length at age for all watersheds (mm), 62 represents the within-watershed

variability in mean length at age, foo represents the between-watershed variability in

mean length at age, and [3 is the intraclass correlation coefﬁcient

(%,,£3 = TOO «2:00 '1' 6'2)

 

 

SPCCICS (age) )700 (95% conﬁdence interval) 6'2 i300 a . b
Bluegill (2) 110.1 (104.6, 115.5)' 5890' 57.8 0.97
Bluegill (3) 137.1 (132.9, 141.3) 11628‘ 0.0 na

Pumpkinseed (2) 106.1 (99.1, 113.2) 1566’ 70.9 4.33
Pumpkinseed (3) 134.3 (128.7, 139.8) 2608‘ 45.4 1.71
Largemouth bass 215.9 (208.5, 223.4) 14440‘ 37.4 0.26
(2)
Largemouth bass 266.2 (253.7, 278.7) 27648“ 264.9 0.94
(3)
Smallmouth bass 214.6 (196.8, 232.4) 29264‘ 0.0 na
(2)
Smallmouth bass 266.5 (246, 287) 35321‘ 0.0 na
(3)
Yellow perch (2) 152.9 (144.9, 161 .0)‘ 5578‘ 214.6‘ 3.70
Yellow perch (3) 172.1 (166.1, 178) 8954. 49.8 0.55
Walleye (2) 318.9 (291.3, 346.6) 19479’ 335.6 1.69

 

72

 

Walleye (3) 395.0 (344, 446.0) 190944' 0.0

Northern pike (2) 490.4 (470.4, 510.3)‘ 28422‘ 1046‘

Northern pike (3) 544.8 (526.9, 562.7)’ 31298' 561.6“

na

3.55

1.80

 

* a o o c a
Varlance estrmate Signiﬁcantly dlfferent from zero (P < 0.05)
a £00 of zero represents variance estimates of near zero.

bIntraclass correlation coefﬁcient was not calculated when foo was estimated near zero.

"P = 0.074, however after controlling for season of sampling there was signiﬁcant

between-watershed variation to model (1’00 = 635.48, P = 0.04).

73

TABLE V

Final multilevel mixed model parameter estimates for the watershed analysis. Summer,

fall, and winter are dummy variables for sampling season (reference category is spring).

No Si gniﬁcant between-watershed variance remained in either northern pike models after

watershed average chlorophyll a was included in the models

 

 

Species (age) Coefﬁcient (if t -value P-value Between-
watershed variance
explained (%)
Northern pike (2) 100*
Intercept 456.8 17 48.1 1 <0.0001
Summer 25.5 89 1.97 0.052
Fall 45.6 89 3.31 0.001
Winter 73.0 89 4.31 <0.0001
Chlorophyll a -7.8 89 -2.55 0.013
Northern pike (3) 100'
Intercept 508.9 1 7 62.46 <0.0001
Summer 42.3 91 3.28 0.0015
Fall 51.9 91 4.04 0.0001
Winter 80.1 91 3.90 0.0002
Chlorophyll a -10.1 91 -3.86 0.0002

 

tVariance estimates were not Signiﬁcantly different from zero (P > 0.05).

74

TABLE VI
Final multilevel mixed model parameter estimates for the ecoregion analysis. Summer,
fall, and winter are dummy variables for sampling season (reference category is Spring),
TN = total nitrogen, TP = total phosphorus, Chla = chlorophyll a, GDD = growing degree

days, SDF = Shoreline development factor, NS = no Signiﬁcant covariates

 

Species (age) Coefﬁcient df t -value P-value Total Variance
variance explained after

explained controlling for

 

(%) season (%)
Bluegill (2)
Intercept 107.2 3 30.0 <0.0001 37 14
Summer -8.1 154 -1.89 0.06
Fall 10.0 154 2.03 0.044
Winter 12.5 154 3.01 0.003
TP 6.6 154 2.98 0.003
Lake area -3.1 154 -1.97 0.050
GDD -22.5 154 -2.98 0.003
Bluegill (3)
Intercept 135.3 3 25.64 0.0001 11 2
Summer -3.0 180 -0.77 0.44
Fall 9.1 180 2.17 0.032
Winter 10.5 180 2.61 0.010
TN 7.7 180 1.99 0.048
Pumpkinseed (2)
Intercept 116.2 3 22.13 <0.001 39 18
Summer 0.7 82 0.15 0.88
Fall 14.3 82 3.18 0.002

 

75

 

Winter
Mean depth
Lake area
Pumpkinseed (3)
Intercept
Summer
Fall
Winter
Mean depth
GDD
Largemouth bass (2)
Largemouth bass ( 3)
Intercept
Summer
Fall
Winter
Color
Smallmouth bass (2)
Smallmouth bass (3)
Intercept
Summer
Fall
Winter
Chla
Yellow perch (2)
Intercept
Summer

Fall

33.5

-ll.l

5.5

134.9

-8.88

3.1

8.3

-37.7

NS

250.8

7.9

14.1

22.7

10.5

NS

224.6

13.1

41.2

33.7

9.8

136.5

15.7

23.5

82

82

82

111

111

111

111

111

158

158

158

158

53

53

53

53

175

175

4.78

-2.70

3.70

26.28

-2.22

0.80

1.00

-2.78

-2.43

22.31

1.25

1.65

3.38

2.84

15.47

1.23

3.72

2.31

2.03

19.55

2.89

3.91

<0.0001

0.009

0.0004

0.0001

0.028

0.42

0.32

0.006

0.017

0.0002

0.21

0.10

0.009

0.005

0.0006

0.22

0.005

0.025

0.048

0.0003

0.004

0.0001

27

26

18

 

76

 

Winter
TN
SDF
Yellow perch (3)
Intercept
Summer
Fall
Winter
GDD
Walleye (2)
Intercept
Summer
Fall
Winter
Alkalinity

Walleye (3)
Northern pike (2)

Intercept
Summer
Fall
Winter
TN
Color
Mean depth
Lake area
Northern pike (3)

Intercept

30.7

9.5

-l3.3

164.5

5.8

10.8

20.0

30.9

317.7

32.6

30.5

NS

466.5

6.7

43.0

67.1

56.6

-l6.0

21.1

16.4

512.5

175

175

175

179

179

179

179

48

48

48

48

124

124

124

124

124

124

124

5.07

2.08

-2.91

36.18

1.41

2.21

4.14

2.35

27.33

-0.04

1.24

2.00

-2.15

56.56

0.62

3.26

4.49

5.03

-2.28

2.42

4.43

26.58

<0.0001

0.039

0.004

<0.0001

0.16

0.028

<0.0001

0.019

0.0001

0.97

0.22

0.052

0.037

<0.0001

0.54

0.001

<0.0001

<0.0001

0.025

0.017

<0.0001

0.0001

19 6
l7 7
35 23
12 6

 

77

 

Summer

Fall

Winter

Lake area

TN

36.9

32.3

68.1

11.8

34.2

128

128

128

128

128

2.83

2.36

3.30

2.58

2.50

0.005

0.020

0.001

0.011

0.013

 

78

 

79

Figure 2

- E “.02

E “.02

5 5:5

E m<>>
- 5 um;
. E um>
- E mam
- 5 use
- 5 ms...
. 3 ms...
. E uma
- E uwa
- E can

- E 0.5

 

 

700—

600 -

500 -

400 -

300 7

see euro

0
0
2

Species (age)

80

CHAPTER 3: CAN HABITAT ALTERATION AND SPRING ANGLING EXPLAIN
LARGEMOUTH BASS NEST SUCCESS?

Abstract

Largemouth bass Micropterus salmoides nest in shallow littoral areas, making them
vulnerable to negative effects of habitat alteration due to development of lake shorelines
and ﬁshing during the spring nesting period. For instance, alteration of shorelines may
reduce the quality and abundance of nesting habitat, and the high visibility of nests and
the aggressive guarding behavior of nesting males increase their vulnerability to ﬁshing.
In 2004, we monitored nest distribution and success, and quantiﬁed local nest habitat
features and lakewide angler effort and lakeshore development patterns, in ﬁve Michigan
lakes in an effort to determine the extent to which habitat alteration and/or ﬁshing limit
the number of nests that produce swim-up fry. Lakes spanned a range of lakeshore
dwelling density (8 — 22 dwellings/km), allowing us to determine the extent to which nest
success varies within and among lakes due to local (e.g., substrate and cover) and
lakewide (e.g., dwellings/km and ﬁshing effort) factors. Surprisingly, local habitat
characteristics were not important determinants of the probability of a nest producing
swim-up fry (P > 0.05). At the whole-lake scale, however, nest success was negatively
related to dwelling density, with the probability of a nest producing swim-up fry
declining from 0.77 in the lowest dwelling density lake to 0.45 in the highest dwelling
density lake (P = 0.018). Lakewide estimates of angling effort could not explain this
difference among lakes, indicating the likely importance of quantifying angling at ﬁner
Spatial scales. Knowledge of the magnitude of anthropogenic effects and the Spatial scale

at which they operate is integral for black bass management.

81

AS keystone predators and a valued sport ﬁsh in North American lakes, black bass —
speciﬁcally largemouth Micropterus salmoides and smallmouth M. dolomieui — possess
life history characteristics that make them vulnerable to perturbations associated with
human development of lake Shorelines. These species Spawn in the Spring when water
temperatures are near or above 15°C. Males construct nests in the substrate of relatively
shallow, littoral areas often in close proximity to physical structure (Annett et al. 1996;
Hunt and Annett 2002; Wills et al. 2004). After attracting and mating with a female, male
bass guard the eggs and deveIOping fry until the brood disperses (Ridgway 1988;
Ongarato and Snucins 1993; Philipp et al. 1997). This period of parental care by males
may last more than a month (Brown 1984), during which time the male bass are highly
active and guard offspring aggressively, while feeding only opportunistically (Ridgway
1988; Hinch and Collins 1991).

Events occurring during these early life stages are important for ﬁrst year
recruitment of bass (Ludsin and DeVries 1997). Therefore, an understanding of
anthropogenic factors affecting black bass early life history is necessary to further our
knowledge of their biology and effectively manage them. Nest success, often deﬁned as
the occurrence of a nest producing swim-up fry (Philipp et al. 1997), is considered to be
an important event in the recruitment process that may affect the abundance of age-0 bass
that will ultimately survive to the ﬁrst winter (Ridgway and Shuter 1997). Although
compensatory mortality may occur, neither the magnitude of the effect on nesting
success, nor the capacity of bass populations to compensate, is fully understood.

Because bass typically nest in shallow littoral areas, human development of lake

Shorelines (i.e., lakeshore dwelling density) and associated activities may negatively

82

affect nesting success in two ways. First, removal of structure (i.e., rooted vegetation or
coarse woody material) and alteration of littoral substrate may increase risk of predation
and/or siltation (Christensen et al. 1996; Radomski and Goeman 2001; Jennings et al.
2003). For instance, Hunt and Annett (2002) concluded that male largemouth bass
selected nest-building sites near physical structure such as woody debris compared to
habitats that lacked structure, suggesting that removal of structure, through activities such
as lakeshore development (LSD), may alter bass nest distributions and ultimately
negatively affect nest success. Second, the high visibility of black bass nests and the
aggressive guarding behavior of nesting males increase their vulnerability to angling
(Ridgway 1988). Removing male bass from the nest, even for short periods of time,
reduces the male’s ability to guard the nest, which ultimately increases predation risk on
bass eggs and larvae, and increases the likelihood that the male will pre-maturely
abandon the nest, thereby negatively affecting production of successful nests (Philipp et
al. 1997; Ridgway and Shuter 1997; Suski et al. 2003).

Most studies of nesting black bass have been conducted in ponds or on a single lake
or reservoir, with the focus often on smallmouth bass (but see Philipp et al. 1997). There
is therefore a paucity of information on the potential impacts and relative importance of
LSD (and associated habitat modiﬁcation) and angling for patterns of nest distribution
and nesting success of largemouth bass within and across lakes. Furthermore, because
most previous studies examining factors affecting nesting success have only been
performed at one spatial scale, that of the local nest, it is unclear as to whether these
assorted factors operate at the local nest scale (i.e., through factors measured at the nest-

scale such as the depth of the nest), lakewide scale (i.e., through factors measured at the

83

lake-scale such as lake productivity), or both. The goals of this study were to determine
whether largemouth bass nest success varies with both local and lakewide features, and to
explore the relative importance of habitat modiﬁcation versus Spring angling to patterns
of nest success. To accomplish these goals we conducted a study examining largemouth
bass reproductive success at multiple spatial scales in six southeast Michigan lakes with a
wide range of lakeshore dwelling density (8 — 22 dwellings/km). Our primary objective
was to determine the extent to which residential LSD and habitat variables, at both local
and lakewide scales, and lakewide angling pressure affect the probability of largemouth
bass producing successful nests. AS a secondary objective, we sought to gain further
insight into our nest success ﬁndings by evaluating the Spatial distribution of bass nests
relative to natural and anthropogenic lakeshore habitat characteristics. We also highlight
the use of generalized linear mixed models, which have properties that make them useful
in the analysis of ﬁsheries data (Venables and Dichmont 2004), but have not been widely
applied in ﬁsheries to date.
Methods

Study area—We monitored Six lakes located in Washtenaw and Livingston counties
in southeast Michigan, USA during May and June 2004 to assess the importance of local
nest and lakewide- scale habitat characteristics to largemouth bass reproductive success
(Figure 1). We selected lakes that were similar morphometrically but that spanned a wide
range of lakeshore dwelling densities from 7.8 — 22.3 dwellings/km (Table 1). All lakes
were mesotrophic, stratiﬁed, and accessible to public ﬁshing.

Lake characteristics—We viewed nest success as a function of lakewide and local

characteristics. We included three whole-lake features: lakeshore dwelling density

84

(lakewide LSD), angler effort, and total phosphorus (TP; Table 2). Lakeshore dwelling
density was determined using visual observations by boat to quantify the number of
riparian dwellings within 50 m of each lake, and then dividing the number of dwellings
by lake perimeter (km). We sampled for TP using integrated epilimnetic water samples
collected using a tube sampler during the month of July. TP was measured using a
persulfate digestion (Menzel and Corwin 1965) followed by standard colorimetry
(Murphy and Riley 1962). We determined angler effort separately for May and June by
conducting two instantaneous angler counts per week in each lake (once per randomly
chosen week day and weekend day). We randomly selected (without replacement) time
of day (morning, mid-day, or evening) for each survey, and surveyed lakes in haphazard
order. During each survey, we visually assessed ﬁshing activity for all boats on the lake
from the vantage of a boat and using binoculars. We recorded the number of anglers per
boat, the location of the boat (near the shoreline or open water), and the gear type used
when possible. Following Philipp et al. (1997), we recorded an angler as potentially
targeting black bass if he/she was using tactics (ﬁshing near the Shoreline and using
appropriate lures or jigs) that could potentially catch nesting bass. We followed the
methods of Lockwood et al. (1999) to expand each survey count to an estimate of the

total number of angler hours, using the equation:

(1) E = FpAdj

pd}
where E = estimated angler hours, F = number of ﬁshable hours during the entire period,
p (e. g. weekends or weekdays during May or June), A = number of anglers, d = day, and j

= count. We calculated two estimates of lakewide angling effort (total hours/km

shoreline): all anglers and just anglers potentially targeting nesting black bass. We

85

generated separate estimates for May 8 — 28, and May 29 — June 27 because it is illegal to
target or harvest bass in Michigan lakes prior to the Saturday of Memorial Day weekend
(May 29 in 2004). Within each month, we averaged weekend estimates and also weekday
estimates, and then summed those means to generate the ﬁnal estimates for each month.
We calculated variance separately for weekend and weekday estimates (as per equation
58 in Lockwood et a1. 1999) and then summed the two values.

Nest location and reproductive success—We surveyed the littoral area for
largemouth bass nests using boats powered by electric trolling motors. We conducted
surveys at least biweekly for new nests and to examine the status of previously located
nests. Once a new nest was located, we marked it with a numbered marker and recorded
its location using a differentiated global positioning system (GPS; Trimble GeoExplorer
®). After marking the nest, we observed local nest characteristics (see below), the
presence/absence of a male bass, eggs, larvae, and/or fry, with either an aqua-scope or by
snorkeling. We considered a nest successﬁll if fry were observed actively swimming
above the nest (Philipp et al. 1997).

Nest characteristics—Once a nest was located, we recorded the dominant substrate
type (e. g., silt, sand, etc.) and the presence of cover (boulders, woody debris,
macrophytes) within a 1 m radius of the nest, along with the depth of the nest. We also
recorded the development type of the nearest shoreline (local LSD type) as either
undeveloped, developed maintained (developed, but with no retaining wall, e. g., a
Shoreline with a maintained lawn), or developed retained (a shoreline with riprap or a
retaining wall). Using the GPS locations, we calculated distance to shore. Also, we

determined wind exposure for each nest from existing GIS coverages. We classiﬁed each

86

nest as having high or low wind exposure based on the location of the nest in relation to
the prevailing SW winds (Table 2). In addition, we used the existing GIS coverages to
quantify the total amount of spawning habitat with regards to local LSD type and wind
exposure.

Statistical analyses

Nest success.— We omitted nests from our analysis if their fate could not be
determined. We only included predictor variables in our analysis for which we had
mechanistic hypotheses regarding their likely effects on bass nest success. We recognized
two general mechanisms through which local habitat features and/or angling pressure
could affect nest success. First, habitat features may directly affect nest success through
physical and chemical constraints on egg survival. Second, local habitat features and
angling pressure, in combination, may indirectly inﬂuence the vulnerability of nests to
failure through parental male abandonment and nest predation. Two additional factors
potentially affecting nest success must also be factored into the analysis. First, nest site
features not subject to anthropogenic alteration may inﬂuence nest success. Second,
attributes at the whole-lake scale may affect the average probability of nest success for a
given lake.

We used a generalized linear mixed model to determine if local nest Site
characteristics or whole-lake characteristics affected the probability of a largemouth bass
nest successfully producing swim-up fry (Table 2). Generalized linear mixed models
(GLMMS) are extensions of generalized linear models (GLMS) with the inclusion of
random effects. Fixed effects models (e.g., GLMS) assume that all observations are

independent of each other, and thus are not appropriate for analysis of hierarchical or

87

correlated data structures (see Wagner et al. in press). In our analysis, GLMMS are used
to accommodate dependence among observations within lakes and to accommodate the
hierarchical nature of the data (e.g., bass nests nested within lakes). Both GLMS and
GLMMS are extensions of the general linear model that allow response variables to
follow any probability distribution in the exponential family (e. g., normal, binomial, and
Poisson). GLMMS are composed of three model components including: (1) a linear
predictor that is a linear combination of regression coefﬁcients; (2) a link function that
relates the mean of the response data to the linear predictor; and (3) a response
distribution from the exponential family of distributions. For a more detailed overview of
the theory and use of GLMS and GLMMS in ﬁsheries research see Venables and
Dichmont (2004).

To begin, we built separate models of nest success as a function of each covariate
hypothesized to affect nest success. After Signiﬁcant, uncorrelated predictors were
identiﬁed we then included them in a Single model. The model can be described as a two
level model, with the ﬁrst level modeling the probability of a nest succeeding as a
function of local nest characteristics and the second level modeling the average
probability of nest success for each lake as a function of lake characteristics. The
probability of success was assumed to be Bernoulli distributed. The response

variable er'j) is binary, where Yij = 1 if nest i in lake j was successful and Yij = 0 if nest i

in lake j failed. The probability of success of nest i in lake j is deﬁned as (pl-j = Pr (Yij = l).

The general form of the two-level model is as follows.

Level 1 model:

88

Q
(2) ’79 = For + Z ﬂquij
q=1

where 77,-j is the log odds of success for nest i in lake j, 77,-j is the level 1 link function

(logit link), 77,]- : log[1—¢L] , 601- is the mean log odds of success for lake j, ,qu is the

’1

effect of covariate X qij on the log odds of success, q = 1 to Q, with Q equaling the total

number of level 1 covariates.
Level 2 model:
S
(3) ﬂoy' =700 + Z7stsj +qu ~61): = 710’°'°ﬂqj = 7q0
s=1

where 700 is the average log odds of success when all level 2 covariates (Wstjare equal to

zero (3 = 1 to S, with S equaling the total number of level 2 covariates) and represents a

grand mean value, 75]- is the effect of covariate Wsj on the average log odds of success,

uo j is the random effect associated with lake j, and uoj ~ N (0, too) , where 2:00 is the

variance between lakes in lake-average log odds of success. A predicted log odds of
success can then be converted to a probability by calculating

1
(4) (0y _ 1+ exp{— 771]}

 

To provide further illustration of the model structure, assume that we are interested
in modeling nest success as a function of a single nest level covariate (level 1), nest depth
and a single lake level covariate (level 2), lakeshore development (LSD). The model can
be viewed in two levels and in combined form as follows, with parameters and subscripts

deﬁned as above:

89

Level 1:
(5) r7,- = poj + ,Blj(nest_depth)ij
Level 2:
(6)/301' = 700 + 701050),- +“0j’ ﬂlj = 710
Combined form:
(7) 77g- = 700 + 7100795t _deplh),_-,~ + 701(LSDlj + “0 j

We performed generalized linear modeling using the GLIMMIX macro of the
MIXED procedure in SAS (SAS Institute Inc. 2000). When using many generalized
linear models, there is a possibility that the conditional variance of the errors may differ
from theory. The GLIMMIX macro allows for the possibility that the conditional error
variance differs from theory by adding an additional parameter to the conditional

variance, the extra-dispersion parameter (4;). If (I; < 1, the distribution of the conditional

errors is said to be underdispersed and if (f > 1 the distribution is overdispersed. If (ii is

close to 1, the variance is consistent with the assumed distribution (Littell et al. 1996).
Underdispersion can lead to inﬂated standard errors, while overdispersion can lead to
underestimated standard errors and thus inﬂated type I error rates. Therefore, we assessed
the ﬁnal model for over- or under-dispersion by examining the extra-dispersion
parameter.

Nest habitat features—Because we hypothesized that nest depth, substrate type, and
the presence/absence of cover would be inﬂuenced by anthropogenic effects associated
with LSD, we modeled these nest attributes as a function of local LSD type and lakewide

LSD. For nest depth, we used a two-level mixed model, with lake as a random effect and

90

local LSD type and lakewide LSD as ﬁxed effects. Local LSD type was included in the
model by designating developed maintained and developed retained shorelines as dummy
variables (undeveloped shorelines were reference cells). For substrate type and the
presence/absence of cover, we used a generalized linear mixed model, with predictor
variables designated as above. The analyses were preformed using the GLIMMIX macro
and MIXED procedure in SAS (SAS Institute Inc. 2000).

Nest distribution—To explore if patterns of nest distribution relative to available
habitat, we used a chi-square goodness of ﬁt test to determine if habitat used for
constructing nests was signiﬁcantly different from the distributions of available habitat.
We reasoned that if most nests were located in a relatively rare habitat type, it would be
indicative of high nest site selectivity and potential limitation of preferred nesting habitat.
Habitat was categorized into proportions of each development type and wind exposure
combination. The analysis was performed for each lake individually.

Results

A total of 178 largemouth bass nests were located during the study period (Table 3).
The number of largemouth bass nests located in each lake ranged from 0 (in Blind Lake)
to 51 (in North Lake). Because largemouth bass did not Spawn in Blind Lake it was
excluded from further analyses. Largemouth bass initiated nest building in early May,
with the number of nests peaking in all lakes in mid-May. Both the last, new nest and the
last successful nest were located on 8 June.

Nest success—To determine the magnitude of variation among lakes in the
probability of nest success, we estimated an unconditional model, with no predictors at

either the nest or lakewide level. The average log-odds of success across lakes was )900 =

91

0.26. Therefore, the probability of success in an “average” lake, with a random effect of

1in = 0, was 0.56. The variance between lakes in lake-average log odds of success was

estimated as foo = 0.193; thus we would expect that 95% of the lakes in our study have a

probability of nest success between 0.35 and 0.75.

Surprisingly, no nest-scale habitat characteristics were Si gniﬁcantly associated with
the probability of a nest successfully producing swim-up fry (P 2 0.10). At the whole-
lake scale, however, the probability of a nest producing swim-up fry decreased markedly

with increasing LSD (intercept (7‘00) = 1.96, standard error (s.e.) = 0.748, P = 0.078;
Slope, effect of LSD ()301) = -0.096, s.e. = 0.04, P = 0.018). The predicted probability of

success ranged from 0.77 in Bruin Lake, the lowest LSD lake to 0.45 in Patterson Lake,
the highest LSD lake (Figure 2). No other lakewide covariates were signiﬁcant (all P >

0.20). Over or underdispersion were not evident in our analysis, with the extra-dispersion
parameter estimated very close to 1 ((13 = 1.02, Littell et al. 1996).

Angling effort—Our estimate of total ﬁshing effort (total angler hours per km of
Shoreline) were quite variable among lakes, but did not vary predictably with LSD in
May or June (May, P = 0.75; June, P = 0.21). Estimated total angler hours were much
lower during the May period (ranging 0 — 227 hrs/km; standard deviations ranged 0 —
64.5), when the majority of nesting occurred, than in June (ranging 65 -— 453 hrs/km;
standard deviations ranged 29.3 — 158.3), when the legal season for bass ﬁshing was
open. Anglers using techniques likely to target bass represented a substantial component
of total angling effort both before and after opening of the legal season for targeting bass

(35% and 42% of angling effort in May and June, respectively). Thus, even though the

92

predominance of angling that potentially targets nesting bass increased in June, it still
occurred in May to a substantial degree despite the ﬁshing regulations.

Nest habitat features—Nest depth was the only nest habitat feature that differed
Signiﬁcantly among shoreline development types. Local LSD type explained 8.5% of the
variation in depth of largemouth bass nests. According to our model, on average, if a
largemouth bass nest was constructed near an undeveloped Shoreline it was shallower
compared to nests constructed near developed shorelines, and nests constructed near
retaining walls were, on average, constructed in yet deeper water (intercept = 0.845, s.e.
= 0.065, P = 0.002; ﬁxed effect of developed maintained shoreline = 0.135, s.e. = 0.047,
P = 0.004; ﬁxed effect of developed retained Shoreline = 0.197, s.e. = 0.058, P = 0.0009).
The grand-mean depth at which largemouth bass nests were constructed was 0.92 m
(95% conﬁdence interval = 0.83, 1.01) and did not vary Signiﬁcantly among lakes
(between lake variance estimate = 0.008, P = 0.12). Surprisingly, substrate type and the
presence/absence of cover did not signiﬁcantly differ among either local LSD types or
among lakes according to lakewide LSD.

Nest distribution—Largemouth bass used Shoreline habitats to construct nests in
different proportions compared to what was available in 4 of 5 lakes (Figure 3), although
patterns of selection varied among lakes. The only lake in which largemouth bass used
habitat in proportion to what was available was Bruin Lake (7.8 dwellings/1cm), with the
majority of habitat, and nest sites, comprised of undeveloped shoreline. For East Crooked
(14.6 dwellings/km) and Patterson (22.3 dwellings/km) lakes, largemouth bass selected
undeveloped shorelines for nest construction, as we had expected. In East Crooked, bass

utilized undeveloped Sites that were both exposed to low and high wind, whereas bass in

93

Patterson Lake primarily used undeveloped sites that were located in low wind exposure
sites in greater proportion compared to what was available. Contrary to our expectations,
in both Halfrnoon (17.7 dwellings/km) and North lakes (21.5 dwellings/km), largemouth
bass primarily used developed maintained Shorelines in low wind exposure areas for
nesting. In Halfrnoon Lake, in particular, largemouth bass nests were located in
undeveloped sites less than expected given the available proportion of this habitat type.
Discussion

We expected local and lakewide features to inﬂuence the distribution and success of
largemouth bass nests. In particular, we hypothesized that nests would be concentrated
along undeveloped shorelines within lakes, and that these nests would have a higher
probability of success than nests located along developed Shorelines. We thought that
availability of cover and visibility to anglers (i.e., nest depth) would explain, in large part,
differences in nest success between developed and undeveloped Shorelines. We also
expected nest success to vary predictably among lakes, with nest success declining with
increasing lakewide LSD, due to higher levels of angling pressure and generally lower
availability of preferred nesting habitat. AS expected, at the whole-lake scale, nesting
success declined with increasing lakewide LSD; but surprisingly, whole-lake angling
effort could not explain the differences in nest success among lakes. Further, we saw no
evidence that local nest features, such as availability of cover or nest depth, could explain
variability in success among nests. Patterns of nest distribution relative to available
habitat varied among lakes, with some indication that preferred habitat becomes limiting
at high LSD, but also that additional reﬁnement of habitat categories is required (see nest

distribution, below).

94

Nest success—Contrary to our expectations, neither nest depth, nor other local nest
features, could explain a Si gniﬁcant amount of variation in nest success. Although this is
consistent with ﬁndings by Gross and Kapuscinski (1997), where local habitat
characteristics such as nest depth and dominant substrate type could not predict
reproductive success of smallmouth bass in Lake Opeongo, Ontario, Canada, we view
these ﬁndings as somewhat surprising given the attention in the literature on local nest
habitat features and the documented habitat preferences of black bass (Hunt and Annett
2002; Saunders et al. 2002; Wills et al. 2004). Why did we detect no local effects on nest
success? The answer may be in part that a more detailed quantiﬁcation of structure is
needed. In our ﬁeld observations, available structure was treated as a categorical variable
(presence/absence), such that we failed to consider varying degrees of cover. For
example, an extensive stand of vegetation and a few sprigs of macrophytes in close
proximity to nests were both considered equal vegetative cover, when they may, in fact,
inﬂuence the fate of an individual nest differently. Also, angling may need to be observed
at a ﬁner (i.e., local) Spatial scale (see below), and/or variation in the abundance and
spatial distribution of nest predators (a factor that we did not quantify), both within and
across lakes, may play a predominant role in determining variation in nest success. In fact
the interaction between ﬁshing pressure and nest predator abundance may be important,
as the removal of guarding male bass during ﬁshing, even for a brief period of time,
increases the probability of nest failure due to predation (Kieffer et al. 1995; Phillipp et
al. 1997).

Contrary to our expectations, ﬁshing effort did not increase with lake dwelling

density. Hence, ﬁshing pressure could not account for the ~35% decline in probability of

95

nest success across lakes. Fishing pressure may not increase with dwelling density in our
lakes because they all have public access. Therefore, a large component of the anglers
likely do not reside on the lake. Still, we were initially surprised that ﬁshing effort could
not explain the variation in nest success because the effects of ﬁshing on nest success
have been investigated in ponds and sections of lakes, with convincing evidence that
ﬁshing negatively affects the success of individual nests (Neves 1975; Ridgway 1988;
Kieffer et al. 1995). This reduction in nest success is often due to nest predation either
while the male bass is off the nest, or even after the male bass has returned, because such
males Show decreased ability to defend the nest and increased likelihood of abandoning
the nest (Philipp et al. 1997; Suski et al. 2003).

Our working hypothesis for why ﬁshing effort did not explain a signiﬁcant amount
of variation in nest success is that the spatial distribution of angling, relative to nest
distribution, is a critical factor to observe. Our angling surveys may have been conducted
at too broad of a scale. For example, anglers in Patterson Lake were observed to be using
methods that targeted nesting bass in a small cove with a high number of bass nests. Nest
predators also appeared to be particularly abundant in this cove. Nest failure rate in this
cove was particularly high. It is likely that the spatial distributions of ﬁshing and of nest
predators interact to inﬂuence nest success, such that both factors should be observed at
ﬁner Spatial scales to be able to determine their combined effect on nest success. It may
be that high levels of shoreline development result in concentration of nesting bass and
potential nest predators, such as other centrarchid species.

Finally, although we chose our lakes to be Similar morphometrically, we cannot

conclusively rule out the possibility that other unmeasured features of our study lakes,

96

either natural or due to human activities, covaried with LSD, and provided the
mechanism driving the observed negative relationship between nest success and LSD.

For example, it is possible that some feature of a lake, such as an unmeasured indicator of
littoral habitat quality, which makes it unfavorable for bass reproduction also makes it
preferable for human development. Future studies examining the relative importance of
LSD on nest success that include more study lakes and contain more detailed
measurements of habitat will help address such questions.

Nest habitat features—We hypothesized that nest habitat features (e.g., nest depth,
substrate type, and presence/absence of cover) would vary predictably among local LSD
types and lakewide LSD. Nest depth was the only variable that varied, differing among
local LSD types. The construction of retaining walls, and to some extent maintained
shorelines, apparently reduced the availability of Shallow-water spawning habitat,
resulting in bass constructing nests in deeper water. However, because neither nest depth
nor local LSD type were signiﬁcant in predicting nest success, the difference in nest
depth among local LSD types does not appear to have substantive effects on nesting
success. Research has demonstrated that local modiﬁcation affects substrate type,
vegetation cover, and course woody material abundance in these lakes and others in
Wisconsin and Minnesota (Radomski and Goeman 2001; Jennings et al. 2003; Jubar
2004). Therefore, the fact that these factors did not vary predictably among nest Sites
according to modiﬁcation type indicates that bass effectively seek out these features,
even if they are relatively less abundant at developed sites.

Nest distribution—Habitat availability may affect the overall outcome of nesting for

a population through altering the number of nests, the distribution of those nests, and/or

97

the success of those nests in producing swim up fry. The number of largemouth bass
nests that we detected ranged from 0 — 51 across lakes, with 5 of the 6 lakes having at
least 21 largemouth bass nests. We can not decisively discern the inﬂuence of the
abundance of adult male bass on nest number across lakes; however, bass catch per effort
ranged from 47 - 92 largemouth bass per hour and was not correlated with the number of
nests located in each lake (r = 0.28, P = 0.59), nor was it related to the average
probability of success in each lake (P = 0.30; A. K. Jubar and M. T. Bremigan,
unpublished data). Determining the potential inﬂuence of male bass abundance on the
number of nests and nest success is further complicated by the fact that not all adult
males breed each year (Raffetto et al. 1990).

We reasoned that if nests were disproportionately abundant along undeveloped
Shorelines and rare along developed Shorelines, that this would be an indication that local
LSD inﬂuences nest site choice (or the very early success or failure of nests, i.e., failure
before we detected them). Although local habitat features of nest sites have been studied
(Gross and Kapuscinski 1997; Rejwan et al. 1999), to our knowledge, the distribution of
nest sites relative to local LSD status has not been evaluated. Given the propensity of
baSS to select nest Sites with nearby structure (Bozek et al. 2002; Hunt and Annett 2002),
one would expect fewer nests to occur along developed shorelines, due to the reduction in
coarse woody material that occurs due to residential LSD, which has been documented in
northern Wisconsin lakes (Christensen et al. 1996) and our study lakes (Jubar 2004).

There was substantial variation among lakes with regards to the distribution of nests
relative to development type. Overall, patterns appeared to roughly correspond to

lakewide LSD. For example, Bruin Lake, our lowest development lake with bass nests,

98

was the only lake in which nest distribution did not differ from random, with respect to
development type and wind exposure. From this pattern we infer that strong selection for
development status or wind exposure did not occur. The majority of nests in Bruin Lake
were located along undeveloped shoreline, indicating that strong “selection” was not
necessary because the majority of available shoreline was of this type. In contrast, in
Patterson Lake, our highest development lake, strong selection for nesting along
undeve10ped Shoreline with low wind exposure was evident. The majority (~65%) of
nests were located in this category that comprised only ~10% of the shoreline. In the
remaining three lakes, we saw intermediate results, generally with selection for
undeveloped and developed maintained shoreline, and avoidance of developed retained
Shoreline. In fact, developed retained shoreline was avoided in all but one lake
(Halfmoon). It may be that additional habitat features need to be taken into account to
explain the distribution of bass nests in lakes. For example, in Halfrnoon Lake, where
nests were concentrated along developed maintained shorelines with low wind exposure,
much of the undeveloped Shoreline was of poor habitat quality for nesting, consisting of
shallow (< 0.5 m) depths, and consolidated, compacted substrates with little cover. Poor
“natural” habitat likely also explains the lack of nests in Blind Lake, where most of the
littoral substrate consisted of consolidated clay (A. K. J ubar, pers. observation). Although
the observed patterns did roughly correspond to LSD patterns, we cannot rule out other
factors that may inﬂuence nest distribution. For example, Rejwan et al. (1999) identiﬁed
a positive relationship between smallmouth bass nest densities and temperature and

Shoreline reticulation in Lake Opeongo, Canada.

99

Conclusions.—Elucidating the spatial scale at which controlling factors operate is a
challenge in ecological studies. The use of multilevel models, however, as were used in
our study, allows for the investigation of potential controlling factors (i.e., covariates) at
multiple spatial scales in a Single statistical model. We determined that, although local
habitat characteristics are likely important factors affecting nesting success, lakewide
features of lakes are also important (actually more important in our study) and they help
explain large-scale patterns in nesting success that would be missed if only local habitat
characteristics or Single lakes were considered.

Understanding the ecology and management of black bass is challenged by the
disconnect between the effects of ﬁshing and habitat on individual nests, and the ultimate
population level effects. Certainly events after nesting are also important contributors to
recruitment. To date, most research on black bass nesting success has been done in ponds
or sections of lakes, in an experimental context. Such work is important, but it does not
quantify the magnitude of anthropogenic and natural effects at the whole-lake scale. Our
ﬁndings demonstrate that dwelling density warrants more attention. It provides valuable
information for modelers by quantifying the scope of the response and hence it begins to
deﬁne the compensatory capacity (in subsequent life stages) needed to nullify negative
effects of lakeshore dwelling density on nest success. This constitutes a critical step in
ultimately determining the population level effects of habitat modiﬁcation and ﬁshing on

black bass recruitment.

100

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103

 

TABLE 1.—Lake morphometry and water quality characteristics for the Six study
lakes surveyed for black bass reproductive success. Shoreline complexity is deﬁned as

the ratio of the length of the Shoreline to the circumference of a circle of area equal to that

 

 

of the lake.
Lake Dwelling density Lake area Mean depth Total Shoreline
(dwellings/km) (ha) (m) phosphorus Complexity
(rig/L)
Bruin 7.8 52.7 3.74 15.3 1.20
Blind 9.5 28.8 4.05 12.5 1.32
East Crooked 14.6 100.5 3.97 19.9 1.84
Halfrnoon 17.7 97.4 6.77 13.1 2.12
North 21.5 90.5 3.53 16.6 1.67
Patterson 22.3 64.1 5.58 22.0 1.79

 

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TABLE 2.— List of covariates used in the analysis of largemouth bass nest success
using a generalized linear mixed model. Level 1 covariates are those measured at the

nest-scale; level 2 covariates are those measured at the lake scale.

 

 

Level 1 covariates Level 2 covariates
Dominant substrate type Lakeshore development (dwellings/km)
Presence/absence of cover (boulders, Angler effort (hrs/km)

woody debris, macrophytes)

Depth (m) Total phosphorus levels (pg/L)
Lakeshore development type

Distance to shore (m)

Wind exposure (high, low)

 

105

TABLE 3.—The total number of largemouth bass nests and the number of successful

and failed nests located at each study lake. The sum of the numbers of successful and

failed nests is leSS than the total number of nests because the total number of nests

includes those nests for which the fate could not be determined. Lakes are ordered

according to increasing dwelling density.

 

 

Lake Total number of Successful nests Failed nests l
nests
Blind 0 - -
Bruin 21 12 5
East Crooked 48 23 9
Halfmoon 24 9 9
North 51 19 18
Patterson 34 10 16

 

106

 

Figure 1

    
       

East Crooked »‘

Patterson

Livingston Co.

  

Bruln‘ Halfmoon

107

Figure 2

 

Probability of success

 

 

 

Lakeshore development (dwellings/km)

108

Figure 3

Percent

801

Bruin

60 P=0.15

 

 

80 East Crooked
50. P = 0.003

 

 

80‘ Halfmoon
60 P = 0.002

 

 

 

 

Patterson
50 P < 0.0001

 

 

DR high
DR low
UD high
UD low

.:
22
a:

109

 

CHAPTER 4: REGIONAL TRENDS IN FISH MEAN LENGTH AT AGE:
COMPONENTS OF VARIANCE AND THE POWER TO DETECT TRENDS

Abstract

We examined statewide time-series (1940s —— 2002) of mean length at ages 2, 3, and 4
for seven ﬁsh species sampled from Michigan and Wisconsin inland lakes for temporal
trends. We also used a components of variance approach to examine how total variation
in mean length at age was partitioned into ﬁve components, including several sources of
spatial and temporal variation. Using these estimated variance components, we Simulated
the effects of different variance structures on the power to detect trends in mean length at
age. Of the 42 datasets examined, only four demonstrated Signiﬁcant regional (statewide)
trends. The slope estimate for age 4 largemouth bass from Wisconsin lakes was
signiﬁcant, with an increase of about 0.7 mm°yr'1 in mean length at age. In contrast, ages
2, 3, and 4 walleye from Wisconsin lakes showed a negative trend, decreasing between
0.5 and 0.9 mm-yr". The structure of variation differed substantially among datasets and
these differences strongly affected the power to detect trends. To maximize trend
detection capabilities, ﬁsheries management agencies should consider variance structures
prior to choosing indices for monitoring and realize that trend detection capabilities are

species-Speciﬁc.

110

 

Introduction

Knowledge of trends in ﬁsh growth rates is important ecologically, as growth rates
inﬂuence ecological interactions and population dynamics, and are often used along with
recruitment and mortality information to assist management decisions (Trippel 1993).
Furthermore, growth rates are inﬂuenced by environmental conditions and can represent
an integrative measure of conditions experienced by a ﬁsh over its lifetime.
Consequently, one goal of many ﬁshery monitoring programs is to determine whether
growth of ﬁsh populations (e. g., mean size at age) is changing with time and if so, if such
changes are consistent across Species and across systems. Most work on evaluating trends
in ﬁsh growth have focused on individual populations (e.g., Reckahn 1986). There have
been some regional evaluations of trends in ﬁsh demographics, although most have
emphasized abundance (McDonough and Buchanan 1991; Beard and Karnpa 1999;
Maceina and Bayne 2001; Grant et al. 2002), the majority of aquatic work evaluating
trends has emphasized single systems and water quality across rivers (Antonopoulos et al.
2001), lakes (JaSSby et al. 1999), and seas (Sandén and Hékansson 1996). Although
investigations into temporal trends within individual systems provide valuable
information, the ability to detect regional (e.g., statewide) temporal trends is crucial for
the evaluation of many management actions and to examine responses to natural or
anthropogenic perturbations. Furthermore, the early detection of regional changes iS
important in many cases to allow time for managers and policy-makers to respond and
take appropriate action (Vaughan et al. 2001). This said, detection of regional trends in
ﬁsh growth (or other parameters) is a challenge, both because available data are often

limited, and because regional trends can become obscured by the large amount of

111

 

temporal variation common to the region and unique to particular populations within a
region. In this study we provide one approach to evaluating regional trends in ﬁsh growth
(mean size at age), and then use the estimated structures of variance to evaluate the
statistical power of different sampling designs for detecting regional trends in ﬁsh growth
to lend insight into design and feasibility of reliable monitoring programs.

Trends and components of variance

A components of variance approach has been advocated to address the issue of
variability in ecological data when evaluating regional temporal trends and monitoring of
ecological systems (Urquhart et al. 1998; Larsen et al. 2001; Kincaid et al. 2004). Under
this framework, total variance is partitioned into four components including, (1) site-to-
site (Spatial) variation, (2) coherent (year-to-year) variation affecting all sites (e. g., lakes)
in a Similar manner, (3) ephemeral temporal variation (e.g., site-by-year interaction)
corresponding to independent yearly variation at each site, and (4) residual variation
(Larsen et a1. 2001; Kincaid et al. 2004). A ﬁfth component can be included in this
framework. In this approach, each site has its own trend (i.e., trend variation: allowing
the slope of the response variable versus time at each site to be a draw from a distribution
and estimate the variance of the distribution of slopes).

Although the total variance of the data is one of the primary factors affecting the
ability to detect trends (Stow et al. 1990), the partitioning of the total variance among
these sources also inﬂuences statistical power. Power analysis is a useful tool for
evaluating the performance of ecological monitoring programs (Peterrnan 1990;

F airweather 1991; Hatch 2003) and in particular for investigating how speciﬁc variance

components affect the power to detect trends. Ideally, a monitoring program should have

112

high statistical power, the ability to detect a speciﬁc deviation from the null hypothesis.

More formally, power is deﬁned as 1 - )6 , where ,6 is the probability of a type 11 error

(failing to reject the null hypothesis when it is actually false).

To our knowledge, a components of variance approach has not been applied to ﬁsh
growth data (i.e., mean length at age data) within the context of trend detection over a
large Spatial region (although random effects models have been used to partition
variability in ﬁsh growth data to test other hypotheses; e.g., Osenberg et al. 1988), even
though ﬁsheries agencies are collecting ﬁsh growth data through time to monitor regions
of lakes and streams (e.g., Hayes et al. 2003). The speciﬁc objectives of this study were
to (1) determine if trends are evident in mean length at age for seven ﬁsh Species in
Michigan and Wisconsin inland lakes, (2) quantify the components of variance for mean
length at age and (3) perform power analyses to investigate the effects of the different
components of variance on the statistical power to detect trends, and to evaluate

alternative sampling designs.
Methods

Datasets

We obtained mean length at age data for seven ﬁsh species from ﬁsh growth surveys
of inland lakes conducted by the Fisheries Division of the Michigan Department of
Natural Resources and the Wisconsin Department of Natural Resources. We included
bluegill Lepomis macrochirus, pumpkinseed L. gibbosus, largemouth bass Micropterus
salmoides, smallmouth bass M. dolomieu, yellow perch Percaflavescens, walleye Sander
vitreus, and northern pike Esox lucius because of their prevalence in the historical data. In

each lake survey, ﬁsh growth had been recorded as the mean length at age for a given

113

species and age. The corresponding number of ﬁsh that contributed to the mean was also
recorded along with the day of year that sampling occurred. We restricted our analyses to
mean length at ages 2, 3, and 4 for each species because the reliability of ﬁsh aging
decreases with increasing age (Ricker 1975) and because these ages had adequate sample
sizes.

Mean length at age time series were available beginning in the early 19603 to the
early 2000s for ﬁsh collected in Michigan and from the late 19403 or late 1950s to the
early 20003 for ﬁsh collected in Wisconsin (Table 1). Fish were collected using a variety
of gear types over the time series. Thus, in an effort to reduce potential biases introduced
by using different sampling gear, we only retained ﬁsh collected using the same gear type
in the analyses for each species, age, state combination (Table 1). For nets, however,

(e. g., trap nets and fyke nets) the mesh size was not recorded over time; thus we could not
control for any potential changes in mesh size. Historically, ﬁsh were not sampled in a
truly random design by the state agencies. However, the ﬁsh growth surveys used in this
analysis represent a large sample of public lakes broadly distributed throughout both
states, thus reducing the likelihood of substantial bias.

Temporal trend statistical analysis

A weighted mixed model was used to assess the presence of regional (statewide)
linear trends in mean length at age for each Species, similar to that suggested by Piepho
and Ogutu (2002). Although we restricted our analysis to the investigation of linear
trends, if a monotonic increase or decrease is present then a linear trend will be present
(Urquhart and Kincaid 1999). Each state, Species/age dataset was analyzed separately.

States were analyzed separately to reduce potential biases introduced by differences in

114

sampling methodologies between agencies. Each data point (mean length at age) was
weighted by the number of ﬁsh that contributed to each mean for each lake. To account
for potential biases introduced by ﬁsh being sampled during different times of the year
(i.e., seasonal trends in mean length at age), seasonal trends were examined prior to the
interannual analysis by ﬁtting linear and quadratic least-squares regression models (Grant
et al. 2004). For each Species/age combination with a signiﬁcant seasonal trend, the
regression equation was used to adjust mean length at age to the median sample date.

Because we could not estimate the lake x year interaction effect for most datasets
(e.g., the data sets did not contain sufﬁcient data on lakes sampled multiple times within a
year or overall sample size was small), we used a simpler model to examine temporal
trends that excludes the estimation of the variance due to lakex year interaction. In this
case the variance due to the lakex year interaction is contained within the residual error
term. Not estimating this parameter, however, does not affect the estimate of the slope.
The mixed model ﬁt to detect interannual trends was

(I) Ylj =,u+a,- +y(/l.+li)+bj +31]

where Yij is the mean length at age for lake i in year j, ,u and ,1 are the ﬁxed intercept and

Slope (ﬁxed regional trend), respectively, y is the jth year minus the mean year used in the

analysis. This standardization of year was performed to provide numerical stability. a ,- is

a random effect for lake i, representing lake-to-lake variability, iid as N (0, 0'02),bj is a

random effect for the j‘h year (coherent temporal variability), iid as N (O, 07,2 ), t,- iS a

115

random effect for the trend for lake i, iid as N (0, 0,2 ), and eg- is the unexplained error

(residual error), iid as N (0, 0'32 ).
Components of variance

To partition the total variance among the various components, where possible, we
also ﬁt a mixed model identical to equation 1, except that an additional random effect for

the lakex year interaction (c0. )was added to the model, yielding

(2) Yij =,u+a,- +y(/1+t,)+bj +c +e

where all parameters are deﬁned as in equation 1 and cij is the random effect for
lakex year interaction (ephemeral temporal variability). Note that eg- represents sampling

error that inﬂuences the observed mean and its variance and its variance is inversely
related to sample Size. In practice this means that the model was ﬁt by weighting
observations (means for a year and age) by their sample Sizes. We estimated variance
components using restricted maximum likelihood and P-values were estimated using a
likelihood ratio test (Self and Liang 1987). We considered all analyses signiﬁcant at P <
0.05.
Power analysis

We used a simulation approach to examine the statistical power to detect temporal
trends using the variance components estimated from equation 2. For each simulation,
one thousand datasets were generated containing species Speciﬁc mean length at age data
for a population of lakes (50 or 1,000 lakes, see below) over 25 years. First, a ‘true’ mean
length at age for each lake in the population was generated over the 25 year time period.

A trend of known magnitude (e.g., a decease of 1 mm-yr") was also incorporated into the

116

dataset. Using the ‘true’ mean lengths at ages for each lake, an ‘observed’ mean length at
age was then generated for each lake. The observed mean length at age was created by
randomly generating lengths for a pro-speciﬁed number of ﬁsh (ranging from 5 — 30) for
each of the lakes from a normal distribution with a mean equal to the “true” mean and
variance equal to the estimated residual (sampling) variance from equation 2. From these
1,000 datasets, a user-Speciﬁed number of lakes (ranging from 10 — 40) were then
randomly sampled from the population 50 or 1,000 lakes each year. When the number of
ﬁsh sampled per lake was held constant, we used the mean number of ﬁsh sampled per

age class from our surveys (97 = 10). Thirty lakes sampled per year were used as a realistic

number of lakes that could be sampled per year by a management agency when the
number of lakes sampled per year was held constant (K. Wehrly, Michigan Department
of Natural Resources Fisheries Division, Institute of Fisheries Research, Pers. Comm).
Lakes were sampled without replacement within a year, but all lakes were available for
selection each year. Data were analyzed for different sampling durations from 5 up to 25

years and analyzed for the presence of a trend. The model speciﬁed in equation 1 was

used to test the null hypothesis that 21 = O for each dataset and the test statistic was
calculated and compared to a critical value ( or = 0.05). Because the data generated depict
a Situation in which we know the null hypothesis is false (i.e., a trend of known
magnitude was incorporated into the data), power was estimated as the percentage of
trials (out of 1,000) that rejected the null hypothesis.

We investigated the extent to which the following factors affected the ability to
detect a trend (1) increasing trend magnitude (/1 ranged from -0.5 — 2.0 mm-yr"), (2)

increasing number of ﬁsh sampled per lake (ranging from 5 — 30 ﬁsh per lake), (3)

117

increasing the number of lakes sampled per year (ranging from 10 — 40 lakes per year),
(4) decreasing lake effect variance, and (5) sampling from a population of 50 or 1,000
lakes. We address factor 1 to provide information on the effects of trend magnitude on
power. We address factors 2 and 3 because the number of ﬁsh and lakes sampled is an
important consideration for sampling designs with respect to allocating personnel and
ﬁscal time and money resources. We address factor 4 to understand how power would
increase if lake-to-lake variance was reduced, for example, by using a lake classiﬁcation
scheme. To this end, we reduced lake-to-lake variance by 50% and then reduced it to
zero. Finally, we examined factor 5 to examine how the proportion of lakes sampled each
year inﬂuences statistical power. For simulations for which sampling from a population
of 50 or 1,000 lakes did not change the general patterns observed, we report only those

results for sampling from a 50 lake population, unless otherwise stated.
Results

Temporal trend

Not all datasets contained enough information to ﬁt model 1. Of 42 datasets
examined (7 species X 3 ages X 2 states), we were able to examine temporal trends for
only 26 datasets (Table 2). Of the 26 analyses, only four demonstrated signiﬁcant
temporal trends. The slope estimate for age 4 largemouth bass from Wisconsin lakes was
signiﬁcant, with an increase of about 0.7 mm°year’l in mean length at age. Ages 2, 3, and
4 walleye from Wisconsin lakes showed a negative trend, decreasing between 0.5 and 0.9
mm°year'l in mean length at age (Table 2). For all other analyses, estimates of the slope
for the ﬁxed regional trend had absolute values of 0.43 or less, which were not

Si gniﬁcantly different from zero (P > 0.05).

118

Variance components

We could not estimate the lakex year interaction effect for 20 of 26 of the datasets

used in trend estimation. For the datasets where estimation was possible, the structure of

variation differed substantially among datasets (Figure 1). Mean residual variation (6'3)

was 54%, and ranged from 18.1 — 75.7% of the total variation. Mean ephemeral temporal

variation (0‘02) was 17.2% and ranged from 4.9 — 30.6% of the total variation. The mean

percent of total variation attributed to coherent temporal variation (ébz) was 3.5% and

ranged from 0.5% to 8.7%. The mean percent of total variation attributed to lake-to-lake

differences (otaz) was 25.4% and ranged from 5.5 — 50.5%. The mean percent of the total

variation due to trend variation (6,2) was small (mean = 0.1%), ranging from 0.01% to

0.24%.
Power analysis

We investigated the effects of variance structures on statistical power by contrasting
two carefully chosen datasets, which had strikingly different variance structures, namely
age 4 walleye sampled in Michigan and Wisconsin (Figure 1). Because the slope
estimates for the Signiﬁcant analyses of temporal trends ranged from -0.5 to -0.9, we used
,1 = -1.0 mm°year'1 for Simulations in which 2 was held constant. Trends less than this
would likely not be considered biologically “signiﬁcant” in the Short-term.

The power to detect trends in mean length at age increased, as expected, with
increasing trend magnitude (Figure 2). For example, after 15 years of sampling, the
power to detect a trend increased from 0.2 — 1.0 as ,1 decreased from -0.5 — -2.0 mm-year'

I for age 4 walleye sampled from Michigan lakes. For age 4 walleye sampled from

119

Wisconsin lakes, power also increased with trend magnitude, but power at a given
number of years and trend magnitude was markedly lower in Wisconsin as compared to
Michigan, demonstrating the inﬂuence of states’ different variance structure.

In an effort to visualize the trade-offs between sampling more ﬁsh per lake versus
sampling more lakes per year, we plotted power curves for both Michigan and Wisconsin
walleye across 10 and 25 year sampling periods (Figure 3). For walleye sampled in
Michigan, the greatest increase in power at 10 years of sampling was gained by
increasing the number of lakes sampled each year, with only a slight gain in power
achieved by increasing the number of ﬁsh sampled in each lake. For example, if 30 lakes
were sampled per year, increasing the number of ﬁsh sampled ﬁ'0m 5 — 30 increased
power by only 0.05. In contrast, assuming 10 ﬁsh were sampled from each lake,
increasing the number of lakes sampled from 10 — 40 increased power by 0.3. A similar
pattern was observed at 25 years; however, relatively high power (ranging from 0.85 —
1.0) was obtained regardless of the number of lakes or ﬁsh sampled (Figure 3).

A different pattern was observed for walleye sampled from Wisconsin (Figure 3). At
a 10 and 25 years of sampling, although increasing the number of lakes sampled each
year from 10 — 20 increased power, power leveled off and remained relatively low even
as the number of lakes increased from 20 — 40. Increasing the number of ﬁsh sampled
from each lake did increase power; however, this increase was quite small.

Decreasing lake-to-lake variance did not have a noticeable effect on power for either
walleye sampled in Michigan or Wisconsin when 60% of the total population of lakes
was sampled each year (sampling 30 out of 50 lakes each year). Rather, power remained

Similar at all sampling durations (Figure 4), but was consistently higher for Michigan

120

compared to Wisconsin lakes. Under the scenario in which 3% of the lakes were sampled
each year (sampling 30 out of 1,000 lakes each year), decreasing lake-to-lake variance
resulted in an increase in power for walleye sampled in Michigan where lake-to-lake
variance comprised 51% of the total variance; however, this pattern of increasing power
with decreasing lake-to-lake variance was not observed with the walleye sampled in
Wisconsin lakes, where lake-to-lake variance was smaller, comprising 15% of the total
variance (Figure 4). Furthermore, when sampling a small percentage (e.g., 3%) of the
population of lakes, some models were not estimable over short sampling durations (< 10
yrs) because there were not sufﬁcient data on individual lakes sampled repeatedly over
time. Thus, power estimates reported for sampling from the 1,000 lake scenario are only

for models that were estimable (i.e., the number of trials was < 1,000).
Discussion

Temporal trend

We detected four signiﬁcant regional trends out of the 26 datasets analyzed, all of
which were from inland lakes sampled in Wisconsin. Of these, one was positive (age 4
largemouth bass) and three were negative (ages 2, 3, and 4 walleye). The magnitude of
the trends ranged from 0.5 — 0.9 mm-year". No signiﬁcant regional trends in mean length
at age were detected from Michigan inland lakes. Although we detected four signiﬁcant
regional trends, any inference regarding causation is difﬁcult (Stow et al. 1998);
however, potential mechanisms can be hypothesized. For instance, potential causal
factors of increasing trends in mean length at age could be due to effective regional
harvest regulations or increases in regional temperatures resulting in increased growth

rates. However, if increases in regional temperature were responsible for the observed

121

increasing trend, then we would expect that more of our datasets would demonstrate such
a trend. Thus, temperature alone is likely not responsible for the observed trend.
Decreases in mean length at age for walleye could be due to effects of anglers or stocking
programs. For example, if stocking rates increased over time or if ﬁsh numbers increased
for some other reason, then increasing competition for resources could lead to reduced
growth rates. This mechanism was also proposed by Li et al. (1996) to explain reduced
mean weights of walleye in stocked lakes in Minnesota. However, the observed trends
could be due to interactions of changing biotic and abiotic conditions over time, which
make it difﬁcult to attribute causality to any single source.
Components of variance

Variance structures (i.e., the proportion of total variance attributed to each
component) varied considerably among the Six datasets we examined. Across all Six
datasets, residual variation (variation due to sampling error) comprised the largest
proportion (37 = 54%) of the total variance, while lake-to-lake and ephemeral temporal
averaged 25% and 17% of the total variation, respectively. In contrast, coherent temporal
variation and trend variation averaged only 3% and 0.1%, respectively. Furthermore,
coherent temporal variation was only signiﬁcantly different ﬁom zero in three out of six
analyses, while Slope variation was only Signiﬁcant in two analyses. However, our
variance estimates are within the percentages reported by Osenberg et al. (1988).
Osenberg et al. (1988) partitioned variance in growth rates of bluegill and pumpkinseed
sunﬁsh into four components, residual error, lake, year, lakeX year. On average, residual
error variance comprised 69% of the total variance, whereas, lake-to-lake variability and

lakeX year variation comprised an average of 20% of the total variance. They found that

122

year effects (coherent variation) did not explain any of the variance. For our analyses, the
relatively high residual variation is likely due to measurement error (e.g., errors made
during the reading of scales for age determination), errors in data processing, crew
effects, and collection protocol sampling errors that may have occurred over the time
period we examined.

Examining variance structures of monitoring indices has been performed for several
lake indicators, primarily using data obtained from the United States Environmental
Protection Agency’s Environmental Monitoring and Assessment Program (EMAP) in the
northeastern U.S.A. The EMAP collected data on a wide range of chemical and
biological data, including water chemistry measures of conservative and nonconservative
ions and biological measures such as ﬁsh and zooplankton species richness (Stemberger
et al. 2001; Kincaid et al. 2004). The variance structures in our analysis of ﬁsh mean
length at age were within the ranges for zooplankton abundance indicators from the
EMAP described by Stemberger et a1. (2001), although these authors did not estimate
slope variation in their study. For zooplankton abundance indicators, percent lake-to-lake
variation ranged from 0 — 69%, coherent temporal variation was “small or negligible”,
ephemeral temporal ranged from 0 — 16%, and residual variation ranged from 14 — 43%
(Stemberger et al. 2001).

For some biological indicators, such as ﬁsh mean length at age in our study and
zooplankton abundances and species richness estimated for the EMAP data, the
proportion of residual variance is much higher compared to conservative chemical
indicators, such as calcium and magnesium (Kincaid et al. 2004). For conservative

chemical indicators, lake-to-lake variation comprises a majority of the total variation and

123

there is relatively low residual variance (Kincaid et al. 2004). The high spatial variation
among lakes and low residual variation for conservative ions likely reﬂects the relative
stability of these indicators within lakes over time and space compared to nutrients and
biological measurements that are controlled more by within-lake processes and which are
more prone to sampling biases (e.g., have higher within-lake spatial and temporal
variation). These differences between conservative chemical indicators and biological
indicators need to be acknowledged and incorporated into the expectations of monitoring
programs. For example, detecting a pre-speciﬁed trend for a biological indicator with a
large residual variance component will require a longer sampling period compared to
indicators with lower residual variances to detect the same trend, all else being equal.
Furthermore, agencies should take steps to reduce sampling errors associated with
biological indicators in order to improve trend detection. All other sources of variation,
with the exception of coherent temporal variation, can also be reduced by manipulating
certain aspects of the sampling design (see Larsen et al. 2001 and Urquhart et al. 1998 for
details).
Trend detection

We observed the expected increase in power with increasing trend magnitude and
sample duration for both the Michigan and Wisconsin analyses. This pattern was also
demonstrated using the EMAP data (Urquhart et al. 1998). A striking difference between
the Michigan and Wisconsin power analyses, however, was the overall low power
observed for the Wisconsin data. Although, we expected power to be lower for the
Wisconsin analyses due to the higher proportional and absolute value of the estimated

coherent temporal and residual variation compared to the Michigan analyses (see below),

124

we were not certain as to the relative affects of each component (coherent temporal or
residual) was on power. Furthermore, because Urquhart et al. (1998) demonstrated the
importance of coherent temporal variance in reducing trend detection, we wanted to
examine its relative affect compared to the much greater proportion of variance attributed
to sampling error. To examine this in more detail, we performed a sensitivity analysis
using the Wisconsin data. Again, because the Wisconsin variance components that

differed most from the Michigan dataset were the residual variance (comprising 76% if

the total variation for WI (6'82 = 4936) versus 18% for M1 (63,2 = 550) and coherent

temporal variance (comprising 4% of the total variation for WI (ribz = 261) versus

nonsigniﬁcant for M1), we concentrated our sensitivity analysis on these two
components. We set the residual and coherent temporal variance to 50 and 25% of the
estimated values while holding all other variance components at their estimated values.
We then reduced them simultaneously while holding all other variances at their estimated
values and calculated the mean percent increase in power compared to the “baseline”
Situation when only estimated values were used. We report the mean percent power
increase representing the average percent increase in power over the sampling period (5 —
25 years) compared to a Situation using the estimated variance components. The mean

percent change was calculated as

25
(( power _ reduced - — power _ full - ) /( power _ full - ) x 100
l l l

 

21
Where power_reduced,~ is the power to detect a -l .0 mm'year'1 trend under the scenario of

reduced residual or coherent temporal variation (or both) in year i and power full,- is the

125

power to detect the same trend under the scenario using the estimated variance
components from equation 2 in year i.

The sensitivity analysis revealed that the coherent temporal variation had a large
effect on the power to detect trends (Table 4). Reducing the coherent temporal variation
to 50 and 25% of the estimated value led to an average percent increase in power of 35
and 95%, respectively. Conversely, setting the residual variance to 50 and 25% of
estimated values led to only 3 and 5% increases in power, respectively. Thus, even
though coherent temporal variation comprised only 4% of the total variation for
Wisconsin and residual variation comprised 75% of Wisconsin’s the total variation;
coherent temporal variation had a disproportionately large inﬂuence on the power to
detect trends. However, once the coherent temporal variance was set to 25% of estimated
value, setting the residual variance to 25% of estimated value did lead to a slightly larger
increase in power, a further 8% increase over the baseline estimates when compared to
just setting coherent temporal variance to 25% of estimated value. The strong effect of
temporal coherent variation to reduce trend detection capabilities was also demonstrated
by Urquhart et a1. (1998). Because this source of temporal variation cannot be reduced by
changing the design of a monitoring program, only an increased sampling duration will
lead to an increase in statistical power (Urquhart et al. 1998; Kincaid et al. 2004). This
example illustrates the importance of examining variance components of potential
monitoring indices, because even a small (as estimated as percent of the total variation)
coherent temporal variation component can reduce trend detection capabilities over the

short-terrn.

126

Although coherent temporal variation can greatly reduce power, the power to detect
trends can also be affected by the allocation of resources to either sample more lakes per
year or sample more ﬁsh per lake. The effect of increasing the number of lakes sampled
each year versus increasing the number of ﬁsh sampled from each lake on the power to
detect trends is important from a management perspective because this issue represents a
trade-off between resource allocations. Should resources be allocated towards sampling
more ﬁsh from each lake (e. g., obtaining a more precise estimate of each lake’s status) or
on sampling more lakes within the region? In our analysis of the age 4 walleye Michigan
data, obtaining a more precise estimate of a lake’s status did not improve trend detection
as much as increasing the number of lakes sampled each year. For the age 4 walleye
Wisconsin data, again relatively high coherent temporal variation resulted in relatively
low power regardless of the sampling design used.

High lake-to-lake (spatial) variance has been Shown to reduce the power to detect
trends (e.g., Urquhart et al. 1988). However as we Show here, the relative importance of
lake-to-lake variance is dependent on the proportion of lakes sampled from the
population of lakes each year. For example, in our analysis of the age 4 walleye Michigan
data, we were able to obtain a better estimate of lake-to-lake variance when we sampled
60% of the lakes each year compared to sampling 3% of the lakes each year.
Consequently a reduction in lake-to-lake variance did not have an appreciable effect on
power under the 60% sampling scenario. However, when sampling only 3% of the
population of lakes each year, lake-to-lake variation became more important and
reductions in this source of variation led to an increase in power. Thus, in Situations with

a large lake-to-lake variance component, it may be advisable to sample some lakes

127

repeatedly (e.g., sample ﬁxed sites) in order to obtain a better estimate of lake-to-lake
variance to increase power. However, as illustrated with the Wisconsin analysis, if
coherent temporal variation is present, even a large reduction in other sources of variance
may not lead to an improvement in power.

Furthermore, the statistical model used to estimate trends Should be considered
during the design stage of a monitoring program. In our analyses, some models were not
estimable over a short sampling duration when only 3% of the population of lakes were
sampled each year. This illustrates how the sampling design (e. g., a simple random
sample in our analyses) can affect what kind of statistical model can be used for trend
detection. If detecting trends over a Short time period is of interest, then having ﬁxed sites
in addition to randomly selected sites iS desirable. The use of ﬁxed sites will ensure that
some lakes are sampled repeatedly over time and thus allow some models to be
estimable. Although it was not within the scope of this paper to explore the many
alternative sampling designs, the type of sampling design employed, such as the use of
ﬁxed Sites in combination with a random selection of lakes each year, can affect power to
detect trends (Urquhart et al. 1988). With information on the components of variance for
desired monitoring indices, management agencies can explore alternate designs in an

effort to maximize power.
Conclusions

The use of historical data from state and federal agencies provides one source of data
that can be used to investigate the presence of trends in ﬁsheries data for multiple
populations (e.g., this study, Reckahn 1986; Beard and Kampa 1999). Much of the

historical data, however, were not collected following probability sampling methods, in

128

which every sampling unit has a known probability of being sampled (Olsen et al. 1999).
Rather, waterbodies were often sampled based on expert choice (i.e., judgment sampling;
Olsen et al. 1999), selected by convenience, or in response to local or regional political
concerns (e.g., convenience sampling; Olsen et al. 1999). Although it must be
acknowledged that the non-probability based sampling associated with the historical data
we used has implications when making statistical inference to the population of lakes or
streams as a whole, these data provide a unique opportunity to examine regional trends.
Furthermore, because the implementation of probabilistic sampling designs is only now
becoming more prevalent, historical data often represent the only source of information
that can be used to inform the development of monitoring programs designed to describe
the status and to detect trends of aquatic indices.

Although the statistical power to detect trends is important to consider when
developing a monitoring program, there are other components of a monitoring program
that should also be considered. For example, the costs and beneﬁts of implementing a
monitoring design Should be considered along with the uncertainties associated with
alternative designs (MacGregor et al. 2002). Thus, power analysis represents one source
of information to be used in the processes of designing an ecological monitoring
program. Examining variance components of desired indices, power analysis, and other
quantitative analyses that take into account uncertainties and expected beneﬁts of
monitoring programs, represents powerful tools that will help guide ﬁsheries

management agencies develop effective monitoring programs.

129

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132

Table 1. Fish species, age, sample size (N, number of observations used in the analyses),
gear type used to collect ﬁsh, and sampling years used in the trend analysis for Michigan
and Wisconsin inland lakes. M1 = Michigan, WI = Wisconsin, BLG = bluegill, PSF =
pumpkinseed sunﬁsh, LMB = largemouth bass, SMB = smallmouth bass, YEP = yellow

perch, NOP = northern pike, WAE = walleye, EF = electroﬁshing, TN = trap net, FN =

 

 

 

fyke net.
N Gear type Sampling years
Species (age) MI WI Ml WI MI WI
BLG (2) 261 162 EF EF 1961-2002 1959-2003
BLG (3) 265 216 EF EF 1962-2002 1958-2003
BLG (4) 261 245 EF EF 1963-2002 1958-2003
PSF (2) 51 66 TN EF 1960-2002 1959-2003
PSF (3) 120 132 TN EF 1960-2003 1959-1992
PSF (4) 143 146 TN EF 1958-2003 1959-1992
LMB (2) 277 227 EF EF 1961-2002 1958-2003
LMB (3) 275 285 EF EF 1963-2002 1959-2003
LMB (4) 243 273 EF EF 1963-2002 1959-2002
SMB (2) 93 52 EF EF 1963-2001 1957-2003
SMB (3) 74 47 EF EF 1963-2001 1957-2003
SMB (4) 61 44 EF EF 1963-1999 1956-2003
YEP (2) 266 167 EF EF 1961-2002 1958-2003
YEP (3) 229 203 EF EF 1961-2002 1958-2003
YEP (4) 185 187 EF EF 1961-2002 1958-2003

 

133

 

Nora)
NOP (3)
NOP (4)
WAEQ)
WAEB)

WAE (4)

157

161

151

236

210

176

166

176

183

303

401

434

FN

FN

FN

EF

EF

EF

FN

FN

FN

FN

FN

1960-2002

1957-2002

1957-2002

1967-2002

1967-2002

1967-2002

1947-2002

1947-2002

1947-2002

1 946-200 1

1 946-2001

1 946-2001

 

134

Table 2. Parameter estimates for the ﬁxed effect of sampling year (ﬁxed regional trend

(mm-year"),/IA) followed by standard error (s.e.) in parentheses, F -value, and P-value for

mean length at age of seven warm and coolwater ﬁsh Species in Michigan and Wisconsin

inland lakes. Signiﬁcant regional trends are Shown in bold (or =0.05). M1 = Michigan, WI

= Wisconsin, BLG = bluegill, PSF = pumpkinseed sunﬁsh, LMB = largemouth bass,

SMB = smallmouth bass, YEP = yellow perch, NOP = northern pike, WAE = walleye,

n.e. = not estimable.

 

 

 

j (s.e.) F-value P-value

Species MI WI MI WI MI WI

(386)

BLG (2) -0.176 n.e. 1.20 n.e. 0.282 n.e.
(0.160)

BLG (3) -0.012 -0.425 0.01 4.73 0.944 0.118
(0.173) (0.195)

BLG (4) 0.004 -0.413 0.00 4.43 0.983 0.059
(0.198) (0.196)

PSF (2) n.e. n.e. n.e. n.e. n.e. n.e.

PSF (3) -0.046 n.e. 0.03 n.e. 0.873 n.e.
(0.262)

PSF (4) 0.066 -0.381 0.08 2.48 0.788 0.176
(0.237) (0.242)

LMB (2) -0.221 n.e. 0.69 n.e. 0.412 n.e.
(0.265)

 

135

 

LMB (3)

LMB (4)

SMB (2)

SMB (3)

SMB (4)

YEP (2)

YEP (3)

YEP (4)

NOP (2)

NOP (3)

NOP (4)

WAE (2)

WAE (3)

-0390
(0.267)
-0292
(0.285)
-0.202
(0.425)
-0392
(0.743)
n.e.
-0077
(0.176)
-0.271
(0.210)
0.165
(0.260)
-0430
(0.753)
11.6.

11.6.

0.096
(0.448)

0.074

0.306

(0.314)

0.672

(0.313)

n.e.

11.6.

11.6.

11.6.

n.e.

11.6.

11.6.

11.6.

-0.036

(0.435) ‘

-0.917
(0.283)

-0.530

2.13

1.05

0.23

0.28

11.6.

0.19

1.69

0.40

0.33

11.6.

11.6.

0.05

0.01

0.95

4.59

11.6.

11.6.

11.6.

11.6.

n.e.

11.6.

11.6.

11.6.

0.01

10.52

4.26

0.157

0.326

0.655

0.626

11.6.

0.665

0.213

0.545

0.577

11.6.

11.6.

0.831

0.936

0.338

0.045

11.6.

11.6.

11.6.

11.6.

11.6.

11.6.

11.6.

11.6.

0.947

0.002

0.042

 

136

 

(0.918) (0.257)
WAE(4) 0.138 -0.676 0.03 8.13 0.867 0.005

(0.816) (0.237)

 

137

Table 3. Estimated variance components followed by standard error in parentheses from

a weighted mixed mode] examining mean length at age over time for Michigan and

Wisconsin inland lakes. Variance components signiﬁcantly different from zero are shown

in bold (a =0.05). YEP = yellow perch, LMB = largemouth bass, WAE = walleye.

 

 

Species Lake-lake Coherent Ephemeral Trend Residual
(age) (6'02) temporal temporal variation error
(4 2) (6.2) (42) (6 2)
Michigan
YEP (2) 59.1 31.6 227.1 0.4 765.9
(91.4) (23.5) (100.4) (0.43) (200.4)
LMB (3) 240.9 32.8 455.4 1.4 1145.0
(108.8) (40.1) (121.4) (1.1) (261.0)
WAE (3) 1526.4 95.5 533.7 8.2 1238.8
(368.8) (101.6) (168.8) (4.7) (315.4)
WAE (4) 1531.8 16.1 928.4 4.9 549.9
(402.0) (88.4) (268.2) (4.2) (216.1)
Wisconsin
WAE (3) 833.5 313.2 225.6 0.4 2230.9
(139.9) (179.1) (63.9) (0.4) (504.9)
WAE (4) 1001.8 260.7 319.3 0.8 4936.2
(167.6) (155.6) (87.9) (0.5) (1063.9)

 

138

Table 4. Mean percent increase in statistical power due to setting the estimated residual

and coherent yearly variance to 50 and 25% of estimated values. The power estimates

correspond to a temporal trend of -1 .0 mm-year'I in mean length at age for age 4 walleye

sampled in Wisconsin inland lakes. The mean percent increase reported is the average

percent increase in power over the sampling period (5 — 25 years) compared to a situation

using the estimated variance components from historical data (see Table 3 for variance

estimates; population of lakes = 50, 30 lakes sampled each year for 25 years, 10 ﬁsh

 

 

sampled per lake).
50% of 25% of 50% of 25% of 25% of coherent
residual residual coherent coherent temporal and
variance variance temporal temporal residual variance
variance variance
Mean percent 3 5 35 95 103
increase

 

139

 

Figure 1.

 

 

 

 

 

      

    

 

100 ] —

80 ‘ DreSIdual !
1 I ephemeral temporal}
; lcoherenttemporal ‘

.1 %
1 gﬂmgbm
1

4o 1

20 ‘
1

0 . ........ ,iyr.

 

   

YEP (2). MI LMB(3),M| WAE(3).M| WAE(4).M| WAE(3).W| WAE(4).W|

140

Power

Figure 2.

1.0 -
0.9 -
0.8 -
0.7 -
0.6 .
0.5 -
0.4 -
0.3 .
0.2 -
0.1 4

 

  

Michigan

 

 

0.0

1.0 -
0.9 a
0.8 ~
0.7 4
0.6 -
0.5 4
0.4 3
0.3 -
0.2 ~
0.1 -

 

 

Wisconsin

1 = -0.5

 

 

0.0
O

7 l r T I

10 12 14 16 18 20 22 24

Sample duration (yrs)

141

Power

Figure 3.

Michigan

 

 

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0'8 8 ﬂ “-- fO'ﬁsh

"""" 20 ﬁsh
07 ——- 30 ﬁsh

0.6 -'
0.5 4
0.4 i
0.3
0.2
0.1

 

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0.9 ‘-
0.8 4.
0.7 =
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”’

 

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'o- ' '-
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0.4 - -----
0.3 .
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"'

Number of lakes

142

 

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