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THE VERTICAL DISTRIBUTION OF PHYTOPLANKTON:
OBSERVATIONS, THEORY, EXPERIMENTS

presented by

JARAD P. MELLARD

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SIOB KIProj/AocaPreleIRClDatoDqundd

 

THE VERTICAL DISTRIBUTION OF PHYTOPLANKTON: OBSERVATIONS,
THEORY, EXPERIMENTS

By
J arad P. Mellard

A DISSERTATION

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

DOCTOR OF PHILOSOPHY

Plant Biology
Ecology, Evolutionary Biology, and Behavior

2010

ABSTRACT

THE VERTICAL DISTRIBUTION OF PHYTOPLANKTON:
OBSERVATIONS, THEORY, EXPERIMENTS

By
J arad P. Mellard

Extrinsic and intrinsic factors have been shown to determine spatial pattern for-
mation of populations and we show how both of these factors interact to determine
spatial patterns in phytoplankton communities. Determinants of the spatial (ver-
tical) distribution of phytoplankton remain under-investigated and untested. One
of the leading hypotheses to explain phytoplankton vertical distribution patterns is
that competition for essential resources, nutrients and light, in opposing gradients
determines vertical distribution. We used a combination of mathematical modeling,
experiments in plankton towers, and lake surveys across major environmental gradi-
ents to study what determines the vertical distribution of phytoplankton, focusing on
competition for nutrients and light.

In chapter 2, we combined two previous bodies of theory on well-mixed and poorly-
mixed water columns to develop a model for a stratified water column. In addition,
we considered multiple nutrient sources— one source to the bottom of the water column
and one source to the surface mixed layer. Employing this combination of stratifica-
tion and multiple nutrient sources in our model, we found eight distinct evolutionarily
stable strategy (ESS) distributions. The predicted ESS distributions from our model
accurately reflected phytoplankton distributions we have observed in lakes. Algae
can exist in the mixed layer, deep layer, or in the mixed layer and deep layer to—
gether. Algae in either of these locations can be limited by nutrients or colimited by
nutrients and light, but counterintuitively, only the mixed layer can be light limited.
We predict how the E88 distribution should change as a function of relevant major

environmental parameters known to vary across bodies of water.

In chapter 3, we conducted experiments to examine how spatial patterns in algae
form as the result of interacting processes: active movement and habitat selection,
growth, and depletion of resources. These experiments were conducted to test prior
theory that predicted that algae will aggregate into a thin layer at a depth and that
that depth depends on resource supply rates. In all experimental plankton towers, al-
gae formed thin layers at the surface, which disappeared at low-nutrient supply by the
end of the experiment. Higher nutrient supply rates created more biomass and made
the algae relatively more light limited. Thus, results qualitatively supported many
of our theoretical predictions. In addition, algae exhibited spatial dynamics consis-
tent with niche construction processes, i.e. modification of their environment and
responses to these modifications through behavioral movement. These experiments
explain how intraspecific competition can drive vertical distributions.

In chapter 4, we surveyed stratified lakes to measure the variation in vertical
distributions of phytoplankton and ascribe environmental conditions to the vertical
distributions. A primary purpose was to evaluate model predictions of the vertical
distribution of phytoplankton in stratified lakes with multiple nutrient sources, while
also considering that the phytoplankton communities are made up of many different
species. Lakes with single pronounced peaks of algal biomass mostly conformed with
model predictions of how environmental variables affect vertical distribution. Phy-
toplankton also frequently formed multiple peaks in biomass within a water column.
The number of peaks that formed depended on the physical space available and the
amount of resource heterogeneity in that space. Peaks were typically dominated by
a single species and each peak in a water column existed at different nutrient and
light conditions. Taxonomic groups sorted across lakes and with depth within lakes
and surface and deep vertical niches could be filled by different taxonomic groups
and species. Competition for nutrients and light appears to be a primary driver of

phytoplankton community structure and vertical distribution.

DEDICATION

I dedicate this work to my family, thank you for supporting me through the years,

and to all those who toil in obscurity.

iv

ACKNOWLEDGMENT

First and foremost, I would like to thank my advisors, Chris Klausmeier and Elena
Litchman. This work is very much influenced by and in collaboration with them. I
would also really like to thank another collaborator, Kohei Yoshiyama, for all the
good detailed work and ideas contributed to these studies. I would like to thank
Mary Anne Evans for her hard field work and Don Schoolmaster for much conceptual
help in analyses. I would like to thank Pam Woodruff, Darice Shumway, and Ally
Hutchens for help with lab and field work. I would also like to thank Paula Tezanos for
help in identification of phytoplankton species and Stuart Jones for providing many
useful comments on the thesis and helping in statistical analyses used in chapter 4.
This work could not have been completed without the help of all of you.

In addition, I would like to thank Kelly Amrhein, Paula Tezanos, Chris Steiner,
Anne Schwaderer, and Claes Becker for contributing in discussions of chapter 3, and
Stuart Jones and Jay Lennon for helpful discussions of analyses used in chapter 4.
Comments from Jim Grover, and several anonymous reviewers greatly improved chap-
ter 2 and I would like to thank Jason Cepela, Emily Grman, and Todd Robinson for
helpful comments on chapter 3 and Emily Grman, Kali Bird, and Colin Kremer for
comments on chapter 4. This work was supported by funding from National Science
Foundation Division of Environmental Biology 06-10531 and 06-10532 and the J .S.

McDonnell Foundation.

TABLE OF CONTENTS

List of Tables ................................. ix
List of Figures ................................ xii
Introduction ........................... 1
1.1 Context .................................. 3
1.1.1 Well-mixed water columns .................... 4
1.1.1.1 Observations ...................... 4

1.1.1.2 Theory and empirical tests of theory ......... 5

1.1.2 Poorly-mixed water columns ................... 6
1.1.2.1 Observations ...................... 6

1.1.2.2 Theory and empirical tests of theory ......... 7

1.1.3 Stratified water columns ..................... 9
1.1.3.1 Theory and empirical tests of theory ......... 9

1.2 Outline ................................... 12

The vertical distribution of phytoplankton in stratified water columns
16

2.1 Abstract .................................. 16
2.2 Introduction ................................ 18
2.3 Methods .................................. 23
2.3.1 Full Model ............................. 23
2.3.1.1 Simulating the full model ............... 27

2.3.2 Simplified model ......................... 27
2.3.2.1 Definitions and assumptions .............. 29

2.3.2.2 Equilibrium conditions ................. 30

2.4 Results ................................... 34
2.4.1 Spatial distribution states .................... 34
2.4.2 Possible distribution states .................... 38
2.4.2.1 Two special cases if RinML = 0 ............ 40

2.4.3 'Ifansitions along environmental gradients ........... 43

2.5 Discussion ................................. 49
2.5.1 Assumptions, limitations, and extensions ............ 52
2.5.2 Model predictions ......................... 54
2.5.3 Relevance ............................. 56

2.6 Appendix ................................. 58

vi

3 Experimental test of phytoplankton competition for nutrients and

light in poorly-mixed water columns ............... 76
3.1 Abstract .................................. 76
3.2 Introduction ................................ 78
3.3 Theory ................................... 80
3.4 Experiment methods ........................... 87
3.5 Experiment results ............................ 91
3.5.1 Physiology ............................. 103

3.6 Discussion ................................. 106
3.7 Appendix ................................. 114
3.7.1 Model ............................... 115
3.7.2 Appendix figures ......................... 120

4 Community-wide phytoplankton vertical distribution in stratified

temperate lakes ......................... 127
4.1 Abstract .................................. 127
4.2 Introduction ................................ 130
4.2.1 Predictions from previous theory: ................ 133

4.3 Survey methods .............................. 137
4.3.1 Sampling in field ......................... 137
4.3.2 Laboratory measurements .................... 138
4.3.3 Survey analysis .......................... 141

4.4 Results ................................... 145
4.4.1 Ecosystem ............................. 145
4.4.1.1 Vertical distributions of phytoplankton ........ 145

4.4.1.2 Environmental parameters ............... 147

4.4.1.3 Vertical distributions across environmental gradients 147

4.4.1.4 Biomass ......................... 156

4.4.1.5 Multiple peak coexistence ............... 157

4.4.1.6 Number of peaks .................... 157

4.4.2 Community ............................ 160
4.4.2.1 Species Diversity .................... 160

4.4.2.2 Whole-community comparisons ............ 162

4.4.2.3 Taxonomic group and species ............. 165

4.5 Discussion ................................. 170
4.5.1 Variation in phytoplankton vertical distributions ........ 170
4.5.2 Depth of algae ........................... 172
4.5.3 Amount and distribution of biomass .............. 175
4.5.4 Multiple peaks and the environment .............. 176
4.5.5 Community ............................ 177
4.5.6 Future work ............................ 181
4.5.7 Further importance and conclusions ............... 182

4.6 Appendix ................................. 183

vii

Bibliography................... ...... 194

viii

2.1

2.2

2.3

2.4

3.1

4.1

4.2

4.3

4.4

4.5

LIST OF TABLES

Variables in the model ...........................

Parameter values unless noted otherwise. Ranges explored here are in
parentheses. ................................

Combinations of equilibrium spatial distribution states of the mixed
layer and deep layer. X indicates the combination is infeasible. All
other combinations are possible subject to criteria listed and their cor-
responding figures and sections in the appendix are indicated.

Effect of environmental parameters on state variables ..........
Parameter values unless noted otherwise .................
Summary of major environmental variables ...............

Multiple linear regression results for depth of global fluorescence max-
imum versus all environmental variables. Only relationships from the
best model were included in the table. The intercept was not significant
(P< 0.05) so it was not included in this table. .............

Multiple linear regression results for depths of fluorescence peaks versus
all environmental variables. Only relationships from the best model
were included in the table. ........................

Multiple linear regression results for depths of single fluorescence peaks
versus all environmental variables. Only relationships from the best
model were included in the table. ....................

Multiple linear regression results for integrated fluorescence (“biomass”)
versus all environmental variables. Only relationships from the best

model were included in the table. ....................

ix

25

26

35

37

119

147

150

151

4.6

4.7

4.8

4.9

4.10

Multiple linear regression results for number of peaks versus the fol-
lowing loglo transformed environmental variables: deep layer span, TP
gradient in the deep layer, light gradient in the deep layer, and back-
ground light attenuation; as well as day-of—year. Only relationships
from the best model were included in the table. ............

Multiple linear regression results for Shannon diversity versus all envi-
ronmental variables in the best model. Environmental variables con-
sidered were the same for the mixed layer and main DCM and included:
turbulent mixing, water column depth, Daphnz'a densities, other major
grazers densities, background light attenuation, total phosphorus at
the bottom, total phosphorus in the mixed layer, and the light level at
the bottom of the mixed layer. Only relationships from the best model
were included in the table. ........................

Multiple linear regression results for dissimilarity versus the following
loglO environmental variables as indicated by the DCA to potentially
play a role: TP at the bottom, and abg’ Daphm'a, and other major
grazers. Only relationships from the best model were included in the
table. Note that TP at the bottom in the best model could be replaced
by TP gradient in the deep layer (P=0.05) but the model cannot in-
clude both due to multicollinearity. ...................

Multiple linear regression results for relative abundance of taxonomic
groups versus all environmental variables in the best model. Environ-
mental variables considered were: turbulent mixing, mixed layer depth,
water column depth, Daphm'a densities, other major grazers densities,
background light attenuation, total phosphorus at the bottom, total
phosphorus in the mixed layer. .....................

Multiple linear regression results for relative abundance of taxonomic
groups versus local environmental variables in the best model. Envi-
ronmental variables considered were: light at the sample depth and
dissolved phosphorus at the sample depth. For integrated mixed layer
samples, the light level at the bottom of the mixed layer was used as
the light at the sample depth. NS indicates that the best model was
not significant (P< 0.1). .........................

X

158

161

165

171

4.11 Logistic regression results for whether a lake switches identity of the
dominant species within the water column (by comparing all samples
within a water column) versus the following loglO environmental vari-
ables: water column depth, mixed layer depth, turbulent mixing co-
efficient, background light attenuation, T P at the bottom, and TP in
the mixed layer. Only relationships from the best model were included
in the table. ................................ 172

4.12 Appendix Table of dominant species for all samples. Shown are relative
abundances for species densities that are > 5% of the total community
density of a sample ............................. 184

xi

LIST OF FIGURES

2.1 Example phytoplankton vertical distributions observed in stratified
lakes. ...................................

2.2 A) Example numerical simulation output of full model showing a DCM
and nutrient-limited mixed layer at steady-state. Solid line is biomass
(cells mL’l), dashed line is nutrient concentration (pg dissolved P

LTl), and dotted line is log light (pmol photons m—Zs" 1). Parameters
are as in Table 2.1 except Rsed = 220 pg P L—liDML = 102 m2
d—1;Rin(z) = 0.6 pg P L-1 d—1 for 0 g 2 S 5, Rin(z) = 0 for z > 5.
B) Example representation of simplified model showing a DCM and
nutrient-limited mixed layer as in the output of the full model.

2.3 Equilibrium vertical profiles. ......................

2.4 Effect of environmental parameter on biomass and vertical distribution.

2.5 Two dimensional bifurcation plot of sediment phosphorus concentra-
tion, Rsed’ and mixed layer nutrient input, RinML' Note that the Ben-
thic Layer and DCM regions are directly on the Rsed axis (RinML =

0). Environmental parameters: abg = 0.1 m‘l; zm = 5 m. .....

2.6 Two dimensional bifurcation plot of background light attenuation, abg’

and mixed layer depth, Zm- Increases in both parameters can lead
to extinction. Environmental parameters: Rsed = 200 pg P LTl;

RinML = 0.1 mg P m—2 (1.1.

3.1 Predicted total and depth distribution of biomass through time. . . .

xii

28

47

48

3.2

3.3

3.4

3.5

3.6

3.7

Points are resource conditions within different water columns at dif-
ferent depths. Resource conditions for a low-nutrient supply water
column (hollow points), mid-level nutrient supply water column (gray
donuts), and high-nutrient supply water column (solid points, some
on tOp of one another) are shown. Since light declines with depth, the
point with the highest light value for each water column is also the shal-
lowest depth. Note that the arrows show the resource conditions for
the different predicted vertical distributions of a benthic layer, DCM,

and surface layer corresponding to the depth distributions in Figure 3.1.

Predicted integrated biomass (a) depth of algal layer and (b) depth of
the algal layer as a function of nutrient concentration at the bottom.
Both (a) and (b) have a solid line representing simulations from the
full model averaged over days 30—50 and a dashed line representing the

equilibrium biomass (a) and z* depth (b) predicted by the E88 model.

Observed total and depth distribution of biomass through time.

Amount of biomass in surface layer (if present) and background through
time for all eight treatments (a is lowest nutrients increasing to h, the
highest nutrients). ............................

Data points are resource conditions within different water columns at
different depths. Resource conditions for a low-nutrient supply tower
(hollow points), mid-level nutrient supply tower (gray donuts), and
high-nutrient supply tower (solid points, some on top of one another)
are shown corresponding to nutrient treatments Rin =5, 50 and 5000

pg P L"1 respectively. Since light declines with depth, the data point
with the highest light value for each tower is also the shallowest depth.
Note that the arrows point out the different treatments corresponding
to the depth distributions in Figure 3.4. ................

Effect of nutrient treatment on equilibrium biomass and depth distri-
bution. a) Observed integrated biomass averaged over days 30—50 as a
function of nutrient treatment. Shown is the almost significant linear
relationship between biomass and log nutrient supply (slope: 22503,
t = 2.28, P = 0.06) and not shown is the significant linear relationship
between log biomass and log nutrient supply (slope: 0.26, t = 2.77,
P < 0.05). b) Observed modal depths for days 30-50 as a function of
nutrient treatment. Note that points for the nutrient treatments of 5,
10, and 50 pg P L—1 have been offset 0.025 m for clarity while the
points for nutrient treatments of 100, 250, 500, 1000, 5000 pg P L—1
all fall directly on top of one another and have not been offset.

xiii

85

86

94

96

97

99

3.8

3.9

3.10

3.11

3.12

3.13

3.14

4.1

4.2

4.3

4.4

Proportion of biomass in the surface layer and the background at the
end of the experiment versus nutrient treatment. ...........

Characteristic layer thickness for all treatments and times. Points are
only plotted if a surface layer was calculated to exist. .........

At the end of the experiment, the light level leaving the bottom of
the water column, 10111;, is shown as a function of nutrient treatment.
There was a significant linear relationship between log [out and log
nutrient treatment (slope: —1.18, t = —3.88, P < 0.01). .......

Chlorophyll a, nutrient, and stoichiometric quantities. ........
Biomass profiles for all towers at two time points: day 1 and day 50.
Profiles of chlorophyll a at the end of the experiment for all towers.
Picture 1: Picture of experimental plankton towers. .........

Relationship between chlorophyll a as measured in the laboratory with
standard protocols using ethanol extraction and on a laboratory fluo-
rometer and fluorescence as measured in the field using SCAMP built-
in fluorometer for all lakes, times, and samples (including mixed layer
and discrete depths). Regression equation: chlorophyll a = 23x fluo-

2 _
rescence —0.55, P<0.001, Radj. —— 0.58 ..................

Depths of a) global fluorescence maximum, b) peaks in fluorescence,
and 0) water column. Depths relative to water column depth of d)
global fluorescence maximum and e) peaks in fluorescence. Histograms
include all lakes and times (n=104 for fluorescence maximum and water
column and n=170 for all peaks). ....................

Nitrogen and phosphorus relationships in the data. a) Molar N :P ratio
for total nitrogen and total phosphorus measured in the mixed layer
(mean=115, median=97, minimum=35, maximum=932). b) Relation-
ship between loglO Total nitrogen and loglo Total phosphorus for all
lakes, times, and samples (including mixed layer and discrete depths).
Pearson’s correlation r=0.75, P <0.001, df=278). ...........

Phosphorus gradient present in most lakes and times (paired t-test,
t=2.27, P=0.013, df=105). Note that in the plot, nutrient concentra-
tions are log scaled .............................

xiv

100

101

102

105

121

125

126

140

146

148

149

4.5

4.6

4.7

4.8

4.9

4.10

4.11

4.12

4.13

Logistic regression relating probability of a benthic layer forming to
loglo light at the bottom of the water column (.2 statistic=3.57, P<
0.001). ...................................

Depth of peak of single peak lakes versus environment. ........
Partial residual plots for the depth of peak of single peak lakes.

Partial residual plots for total biomass (integrated fluorescence) versus
environmental variables in the best model. ...............

Partial residual plots for deep layer biomass (integrated fluorescence in
the deep layer) versus environmental variables in the best model. . . .

Partial residual plots for mixed layer biomass (integrated fluorescence
in the mixed layer) versus environmental variables in the best model.

Type II regression of log light values at a peak versus log dissolved
phosphorus values at a peak ........................

Partial residual plots for number of peaks versus environmental vari-
ables in the best model. .........................

Detrended correspondence analysis plot (DCA) of all communities (all
lakes and depths). Also plotted are environmental vectors for loglo
transformed environmental variables that did not overlap too strongly
with another variable (excluded turbulent mixing coefficient because
it overlapped with abg and TP measured at the depth of the sample

because it overlapped with TP measured at the bottom). Other vari-
ables and their scores (vectors scaled by correlation coefficient) for axis
1 and 2 respectively: DP is soluble reactive phosphorus (-0.24397522,

0.257411923) and light is irradiance (0.02501621, 0.181052901) at the
depth of the community sample, abg is background light attenuation

(-0.01306323, 0.341490988), TP(zb) is total phosphorus measured at
the bottom (0.12299715, 0.387226041), Daphnia is Daphnia density
(0.10589080, 0.297177857), and Zoop is density of other major grazers
(-0. 13330044, 41008967929). .......................

XV

150

157

158

159

160

160

163

4.14 Frequency distributions for Bray-Curtis community dissimilarity in-
dices of different community samples. Dissimilarity is maximum at a
value of 1. a) Dissimilarity for samples taken within a lake. b) Across
lake dissimilarity for communities. c) Dissimilarity of mixed layer com-
munities compared to other mixed layer communities. (I) Dissimilarity
of main DCM communities compared to other main DCM communi-
ties. e) Correlation between dissimilarity of mixed layer communities
(part c) and dissimilarity of main DCM communities (part e). f) Dis-
similarity between paired mixed layer and main DCM samples for each
lake. .................................... 164

4.15 Partial residual plots for community dissimilarity between the mixed
layer and main DCM versus environmental variables in the best model. 165

4.16 Relative abundance of taxonomic groups across lakes and with depth. 168

xvi

Chapter 1

Introduction

“Space complicates ecological interactions by two fundamental mecha-
nisms: it allows for non-uniform patterns of environment and population
density, and for movement (dispersal or migration) from one location to
another.”
-S. Levin

Ecological communities are structured in space across multiple scales. The hetero—
geneous nature of the environment (Burrough 1981) translates to community compo-
sitional patterns at local, regional, and even global scales (MacArthur 1972). Different
ecological processes may determine species distributions at different scales and these
processes can feed back on one another (Levin 1992, Tilman and Kareiva 1997, Lei-
bold et al. 2004). A community is comprised of individual populations and each
is distributed in space according to its tolerances to stresses and requirements for
resources (Levin 1976, Tilman and Pacala 1993). Spatial heterogeneity may be key
to explaining the coexistence of many similar species (Hutchinson 1961).

Spatially heterogeneous distributions of populations have important consequences
for ecosystem-level processes (Loreau et al. 2003a). Production can vary in space
which influences the spatial distributions of consumers and transfer of energy to

higher trophic levels (Johnsen and Jakobsen 1987) as well as spatial coupling between

1

systems due to consumer behavior (McCann et a1. 2005). Populations distributed
in space also change the flux of matter, energy, and nutrients between ecosystem

components and ecosystems, creating meta-ecosystems (Loreau et al. 2003b).

I will use phytoplankton (algae) to illustrate how spatial heterogeneity can be gen-
erated. Algae exhibit striking spatial patterns that are likely the result of opposing
resource supply gradients (Fee 1976, Klausmeier and Litchman 2001). Light is sup-
plied from the surface and declines exponentially with depth due to abiotic and biotic
absorbance and scattering (Kirk 1975a). Nutrients usually enter the water column
from the sediments at the bottom (Wetzel 1975). These opposing resource gradients
create a dilemma for algae, as they require both resources for growth. Many algae
are motile (Reynolds 1984) or have other ways to control their location in the water
column, such as regulation of buoyancy (Cullen and Maclntyre 1998), and thus are
not passively drifting about as the name plankton suggests. Where is the optimal

location in an environment with opposing resource gradients?

For algae, the optimal location within the water column is the depth where an
individual is equally limited by both light and nutrients (Klausmeier and Litchman
2001). This depth of colimitation depends on the resource supply rates. It also de-
pends on all the other algae in the water column. Algae can be at different depths
in the water column; physiological traits may determine each species depth of colim-
itation or “strategy.” As they grow, algae modify their environment due to resource
depletion, taking up nutrients and shading one another. These processes of move-
ment, resource depletion, and growth create feedbacks among algal strategies in the
aquatic environment. This is what I will refer to as algal games (Klausmeier and
Litchman 2001). This game will be key to my approach in understanding studying

vertical distributions.
The spatial distribution of algae is important because it controls ecosystem pro-

cesses such as whole-system primary production (Fee 1976), the flux of carbon to

2

deeper parts of a water body (Suess 1980), the flux of nutrients from the deep to
shallower waters (Garside 1985), and even the thermal properities and physical struc-
ture of the water body (Mazumder et al. 1990). Spatial heterogeneity in the aquatic
environment may also impact community-level processes and patterns such as resource
competition and species coexistence (Tilman 1982). Observed spatial distributions
may be the result of resource competition interactions within the community and
vertical niche partitioning between species may result in their coexistence (Carney
et al. 1988).

Before I outline my dissertation work, I will review relevant literature to provide a
context for my graduate research. Then I will briefly introduce each of my dissertation

chapters.

1.1 Context

The major axis of heterogeneity in lakes and oceans is the vertical dimension. Depth-
varying irradiance and turbulent mixing are prominent forms of vertical heterogeneity.
The foundations for present day ecosystem-level investigations focused on how light
and mixing impact phytoplankton populations and I will focus on studies that con-
sider these processes.

Phytoplankton spatial models generally focus on one-dimensional water columns
and come in two forms: well-mixed and poorly-mixed water columns. Phytoplankton
spatial models of light competition began with considering well-mixed populations
for simplicity, but include the underlying spatial heterogeneity in light. In well-mixed
water columns, algae are homogenized, hence no spatial patterns can form. In poorly-
mixed water columns, algae can be distributed heterogeneously with depth and may
aggregate into a thin layer. I consider a model to address poorly-mixed conditions

if it allows for any heterogeneous distribution of algae. Some of these studies that

3

address poorly-mixed conditions varied mixing levels to create conditions between
well-mixed and extremely poorly-mixed, where algae can still form patterns but the
mixing prevents the population from forming a thin layer. Although I have categorized
light competition studies into well-mixed and poorly-mixed water column categories,
note that many of the studies contain other aspects that makes them different from
each other, such as whether they include competition for nutrients, multiple species,
and traits related to buoyancy and swimming.

I will introduce theoretical developments and empirical tests of theory, empha-
sizing those studies that consider mixing and competition for light. Many of the
theoretical studies have been tested empirically. This is an area in ecology that has
advanced significantly, likely due to the close relationship between the modeling being
conducted and the explicit tests of predictions from those models. Of course it helps
that phytoplankton populations are amenable to experiments due to their small size

and fast generation time.

1.1.1 Well-mixed water columns

Phytoplankton spatial models of light competition start with well-mixed populations
(Huisman and Weissing 1994), but include heterogeneity in the form of the under-
lying light gradient. Many later models and experiments build on these well-mixed-

population results.

1 .1.1.1 Observations

Early observations of phytoplankton populations in the surface layer focused on the
importance of water column stability, specifically mixed layer depth, as a primary
determinant of spring algal blooms in temperate waters (Riley 1942). One of the first
examinations of how light sets the conditions for population growth showed that for

phytoplankton in a well—mixed layer, there is a critical depth for the mixed layer in

4

order for a population to persist there. That critical depth is set by the metabolic

balance between energy production and destruction (respiration) (Sverdrup 1953).

1.1.1.2 Theory and empirical tests of theory

Several very influential theoretical studies on effects of light competition and mixing
on phytoplankton populations were published in the mid-19905. Huisman and Weiss-
ing (1994,1995) put forth the theory of how light acts as a resource in a well-mixed
environment, which is similar but not identical to a nutrient: the light at the bot-
tom of a water column at equilibrium, Iout: predicts the outcome of competition for
light in a well-mixed water column, that is, the species with the lowest Iout wins
in competition, similar to R*. However it differs from R* in nutrient competition
in two ways: 1) [out depends on the light supply, [in 2) [out is a global measure
of the effects of a population on light, which is not the same as the local measure
of the effects of a population on light, 1*. Actually, [out < 1*, which means that
part of the population is experiencing negative growth. How can the population be
maintained then, without going extinct? It can be maintained because the losses from
that negative growth rate at depth are balanced by production above it (Huisman
and Weissing 1994). However, if the water column is too deep, the population can go
extinct because there is not enough production to balance those losses.

Light competition theory was tested and verified for monocultures (Huisman
1999) and multispecies mixtures (Huisman et al. 1999a). Huisman and Weissing
(1994,1995) also examined competition for light and nutrients and those predictions
were tested and verified as well (Passarge et al. 2006).

An in-depth analysis of how mixing depth, nutrient supply, light, biomass, sinking,
and recycling was undertaken by Diehl (2002) in a model that built on Huisman
and Weissing (1994,1995), and thus assumes a well-mixed phytoplankton population.

Diehl (2002) predicts biomass in the mixed layer to show a unimodal response to

5

mixed layer depth. Model predictions from Diehl (2002) were evaluated in several
field enclosure experiments (Diehl et al. 2002, Ptacnik et al. 2003). Predictions
of how mixing depth affects phytoplankton production, sedimentation, and resource
levels (Diehl 2002) were tested and verified, as well as how mixing depth differentially
affects sinking and nonsinking taxa (Ptacnik et al. 2003). Kunz and Diehl (2003)
also showed some evidence that consistent with field observations in lakes differing in

mixed layer depth.

1.1.2 Poorly-mixed water columns

Poorly-mixed conditions are necessary to examine spatial pattern formation. General
spatial models of continuous space start with the relatively simple (Skellam 1951) and
increase in complexity as outlined in Okubo (1980). Spatial models for phytoplankton
populations are related to these general models (Huisman et al. 1999c), and in some

ways, mimic their development.

1.1.2.1 Observations

Heterogeneous depth distributions of phytoplankton were observed and shown to be
a significant component of the ecosystem (Fee 1976). Fee (1976) showed that sig-
nificant phytoplankton populations and primary production occur below the mixed
layer in lakes. Fee (1976) explained how light and nutrient gradients could lead to the
formation of a deep chlorophyll maximum, DCM, which is a peak in chlorophyll well
below the surface, often at apparently suboptimal light levels (Camacho 2006). Fee
(1976) emphasized that the position of the DCM should be related to light penetra-
tion, but also hypothesized that sedimentation, grazing, and minimization of loss due
to respiration could be responsible for the large amount of deep layer biomass. Since
then, numerous hypotheses for DCM formation and vertical distribution patterns of

phytoplankton have been proposed (see Lindholm 1992 and references therein. For

6

example, offshore advection (Cullen et al. 1982), near-inertial internal wave shear
(Franks 1995), sinking in a density stratified water column (Condie and Bormans
1997), depth dependent grazing by zooplankton (Johnsen and Jakobsen 1987) or
mixotrophs (Tittel et al. 2003), lateral intrusions of nutrient rich water that may
stimulate growth (S. MacIntyre pers. comm), diel vertical migration of algae (Som—
mer and Gliwicz 1986, Gasol et al. 1991), preferential movement of algae to depth
that favors growth (Klausmeier and Litchman 2001), in situ growth (Fee 1976), and
behavioral responses to chemoclines or other information acting as sensory cues (Ger-

vais 1998, Clegg et al. 2007) have all been proposed to explain DCM formation.

1.1.2.2 Theory and empirical tests of theory

Spatial heterogeneity of a population was examined by relaxing the assumption of a
well-mixed water column and examining neutrally buoyant species in this environ-
ment. Huisman et al. (1999c) used numerical simulations of a spatially explicit model
to Show how bloom formation depends on physical mixing: if the water column depth
is less than a critical depth and turbulent mixing is less than a critical turbulence
level, then blooms can form. In this poorly-mixed environment, multispecies com-
petition for light showed that neutrally buoyant species competing for light should
always decline with depth, hence no DCM formation should occur under these con—
ditions (Huisman et al. 1999b). In addition, species were not likely to vertically
segregate, and in this kind of environment with just light competition, there are very
limited opportunities for coexistence (Huisman et al. 1999b).

Under poorly-mixed conditions, the species or individuals that obtain the best
position in the water column are favored (Huisman et al. 1999b, Klausmeier and
Litchman 2001). Considering a motile species competing for light and nutrients in
a poorly mixed water column, Klausmeier and Litchman (2001) showed there is an

evolutionarily stable strategy (ESS) depth that prevents growth in the rest of the

7

water column. Of note, Klausmeier and Litchman (2001) assume that the system
is adaptive, i.e. algae move to where conditions are best for growth. This adaptive
strategy can lead to non-intuitive results. For example, algae in a benthic layer are
far from their light source so one might predict them to be limited by light. However,
with adaptive movement, if there was not enough light at the bottom, the algae
would not move there. Therefore, Klausmeier and Litchman (2001) predict algae in

a benthic layer to be limited by nutrients, not light.

Studies that explicitly test the theory of how opposing resource gradients in
poorly-mixed water columns can generate vertical distributions of phytoplankton
were needed. I, in collaboration with Kohei Yoshiyama, Christopher Klausmeier,
and Elena Litchman, tested this theory (Klausmeier and Litchman 2001) in exper-
imental water columns (Chapter 3). We examined the dynamics and equilibrium
vertical distribution of phytoplankton along a gradient in nutrient loading and found
evidence for many of our dynamic and some equilibrium theoretical predictions in our

experiment.

Huisman et al. (2002) builds on previous work (Huisman et al. 19990) by adding
sinking to a light-limited population in a uniformly mixed water column, effectively
adding sinking to the arguments of Riley (1942). Previous work (Huisman et al.
1999c) showed there was a maximal water column depth and a maximal turbulent
mixing level for a population to persist, but with the addition of sinking, there is
also a minimal turbulent mixing level in order to keep the population from sinking
out of the photic zone. A theoretical study that varied sinking rate demonstrated
the maximal sinking rate in different environments (Huisman and Sommeijer 2002).
Theory predicts that the outcome of competition for light between sinking and buoy—
ant species can depend on turbulent mixing, with sinking species dominating at high
turbulent mixing levels and buoyant species dominating at low turbulent mixing lev-

els (Huisman and Sommeijer 2002, Huisman et al. 2004). An artificially mixed lake

8

that could be intermittently mixed was used to test this prediction. Comparison of
periods with artificial mixing versus periods without verified the predicted shift in
species dominance (Huisman et al. 2004).

More recently, an empirical study (Jaeger et al. 2008) examined some of the pre—
dictions related to Huisman et al. (2002) of how mixing intensity, water column depth,
sinking, and light affect phytoplankton populations. However, this study was also
complicated by the fact that there were community-level interactions and responses.
The combination of low mixing intensities, deep water columns, and diflerent species
with different motility and buoyancy related traits was shown to create vertical niche
partitioning in the experimental enclosures in the lake (Jaeger et al. 2008). Further-
more, Jaeger et al. (2010) conducted a theoretical study that extended the interactive
effects of mixing intensity, water column depth, sinking, and light (Huisman et al.
2002) to include nutrients. In these uniformly mixed water columns, Jaeger et al.
(2010) predicts that the population could be light or nutrient limited, depending on

the mixing intensity and water column depth.

1.1.3 Stratified water columns

Many bodies of water stratify, resulting in division of the ecosystem into distinct parts:
a well-mixed surface layer and a poorly-mixed deep layer. However, few theoretical
studies that include the feedbacks between phytoplankton and light have considered

the impacts of stratification on the vertical distribution of phytoplankton.

1.1.3.1 Theory and empirical tests of theory

Studies mentioned previously have generally focused on phytoplankton only in the
mixed layer (Huisman and Weissing 1994,1995, Diehl 2002). However, some consid-
ered a completely poorly-mixed water column (Huisman et al. 1999c, 1999b, Klaus-

meier and Litchman 2001) and one considered a stratified water column (Yoshiyama

9

and Nakajima 2002). Illustrating some of the complications that spatially-explicit
competition for nutrients and light can create, Yoshiyama and Nakajima (2002) used
numerical simulations of a sinking population to show bistability of alternative ver-
tical equilibria in a coupled well-mixed surface layer and poorly-mixed deep layer
separated by a thin thermocline region that reduced exchange between the two lay-
ers. The bistability of surface layer maxima and deep layer maxima is created by
positive feedback in both layers. This positive feedback is due to asymmetric com-
petition, as phytoplankton in the surface layer reduce light supply to phytoplankton
in the deep layer and phytoplankton in the deep layer decrease nutrient supply to

phytoplankton in the surface layer (Yoshiyama and N akajima 2002).

In order to get more insight into stratified bodies of water, I, in collaboration with
Kohei Yoshiyama, Christopher Klausmeier, and Elena Litchman, combined elements
from these previous studies to show how spatially-varying mixing (stratification),
can drive the vertical distribution of phytoplankton (Chapter 2). In addition we
used analytical results from our game theoretical model to better define and analyze
parameter space. Stratification was not the only extra environmental complexity
we added. We also added multiple nutrient sources, which can create previously
unpredicted depth distributions. Specifically, multiple nutrient sources allows for

multiple vertical biomass maxima.

Multiple species may compete for nutrients and light in poorly-mixed environ-
ments. Huisman et al. (2006) examined how sinking species with different nutrient
and light competitive abilities may coexist in a nonequilibrium environment caused
by seasonal changes in incoming light. Yoshiyama et al. (2009) delineated the areas
in parameter space where two species competing for nutrients and light in stratified
water columns may coexist. Yoshiyama et al. (2009) use the same ESS approach as
Chapter 2, extending it to multiple species, but including just one nutrient source.

Yoshiyama et a1. (2009) provide another explanation for bimodal phytoplankton dis-

10

tributions, hence when we observe two modes, then according to our theory, it could
be one species (Chapter 2) or two species (Yoshiyama et al. 2009). Yoshiyama et al.
(2009) show that for two species with a tradeoff in light and nutrient competitive
abilities, the species can divide the water column according to their requirements. In
addition, stratification in combination with multiple species creates distinct disjunct
niches of the same species. For example, along an environmental gradient of nutrient
loading or mixed layer depth, one species can live under the shade of the other, then
disappear completely at higher nutrient loading or deeper mixed layer depth, but
then reinvade and outcompete the other species to take over the mixed layer at even

higher nutrient loading or deeper mixed layer depth conditions.

In 2007, I, in collaboration with Mary Anne Evans, Kohei Yoshiyama, Christopher
Klausmeier, and Elena Litchman, set out to examine how model predictions, specifi-
cally Chapter 2 and Yoshiyama et al. (2009), are upheld in the field (Chapter 4). We
found a great deal of variation in vertical distributions of phytoplankton in lakes and
that major environmental variables explained much of this variation as theory pre-
dicted (Chapter 2). In addition we uncovered pronounced community compositional
patterns across lakes and within lakes with depth that should fuel further studies,

both theoretical and empirical.

A recent community study has shown how groups of phytoplankton that differ in
their pigment composition are distributed differently with depth. Across lakes, the
environmental variables of color (DOC), total phosphorus, and CV of temperature
were shown to determine vertical distribution of the bulk community of phytoplank—
ton as well as individual groups of phytoplankton distinguished by their pigment

composition (Longhi and Beisner 2009).

11

1 .2 Outline

The aim of this dissertation was to determine what drives vertical distributions of
phytoplankton. To this end, we developed generalized theory and rigorously tested
theoretical predictions in experimental water columns and in lakes existing across
environmental gradients. No experimental tests had been conducted of how intraspe-
cific competition for nutrients and light in poorly-mixed water columns could create
different vertical distributions of phytoplankton. Most of the previous theory was
limited to the two extremes of completely well-mixed or poorly-mixed water columns
and could not replicate real vertical distributions of phytoplankton. In addition, few
previous studies had explicitly tested predictions from previous theory on how com-
petition for nutrients and light determines vertical distributions of phytoplankton in

many lakes along environmental gradients.

In Chapter 2, we combine two bodies of theory, that of well-mixed and poorly-
mixed water columns, into one theoretical framework in order to describe stratified
water columns. I, in collaboration with Kohei Yoshiyama, Elena Litchman, and
Christopher Klausmeier, made previous theory more realistic, by extending previ-
ous models of spatially heterogeneous competition for nutrients and light to include
stratification and multiple nutrient sources. We asked, how does stratification affect
vertical distribution and how do multiple nutrient sources, in addition to stratifica-
tion, affect vertical distribution? A key issue we faced was how to create stratification
in a simplified model that would provide analytical results. We created stratification
by merging two theories, that of a completely well-mixed water column with that of a
completely poorly-mixed water column. We found the E88 distribution of algae to be
a function of different environmental parameters. A difference with a previous study
that considered motile algae (Klausmeier and Litchman 2001), is that the algae in

the surface layer are well mixed, hence cannot aggregate at their ESS depth. In this

12

situation, if the depth of colimitation is in the mixed layer, the shallower part of the
population is limited by nutrients and the deeper part of the population is limited by
light.

We also add depth-dependent nutrient sources, which can create previously unpre-
dicted depth distributions. Specifically, multiple nutrient sources can create multiple
vertical biomass maxima. Perhaps counter intuitively (especially considering previ-
ous theory that predicts a single best location for growth (Klausmeier and Litchman
2001)), a vertical distribution with multiple maxima is an ESS under some condi-
tions. When this additional environmental complexity of multiple nutrient sources
is coupled with stratification, phytoplankton can exist in the mixed layer and deep
layer simultaneously. Although the same species is in the mixed layer and deep layer,
they are not necessarily the same physiologically: the mixed layer algae are nutrient
limited and the deep layer algae are nutrient limited or colimited if in a benthic layer
or DCM respectively. The goal of our contribution was not to further obfuscate what
is already known about phytoplankton in vertical light and nutrient gradients but
rather provide an encompassing picture of many of the possible outcomes by gen-
eralizing previous models. We provided detailed mathematical descriptions of the
environment and how the organism interacts with it, explicitly considering vertical

strategies in that environment.

In Chapter 3, I, in collaboration with Kohei Yoshiyama, Christopher Klausmeier,
and Elena Litchman, tested the algal games theory (Klausmeier and Litchman 2001)
in experimental plankton towers designed to mimic poorly-mixed water columns. In
this experiment, we asked, will algae form a thin layer and will the depth of the thin
layer be related to resource conditions? Specifically, will the thin layer be shallower
under higher nutrient conditions? We also extended the theoretical predictions to in-
clude predictions of spatio—temporal dynamics. For example, we asked, where should

the algae aggregate initially? One might think it depends on environmental condi-

13

situation, if the depth of colimitation is in the mixed layer, the shallower part of the
population is limited by nutrients and the deeper part of the population is limited by

light.

We also add depth-dependent nutrient sources, which can create previously unpre-
dicted depth distributions. Specifically, multiple nutrient sources can create multiple
vertical biomass maxima. Perhaps counter intuitively (especially considering previ-
ous theory that predicts a single best location for growth (Klausmeier and Litchman
2001)), a vertical distribution with multiple maxima is an ESS under some condi-
tions. When this additional environmental complexity of multiple nutrient sources
is coupled with stratification, phytoplankton can exist in the mixed layer and deep
layer simultaneously. Although the same species is in the mixed layer and deep layer,
they are not necessarily the same physiologically: the mixed layer algae are nutrient
limited and the deep layer algae are nutrient limited or colimited if in a benthic layer
or DCM respectively. The goal of our contribution was not to further obfuscate what
is already known about phytoplankton in vertical light and nutrient gradients but
rather provide an encompassing picture of many of the possible outcomes by gen-
eralizing previous models. We provided detailed mathematical descriptions of the
environment and how the organism interacts with it, explicitly considering vertical

strategies in that environment.

In Chapter 3, I, in collaboration with Kohei Yoshiyama, Christopher Klausmeier,
and Elena Litchman, tested the algal games theory (Klausmeier and Litchman 2001)
in experimental plankton towers designed to mimic poorly-mixed water columns. In
this experiment, we asked, will algae form a thin layer and will the depth of the thin
layer be related to resource conditions? Specifically, will the thin layer be shallower
under higher nutrient conditions? We also extended the theoretical predictions to in-
clude predictions of spatio-temporal dynamics. For example, we asked, where should

the algae aggregate initially? One might think it depends on environmental condi-

13

 

 

tions such as nutrient loading. Perhaps non—intuitively, our theory predicts that algae
should always swim to the top because they should be light limited initially for the
reasonable range of nutrients explored in our experiment. Once sufficient growth has
occurred, the nutrients should be depleted at the surface in low-nutrient treatments

so that the algae swim down to acquire more nutrients.

We found that algae formed a thin layer at the surface during the first part of
our experiment in all treatments because that is the best location for growth. This
thin layer persisted throughout the experiment in high-nutrient treatments, but in
low-nutrient treatments, the thin layer dissipated midway through the experiment as
algae redistributed throughout the water column. We found qualitative support for
predictions of equilibrium biomass and resource limitation status across our treat-

ments.

In Chapter 4, I, in collaboration with Mary Anne Evans, Kohei Yoshiyama,
Christopher Klausmeier, and Elena Litchman, conducted a lake survey to measure
vertical distributions of phytoplankton and environmental variables. We focused on
environmental variables predicted from Chapter 2 to be important in determining
phytoplankton vertical distributions. We asked, what phytoplankton vertical distri-
butions exist in different lakes and what determines them across major environmental
gradients? On the empirical side, theory on how mixing and light interact to affect
phytoplankton populations had already had some success in explaining whole lake
systems across lakes (Kunz and Diehl 2003) and within a lake that was experimen-
tally manipulated (Huisman et al. 2004). However, we wanted to better know how
well it can describe other situations, particularly when other factors are involved,
such as nutrients, stratification, and motility, that recent theory had shown to be im-
portant in being able to replicate patterns in the field. We aimed to test predictions
across large environmental gradients to examine how nutrient and light competi-

tion can drive patterns in different lakes. In addition, with the many complications

14

presented by stratification and multiple species with presumably different motility,
nutrient, and light traits (Yoshiyama et al. 2009), we wondered if we would see any
evidence supporting our predictions for how vertical distribution should change across
environmental gradients.

We found a great deal of variation in vertical distributions of phytoplankton in
lakes and that major environmental variables explain much of this variation as the-
ory predicted (Chapter 2). We found that multiple peaks of algae within the water
column is a common phenomenon and that these peaks exist at different light and
nutrient resource levels. Across all peaks, there is a negative relationship between
nutrient and light levels. We found that taxonomic groups of phytoplankton are dis-
tributed across lakes according to environmental variables, exhibit contrasting depth
distributions between lakes, and respond differently to nutrient and light levels within
lakes. Furthermore, vertical niches such as DCMs, are composed of many different

species across lakes but each DCM is usually dominated by a single species.

15

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Chapter 2

The vertical distribution of
phytoplankton in stratified water

columns

Jarad P. Mellard
with

Kohei Yoshiyama, Elena Litchman, and Christopher A. Klausmeier

2. 1 Abstract

What determines the vertical distribution of phytoplankton in different aquatic en-
vironments remains an open question. To address this question, we develop a model
to explore how phytoplankton respond through growth and movement to opposing
resource gradients and different mixing conditions. We assume stratification creates
a well—mixed surface layer on top of a poorly-mixed deep layer and nutrients are
supplied from multiple depth-dependent sources. Intraspecific competition leads to

a unique strategic equilibrium for phytoplankton, which allows us to classify the dis-

16

 

tinct vertical distributions that can exist. Biomass can occur as a benthic layer (BL),
a deep chlorophyll maximum (DCM), or in the mixed layer (ML), or as a combination
of BL+ML or DCM+ML. The ML biomass can be limited by nutrients, light, or both.
We predict how the vertical distribution, relative resource limitation, and biomass of
phytoplankton will change across environmental gradients. We parameterized our
model to represent potentially light and phosphorus limited freshwater lakes, but the
model is applicable to a broad range of vertically stratified systems. Increasing nu—
trient input from the sediments or to the mixed layer increases light limitation, shifts
phytoplankton towards the surface, and increases total biomass. Increasing back-
ground light attenuation increases light limitation, shifts the phytoplankton towards
the surface, and generally decreases total biomass. Increasing mixed layer depth in-
creases, decreases, or has no effect on light limitation and total biomass. Our model
is able to replicate the diverse vertical distributions observed in nature and explain

what underlying mechanisms drive these distributions.

17

 

2.2 Introduction

The aquatic environment of phytoplankton creates an opportune situation to study
the feedbacks between resource gradients, behavioral movement, population dynam-
ics, and passive dispersal. The major axis of spatial heterogeneity for phytoplankton
is the vertical dimension. The vertical distribution of phytoplankton affects pri-
mary production as well as energy transfer to higher trophic levels (Leibold 1990;
Williamson et al. 1996; Lampert et al. 2003). Therefore, there is an immediate
need to understand the fundamental principles that govern the vertical distribution
of phytoplankton, ecologically important organisms that contribute roughly half of
global net primary productivity (NPP) (Field et al. 1998) and continue to be affected

by climate change (Hays et al. 2005).

A dizzying diversity of phytoplankton vertical distributions have been observed
(see Fig. 2.1 for a few examples). Density stratification breaks the water column into
distinct strata resulting in non—uniform mixing, often with a well-mixed surface layer
on top of a poorly-mixed deep layer (Wetzel 1975; Wiiest et al. 2000). Phytoplankton
may be found in high abundance in the mixed layer, in the deep layer, directly on the
bottom, or in some combination of these locations. What determines their vertical
distribution in stratified water columns? Light is in greatest supply at the top of
the mixed layer and phytoplankton are hypothesized to exist there when there is
adequate nutrient supply (Reynolds 1984; Paerl 1988). Frequently, phytoplankton
form a peak in abundance known as a deep chlorophyll maximum, or DCM, in the
deep layer. Low turbulence and suflicient light penetration have been hypothesized
as necessary for a DCM to persist (Fee 1976) and the light and nutrient gradients
control the depth of the peak (Fee 1976; Klausmeier and Litchman 2001). Under low
nutrient concentrations and if sufficient light penetrates to the bottom, phytoplankton

may form a benthic layer on the sediments and access nutrients diffusing through the

18

 

sediment pore water before it enters the water column (Sand-Jensen and Borum 1991).

19

Figure 2.1. Example phytoplankton vertical distributions observed in strat-
ified lakes in Southern Michigan. A) Benthic layer biomass only. B) DCM
biomass only. C) Mixed layer biomass only. D) Benthic layer and mixed layer
biomass. E) DCM and mixed layer biomass. Vertical distributions are chloro-
phyll a fluorescence profiles and mixed layer depth, zm, is defined from the
temperature profile to be the depth 1 oC cooler than the surface temperature.
Profile A) is from Sherman Lake, Kalamazoo County MI, October 12, 2007.
Profile B) is from Bristol Lake, Barry County MI, October 3, 2007. Profile
C) is from Fine Lake, Barry County MI, October 3, 2007. Profile D) is from
Hogsett Lake, Kalamazoo County MI, October 22, 2007. Profile E) is from
Bassett Lake, Barry County MI, October 15, 2007.

20

Fluorescence
.012. nOA . 9.6.10.8 4 LQ 1.2.- 1.4

 

 

 

 

 

 

a l A
a 2f
O.
Q) .
Q Benthic layer
0 . . . .01 .1 -OriznaQrfstrflffilzsi Or6 .917 A
B
E 2
33 2mg --------------------------
5 8 Deep chlorophyll
10 maximum (DCM)
12
14
. .- 940.5 . 0.10. . 0.1.5 0.7—0 - 0425
A C
5 2
.2:
Te-
Q Mixed layer
biomass

 

 

Benthic layer +
mixed layer

Depth (111)

 

 

 

0....0.-1 0:2.-0:3..9.-4- 0,5, 0,6

DCM +
mixed layer

Depth (m)

 

 

Figure 2.1: Example phytoplankton vertical distributions observed in stratified lakes.

21

In a well-mixed water column, phytoplankton and nutrients are homogenized
throughout the water column; however a light gradient is inevitable. As a conse-
quence, phytoplankton experience varying local light levels and therefore varying
growth rates. The light level at the bottom of the water column, Ioutw predicts the
outcome of competition for light (Huisman and Weissing 1994, 1995) in a way similar
to R* for nutrients (Tilman 1982). In contrast, in a poorly-mixed water column,
motile phytoplankton can be thought of as playing a competitive game in opposing
essential resource gradients. A shallower position allows a cell to shade those below it
but a deeper position allows it to intercept nutrients mixing up from below. Eventu-
ally phytoplankton will aggregate at their evolutionarily stable strategy (ESS) depth
2*, which is the depth of equal limitation by nutrients and light and prevents growth
elsewhere in the water column (Klausmeier and Litchman 2001). These studies are
applicable to the two extremes of whole water columns, one of well-mixed and one of

poorly-mixed.

Many bodies of water stratify. Several models have considered stratified water
columns, ranging from complex simulation models particular to specific ecosystems
(Lucas et a1. 1998; Fennel and Boss 2003; Peeters et al. 2007; Ross and Sharples
2007) to simpler models aimed at general understanding. Condie and Bormans (1997)
and Hodges and Rudnick (2004) included sinking but neglect the feedback of phy-
toplankton on light. Huisman and Sommeijer (2002a,b) incorporate the feedback of
phytoplankton on light, but omit nutrients and assume no mixing in the hypolimnion.
Yoshiyama and Nakajima (2002), Yoshiyama et al. (2009), and Ryabov et al. (2009)
do not include nutrient loading to the mixed layer. Our study systematically explores
the different vertical distributions of phytoplankton that can arise from intraspecific

competition for nutrients and light in a stratified water column.

In this paper, we build on previous work by considering a stratified water column

with a well-mixed surface layer on top of a poorly-mixed deep layer, a combination

22

of approaches by Huisman and Weissing (1994, 1995) and Klausmeier and Litchman
(2001). We relax the assumption of an infinitely thin layer (Klausmeier and Litchman
2001) to a layer of finite depth and show what resources limit growth at different
depths within the layer. Furthermore, we consider multiple nutrient inputs, including
input directly to the mixed layer, expanding on Diehl (2002). Current models for
poorly-mixed water columns consider only nutrient supply from below (Klausmeier
and Litchman 2001; Huisman et al. 2006; Beckmann and Hense 2007). We enumerate
the possible equilibrium algal vertical strategies and show under what conditions each

should occur.

2.3 Methods

2.3.1 Full Model

The full model consists of partial differential equations for biomass, b(z, t) and nutri-
ents, R(z, t) which in our examples represents phosphorus, and an integral equation
for light, I (z, t). We consider a one-dimensional water column where z is depth with
the surface at z = 0 and the bottom at z = 2b.

Phytoplankton biomass b grows according to Liebig’s law of the minimum, so
gross grthh rate at depth 2 is g(R,I) = min(fI(I(z,t)),fR(R(z,t))). Functions
f [(1 ) and f R(R) are the potential growth rates as a function of the resource I or R
when that resource is limiting. We use the Michaelis-Menten form for the functions
in our numerical solutions, fI(I) = rI/(I-l- KI) and fR(R) = rR/(R-l- KR) where r
is the maximum growth rate and K I and K R are half-saturation constants for light
and nutrients respectively. Our qualitative results, hoWever, should hold for other
bounded, strictly increasing functions. Biomass is lost at density independent rate
m, which encompasses all sources of mortality. Net growth rate is 9(2) — m. Net

growth at depth 2 is only possible if both I is greater than the break even light

23

level, 1* = fI—1(m), and R is greater than the break even nutrient concentration,

12* = El(m) (Tilman 1982).

A depth-dependent turbulent eddy diffusion coefficient D(z) describes passive
movement. Active movement is described by a taxis term (Okubo 1980). Phytoplank-
ton behavior is governed by simple rules. They move up if conditions immediately
above are better than immediately below, move down if conditions immediately below
are better than immediately above, and do not move if conditions are worse imme—
diately above and below. To describe this behavior, we let phytoplankton velocity v
depend on the gradient in growth rate, 89/82. We assume 1) to be an odd decreasing
function that approaches Umax as 89/82 approaches negative infinity (positive '0 is
upward), approaches —’Umax as 89/82 approaches positive infinity, and 22(0) = 0. See
the section titled Assumptions, limitations, and extensions in the Discussion for how

relaxing the assumption of active motility affects results.

Change in biomass at depth 2 is the balance of growth, death, and passive and

active movement.
6b _ 6 0b By
a — W, I) ‘ m)“ 5; (0(2):; +” (6—) b) ‘2'”

Nutrients R are taken up by phytoplankton with a yield of Y biomass per unit nutrient
consumed, are mixed with eddy diffusion coefficient D(z), are supplied directly to the
water column at depth 2 at rate Rin(z), and are recycled from dead phytoplankton

with proportion 5.

6R b 3 6R b
5t- - "9(R, 1)? + E ONCE) + Rink?) + am? (2'2)

Light follows Lambert-Beer’s law, decreasing due to attenuation from biomass and

background turbidity (Kirk 1975a). The attenuation coefficient due to biomass is a

24

and due to background is abg'

— (abgz+foz ab(Z,t)dZ)

I(z,t) = ine (2.3)

Phytoplankton do not leave or enter the water column, so boundary conditions are:

(09);; + '0 (g—:) b)

Nutrients have no surface flux but diffuse into the water column from the sediments

= 0 (2.4)
z=0,zb

 

where they have fixed concentration Rsed at a rate proportional to the concentration

difference across the interface. The permeability of the interface is described by h.

8R 8R,
— = 0 and —— = MR '- sz )) (2'5)
62 2:0 az Zzzb 36d I)

See Table 2.1 for a list of variables and Table 2.2 for a list of parameters and their

default values.

Table 2.1: Variables in the model.

 

 

Variable Units Meaning
b(z, t) cells mL—F biomass concentration
BML cells cm—2 biomass in ML
BDL cells cmTZ biomass in DL
2* m depth of co—limitation in DL
2e m depth of co—limitation in ML
R(z, t) pg P LT1 phosphorus concentration
RML pg P L—1 average phosphorus concentration in ML
I (z, t) pmol photons m—2s_1 . irradiance
g(R, I ) (1‘1 growth rate
57ML (1"1 average growth rate in ML

 

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2.3.1.1 Simulating the full model

The system of reaction-diffusion equations that define our model (Eqs. 1—5) defies
analytical treatment, so we begin with numerical solutions of the model to gain insight
into its behavior. We spatially discretized and numerically simulated the full model
using VODE (Brown et al. 1989) following Huisman and Sommeijer (2002). The
specific equation we use for v is v = vmax - g—g/ (g; + szim)’ where szim =
0.001 deI. We simulate a stratified water column with mixed layer depth 2m,
setting D(z) = 102 m2d_1 for 0 S 2 g zm and D(z) = 1 mzd"1 for zm < z 3
2b, realistic values for D(z) in the epilimnion and hypolimnion (MacIntyre et al.
1999). An example equilibrium vertical profile shows that biomass is almost uniformly
distributed in the mixed layer and forms a deep chlorophyll maximum (DCM) in the
deep layer (Fig. 2.2A). The DCM thickness decreases as the swimming speed of the
phytoplankton is increased until it can be approximated by an infinitely thin layer
(Klausmeier and Litchman 2001, unpub. results). Nutrients are almost uniformly
distributed in the mixed layer, relatively constant below the mixed layer down to
the DCM, and increase linearly below the DCM to the sediments. These numerical
results and previous research (Huisman and Weissing 1994; Klausmeier and Litchman
2001) suggest that the full model can be approximated by a simplified model (Fig.
2.2B) with a completely homogenous mixed layer above a poorly-mixed layer where

phytoplankton can form a thin layer.

2.3.2 Simplified model

In order to obtain analytical results, we use a simplified model to approximate the
equilibrium distribution of the full model. Evidence that the full model can be reduced
to a simpler model comes from simulations (Klausmeier and Litchman 2001, Mellard

et al. unpublished) and a rigorous mathematical proof (Du and Hsu 2008). We later

27

A) Full model B) Simplified model

 

 

 

 

 

 

R=R* fin
I :r 0 i l
I ' '
I I
l . '
Zm I 5: 2m ' g
l 5 '
I 5 '
I I: ' 5
z I 5 '
II .. L i
s __ z e r L
\\ E \\\::-
\\ i
\ f.“
\ ' s
\ , \
\ :: \\
2b. \\ 2b.. 3 I \ I
1* Rsed
— biomass (b) ---- nutrient (R) -—--log light (log 1)

Figure 2.2: A) Example numerical simulation output of full model showing a DCM
and nutrient-limited mixed layer at steady-state. Solid line is biomass (cells mL—l),
dashed line is nutrient concentration (pg dissolved P L_1), and dotted line is log
light (pmol photons m_2s-1). Parameters are as in Table 2.1 except .Rsed = 220 pg
P L—1;DML = 102 m2 d—1;Rm(z) = 0.6 pg P L—1 d—1 for 0 g z s 5,Rin(z) = 0
for z > 5. B) Example representation of simplified model showing a DCM and
nutrient—limited mixed layer as in the output of the full model.

give criteria for when our simplified model does a good job of approximating the full
model as well as discuss specific cases for when it may do a poor job (see Assumptions,

limitations, and extensions in the Discussion).

In addition to providing intuitive insight, algebraic expressions, and ease of nu-
merically exploring parameter space, the simplified model provides a skeleton of the
full model showing where the peaks in biomass occur, the depth of co—limitation, and
the amount of biomass in the mixed layer and deep layer (compare Fig. 2.2B with Fig.
2.2A). We break up the water column into a perfectly-mixed upper layer (Huisman
and Weissing 1994) and a poorly-mixed deep layer (Klausmeier and Litchman 2001).

This water column approximates stratified temperate lakes (Wetzel 1975; Wiiest et al.

28

2000) and oceans (Osborn 1980; Mann and Lazier 1996).

2.3.2.1 Definitions and assumptions

Well-mixed surface layer (ML)

In the mixed layer, 0 __<_ z s zm, we assume D(z) is large enough to homogenize
the nutrients and phytoplankton, overcoming phytoplankton motility, growth, and
nutrient consumption (D(z) >> vmaxzm and D(z) >> gzrzn for 0 3 z 5 2m). Phy-
toplankton and nutrient distributions observed in thermally stratified lakes are often

consistent with this assumption (Fig. 2.1, J. Mellard unpublished data).

Define BML to be the depth—integrated biomass in the mixed layer

BML -_— [Ozmb(z)dz (2.6)

and RML to be the average nutrient concentration in the mixed layer

_ 1 2m
RML = 23;“) R(Z)dz (2.7)

To explore the effect of changing 2m without changing the nutrient supply to the
mixed layer, we assume the only source of nutrients besides the sediments is direct

surface input by setting Rin(z) as a delta function at z = 0 with total nutrient input

rate RinML
Zm
RinML 2/0 Rin(z)dz (2-8)
Define gML to be the average growth rate in the mixed layer

_ 1 2m
m = Zn‘ [0 g(z)dz (2.9)

29

and 29 to be the depth of equal limitation where

fR(R(Ze)) = fIUIZell (2-10)

Poorly-mixed deep layer (DL)

In the deep layer, Zm < 2 3 2b, we assume that phytoplankton motility or growth
can overcome mixing to form a thin layer (’Umax(zb -- 2111) >> D(2) or g(2b — 2m)2 >>
D(2) for Zm < 2 S 2b). Following Klausmeier and Litchman (2001), we assume that
algae will aggregate at their ESS depth 2*. Note that there are two ways for the
algae to achieve their ESS depth 2*. According to the inequalities, either swimming
or growth can overcome mixing. For a DCM, 29 = 2*. We use a delta function to

approximate the biomass distribution at depth 2* (Klausmeier and Litchman 2001),
b(z) = BDL5(Z*) (2.11)
where depth integrated biomass in the deep layer is

BDL = /:b b(2)dz (2.12)

111

2.3.2.2 Equilibrium conditions

We focus on vertical distribution at both dynamic (d/dt = 0) and strategic (ESS)

equilibrium. At equilibrium, net growth rate is 0 wherever biomass exists

‘ — m = 0 if B > 0;
ML ML (2.13)

g(z*)—m=0 ifBDL >0.

30

In other words, at equilibrium, if the population exists in the mixed layer or deep

layer, it is neither increasing or decreasing there. For an equilibrium to be an ESS,

§ — m S 0 and
ML (2.14)

g(2)—-m§0 for2m<z§2b.

In other words, phytoplankton cannot invade the mixed layer or deep layer. In terms
of resource conditions in the deep layer, I (2*+) = 1* and R(z*) = R* when BDL > 0
meaning that light is at the break-even level immediately below the thin layer and
nutrients are at the break—even level at the depth of the thin layer (Klausmeier and

Litchman 2001).
Simplified model derivation

Nutrients are constant in the surface layer (R(2) E RML for 0 S 2 3 2m), and
are linear with depth wherever there is no biomass in the deep layer (dZR/dz2 = 0
for 2m < 2 < 2), where b(2) = 0). For convenience, we specify vertical diffusion

coefficient in the deep layer as DDL'

At steady state, net nutrient flux equals net nutrient consumption by phytoplank-
ton. In the surface layer, we have
‘ B smB dR
__9_M_L__1\L + A + RinML + DDL — = 0. (2.15)
Y Y d2 2=2+
m
The first two terms of the left-hand side of (Eq. 2.15) represent consumed and recycled
nutrients within the surface layer, and the third and fourth terms, direct nutrient
input to the surface layer and nutrient flux from the deep layer, respectively. Because
gML -— m = 0 when BML > 0, (Eq. 2.15) can be modified to:
m(l—£) BlWL dR

- Y + RinML + DDL g; Z_Z+ = 0- (2'16)
_ m

 

31

Note that (Eq. 2.16) also holds when BML = 0. Nutrient flux from the deep layer
depends on whether biomass is present in the deep layer (BDL > 0) or not (BDL = 0).

When BDL == 0, dR/dz is constant in the deep layer:

(112 _ R(Zb) - RML

 

 

— — 2.17
(12 2b — Zm ( )
From the boundary condition at 2 = 2b (5) and (Eq. 2.17) we have
R(Zb) - RML
= . — . 2.1
Zb _ Zm h (Rsed R(Zb)) ( 8)

Rearranging (Eq. 2.18), we obtain R(zb), and substituting R(2b) in (Eq. 2.17),
dR/dz is expressed by:
613 _ Rsed — RML

— —— . 2.1
d2 2b+1/h-zm ( 9)

 

According to Klausmeier and Litchman (2001), a stable DCM should be co-limited
by nutrients and light (i.e., R(2*) = R* and I(2*+) = 1*), and a stable benthic layer
should be limited by nutrients (i.e., R(2b) = R* and 1(23‘) 2 1*). Therefore, when
BDL > 0, R(2*) = R*, and dR/dz is expressed by:

dR _ 12* — RML

— — — 2.20
d2 222$ 2* — Zm ( )

Substituting dR/dz in (Eq. 2.16) with (Eq. 2.19), and (Eq. 2.20), we have equalities

for nutrient balance in the surface layer:

m(1—5)B DDI (ngd—RMl) _ _
-——Y—ML + Rink/IL + Zb‘l‘l/h-Zm — 0 when BDL — 0,

_ *_ -
_m(1 €)B + RinML + D (R R ) = 0 when BDL > 0.

2 —2m

(2.21)

Similarly in the deep layer, we have an equality for nutrient balance at a depth

32

with positive biomass 2*. When Zm < 2* < 2b (DCM), we have

 

B
_ DL + DDL _ Z _ DDL It: 2 0. (2.22)

_ *—
25—2

The second and third terms of left-hand side of (Eq. 2.22) respectively denote nutrient
fluxes from below and above 2*. Because R(2*) = R* (Klausmeier and Litchman

2001), these fluxes can be expressed by:

 

 

DDL $13 = DDL (Rsed _ R*)
d2 Z=Z*+ Zb + l/h -—-2* (2.23)
D 915 _ DDL (3* - RML)
DL _ " >1: _ ‘
d2 3:21: 2 Zm

 

Substituting the fluxes in (Eq. 2.22) with (Eq. 2.23) we have an equality for nutrient

balance at depth 2*,

__m (1 - 8) BDL DDL (Rsed - R*l _ DDL (3* — RML) = 0 (2 24)
Y 2b+1/h-2* Z*-Zm ' .

 

 

 

When 2* = 2b (benthic layer), net nutrient flux is the sum of nutrient fluxes at
sediment-water interface [hDDL (Rsed -— R(2b)) = hDDL (Rsed — R*)] and from
above 2b. Thus nutrient balance at benthic layer is written as
m (1 - 8) BDL * DDL (3* ‘- RML)
— — — = . 2.2
Y + hDDL (Rsed R ) Zb _ Zm 0 ( 5)
We can see that (Eq. 2.24) implies (Eq. 2.25) when 2* = 2b. Therefore the equality

(Eq. 2.24) holds for 2m < 2* 3 2b, which expresses nutrient balance at either a

DCM or a benthic layer.

33

The light profile is expressed by

— 2+aB , 2 )
line (abg ML /Zm for 0 S 2 S Zm

7 -— _ + B )
I(~) — line (0'ng 0' ML for zm < Z < 2* . (2.26)
— + B + B
line ((1ng (1 ML 0 DL) for 2* S 2 S 2b

Steady state distributions are obtained by solving equations for zero net growth
(Eq. 2.13), nutrient balance in the surface layer (Eq. 2.21), and nutrient balance in
the deep layer (Eq. 2.24), with the light profile (Eq. 2.26). Conditions (2.14) should

be satisfied for a steady state distribution to be an ESS.

2.4 Results

2.4.1 Spatial distribution states

Stratification and multiple nutrient sources lead to a greater diversity of possible
equilibrium vertical distributions and resource limitation states of phytoplankton than
in previous models. In the mixed layer, four states for phytoplankton are possible:
light-limited (fR(2) > fI(2) for 0 S 2 S 2m), nutrient-limited (fR(2) < fI(2) for 0 S
2 S 2m), co—limited (0 S 23 S 2m), or not present (empty). In the deep layer, three
states for phytoplankton are possible: nutrient-limited in a benthic layer, co-limited
in a deep chlorophyll maximum, or not present (empty). Combinations of these four
mixed layer and three deep layer biomass states result in 4 x 3 = 12 logically possible
vertical distribution states (Table 2.3). However, four of these vertical distribution
states are infeasible. In order to have both mixed layer and deep layer biomass, the
mixed layer biomass must be nutrient-limited (if mixed layer biomass is co—limited

or light-limited then the light level below the mixed layer is less than 1*). This

34

eliminates the four combinations of co—limited or light-limited mixed layer biomass
states with any deep layer biomass state, leaving eight possible vertical distribution

states at equilibrium (for proof see Appendix).

Table 2.3: Combinations of equilibrium spatial distribution states of the mixed layer
and deep layer. X indicates the combination is infeasible. All other combinations are
possible subject to criteria listed and their corresponding figures and sections in the
appendix are indicated.

 

 

Deep layer Mixed layer
Empty R—limited Co—limited 1-limited
Empty Fig. 3A Only if RinM > 0 Fig. 3D Fig. 3E
1 Fig. 6A 3 4
Benthic Layer Only if RinM = 0 Only if RinM > 0 X X
Fig. 3B Fig. 6B
DCM Only if Rin = 0 Only if RinM > 0 X X
Fig. 3C Fig. 6C

1 Appendix page 61, Case 1: Empty.
Appendix page 67, Case 4: Nutrient-limited mixed layer.
Appendix page 63, Case 2: Co—limited mixed layer.
Appendix page 66, Case 3: Light—limited mixed layer.
Appendix page 71, Case 7: Benthic layer.
Appendix page 68, Case 5: Benthic layer and N utrient-limited mixed layer.
Appendix page 73, Case 8: DCM.
8 Appendix page 69, Case 6: DCM and Nutrient-limited mixed layer.

As mentioned above, our model incorporates two new factors beyond Klausmeier
and Litchman (2001): 1) stratification and 2) mixed layer nutrient input. We describe
the possible distribution states and examine how they depend on environmental con-
ditions. In order to do this, we numerically evaluated expressions for the equilibrium
(Eqs. 2.13, 2.21, 2.24, 2.26) and checked the feasibility of each case. We always
found a unique vertical distribution state of phytoplankton for a given set of param-

eters. In addition, we examined how the vertical distribution state changes along

35

environmental gradients and confirmed these results according to methods in Table

2.4.

36

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37

2.4.2 Possible distribution states

There is often appreciable nutrient input directly to the mixed layer, due to riverine
inputs, surface runoff, or atmospheric deposition. This mixed layer nutrient input,
RinML’ can depend on landscape geomorphology and anthropogenic influences sur-
rounding the body of water. Here we consider the case RinML > 0, although some
kettle or other glacial lakes that have very small drainage basins might be reasonably
approximated by an assumption of no mixed layer nutrient input (Hutchinson 1957).

With mixed layer nutrient input, six equilibrium vertical distribution states are
possible (Fig. 2.3, Table 2.3). A benthic layer or DCM by itself are special cases
not possible with positive RinML because they form when sufficient light penetrates
to the deep layer and reduce nutrient concentration above to 12* so any amount of
nutrient input to the mixed layer will sustain a population there (see Two special
cases if RinML = 0 below for their description). We describe the equilibrium vertical

distribution states below; mathematical details are given in Appendix.

1) Empty. An empty state is perhaps trivial because likely all bodies of water have
enough nutrients for some biomass to exist but we describe it here as a possi-
bility. No biomass persists in the water column. Light declines exponentially
with depth due to background attenuation. Nutrient levels are uniform with
depth and at the same concentration as in the sediments (R(2) = Rsed)' See

Fig. 2.3A and page 61, Case 1 in Appendix.

2) Co-lz'mited mixed layer. A co-limited mixed layer is actually only co—limited at
one point in the mixed layer but as a whole, we consider it co—limited because
the population is experiencing the entire range of conditions in it. Biomass is
uniformly distributed throughout the mixed layer and absent below it. The
upper portion of the mixed layer (z < ze) is nutrient-limited and the lower

portion (2 > 29) is light-limited. Light declines exponentially within the mixed

38

4)

5)

layer due to algal and background attenuation and in the deep layer below due to
background attenuation only. Light at the bottom of the mixed layer is actually
less than the break-even level (I (2m) 2 [out 3 1*), but the population can
persist (Huisman and Weissing 1994). Nutrients in the mixed layer are uniform
at or above the break-even concentration (RML 2 R*) and increase linearly

with depth in the deep layer. See Fig. 2.3B and page 63, Case 2 in Appendix.

Light-limited mixed layer. In a light-limited mixed layer, the depth of co-
limitation for the population would be above the water column if it could exist
there. Conditions are the same as a co-limited mixed layer except the entire
mixed layer is limited by light ( f R(RML) > f 1(Iin)). See Fig. 2.3C and page
66, Case 3 in Appendix.

Nutrient-limited mired layer (R-limited ML). A nutrient-limited mixed layer
by itself may be somewhat unlikely as most bodies of water have significant
nutrient input from the sediments. Conditions are the same as co-limited and
light-limited mixed layers except nutrients in the mixed layer are at the break
even concentration (RML = R*) and below the mixed layer, are constant or

decrease linearly to R(zb). See Fig. 2.3D and page 67, Case 4 in Appendix.

Benthic layer + nutrient-limited mixed layer (BL+ML). This is an intriguing
case with the population divided between two locations but with both locations
limited by the same resource. Biomass is uniformly distributed throughout the
mixed layer and resides at the sediment-water interface in the deep layer. The
entire mixed layer and the benthic layer are limited by nutrients. Light declines
exponentially with depth in the mixed layer due to algal and background atten-
uation and in the deep layer below due to background attenuation only. Light at
the bottom of the water column 1(zb) > 1*. Nutrients are uniformly distributed

throughout the water column at the break-even concentration (R(2) = R*). See

39

6)

Fig. 2.3E and page 68, Case 5 in Appendix.

Deep chlorophyll maximum + nutrient-limited mixed layer (DCM+ML). This
is another intriguing and probably common (Mellard et al. unpublished data)
case. Biomass is uniformly distributed throughout the mixed layer and forms a
thin layer at depth z* within the deep layer. The entire mixed layer is limited
by nutrients and the DCM islimited by nutrients and light. Light declines
exponentially with depth in the mixed layer due to algal and background at—
tenuation. In the deep layer, light declines exponentially above and below the
DCM and decreases a finite amount within the DCM. Immediately below 2*,
light is at the break-even level (I(z*+) = 1*). Nutrients in the mixed layer
and below to the DCM are constant at 12*. Below the DCM, nutrients increase

linearly with depth. See Fig. 2.3F and page 69, Case 6 in Appendix.

2.4.2.1 Two special cases if RinML = 0

Benthic layer and DCM are special cases of BL+ML and DCM+ML where RinML =

0.

7)

8)

Benthic layer (BL). (Only possible if RinML = 0) The benthic layer is the only
location in the water column the population exists in this case. Biomass resides
at the sediment-water interface at z = zb. Light declines exponentially with
depth due to background attenuation and there is sufficient light at the bottom
(1(zb) > 1*). Nutrient levels are uniform throughout the water column at 12*.

See Fig. 2.3G and page 71, Case 7 in Appendix.

Deep chlorophyll maximum (DCM). (Only possible if RinML = O) The con-
spicuous DCM (Camacho 2006) is considered to form at the E38 depth (of
co—limitation) in the deep layer. Biomass forms a thin layer at depth 2* within

the deep layer. Light declines exponentially above and below the DCM and

40

decreases a finite amount at the DCM. Immediately below 2*, 1(z*+) = 1*.
Nutrient levels are at R* at and above the DCM and increase linearly below

the DCM. See Fig. 2.3H and page 73, Case 8 in Appendix.

41

Figure 2.3. Equilibrium vertical profiles A—F) with mixed layer nutrient input
(RinML > 0). G) and H) are special cases where RinML = 0. A) Empty.
Here, there is not sufficient nutrients for biomass to persist. B) Co—limited
mixed layer. The solid lines enveloping the mixed layer represents the biomass
there. RML is the nutrient concentration in the mixed layer. C) Light-limited
mixed layer. The mixed layer biomass is completely light-limited due to in-
creased Rsed‘ D) Nutrient-limited mixed layer. Primary nutrient source is
directly to the mixed layer (Rsed < R*). The entire mixed layer is nutrient
limited because 1(zm) > 1*. E) Benthic layer and nutrient-limited mixed
layer. The solid line at the bottom represents biomass in the benthic layer.
1(zg') > 1*. R = R* in both layers. F) DCM and nutrient-limited mixed
layer. The solid line representing biomass in the DCM is at 2*, where R = R*
and 1(z*+) = 1*. R = R* in both layers. G) Benthic Layer. The solid
line at the bottom represents biomass in the benthic layer. There are enough
nutrients from sediment (Rsed > R*) for biomass to exist at the bottom of
the water column and also enough light (> 1*). Nutrients above the benthic

layer are constant at R*. H) DCM. The solid line representing biomass in the

DCM is at z*, where R = R* and 1 = 1*.

42

A) Empty B) Co-limited ML C) I-limited ML

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

13* [in 13*]? fin O- R* R 1'
I I I l
I I
I Ze- l
2m i z 'I Z J.
I I I
I \ I
I \ I
I \ I
I \ I
I ‘ I
I ‘ I
zbj l l 2b- l I “ I 21,- l I l I
Rse 1* Rsed 1* Rsed
D) Nutrient-limited ML E) BL + ML F) DCM + ML
Ig=R* {- 54* 1 m R=R* I,
I I I
I I I
2111 I 2m : zm :
I I I
I I I
Z I Z I Z I /
I' l 2* ‘I
.‘ ' ‘
I : \
J l l ' \‘
2b I 2b 4 : Zb‘ I ~ I
Rsedr" Rsed” 1* Rsed
G) Benthic layer
13* 1i
I
I
biomass (b) ‘ :
Zm I
----- nutrient (R) E
I
------------ log light (log I) :
l
:1 I «J I \'
2b Rs'edr' Zb 1* Rsed

Figure 2.3: Equilibrium vertical profiles.

2.4.3 Transitions along environmental gradients

We now examine how the equilibrium vertical distribution, biomass, and resource

limitation depend on environmental parameters. We focus on three environmental

43

parameters that are known to vary among water bodies or through time and that po-
tentially affect phytoplankton communities: sediment nutrient concentration, Rsed;
mixed layer nutrient input, RinML; background light attenuation, abg; and mixed
layer depth, zm. Sediment nutrient concentration varies widely between lakes. Back-
ground light attenuation depends on the amount and composition of particulate and
dissolved matter suspended in the water column. Mixed layer depth can vary both
between and within bodies of water through time due to seasonal changes (Wetzel

1975). Note that other transitions are possible in addition to those that are described

below.

Effect of sediment nutrient concentration. Nutrient enrichment in the form
of sediment nutrient concentration causes phytoplankton to shift towards the surface.
For example, in Fig. 2.4A, they shift from a BL+ML to a DCM+ML to a co-
limited mixed layer to a completely light-limited mixed layer. Increasing Rsed pushes
2* and ze towards the surface as the biomass becomes more light-limited. Total
biomass increases until it is light-limited. Interestingly, the nutrient-limited mixed
layer biomass is unaffected by increasing sediment nutrient concentration because the

deep layer biomass uses it all for growth.

Effect of mixed layer nutrient input. Nutrient enrichment in the form of
mixed layer nutrient input causes phytoplankton to shift towards the surface. For
example, in Fig. 2.4A, they shift from a BL+ML to a DCM+ML to a co—limited mixed
layer to a light-limited mixed layer. Increasing RinML pushes z* and .23 towards the
surface as the biomass becomes more light limited. Total biomass steadily increases,
but solely due to mixed layer biomass increasing: benthic layer biomass does not

increase and DCM biomass actually slightly decreases with increasing RinML'

Effect of background light attenuation. Increases in background light at-
tenuation causes phytoplankton to shift towards the surface. For example, in Fig.

2.48, the phytoplankton shift from a BL+ML to a DCM+ML to a co—limited mixed

44

layer to a light-limited mixed layer before eventually going extinct. Increasing abg
pushes 2* and ze towards the surface as the biomass becomes more light-limited.
Increasing abg has no effect on completely nutrient-limited biomass (benthic layer or
nutrient—limited mixed layer). However, for all other states, increasing abg decreases
biomass.

Effect of mixed layer depth. Increases in mixed layer depth can cause phyto-
plankton to shift towards the surface due to entrainment once 2m _>_ 2*. For example,
in Fig. 2.4C, the phytoplankton shift from a DCM+ML to a co—limited mixed layer
once the mixed layer entrains the DCM to a light-limited mixed layer and finally
to an empty state when the mixed layer becomes too deep and the phytoplankton
go extinct because of extreme light limitation. Increasing Zm has no effect on 2*
for the DCM; however, 26 for the co—limited mixed layer becomes shallower with in-
creasing mixed layer depth (although this is not universally true). Increasing mixed
layer depth has negative, positive, or no effect on biomass, dependent on the state of
the phytoplankton. Biomass in a BL, DCM, or nutrient-limited mixed layer (when
a BL or DCM is present) is unaffected by increasing mixed layer depth. Biomass
in a light—limited or nutrient—limited mixed layer (by itself) decreases with increasing
mixed layer depth. Biomass in a co—limited mixed layer may increase or decrease with

increasing mixed layer depth.

45

Figure 2.4. Effect of environmental parameter on biomass (top), state (mid—
dle), and vertical distribution (bottom). Top) Amount of biomass in benthic
layer (BL), DCM, and mixed layer. Middle) State of the phytoplankton. Phy-
toplankton can be in a benthic layer + nutrient-limited mixed layer (BL+ML),
DCM + nutrient-limited mixed layer (DCM+ML), co—limited mixed layer (Co—
lim. ML), light-limited mixed layer (1—lim. ML), or extinct (Empty). Bot-
tom) Dotted line is depth of colimitation if in the mixed layer, 26, and solid
line is depth of colimitation if in the deep layer, 2*. Gray shading indicates
that biomass is present in the mixed layer. A) Effect of sediment phosphorus
concentration, Rsed’ on phytoplankton biomass and vertical distribution. En—
vironmental parameters: abg = 0.1 m_1;2m = 5 m; RinML = 1 mg P m—2
d‘l. B) Effect of RinML on phytoplankton biomass and vertical distribution.
Environmental parameters: abg = 0.1 m—l; 2m = 5 m; Rsed = 120 pg P
L_1. C) Effect of abg on phytoplankton biomass and vertical distribution.
Environmental parameters: 2m = 5 m; Rsed = 40 pg P L_1; RinML = 1 mg
P m-2 d—l. D) Effect of 2m on phytoplankton biomass and vertical distri-
bution. Environmental parameters: abg = 0.4 m—l; Rsed = 40 pg P L_1;

—2 —1
RinML = 1 mg P m d .

46

>
w

 

 
  

Mixed layer

Orwwev‘a

 

 

Biomass 107 cells cm'2

Lo_;—- «{ququ

 

grim—“v ‘rssmmr‘rs‘oo “ Rsed
I§I§§IOO C"‘1’m| I-limited ML IfaLJI DCM | Co-lim. ML II-lim. ML

+ML
-2502 i 2500 .Rsed

 

2* or 26

 

 

 

Zb'

 

 

 

 

 

 

 

 

 

 

 

 

     
 

a ‘5 D

E .l' -

g 0-6: m

% 0.5r—-——'I

O

‘2: o.

:2 g; m G.“

a ”I

.2 ab

‘1‘ 2 g G 5‘ 1‘5 20 m
ImIEfiL MI Co-lim ML I IEmpty 33:4 Co- lim. OIMLIS lempty
.92.? 3-0.6.. LQanMabg 5 .. 10 15

 

2* or Ze

 

 

 

ZbI

Figure 2.4: Effect of environmental parameter on biomass and vertical distribution.

47

Interactive effects of environmental parameters. The vertical distribution
as a function of Rsed and RinML is shown in Fig. 2.5. Increasing either of these
parameters makes the phytoplankton more light-limited so that these parameters
jointly determine vertical distribution. The difference between increasing either of
these two parameters is subtle and not illustrated in Fig. 2.5 but can be seen by
comparing Fig. 2.4A and Fig. 2.4B. When biomass is present in both layers, each
exhibits asymmetric control over the nutrient sources so that only mixed layer biomass

increases if RinML increases and only deep layer biomass increases if Rsed increases.

 

  
  
 

   

 

 

 

T

I—l

m 1500

00

3

I:

.2

g Light-limited ML
§ 1000~

c:

O

0

m

E

O

.1:

% Co—limited ML

% 500-

E DCM"

a)

.5.

"O

a 3.1

'8

m I I
‘3 Empty R-limited ML 5 ‘0

RinML’ mixed layer phosphorus input (mg P m'2 d‘l)

Figure 2.5: Two dimensional bifurcation plot of sediment phosphorus concentration,
Rsed’ and mixed layer nutrient input, RinML' Note that the Benthic Layer and
DCM regions are directly on the Rsed axis (RinML = 0). Environmental parameters:

abg = 0.1 m‘1;2m = 5 m.

The vertical distribution as a function of abg and Zm is shown in Fig. 2.6. In-
creasing either of these parameters makes the phytoplankton more light-limited as
well, however, these parameters interact to determine vertical distribution. These

parameters affect the light environment of the phytoplankton more, although mixed

48

layer depth can bring the biomass closer to nutrients at the bottom, and their effects
can be less obvious. For example, some cases are unaffected by mixed layer depth
(BL+ML to a DCM+ML) while others show non—unidirectional relationships (co-
limited ML). All four environmental parameters may interact to determine vertical
distribution. Overall, these four parameters, either individually or combined, shift

the phytoplankton to more light-limited conditions if increased (results not shown).

 

I—u
O
1

Empty

   

abg, baCkground light attenuation (m‘l)

 

 

 

 

0‘5 ‘ Co-limited ML
DCM + ML ‘rnght-lumted ML
BL + ML
5 1‘0 1'5 20

2m, mixed layer depth (m)

Figure 2.6: Two dimensional bifurcation plot of background light attenuation, abg,
and mixed layer depth, 2m- Increases in both arameters can lead to extinction.
Environmental parameters: Rsed = 200 pg P L— ; RinML = 0.1 mg P m_2 d—l.

2.5 Discussion

Aquatic communities exhibit pronounced spatial patterns (Steele 1978). How compe—
tition structures the spatial distributions of organisms through feedbacks in abiotic
and biotic components is important to understanding how biological heterogeneity
is generated. We have shown how externally imposed heterogeneity in the form of

resource gradients and mixing interacts with internally generated heterogeneity in the

49

form of competition, population dynamics, and movement to determine the spatial

distribution of phytoplankton.

Our simplified model is like an x-ray that exposes the skeleton upon which the
vertical distributions of phytoplankton are built. It also incorporates two important
components of the phytoplankton environment required to replicate real patterns in
aquatic systems. First, we add stratification, which creates spatially varying mixing,
expands a thin layer to finite thickness in the mixed layer, and allows for different
relative resource limitation within the mixed layer. Second, we add multiple nutrient

sources, which can create multi—modal phytoplankton distributions.

The inclusion of stratification means that in our simplified model, phytoplankton
can exist at a single point such as in a DCM or benthic layer, or can be homogeneously
distributed throughout the mixed layer. In a DCM in a poorly-mixed water column,
phytoplankton exist in a thin layer at their depth of equal limitation by nutrients and
light, 2* (Klausmeier and Litchman 2001). However, when the depth of equal limita—
tion occurs within the mixed layer, the thin layer is expanded to the thickness of the
mixed layer and phytoplankton exist above and below the depth of equal limitation.
Decreasing the mixed layer depth to zero in our model reveals a subtle mistake in
the surface scum case of Klausmeier and Litchman (2001). They erroneously neglect
the inevitable spatial gradient in light in a surface scum and conclude that a surface
scum must be light-limited. Our current analysis shows this is not the case, because
a surface scum may be co—limited over a range of Rsed' We also correct the formulas

for biomass in this case (see page 63, Case 2 in Appendix).

One of the intriguing results of our study is the possibility that phytoplankton
biomass could maintain source populations in both the mixed layer and deep layer
simultaneously. Without nutrient input directly to the mixed layer, a phytoplankton
population can grow in only one location. However, when there is nutrient input di-

rectly to the mixed layer, phytoplankton populations can grow in the mixed layer and

50

in the deep layer together. This bimodal distribution occurs not merely due to pas-
sive dispersal from a source habitat into a sink habitat, but instead because growing
conditions are favorable in these two locations. Phytoplankton peak biomass in the
mixed layer and deep layer is a common feature in many lakes (Fig. 2.1, J. Mellard
unpub. data), which may be explained as the adaptive response of phytoplankton
to multiple nutrient inputs to the water column. One alternative explanation is the
coexistence of two species exhibiting a trade-off in their light and nutrient require-
ments that competitively divide the water column into separate niches (Yoshiyama

et al. 2009); another alternative explanation is passive dispersal from a source to a

sink habitat.

Other studies that have considered stratification have also found interesting results
such as bistability of biomass between the mixed layer and deep layer (Yoshiyama
and Nakajima 2002, Ryabov et al. 2009) and biomass straddling both layers simulta—
neously due to sinking or actual production in both layers (Huisman and Sommeijer
2002b, Hodges and Rudnick 2004 Beckmann and Hense 2007; also mentioned as a
possibility in Ryabov et al. 2009). Our approach offers a third possibility and con-
siders production in the mixed layer and/ or deep layer but because the deep layer
biomass exists in an infinitely thin layer, phytoplankton produced in that layer cannot
be partially entrained in the mixed layer. Likely one of these results is more represen-
tative of reality, probably where biomass can straddle both layers with proportions

from both layers dispersing across the boundary.

Although our results do not show bistability of biomass distributions, we do see
that in some area of parameter space, a small change in a parameter can cause a
major shift in phytoplankton vertical distribution. For example, in Fig. 2.4A and C,
over a small range of Rsed and abg respectively, the DCM can shift many meters or
the population can even change to a different vertical distribution state. Many bodies

of water may exist in this range in parameter space since many have DCMs (Camacho

51

2006, Mellard et al., unpublished data). This could have important ramifications for
the sensitivity of those bodies of water to environmental change.

The presence of a mixed layer adds complications that few studies have explored
thoroughly (Beckmann and Hense 2007; but see Ryabov et al. 2009, Yoshiyama et al.
2009). The particular form of depth dependent mixing may influence results and
previous studies have used many different forms ranging from no mixing in the deep
layer (Huisman and Sommeijer 2002b) to a step function (Hodges and Rudnick 2004,
Yoshiyama et al. 2009), to a smoothly varying thermocline (Yoshiyama et al. 2009,
Ryabov et al. 2009) to a thermocline region with reduced diffusivities (Yoshiyama
and Nakajima (2002). Future studies should examine the influence that the particular

form of stratification has on results.

2.5.1 Assumptions, limitations, and extensions

In general, our inequalities guide the conditions under which our simplified model
approximates the full model (D(2) >> vmaxzm and D(2) >> 921211 for 0 S 2 g 2m
and ’Umax(2b — 2m) >> D(2) or g(zb -— 2m)2 >> D(2) for 2m < 2 3 2b). The
ESS distribution is convergence stable (Klausmeier and Litchman 2001), and through
either movement or growth the full model will converge on the simplified model when
our inequalities for the deep layer hold.

If the mixed layer is well-mixed according to our inequalities, our simplified model
approximates the full model well. If there is no mixed layer, then we have potential
conditions for a surface bloom (see Model predictions in next section of discussion),
essentially a completely poorly-mixed water column (Zm = 0). In between these
two scenarios, the simplified model may not do a good job of approximating the full
model.

Many phytoplankton groups such as cryptophytes, dinoflagellates, green algae,

and chrysophytes have flagella and are actively motile. Other phytoplankton groups

52

such as cyanobacteria and diatoms regulate their depth through physiological con-
trol of their buoyancy (see review in Cullen and MacIntyre 1998 and Waite et al.
1997 for diatoms in particular). Our model applies broadly to all of these groups of

phytoplankton.

However, not all phytoplankton can taxis along the gradient in growth rate because
their taxis speed is too slow or mixing is too great. Some diatoms are well-mixed in
the surface layer so D(2) >> vmaxzm and D(2) >> 9212n for 0 S 2 S Zm and it would
seem our model would hold under these conditions. However, criteria for the deep
layer must also be met so that ’Umax(2b — 2m) >> D(2) or g(zb - 2m)2 >> D(2) for
2m < 2 g 2b. Some diatoms and other species may not be able to meet these criteria
in the deep layer if mixing there is strong (big D(2)) or the water column is not deep
(small 2b -- 2m)-

Deep water columns allow another way for even neutrally buoyant species to reach
the E88 by making it easier to satisfy the second condition for our approximation,
g(zb — 2m)2 >> D(2). In this case, our model also does a reasonable job of ap-
proximating positively or negatively buoyant species with low but realistic speeds (J.
Mellard, unpublished simulations). However, our simplified model can deviate signif-
icantly from the full model (results not shown) for positively or negatively buoyant
species with faster speeds (> 0.2 m d_1) or in shallower water columns (such as 20
111). Finally, buoyancy does not affect our results if 23 is in mixed layer and we follow
our assumption of perfect mixing and sinking does not affect our results in the case

of a benthic layer.

The assumption of a well-mixed layer can be broken in several ways. If D(2) for
0 g 2 g 2m is small, then the mixed layer may not be considered well-mixed. If 2m
is large then this allows another way for the mixed layer to not be completely mixed,
particularly if ”max is large or for species that are significantly positively or negatively

buoyant. For example, in the case of D(2) = 100 m2 d"1 for 0 S 2 3 2m, a Zm = 4

53

m, and a positively buoyant species with velocities of 6 m d”1, the inequality where
our simplified model approximates the full model breaks down and not only can there
be non-uniform biomass in the mixed layer but addition of the high buoyancy can
make the phytoplankton switch vertical distribution states completely in comparison
to the state of a neutrally buoyant species.

The main cases in which our simplified model will not apply are when the mixed
layer is intermediate between well- and poorly-mixed and when the deep layer thick-
ness (2b — 2m) is small and phytoplankton can not regulate their depth. These cases
will require numerical solution of the full model, possibly with the addition of sinking
or buoyancy (as in Huisman and Sommeijer 2002b, Huisman et al. 2004, Ryabov

et al. 2009).

2.5.2 Model predictions

Increasing sediment nutrient concentration, R decreases the DCM depth and

sed’
increases all biomass until it becomes light-limited (Fig. 2.4A). This prediction is
in accordance with the trophic status hypothesis of M011 and Stoermer (1982) that
nutrient-rich lakes will support a larger, shallower DCM. If we consider Rsed to be
representative of trophic status, a comparison of the DCMs in relatively nutrient-rich
Lake Michigan and nutrient-poor Lake Superior supports both our predictions and
the trophic status hypothesis (M011 and Stoermer 1982).

Increasing mixed layer nutrient input, RinML’ decreases DCM depth and increases
mixed layer biomass, while having little effect on deep layer biomass (Fig. 2.4B). In
Sawtooth Valley, Idaho lakes, experiments and simulations showed that fertilization
in the form of surface nutrient input increases mixed layer biomass but had little effect
on DCM biomass (Gross et al. 1997). Additionally, in Lake Geneva, a reduction in

phosphorus inputs to the surface due to human activity has led to a deepening of the

depth of DCM and annual nutrient depleted zone (Anneville and Leboulanger 2001).

54

Both of these studies support our predictions, contrary to other models which predict

a tradeoff between mixed layer and deep layer biomass (Christensen et al. 1995).

Increasing background light attenuation, abg’ generally decreases DCM depth and
total biomass, especially the mixed layer biomass (Figs. 2.4C). Unfortunately, few
empirical studies examine how background attenuation is related to vertical distribu-
tion and biomass, rather using total attenuation as the light-related environmental
parameter. Total attenuation does however predict how the depth of the DCM varies
both among and within the five Laurentian Great Lakes (Barbiero and 'Iiichman
2001). In a comparison of two Finnish lakes, the dark water lake with high color
values and shallow Secchi depth had a shallower depth distribution of phytoplankton
than the clear water lake with low color values and deep Secchi depth (Holopainen
et al. 2003). The negative effect of abg on mixed layer biomass is supported by
experimental manipulation of background light attenuation in field enclosures (Diehl

et al. 2002).

Mixed layer depth, 2m, can have a negative, positive, or no effect on biomass over
some range of mixing depths dependent on the resource limitation state and verti-
cal distribution of the phytoplankton (Figs. 2.4D). Less physically realistic models
predict a unimodal relationship of mixed layer biomass with mixed layer depth (Huis-
man and Weissing 1995; Diehl 2002). Unfortunately, direct comparison of predictions
from these other models with ours is hampered by additional processes such as nu-
trient input (Huisman and Weissing 1995) and sinking (Diehl 2002) that are directly

proportional to mixed layer depth in their models.

While many environmental parameters vary widely between bodies of water, mixed
layer depth also exhibits large variation seasonally within a body of water. Seasonal
variation in mixed layer depth plays a major role in determining the seasonal cycle in
vertical distribution and can affect the importance of deep layer biomass (Lindholm

1992). Surprisingly, few studies have systematically examined effects of mixed layer

55

depth on phytoplankton spatial and physiological structure. Mixed layer biomass
showed a unimodal relationship with mixed layer depth across lakes (Kunz and Diehl
2003) and within field enclosures (Diehl et al. 2002) which agrees with our prediction
of state-dependent effects of Zm on BML (Figs. 2.4D). Both of these studies also
support our prediction of a shift from nutrient limitation to light limitation with
increasing mixed layer depth.

We also predict the location of the DOM to be at the transition from nutrient
limitation to light limitation, which is supported by data from Lake Tahoe (Coon
et al. 1987). With increased nutrient input, biomass can reach very high levels in
a light-limited mixed layer (J. Mellard, unpublished results). Surface blooms often
contain the most biomass throughout the season in a lake, which may support our
prediction that decreasing 2m to zero in water columns with high nutrient levels can

create extremely high biomass surface layers (Paerl 1988).

2.5.3 Relevance

The fundamental relationships of phytoplankton with nutrients, light, and mixing
revealed in our study may also guide lake management solutions. For example, in
management of nutrient loading, not only the concentrations, but the locations of in—
put to the water column are important. Overall, the best way to reduce algal biomass
is probably to reduce all nutrient inputs (Rsed, RinML)’ but reducing inputs to the
mixed layer (RinML) may be the most effective for decreasing biomass, given our
results. Some hypereutrophic lakes may require very large reductions in phosphorus
loading which may or may not help depending on the severity of phosphorus limita-
tion for the phytoplankton as well as the potential for sediment phosphorus release
(Marsden 1989). If this is the situation, artificial mixing that increases mixing depth
(2m) may be the best option (Lorenzen and Mitchell 1973, Visser et al. 1996), which

we predict will reduce biomass if it enhances light limitation.

56

Climate change affects the heat budget and other physical processes of a lake
which, in turn, determine stratification and mixed layer depth. In particular, climate
change may affect mixed layer depth (Magnuson et al. 1997; Schindler 1997), which
we predict to have state-dependent effects on phytoplankton vertical distribution and
biomass (see Figs. 2.4D). Climate change also alters precipitation, hence the hydro-
logical regime on the surrounding landscape that affects nutrient inputs and water
clarity. Anthropogenically driven atmospheric nutrient deposition is also increasing,
even in pristine areas (Hartmann et al. 2008; Neff et al. 2008). Climate induced
changes in stratification and nutrient budgets have already affected phytoplankton
community biomass and composition in some lakes (O’Reilly et al. 2003; Verburg
et al. 2003; Johnk et al. 2008). However, climate change effects on vertical distri-
bution have so far gone unreported. An important task is to dissect how climate
and other anthropogenically induced changes will be channeled through a number of
‘ environmental drivers to determine phytoplankton vertical distribution and produc-
tion (Karlsson et al. 2009). Our model provides a spatially explicit framework to
explore how multiple feedback loops between biotic and abiotic factors in the aquatic

ecosystem will respond to human-induced environmental change.

57

2.6 Appendix

58

Simplified model

In the following, we first write down QML when growth in the surface layer is limited
by light, limited by nutrients, or co-limited by nutrients and light for later convenience.
Next we Show that four cases out of the twelve logically possible combinations of
biomass in the mixed and deep layers are theoretically infeasible, leaving eight possible
cases (Table 2.3). Then we solve for the steady states of these cases, and evaluate

their stability.

Growth in the surface layer

Growth in the surface layer gML is written as
_ 1 Zm _ _
m = 2; f0 m1n(f1(1(2)),fR(RML)) dz. (A1)
When f R(RML) 2 f [(Iin), growth is limited by light only, and gML is:
_ 1 2m
QML = —/ f1(1(Z))dZ- (A2)
2111 0

When we use a Michaelis-Menten formulation fI(1) = r1 / (1 + K I), the integral can
be computed following Monsi and Saeki (1953) and Huisman and Weissing (1994):

K 1
gML : 7' 10g 1 + 1n
— + B
KI+Iine (abgzm a ML)

 

 

A3
abgzm + aBML ( )

When f R(RML) S f1(1(2m)), growth is limited by nutrients only, and the integral

is trivially computed:

EIML = fR(R1VIL)- (A4)

59

When f 1(1 (2111)) < f RIRML) < f1(1in), growth is co—limited by nutrients and light.
Because f [(1 (2)) — f R(RML) decreases monotonically for 0 S 2 3 2m, there is a

unique co—limitation depth 0 S 29 g Zm that satisfies:

fR(RML) = 11(I(Ze))I (A5)

and the integral splits into a nutrient-limited and a light-limited part:

Ze

0

Zm

fR(RML)dZ +/ f1(1(2))d2] . (A6)

2e

_ 1
9ML = 3;; I
Each integral of (Eq. A6) is computed following (Eq. A3) and (Eq. A4):

— + B

_ Ze _ 7. K1+Iine (abgze a MLZe/Zm)
gML = 35mm“) + ab 2m + aBML 10g ( + B )
g K1 + line abgzm a ML

(A7)

 

 

To summarize, gML is expressed by (Eq. A3) when f R(RML) 2 f 1(1in), by (Eq.

A4) when fR(RML) S f1(1in), and by (Eq. A7) when f1(1(2m)) < fR(RML) <
f1(1in). The co—limitation depth ze is obtained from (Eq. A5).

Four infeasible cases

Under light limitation, 89/61 = de/dI > 0 while 9 is independent of nutrients
(Bg/dR = 0) from our assumption. Light decreases with depth d1 /d2 < 0, and
nutrients are constant in the surface layer dR/dz = 0. Differentiating g with respect
to 2 we have
a _ as 2911?.
d2 81 d2 8R d2.

60

Thus dg/dz < 0 under light limitation. Likewise, dg/dz = 0 under nutrient limitation
in the surface layer. As we saw before, there is a unique co-limitation depth 2e when
growth is co-limited by nutrients and light in the surface layer, and below 29, growth
is limited by light. Therefore the following inequality is satisfied under co—limitation

or light limitation:
g(2) > g(zm) for 0 S 2 < Zm- (A9)

Suppose there is positive biomass in the surface layer, BML > 0, whose growth is
limited by light or co—limited by nutrients and light, and g(zm) — m 2 0. Because of

(Eq. A9) it is obvious that net growth in the surface layer satisfies

2:}; [02m (g(z) — m) d2 > 0. (A10)

This contradicts the first equality of (Eq. 2.13). Therefore g(zm) -— m < 0 when
BML > 0 and the growth is limited by light or co—limited. Because g(zm) — m < 0,
1 (2m) < 1*. Therefore g(z) — m < 0 for 2m < 2 3 2b. This prevents the second
equality of (Eq. 2.13) from being satisfied anywhere in the deep layer, and hence
BDL should be 0.

To conclude, if BML > 0 and the growth is limited by light or co-limited by nu-
trients and light, BDL = 0 at steady state. This excludes four cases, (DCM)+(light-
limited ML), (DCM)+(co—limited ML), (benthic layer)+(co-limited ML), and (ben-

thic layer)+(light-limited ML), from steady state distributions.

Eight possible cases
Case 1: Empty

Knowns: BML = 0, BDL = 0

61

Unknowns: RML

Equations to solve:

Because BML = BDL = 0, we have only one equation derived from (Eq. 2.21) to

solve for one unknown RML:

 

DDL (Rsed - RML)
RlnML+ zb+1/h_zm —07

and obtain

(2b + 1/h — 2m) RinML.
DDL

 

RML = Rsed +

From (Eq. 2.26) light profile is expressed by

1(2) = line-abs?

Consistency/stability criteria:

(A11)

(A12)

(A13)

It is easy to see that gML 2 9(2) for Zm < 2 3 2b. Therefore the case “empty” is

stable when gML - m g 0. From (Eq. A3), (Eq. A4), and (Eq. A7), this condition

is summarized by:

r

 

 

 

K +1-
r log 1 _1n _ m S 0
angm (KI-Hing abgzm)
when fR(RML) Z f[(Iin)I

%fR(RML) + abgzm log ( -- m < 0

 

 

KI-I'Ijne—abgze )
KI+1in€—abgzm

when f1(1(2m)) < fR(RML) < fIUinlv

fR(Rlv1L) - m S 0

\ when fR(RML) S f1(I(Zm))a

62

(A14)

where 29 is obtained from (Eq. A5). The frontier of the first inequality of (Eq. A14),

 

 

abg 2m

K 1-
log 1 J12“ Z — m = 0, (A15)
KI + line bg m

separates empty and light-limited ML regions; the second,

 

 

-0, 29
2 — r K + 1- e bg
—-e-fR(RML) + log I m _a 2m — m = 0, (A16)
2*“ abgzm K I + Iine bg

separates empty and co—limited ML regions. The third inequality of (Eq. A14) implies
RML _<_ R* and the frontier,

 

(2b + 1/h - 2m) RinML : 12*

(A17)
DDL

Rsed +

separates the empty and the benthic layer or DCM or nutrient-limited ML or some

possible combination of these cases.

Case 2: Co-limited mixed layer

Knowns: BDL = 0
Unknowns: BML’ 29, RML
Equations to solve:

Because BML > 0 and BDL = 0 we have equalities from (Eq. 2.13) and (Eq.
2.21) to solve for RML and BML:

 

 

m (1 - 8) BML , DDL (R d - RML) __
" Y + RIDML + Zb + :3}; _ Zm - 0 (A18)
1 2m _
(gML — m =) 7 I] min(f1(1(2)),fR(RML))dz — m = 0. (A19)
In 0

63

where the light profile is from (Eq. 2.26):

e— (abgz‘l'aBMLZ/Zm)

() Iin for0_<_2§2m (A)
1 2 = 20
- + B
line (abgz a ML) for 2111 < Z S 2b

Specifically when growth is co—limited by nutrients and light, gML is expressed by

(Eq. A7 ), and the equality (Eq. A19) is rewritten by

— a 2 +aB 2 2

23 - T KI-I—Iine (bg 6 ML 8/111)
K1 + Iine abgzm a ML

 

 

--m = 0,
abgzm + aBML

(A21)
where 29 is obtained from (Eq. A5). Equations (Eq. A18) and (Eq. A21) are solved

numerically for unknowns BML and RML with 29 from (Eq. A5).

Consistency/stability criteria:

Stability is already ensured because 1(2) < 1 (2m) < 1* for Zm < 2 3 2b (see
“Four impossible cases” section for the proof). Existence of positive steady state
requires positive biomass BML > 0 and equal limitation depth within the surface
layer 0 < 29 < Zm- The frontier of the first inequality is obtained by setting BML = 0
in (Eq. A18), (Eq. A21), and (Eq. A5), which is identical to the second inequality
of (Eq. A16). This separates co—limited ML and empty regions. One frontier of the

second inequality is obtained by setting 29 = 0 in (Eq. A18), (Eq. A21), and (Eq.

64

A5):

 

m(1—€)BML D R -—R ,
Y + R

 

 

— lIlML + Zb+1 h—Zm = 0
ob ZmiaPML log K1+Iin — m = 0 . (A22)
g —( + B )
mum. “ngm 0 ML

f1(11n)- fRIRML) = 0

When we use Michaelis—Menten formulations for f1 and f R, we obtain an equality
algebraically from (Eq. A22). This frontier separates co—limited and light-limited ML
regions. The other one is obtained by setting 29 = 2m in (Eq. A18), (Eq. A21), and
(Eq. A5):

m(1—e)B , DD (R. —R ) _
__7_LIL + RinML + W _ 0
fR(RML) — m = 0 . (A23)

11 (line-(“bg2m+“BML)) — fRo‘zML) = 0

From the second equality of (Eq. A23), RML = R*. From the second and the third

equalities, we have

— + B
Iine (abgzm a ML) = 1*, (A24)
which yields
log (fin/1*) — ab Zm
BML = g . (A25)

 

a

65

Substituting RML = R* and (Eq. A25) in the first equality of (Eq. A23) we obtain

YDDL (Rsed _ 12*) _ log (fin/1*) _ abgzm + YRinML _
m(1—e)(2b+1/h-—2m) a m(1—e)—

 

 

0. (A26)

When RinML = 0, (Eq. A26) is identical with (Eq. A62), and separates co—limited
ML and DCM regions.

Case 3: Light-limited mixed layer

Knowns: BDL = 0
Unknowns: BML’ RML
Equations to solve.

BML > 0 and BDL = 0 in this case, thus the same equalities (Eq. A18) and (Eq.
A19) with the light profile (Eq. A20) hold as in the co—limited ML case. Under light

limitation for growth, gML is expressed by (Eq. A3), and (Eq. A19) is rewritten by

7‘ log K1 + Iin
ab 2m + aBML _ B
g K1 + Iine (abgzm-I-a ML)

 

 

— m = 0. (A27)

Equalities (Eq. A18) and (Eq. A27) are solved numerically for the two unknowns
RML and BML'
Consistency/stability criteria:

Stability is ensured because 1 (2) < 1(2m) < 1* for Zm < 2 3 2b. The existence
of a positive steady state requires BML > 0 and f Iain) < f R(RML). The frontier
of the first inequality is obtained by setting BML = 0 in (Eq. A18) and (Eq. A27),
which is identical with (Eq. A15). The frontier of the second inequality is obtained
by setting f1(Iin) — f R(RML) = 0, which is identical with what is obtained from
(Eq. A22).

66

Case 4: Nutrient-limited mixed layer

Knowns: BDL = 0, RML = R*
Unknowns: BML
Equations to solve:
The same equalities (Eq. A18) and (Eq. A19) with light profile (Eq. A20) hold
because BML > 0 and BDL = 0 in this case. Under nutrient limitation for growth,

gML is expressed by (Eq. A4), and (Eq. A19) is,

fR(RML) — m = 0, (A28)

which means RML = R*. Substituting RML = R* in (Eq. A18), we obtain

_m(1 — E) BML
Y

 

DDL (Rs d - R"‘)
R- e = . A29
+ mML+ zb+1/,,_Zm 0 ( )

Rearranging (Eq. A29) we have BML:

ML m(1-—e) m(1 —e) (2b+1/h—2m)

 

Consistency/stability criteria:

The existence of a positive steady state requires BML > 0 and f1(1(2m)) >
f (RML) (= m). The latter inequality implies 1(2m) > 1*. The frontier of the first
inequality is obtained from (Eq. A30), which is identical with (Eq. A17). The frontier
of the second inequality is rewritten as:
[inte— (abgzm+aBML) = 1*. (A31)

Substituting BML with (Eq. A30) in (Eq. A31), some rearrangement gives the same
equality as (Eq. A26).

67

Stability requires g(z) — m S 0 for Zm < 2 3 2b. When BDL = 0 and Rsed >
RML, dR/dz > 0 from (Eq. 2.19). Because RML = R* here, we have R(2) >
R* for Zm < 2 3 2b in this case. With 1(2m) > 1*, there is 5 > 0 such that
g(zm + 5) — m > 0. Therefore a nutrient-limited ML is unstable when Rsed > R*
and is stable when Rsed S R*. Considering the conditions for existence BML > 0
and stability Rsed S R*, some rearrangement of (Eq. A30) gives an inequality

RinML > 0 that must be satisfied.

Case 5: Benthic layer and Nutrient-limited mixed layer

Knowns: RML = R*
Unknowns: BML) BDL
Equations to solve:
Growth in the surface layer is limited by nutrients, that is, RML = R*. Because

BML > 0, BDL > 0, and RML = R*, we have equalities from (Eq. 2.21) and (Eq.

 

 

 

2.24):
1 — e B
1 - B

—m( if) DL + hDDL (Rsed — R*) = 0, (A33)

and obtain,

_ YRinML
BML —— m (1 _ e)’ (A34)
hYDDL (R d - R*)

B = se . A35
DL m (1 — e) ( )

The light profile is expressed by (Eq. 2.26).
Consistency/stability criteria:

Stability is ensured because R(2) = R* for 0 g 2 3 2b. The existence of a positive

68

steady state requires BML > 0, BDL > 0, and 1(2b) 2 1*. These first two conditions
imply RinML > 0 and Rsed > R*, respectively. The frontiers RinML = 0 separates
(benthic layer + nutrient-limited ML) and benthic layer regions, and Rsed = R*,
(benthic layer + nutrient-limited ML) and nutrient-limited ML regions. Substituting
BML and BDL in (Eq. 2.26) with (Eq. A34) and (Eq. A35), the last condition

1(2b) 2 1* is rewritten as:

 

_ [ab Zb+a_Y_1_finML+ahYDDL (Rsed_R*)

which is rearranged to get:

hYDDL (Rsed - R*) _ 103(11n/1*) - angb + YRinML <
m(1—e) a m(1—-e)—

 

 

0. (A37)

The frontier of (Eq. A37) separates the (benthic layer + nutrient-limited ML) and

(DCM + nutrient-limited ML) regions.

Case 6: DCM and N utrient-limited mixed layer

Knowns: RML = R*
Unknowns: BML’ BDL’ 2*
Equations to solve:

Because BML > 0, BDL > 0, and RML = R*, we obtain equalities (Eq. A32)

and

m (1 — 5) BDL DDL (Rsed — R*)
_ = A
Y + Zb+1/h—z* 0, ( 38)

 

 

from (Eq. 2.21) and (Eq. 2.24). Light profile is expressed by (Eq. 2.26). At 2*,

69

growth is co—limited by nutrients and light, thus 1(2*+) = 1*:

— *+ B ,. + B
11116 (0ng 0 ML a DL) :1...- (A39)

From (Eq. A32) we obtain BML’ which is expressed by (Eq. A34). Equalities (Eq.
A38) and (Eq. A39) are simultaneously solved for BDL and 2*.
Consistency/stability criteria:

DCM and nutrient-limited ML is stable because R(2) = R* for 0 S 2 < 2*
and 1 (2) S 1* for 2* S 2 S 2b. The existence of a positive steady state requires:
BML > 0, BDL > 0, and Zm < 2* < 2b. The first condition is satisfied when

RinML > 0. Rearranging (Eq. A38), we get:

YDDL (Rsed - R*)

 

 

 

 

B = . A40
DL m(1—e)(2b+1/h—2*) ( )
Substituting BML from (Eq. A34), (Eq. A39) is rearranged and we get:
log (fin/1*) — abg2* YRinML
BDL = — . (A41)
a m (1 — 5)
From (Eq. A40) and (Eq. A41) we have an equality:
_ 3* lo (1- /1*) — a 2* .
YDDL (Rsed ) = g In be _ 3’31th (A42)

m(1—e)(2b+1/h—2*) a m(1—e)’

which is solved for 2*. The one frontier of the condition Zm < 2* < 2b is obtained

by substituting 2* = Zm in (Eq. A42):

YDDL (Rsed - R*) _ 103(1111/1’“) ‘ “bgzm YRinML __
m(1-—e)(2b+1/h-2m) a m(1—e)_

 

 

0, (A43)

which is identical with (Eq. A26) and separates (DCM + nutrient—limited ML) and

70

co—limited ML regions. The other one is obtained by substituting 2* = 2b:

hYDDL (Rsed — R*) _ 103 (1111/ 1 *) - angb + YRinML 2
m (1 — e) a m (1 - 5)

 

 

0, (A44)

which is identical with the frontier of (Eq. A37), and separates the (DOM + nutrient-

limited ML) and (benthic layer + nutrient-limited ML) regions.

Case 7: Benthic Layer (BL)

Knowns: BML = 0
Unknowns: BDL, RML
Equations to solve:

When BML = 0 and 2* = 2b, the following equalities are derived from (Eq. 2.21)
and (Eq. 2.24):

 

DDL (R* — RML) ___ 0

 

 

 

 

R- ML +
m 2" _ Zm. (A45)
m (1 - 6) BDL * DDL (13* - RML) _
_ Y + hDDL (Rsed — R ) - 2b _ Zm — 0,
and we obtain two unknowns:
DDL
hYDDL (Rsed — R*) YRinML
= . A47
DL m(1—e) +m(1—e) ( )
From (Eq. 2.26), the light profile is,
line—abgz for 0 S 2 < 2b
1 (2) = B (A48)
Iine— (abg2+a DL) for 2 = 2b

71

Consistency/stability criteria:

First we consider the existence of the positive steady state. From (Eq. A47),

BDL > 0 when
hDDL (Rsed — R*) + RinML > 0. (A49)
Net growth g(zb) — m = 0 when
— + B
1(2b) = 1ine (abgzb a DL) 2 1*. (A50)

The two above inequalities (Eq. A49) and (Eq. A50) ensure the existence of a positive

steady state.

Next we consider the stability criteria. Net growth should be negative or 0 ev-
erywhere for the stability. When RinML = 0, 9(2) —— m = 0 because R(2) = R* for
0 S 2 S 2b, and hence benthic layer is stable. When RinML > 0, the benthic layer
is unstable because RML > R* from (Eq. A46) and 1 (2) > 1* from (Eq. A50).

To summarize, the stability of the benthic layer requires RinML = 0; in this case,
the inequality (Eq. A49) is simplified, and the parameter region where the deep layer

is stable is expressed by:

Rsed - 12* > 0 (A51)
—-(ab zb-I-aBDL) * .
1- e g 2 1

1n

The frontier of the first inequality, R = R*, separates the benthic layer and empty
sed

regions, which is identical with (Eq. A17) when RinML = 0. Substituting BDL with

72

(Eq. A47), the frontier of the second inequality of (Eq. A51) is written as,

 

 

hYDDL (Rsed — R*) _ 103(11n/1*) ‘ “bgzb =

m (1 __ E) a 0, (A52)

which separates the benthic layer and DCM regions.

Case 8: DCM

Knowns: BML = 0
Unknowns: BDL’ 2*, RML
Equations to solve:

When BML = 0, the following equalities are obtained from (Eq. 2.21) and (Eq.

 

 

 

 

2.24):
DDL (3* — RML)
RinML + 2* _ m = 0, (A53)
_m(1— 8) BDL + DDL (R... - R*) _ DDL (R* - RML) = 0 (A54)
:1: * '
Y 2b + 1/h ’ 2 z _ 2’“

From (Eq. 2.26), the light profile can be expressed by

line—abgz for 0 S 2 < 2*
[(3) = —(a 2+aB ) (A55)
Iine bg DL for 2* S 2 S 2b

A stable DCM must be co—limited by nutrients and light. Therefore 1(2*+) = 1*,

that is,

_ *
1- ((1ng +aBDL) = 1*. (A56)

me

Solving (Eq. A53), (Eq. A54), and (Eq. A56), we obtain three unknowns, RML,

73

BDL’ and 2*.
Consistency/stability criteria:

As with the case of a benthic layer, a DCM is unstable when RinML > 0 because
RML > R* from (Eq. A53) and 1(2) > 1* for 0 S 2 < 2* from (Eq. A56). So we

consider RinML = 0. In this case, RML = R*, and rearranging (Eq. A54) we have

YDDL (Rsed _ R*)

 

 

BDL: m(1—e)(2b+1/h—2*)’ (A57)
and rearranging (Eq. A56) we have
BDL = 10% (fin/1:) — abgzak. (A58)
From (Eq. A57) and (Eq. A58) an equality is obtained:
YDDL (Rsed - R*) _ 103(11n/1*) _ abgz*, (A59)

 

 

m(1—e)(2b+1/h—2*)_ a

which is solved algebraically for 2* (Klausmeier and Litchman 2001). The obtained

2* should satisfy
2m < 2* < 2b. (A60)
From (Eq. A57), the existence of a positive steady state requires
Rsed > R*. (A61)

RinML = 0 and inequalities (Eq. A60) and (Eq. A61) define the parameter region
where the DCM is stable.

One frontier of (Eq. A60), 2* = 2m, is expressed by substituting 2* in (Eq. A59)

74

With Zmi

YDDL (Rsed - R*) _ 103(11n/1*) ‘ “ngm
m(1—e)(2b+1/h-2m) a

 

 

= 0, (A62)

which separates DCM and co—limited ML regions, and the other one, 2* = 2b,

hYDDL (Rsed — R*) _ 10g (hm/1*) — abgzb _
m (1 — e) a _

 

 

0, (A63)

separates the DCM and benthic layer regions. Note that this frontier is identical with
(Eq. A52). The frontier of (Eq. A61), Rsed = R*, separates the DOM and empty

regions.

75

Chapter 3

Experimental test of
phytoplankton competition for
nutrients and light in poorly-mixed

water columns

Jarad P. Mellard
with

Kohei Yoshiyama, Elena Litchman, and Christopher A. Klausmeier

3.1 Abstract

Despite the importance of the vertical distribution of phytoplankton for primary pro-
duction and energy transfer to higher trophic levels, our mechanistic understanding
of the phenomenon is poor. Recent theory of the vertical distribution of phytoplank-
ton considers how interacting niche construction processes such as resource depletion,

behavior, and population dynamics contribute to spatial heterogeneity in the aquatic

76

environment. To test this theory, we used a motile phytoplankton species (Chlamy-
domonas reinhardtii) growing in poorly-mixed water columns with opposing resource
gradients of nutrients and light to examine how intraspecific competition determines
the vertical distribution of phytoplankton. Under these conditions, theory predicts
that a species should aggregate at a single depth, an evolutionary stable strategy
(ESS). This depth of aggregation, or biomass maximum, should change through time
due to depletion of available resources. In addition, the depth of the ESS aggregation
should be deeper under low amounts of nutrient loading and shallower under higher
amounts of nutrient loading. We tested these theoretical predictions in our experi-
mental water columns. Supporting predictions, we routinely observed a single biomass
maximum, where much of the population was aggregated, and the equilibrium depth
of the biomass maximum was at the surface under higher nutrient loading. However,
at equilibrium, low nutrient loading led to a non-distinct biomass maximum with the
population distributed over most of the water column instead of the distinct subsur—
face peak predicted by theory. Also supporting predictions, total biomass across water
columns was positively related to nutrient supply. Further supporting predictions, we
also found evidence of light limitation for a surface biomass maximum and nutri-
ent limitation for a deep biomass maximum. In addition, the resource environment
was strongly modified by the behavioral movement, self-shading, nutrient uptake, and
growth of the phytoplankton. The light level leaving the bottom of the water column,
101“, declined through time as the phytoplankton grew and was negatively related to
nutrient loading. Nutrients were strongly depleted where biomass was present by the
end of the experiment. This experimental study shows that the vertical distribution

of phytoplankton may be driven by intraspecific resource competition in space.

77

3.2 Introduction

What determines the abundance and spatial distribution of organisms is one of the
main questions in ecology (Brown 1984). External controls in the form of resources
and stresses distributed in space along with organism-specific preferences and toler-
ances are commonly suspected to determine spatial distributions (MacArthur 1972).
However, it has long been recognized that there are feedbacks on the environment and
often the environment is modified by the activities of organisms themselves (Levins
1979). In self-organizing systems, spatial patterns can form through interactions in-
ternal to the system without intervention by external influence (Klausmeier 1999,
van de Koppel et al. 2008). Studies are needed that explicitly model and measure
how feedbacks between the strategies of organisms and their biotic and abiotic envi-

ronments determine spatial patterns (Laland et al. 1999, Hastings et al. 2007).

Our approach to examining spatial distributions of organisms fuses externally im—
posed heterogeneity with self-organizing dynamics. A verbal model of how external
. and internal heterogeneity interact is: 1) Resource gradients represent external en-
vironmental heterogeneity. 2) Organisms sense these resource gradients and select
habitats based on perceived quality. 3) The organisms’ growth results in population
dynamics. 4) Population dynamics create feedbacks on the resource environment. 5)
The organisms undergo further strategic movement based on the feedbacks in the

resource environment that all the other organisms have created.

Phytoplankton are ideal for examining these interacting processes. Phytoplank-
ton require nutrients and light to grow and these essential resources usually form
opposing gradients in the vertical dimension in the aquatic environment (Reynolds
1984). These gradients in resources are actually set or enhanced by the phytoplankton
themselves due to nutrient uptake and self-shading (Klausmeier and Litchman 2001).

The hypotheses of what determines the vertical distribution of phytoplankton remain

78

largely untested (but see Carney et al. 1988) and few studies have attempted to
recreate vertical distributions under controlled settings based on existing hypotheses

(but see Jaeger et al. 2008).

Vertical distributions of phytoplankton are strongly dependent on the physics op-
erating in a body of water (Huisman et al. 1999c, Jaeger et al. 2008). In a completely
well-mixed water column, phytoplankton are homogenized and form no patterns in
vertical distribution. However, the environment is not always well mixed, in which
case we can expect pronounced patterns. Multiple distinct vertical distributions are
possible in poorly-mixed systems including a benthic layer, where phytoplankton form
a layer directly on the sediment surface, a deep chlorophyll maximum (DCM), where
phytoplankton form a layer in a poorly—mixed portion of the water column away from
the boundaries, and a surface layer, where phytoplankton form a layer at the surface
of the water. Several hypotheses have been proposed to explain the formation of
DCMs, such as near-inertial internal wave shear (Hanks 1995), sinking in a density
stratified water column (Condie and Bormans 1997), depth dependent grazing by zoo—
plankton or mixotrophs (Tittel et al. 2003), diel vertical migration of algae (Sommer
and Gliwicz 1986, Gasol et al. 1991), behavioral responses to sensory cues (Gervais
1998, Clegg et al. 2007), and preferential movement to and growth at an optimal
depth in opposing resource gradients (Fee 1976, Klausmeier and Litchman 2001). We
focus on this last hypothesis, how movement and growth in opposing resource gradi-
ents can determine phytoplankton vertical distributions, because theory (Klausmeier
and Litchman 2001) has made testable predictions related to this hypothesis that are

amenable to experimentation.

Motile algae in poorly-mixed water columns can be thought of as playing a game
in the opposing resource gradients of nutrients and light (Klausmeier and Litchman
2001). Motile algae are common and represent important components of phytoplank-

ton communities in freshwater and marine environments (Reynolds 1984, Cullen and

79

MacIntyre 1998). Using a spatially-explicit dynamical model, Klausmeier and Litch-
man (2001) Show that motile phytoplankton can form a thin layer in poorly-mixed
water columns as is also observed in the field (Fee 1976, Gasol et al. 1991, Gervais
1998, Mellard et al. Chapter 4). They show that their full dynamical model can
be approximated by a game-theoretical model that has the advantage of providing
analytical results for greater insight. The game-theoretical model considers motile
algae to form an infinitely thin layer at their depth of co-limitation. This strategic
depth, 2* , is a convergence stable evolutionarily stable strategy (ESS) and prevents
growth elsewhere in the water column.

The model makes specific predictions about the vertical distribution of algae
(Klausmeier and Litchman 2001): 1) Phytoplankton can form a thin layer, 2) the
depth of the layer depends on environmental conditions, specifically it should be
deeper under low-nutrient conditions and shallower under high-nutrient conditions,
3) biomass should be positively associated with nutrient supply over the range of nu-
trient supply, from adequate to saturating, 4) phytoplankton in a surface layer should
be co-limited (Mellard et al. Chapter 2) or light-limited, whereas phytoplankton in
a benthic layer should be nutrient-limited, and those in a DCM co-limited by nu-
trients and light. We evaluated these predictions with the aid of a dynamic model
and experimental plankton towers focusing on whether algae aggregate and whether

aggregation patterns depend on environmental conditions.

3.3 Theory

We expanded on previously published theoretical work (Klausmeier and Litchman
2001) by examining dynamics of the full model used to verify the more fully explored
game-theoretic model. Because transient dynamics were not explored in Klausmeier

and Litchman (2001) or elsewhere, we present some of these results here because

80

they are directly applicable to results from our experiment. The full model in-
cludes spatially-explicit equations for biomass, b, nutrients, R, and light, 1 in a one-
dimensional water column where 2 is depth with the surface at 2 = 0 and the bottom

at 2 = 2b. See Appendix for a full description of the model.
Model predictions

Under the conditions we are examining, simulations predict algae to aggregate and
form a thin layer, hence the use of the game-theoretic model proposed by Klausmeier
and Litchman (2001) should be valid. However, because the game-theoretic model
assumes the system approaches a stable equilibrium, some of the predictions may not
be valid for the time scale of our experiment (50 days). The game-theoretic model also
assumes an infinite swimming speed that should not be valid for any species we use
in our experiments. Therefore, we present predictions from the full dynamical model,
which have not been presented before, as well as predictions from the game-theoretic

model proposed by Klausmeier and Litchman (2001).

Simulations suggest the following transient dynamics. Algae that start in a uni-
form distribution should behaviorally aggregate at the surface by the end of day
1 (Figure 3.1 bottom left plots). They should grow exponentially initially (Figure
3.1 top left plots) before reaching carrying capacity which will happen sooner in
low-nutrient towers (Figure 3.1a) than in mid-level nutrient towers (Figure 3.1b) or
high-nutrient towers (Figure 3.1c). In low and mid-level nutrient towers, algae should
move down to acquire more nutrients once they are depleted at the surface. In low-
nutrient towers, algae should remain at the bottom of the water column to take up
the little nutrients available if enough light penetrates there (Figure 3.1a bottom right
plot). In mid-level nutrient towers, algae should form a layer somewhere between the
surface and the bottom in a DCM where nutrient and light supply are balanced by
the uptake and self-shading of the algae (Figure 3.1b bottom right plot). High nu-

trient towers results in higher biomass, so algae face intense light competition due to

81

plentiful nutrients and should remain at the surface (Figure 3.10 bottom right plot).

82

Figure 3.1. Predicted total biomass (top left), depth distribution of biomass
through time (bottom left) and equilibrium (day 50) distribution of biomass,
nutrients, and light (bottom right) for a) low-nutrient supply (R,1n =5 pg P
L‘l), b) mid-level nutrient supply (Bin :50 pg P L_1), and c) high-nutrient
supply (Rin 25000 pg P L—l). The top left plot of each part shows biomass
integrated over the entire water column. In the bottom left plot of each part,
biomass density is shaded so that higher biomass is in darker shades. The
solid line on that plot shows the average depth of the biomass and the dashed
line shows the location of the biomass maximum. In the bottom right plot of
each part, the equilibrium (day 50) biomass, nutrients, and light are all scaled
to their maximum to fit on one plot but units above each plot show absolute
quantities. The 1* value on those plots shows break-even light level and is

relativized to the maximum light level as well.

83

low nutrients biomass [105 cells ml'l]
0 Q 0.4 016 0,8

nutrient [pg P L'l]
0 0.025 0.05 0.075 0.10 0.125 .

light [pmol photons m’zs'l]
0 1.0 20 3.0 41 ,
‘—l‘*

9
~

 

 

. . A A g; I ‘
o'
.

 

?

Depth [m] Biomass[107 cells cm'z]

 

 

 

 

 

 

1 *2 mid"°"°'““m°“‘s biomass [105 cells mrl]
9 z i .6 8
0. nutrient [pg P L'l]
0 2 4 6

 

light [pmol photons m'zs'l]
0 10 20 310 40

J

 
 
 
 
 
 

.O
u:

 

Depth [ml Biomass [107 cells cm'zll

p—I
U
Q

 

 

c) high nutrients biomass [105 cells ml'l]
q s 1,0 1,5 20 2;

I"
N'LA

nutrient[ gPL'l]
0 1000 200 3000 4000

light [pmol photons m'zs'l]
0 1,0 20 3,0 4.0 .

 

l . A L

 
  

Depth [ml Biomass [107 cells cm’2]l

 

 

 

 

 

 

0.5
1.0:
l . k k ‘ - .. _ - — biomass (b)
.3
0 10 z'lhme [11.3.3] 40 50 ___ nutrient (R)
— average depth - - - -depth of biomass maximum —-light (I)

Figure 3.1: Predicted total and depth distribution of biomass through time.

84

At equilibrium (predicted to be reached after 50 days), we predict the algae in
the low-nutrient towers to be limited by nutrients, the algae in the mid-level nutrient
towers to be co—limited, and the algae in the high-nutrient towers to be limited by

light (Figure 3.2).

- O O
40 -
- O
.1
O
30 r . O
Q 0
:5 _ 0 Low nutrients (Benthic layer)
'29 20 — Do . .
1-1 _ Mid-level nutrients (DCM)

High nutrients (Surface layer)

10’ / l
_ 0

O
. .-.. ... . .......1 . .......1 L 1+
0.1 l 10 100 1000

l

 

Nutrient (R)

Figure 3.2: Points are resource conditions within different water columns at different
depths. Resource conditions for a low-nutrient supply water column (hollow points),
mid-level nutrient supply water column (gray donuts), and high-nutrient supply water
column (solid points, some on top of one another) are shown. Since light declines
with depth, the point with the highest light value for each water column is also
the shallowest depth.- Note that the arrows show the resource conditions for the
different predicted vertical distributions of a benthic layer, DCM, and surface layer
corresponding to the depth distributions in Figure 3.1.

We further predict the total biomass in a water column to be positively related to
nutrient supply until the algae are completely light limited (Figure 3.3a). In addition,
we predict the vertical position of the thin layer to be shallower under higher nutrient
conditions (Figure 3.3b).

We designed an experiment to evaluate whether these predictions are upheld in

85

2.5

 

 

 

 

 

L '- -----------------
r a ’
I.
((3— 2.0,
e
0
g 1.5:
l\ _
S .
§ 1.0—
e _
.9.
m 0 5; — Simulations offull model
E --ESS model
0* - . . ..-1 . m.-....1 - .-....-l .mmm
1 10 100 1000
Nutrient supply at bottom [pg P L—l]
10 100 1000
0L -m. ._ ...l - . . - .
b
E
E :
13‘ i
E‘ 05:
CI-I _.
O -
5 -
0‘ s.
Q) -
Q :
1.0}
1.5:

 

 

 

Figure 3.3: Predicted integrated biomass (a) depth of algal layer and (b) depth of
the algal layer as a function of nutrient concentration at the bottom. Both (a) and
(b) have a solid line representing simulations from the full model averaged over days
30—50 and a dashed line representing the equilibrium biomass (a) and 2* depth (b)
predicted by the ESS model.

86

F__Y‘.'.‘ -m#

water columns under controlled settings. We manipulated one factor, nutrient supply,

while holding all other factors constant.

3.4 Experiment methods

Experimental setup

We used cylindrical plankton towers to examine spatial distributions of phyto-
plankton (Picture in Appendix). Tower dimensions were 1.5 m height, 0.2 m diameter
and constructed from clear cast acrylic tubes (Total Plastics, Kalamazoo, MI). Towers
had ports along the vertical dimension with silicone stoppers that were punctured with
needle syringes to take samples or inject nutrients. Towers were covered with heavy
duty black plastic sheeting to maintain a unidirectional light source and increase light
attenuation. Towers were illuminated 24 hours a day to maintain the light gradient
with a single cool 42 watt fluorescent light (Technical Consumer Products, Aurora,
Ohio) above each tower. In order to have only one limiting nutrient, phosphorus,
towers were filled with autoclaved WC medium (Guillard 1975) without phosphorus
but with 5X all other ingredients, including bicarbonate in order to eliminate carbon
limitation. Towers were inoculated with cultured Chlamydomonas reinhardtii 2935
(Carolina Biological Supply), a flagellated green alga commonly found in temperate
freshwater lakes (Reynolds 1984). Towers were then mixed by stirring the whole col-
umn vigorously. After inoculation, we injected concentrated phosphorus (KQHPO4)
at 10 depths in each tower to create a nutrient gradient initially in concentrations
corresponding to the experiment treatments (next paragraph). We confirmed that
the algae were homogenously mixed and the nutrient gradient was present initially
by withdrawing samples within an hour after injecting the phosphorus. A clear plas-
tic sheeting (saran wrap) was placed loosely over the top of each tower during the

experiment to reduce probability of contaminants and invaders but still allow gas

87

 

exchange.
Experiment treatments

Our towers represented an environmental gradient in nutrient loading, with in-
creasing phosphorus concentrations injected at the bottom (deepest port). Nutrient
concentrations of 5, 10, 50, 100, 250, 500, 1000, and 5000 pg P L‘1 were injected at
the bottom of towers 1 through 8, respectively. During each sampling, some volume
was removed from each tower. In order to keep the water level relatively constant
as well as maintain a constant nutrient supply into the system, we injected nutrients
back into the system. After most sampling days, we set up a gravity fed nutrient ad-
dition system that slowly injected approximately 250 mL of concentrated phosphorus
WC medium into the bottom port of each tower. This slow injection system took
approximately 12 hours to complete each time. The days we injected nutrients are
indicated by arrows on Figure 3.4.

Sampling

Two main sampling schemes were employed. For the first 15 days of the experi-
ment, 17 relatively evenly spaced ports were sampled for biological analysis and for
days 16 through 50, 21 relatively evenly spaced ports were sampled for biological anal-
ysis. We increased our spatial resolution by adding these four other ports. For the
first four days of the experiment, seven relatively evenly spaced ports were sampled
for nutrient analysis and for days five through 50, eight relatively evenly spaced ports
were sampled for nutrient analysis. We sampled every three to four days for the first
25 days of the experiment and every three to seven days thereafter. We ended the
experiment after 50 days because we observed no further distinct changes in spatial
distribution of algae, biomass was declining in most towers, and our model predicted
towers should have reached equilibrium by then. We refer to the the last 20 days of
the experiment as at equilibrium, since spatial distributions appeared to have reached

steady state.

88

Samples were taken from each port using 22—gauge 3-inch hypodermic needles
(Air-Tite Products Co, Inc., Virginia Beach, VA) in 10 mL B-D syringes (Becton
Dickinson 8: co., Franklin Lakes, NJ), and placed in liquid scintillation vials for phy-
toplankton enumeration or filtered through 0.45 pm nylon, 25 mm syringe filters
(Fisher Scientific, Hampton, NH) and placed in 10 mL centrifuge tubes (Corning
Incorporated, Corning, NY) for nutrient analysis. Cell densities were measured on
CASY cell counter Model TT (Scharfe-System, Reutlingen, Germany) using a. 4-30
pm cell diameter range and preserved afterwards using Lugols solution. Cells were
also examined under an inverted scope to check for signs that they were alive and
possible morphological changes. Dissolved phosphorus was measured using the or-
thophosphate method on Lachat Instruments Quick Chem 8500 (Lachat Instruments
a Hach Co Brand, Loveland, CO). At the end of the experiment we measured the
C:N:P of particulate matter, chlorophyll a, and temperature at the same eight ports
in the tower where dissolved nutrients were measured. Particulate carbon and nitro—
gen were measured by filtering samples on 25 mm Whatman GF/ F pre-combusted
glass fiber filters (Whatman plc, Springfield Mill, UK) before combusting them in a
Costech Elemental Combustion System CHNS—O (Costech Analytical Technologies,
Inc., Valencia, CA). Particulate phosphorus was measured by filtering samples on 25
mm Whatman GF/ B acid-washed glass fiber filters, performing persulfate digestion
on the filters, and then analyzed colorimetrically on a Shimadzu spectrophotometer
UV-240PC (Shimadzu Scientific Instruments, Columbia, MD) at 880 nm. Chlorophyll
a was measured by filtering onto a 25 mm Whatman GF / B filter, which was extracted
with ethanol and measured fluorometrically (Welschmeyer 1994). We also measured
pH at two points in each tower to make sure there was not a vertical gradient in pH.
Light was measured at the surface and bottom of the water columns before the exper-
iment started, at the bottom of the water columns throughout the experiment, and

through the water columns at the end of the experiment. Light was measured using

89

 

a LI—COR Quantum/Radiometer/Photometer model LI-185B (LI-COR Biosciences,
Lincoln, NE).

Data analysis

To summarize the vertical distributions, we fit three functions to the vertical
profiles of biomass and used information criteria to distinguish which function fit best
(see Appendix). The three functions were: a constant (b(2) = c), a line (b(2) = n2+c),
and an exponential plus a constant (b(2) = ne_sz + c). We chose these functions
because our data looked representative of these functions and comparing the line

function and the exponential plus a constant function allowed us to distinguish if

 

a thin layer was present or not. The exponential part of the exponential plus a
constant function describes the biomass in the thin layer. There was never a peak
at depth so the exponential function is pinned at the surface. We used AAICc to
determine the best function (Burnham and Anderson 2002). If the exponential plus a
constant function did not fit best or found a biomass minimum at the surface then we
characterized the profile to have no surface layer present. When no surface layer was
present, layer biomass and width for that profile were not calculated. Surface layer

"’32 over the depth of the tower,

biomass was calculated by integrating b(2) = ne
however, note that only the top few centimeters really contributed to the surface
layer biomass due to the exponential decay in the equation. Background biomass was
calculated as czb from the best fit function, where 2b is tower depth. When a surface
layer was present, total biomass was calculated as the sum of surface layer biomass
and background biomass. The characteristic layer thickness was calculated as 1/s.
When a surface layer was not present, the line function always fit better than the

constant so total biomass was calculated using the line function and integrated using

the trapezoid rule.

Linear regression was conducted on equilibrium biomass and log biomass ver—

sus log nutrient supply because biomass appeared to show heteroscedasticity. How-

90

L
. |

 

ever, we present the untransformed biomass data because we present the model pre-
dicted biomass untransformed as well. Relationships were also checked for significant
quadratic terms but none were found. Linear regressions were also conducted on log
light at the bottom, and all chlorophyll, nutrient, and stoichiometric response vari-
ables with log nutrient supply as the independent continuous variable for all towers.
AN COVAs were conducted on all chlorophyll, nutrient, and stoichiometric response
variables with log nutrient supply as the independent continuous variable and surface
versus deep as the independent categorical variable for towers that had a surface layer
present at the end of the experiment (treatments 100—5000 pg P L_1). Statistical
analyses were performed in M athematica v7 (Wolfram Research, Inc., Champaign,

IL) and R v2.10 (The R Foundation for Statistical Computing, Vienna, Austria).

3.5 Experiment results

All towers showed initial behavioral aggregation of the algae in response to resource
gradients, where algae went from a uniform distribution on day 0 to aggregating at
the surface by day 1 (Figure 3.4 shows representative results). Once aggregated (Fig-
ure 3.4 top left plots), algae depleted nutrients locally through growth and moved
down if nutrients were limiting (Figure 3.4a,b bottom left plots). At the end of the
experiment, algae in the lowest nutrient treatment were relatively evenly distributed
with a biomass minimum at the surface (Figure 3.4a bottom right plot). Sufficient
light penetrated to the bottom so that [out > 1*. Nutrients were in low abundance
throughout the water column (Figure 3.4a bottom right plot). In the mid-level nutri-
ent treatment, biomass was spread throughout the water column (Figure 3.4b bottom
right plot). In the highest nutrient treatment, algae exhibited a biomass maximum at
the surface (Figure 3.4c bottom right plot). Light was depleted and below 1* beneath

the surface maximum. Nutrients were depleted at the surface and in high abundance

91

at depth.

92

   

Figure 3.4. Observed total biomass (top left), depth distribution of biomass
through time (bottom left) and equilibrium (day 50) distribution of biomass,
nutrients, and light (bottom right) for a) low-nutrient supply (Rin =5 pg P
L‘l), b) mid-level nutrient supply (Rin =50 pg P L_1), and c) high-nutrient
supply (Rin =5000 pg P L_1). The top left plot of each part shows biomass
integrated over the entire water column. In the bottom left plot of each part,
biomass density is shaded so that higher biomass is in darker shades. The
solid line on that plot shows the average depth of the biomass and the dashed
line shows the location of the biomass maximum. The small arrows along
the bottom of that plot indicates the days that phosphorus was injected at
the bottom of the towers. In the bottom right plot of each part, biomass,
nutrients, and light are all scaled to their maximum to fit on one plot but
units above each plot show absolute quantities. The 1* value on those plots
shows break-even light level and is relativized to the maximum light level as

well.

93

Depth [m] Biomass [107 cells cm'z]

 

 

biomass [105 cells ml'l]
0 0,05 011 0.115 04.2,

 

- -l
I. nutrient [fig P Lg ]

() 05 2,5

 

light [pmol photons m'zs'l]
9 1.0 2.0 3.0 4.0 -

 

 

 

 

Depth [m] Biomass [107 cells cm'2]|

b) mid-level
nutrients

 

biomass[105 cells ml'l] I .
0 0,1 0,2 0,3 0,4 I

 

nutrient [pg P L'l] 1
L 110 15 '

light [pmol photons m'zs'l]
p 110 210 310 49 ,

 

 

 

    

W

.0‘
....
.......
.......
...
......

 

Q
.....
.-
‘~
'.
I -'
. U"
..........
.-
0000

 

Depth [m] Biomass [107 cells cm'2]l

 

 

biomass [105 cells ml'l]
0 20 49 69 39.

 

nutrient [pg P L'l]
0 250 500 750 1009
light [pmol photons m'zs'l]
0 1,0 20 3,0 4.0 .

 

 

AAAAAAAAAA

 

 

gmg

 

 

 

0

1115i
10

— average depth

204 l

30

Time [days]

- - - -depth of biomass maximum

 

— biomass (b)
--- nutrient (R)
-—light (1)

Figure 3.4: Observed total and depth distribution of biomass through time.

Algae were present in a distinct surface layer at most times in all of the towers
(Figure 3.5a—h). However, the surface layer disappeared in low-nutrient treatments
by the end of the experiment (Figure 3.5a—c). The surface layers in most of the
towers (Figure 3.5b—d,f,g) show an early peak in biomass where it is higher than
the background followed by a decline in surface layer biomass till the end of the
experiment. Two of the towers never had a surface layer with more biomass. than the
background (Figure 3.5a,e) and the highest nutrient tower only had more biomass
in the surface layer than the background during the last two sampling times of the

experiment (Figure 3.5h).

95

a)5ngL-l j e) 250 (IgPL'l

Biomass [107 cells cm’z]

 

Biomass [107 cells cm‘z]

 

—s
{It
v r

Biomass [10‘7 cells cm'z]

 

 

 

Biomass [107 cells cm'z]

 

 

 

0 10 20 30 40 50 0 10 20 30 40 50
Time [days] Time [days]

— background biomass --- surface layer biomass

Figure 3.5: Amount of biomass in surface layer (if present) and background through
time for all eight treatments (a is lowest nutrients increasing to h, the highest nutri-
ents).

96

Concerning the limiting resource, by day 50, the algae at all depths in the lowest
and mid-level nutrient towers were relatively more nutrient limited than the highest
nutrient tower (Figure 3.6 and note that nutrient axis is on log scale). The algae
at all depths in the highest nutrient tower appear to be primarily limited by light
as evidenced by their extremely low light levels at all depths (see also Figure 3.4c.

bottom left plot).

 

 

. O
40 — °
- O
o
_ O
30 : O 0 Low nutrients
§ - O O Mid-level nutrients
‘63) 20 i o
:1. _ 0 O
: O
10 -_ . High nutrients (Surface layer)
1 . . ......l . . .l....l . . .l....l A AAL“ x -. L
0.1 l 10 100 1000
Nutrient (R)

Figure 3.6: Data points are resource conditions within different water columns at
different depths. Resource conditions for a low-nutrient supply tower (hollow points),
mid-level nutrient supply tower (gray donuts), and high-nutrient supply tower (solid
points, some on top of one another) are shown corresponding to nutrient treatments

Bin =5, 50 and 5000 pg P L-1 respectively. Since light declines with depth, the
data point with the highest light value for each tower is also the shallowest depth.
Note that the arrows point out the different treatments corresponding to the depth
distributions in Figure 3.4.

Total biomass averaged over the last 20 days of the experiment was positively
related to nutrient supply (Figure 3.7a) with a near significant linear relationship
between biomass and log nutrient supply (P = 0.06) and a significant linear rela-

tionship between log biomass and log nutrient supply (not shown, P < 0.05). The

97

 

depth of the biomass maximum was negatively related to nutrient supply, i.e. deeper
under low-nutrient loading and shallower under higher nutrient loading (Figure 3.7b).
The biomass maximum was always at the surface for the five highest nutrient supply

towers.

98

 

 

 

 

: O
2.5: a
QT” I
a 2.0-
o .
‘3
h 1.5-
S
g 1.0:
.9
m I
0.5_—
O
9* l 1 1 l 1 l l l
10 100 1000
Nutrient supply at bottom [pg P L"1]
0 . 19 1&0 i $1030 it
:b I T
i e
E. 0.5:
o I.
13 _
O t
g .
,H .
o 1-
43 I
g“ 1.0}
L
f O
1.53 8 ' 3

 

Figure 3.7: Effect of nutrient treatment on equilibrium biomass and depth distribu-
tion. a) Observed integrated biomass averaged over days 30—50 as a function of nu-
trient treatment. Shown is the almost significant linear relationship between biomass
and log nutrient supply (slope= 22503, t = 2.28, P = 0.06) and not shown is the sig-
nificant linear relationship between log biomass and log nutrient supply (slope= 0.26,
t = 2.77, P < 0.05). b) Observed modal depths for days 30—50 as a function of nutri-

ent treatment. Note that points for the nutrient treatments of 5, 10, and 50 pg P L'"1
have been offset 0.025 m for clarity while the points for nutrient treatments of 100,
250, 500, 1000, 5000 pg P L—1 all fall directly on top of one another and have not
been offset.

99

Algae were present throughout the water column, without a distinct aggregation at
the end of the experiment in low to mid-level nutrient towers (Rin =5—50 pg P L-l).
The portion of the biomass in the layer, where present, shows an increasing trend with
nutrient treatment (Figure 3.8). Although the surface layer was very pronounced
when present, only in the highest nutrient treatment was there more biomass in the

layer than in the background at the end of the experiment (Figure 3.8).

 

 

 

 

 

g 1.0 r
‘5
1:
g 0.8 —
8‘0
A: - .
8 0.6 ~ . I
'2 . — background blomass .
B _ --surface layer biomass ,
(3 I
E 0.4 — '0
.9 " o
.o o
e . x
'g 0.2 ~ "
H 0
a E o. x...
o" 00 1 . . . 1m.--1 ~-‘.: 1L.--l . . . 1
10 50 100 500 1000 5000

Nutrient supply at bottom [pg P L‘l]

Figure 3.8: Proportion of biomass in the surface layer and the background at the end
of the experiment versus nutrient treatment.

The thickness of the layer (if present) peaked early in the experiment and then
declined and disappeared in low to mid-level nutrient towers (Figure 3.9a—c), while

generally declining in the higher nutrient towers (Figure 3.9d-h).

100

a)5ngL‘1 e) 250 ngL‘1

   

 

 

 
   
  
   
 

 

 

 

 

 

 

 

E 0.06
3
.g 0.04
g
t
E, 0.02
b) 10 ngL'1 0500 ngL'1
._. 0.06
E. 0.06
g 0.04 0.04
.2
'5
£0.02 0-02
:3
v, .............. H. 0
c) 50 pg P L'1
.— 0.03
:3... _
E, 0.06:
g 0'04 0.04:
:3 .
>~0.02 L
3 0.02+
0 _- . .A. . A_1_ n
d) 100 ngL‘1 105000 ngL'1
20.06
3 0.01
730.04
S 0 05
3,002 -
_J

   

50 "0 10 20 30 40 50
Time [days] Time [days]

0

 

 

Figure 3.9: Characteristic layer thickness for all treatments and times. Points are
only plotted if a surface layer was calculated to exist.

101

 

The light level at the bottom of the water column, 10m, declined through time in
all treatments (not shown). At the end of the experiment, [out was lower in the higher
nutrient treatments (Figure 3.10) with a significant linear relationship between log
Iout and log nutrient treatment (P < 0.01). At the end of experiment, chlorophyll
concentration exhibited subsurface maxima in the three lowest nutrient treatment
towers, although the subsurface maxima were not well-defined peaks. Conversely,
the five highest nutrient treatment towers exhibited surface maxima for chlorophyll
concentration (Appendix Figure A2a-h). In this way, chlorophyll mimics the biomass
distributions (Appendix Figure A1). Log chlorophyll concentration was positively

related to nutrient supply of the experimental treatments (P < 0.001, not shown).

 

2%
1*1
01
E‘
E. ”Zr
Na
8“ -4_
r—l _
-6:
C o
1
_8 1 1 1 1 1 1 1 1

 

 

5 10 50 100 500 1000 5000

Nutrient supply at bottom [pg P L—l]

Figure 3.10: At the end of the experiment, the light level leaving the bottom of
the water column, [outa is shown as a function of nutrient treatment. There was a
significant linear relationship between log [out and log nutrient treatment (slope=
—1.18, t = —3.88, P < 0.01).

102

 

 

 

3.5.1 Physiology

Although theory assumes constant physiology, we measured considerable physiologi-
cal variation in our experiment. Chlorophyll concentrations per cell were positively
related to nutrient supply of the experimental treatments (P < 0.001, Figure 3.11a).
Carbon per cell was not related to nutrient supply (results not shown). However,
the chlorophyll-to—carbon ratio was positively related to nutrient supply (P < 0.001,
Figure 3.11b). The nonlimiting nutrient, nitrogen per cell was not related to nutrient
supply (results not shown). In towers where peaks occurred (high—nutrient supply
towers), cellular phosphorus quota was positively related to nutrient supply across
all towers (P < 0.001, results not shown) and nutrient supply had a larger effect on
deep biomass (different slopes, P < 0.001, Figure 3.11d). To distinguish the effects of
nutrients on surface layer populations versus deep populations, we divided the data
into two categories: surface layer and deep. The s is for surface layer data points and
d is for deep data points in Figure 3.11d-f, and in those figures, we are focusing only
on towers with a distinct layer.

Particulate C:N ratio was negatively related to nutrient supply (P < 0.005, Figure
3.11c). Particulate C:P ratio was also negatively related to nutrient supply across all
towers (P < 0.001, results not shown) and the surface biomass had a higher C:P
than the deeper biomass in the higher nutrient treatment towers (different intercepts,
P < 0.001, Figure 3.11e). Particulate N :P ratio was negatively related to nutrient
supply across all towers (P < 0.001, results not shown) and the surface biomass had a
higher N :P than the deeper biomass in the higher nutrient treatment towers (different

intercepts, P < 0.001, Figure 3.11f).

103

 

Figure 3.11. Chlorophyll a, nutrient, and stoichiometric quantities at the end
of the experiment as a function of nutrient supply. Plots a—c show the re-
gression lines from all treatments and sampling depths. Plots d-f show the
regression lines from ANCOVAS conducted only on treatments with a sur-
face layer present at the end of the experiment. The solid line is for the
d=deep data points and the dashed line is for the s=surface data points.
Only significant relations are shown and if the AN COVA was significant for
a variable, those results are shown rather than the linear regression results
for all treatments. a) Chlorophyll a per cell is positively related to log nu-
trient treatment (N=60, slope = 3.77 x 10—7, t = 11.21, P < 0.001, as is
chlorophyll, not shown, N=60, slope = 1.34, t = 9.25, P < 0.001). b) Chloro—
phyll a to carbon ratio (ChlzC) is positively related to log nutrient treatment
(N=60, slope = 3.95 x 10_3, t = 12.45, P < 0.001). c) Carbonznitrogen ratio
of particulate matter is negatively related to log nutrient treatment (N=60,
slope = —0.69, t = —3.01, P < 0.005). d) Phosphorus cellular quota is posi-
tively related to log nutrient treatment but the slopes differs between the deep
(N=33, slope = 2.04 x 10-6, t = 16.747, P < 0.001) and surface data points
(N=4, slope = 1.74 x 10—6, t = 12.52, P < 0.001). e) Carbonzphosphorus
ratio of particulate matter is negatively related to log nutrient treatment but
the intercept differs between the deep (N=33, intercept = 169.76, t = 8.269,
P < 0.001) and surface data points (N24, intercept = 192.39, t = 25.117,
P < 0.001). f) N itrogenzphosphorus ratio of particulate matter is negatively
related to log nutrient treatment but the intercept differs between the deep
(N=33, intercept = 145.50, t = 20.53, P < 0.001) and surface data points

(N24, intercept = 164.91, t = 25.117, P < 0.001).

104

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

A.” flux
8H3 Swan 8.13 SE 2.: ow ow of cw ow cm. of o.”
:53 m 9: Sosa maonamonm 0:8 $0 .832 038 $2 .832

I I . I m

T 1 ..

- . . am
mm \c;

8a? 8.84 8-3a 83 was 23 83 3 3 N._ a a

:-=8 __Eaeoza as :8an ”728.8 was :3?ng a: onzo 0:8 20 as:

Nutrient supply at bottom [pg P L‘l]

Figure 3.11: Chlorophyll a, nutrient, and stoichiometric quantities.
105

Nutrient supply at bottom [pg P L‘ 1]

3.6 Discussion

We examined how externally imposed heterogeneity and biological self—organization
interact to determine phytoplankton spatial distributions. We explained how the
spatial distribution and abundance of a species may be driven by feedbacks between
resource gradients, behavioral movement, and population dynamics. We have shown
how intraspecific competition can drive the vertical distribution of phytoplankton in

poorly mixed environments.

Other studies have shown how particular processes may influence vertical distri-
butions. Carney et al. (1988) convincingly showed with field studies how interspecific
resource competition for nutrients and light can structure vertical distributions of
phytoplankton. Several studies have used experimental water columns to examine
other processes that have been hypothesized to explain the vertical distribution of
phytoplankton such as diel vertical migrations (Arvola et al. 1991), sedimentation

losses (Pannard et al. 2007), and mixing (Jaeger et al. 2008).

Our goal was to examine if model predictions are supported by our experimental
test of how competition determines the vertical distribution of phytoplankton. We
focused on qualitative patterns due to uncertainty in several of the model parameters.
The first prediction we considered was that algae will form a thin layer (Klausmeier
and Litchman 2001). This prediction was supported for the surface layer case, as in
high-nutrient treatments, we observed surface aggregations (Figure 3.5). Additionally,
algae were aggregated in a thin surface layer in most treatments over the whole
duration of the experiment and in low and mid-level nutrient treatments over most of
the duration of the experiment. However, the prediction that algae will form a thin

layer was not supported for the DCM or benthic layer case.

The second prediction was that the depth of the thin layer should be deeper under

low-nutrient conditions and shallower under high-nutrient conditions. Support for this

106

 

prediction was mixed (Figure 3.7b), as the equilibrium depths of the biomass maxima
were deeper in the low-nutrient treatments than the high-nutrient treatments. The
five highest nutrient treatments all had surface biomass maxima, but, in the three
lowest nutrient treatments, there was no clear relationship between equilibrium depth

of the biomass maximum and nutrient supply.

The third prediction was that over a range of nutrient concentrations, the total
biomass should be positively associated with nutrient concentrations at the bottom of
the water column. This prediction was supported (Figure 3.7a), as equilibrium total
biomass was higher in the higher nutrient treatments. While it may seem obvious
that more biomass should grow at higher nutrient levels, in our experimental water

columns, nutrient supply and algal biomass can be spatially separated.

The fourth prediction was that a surface layer should occur under high-nutrient
supply conditions and be co- or light limited, a benthic layer should occur under low-
nutrient supply conditions and be nutrient limited, and a DCM should occur under
mid—level nutrient supply conditions and be colimited. This prediction was somewhat
supported (Figure 3.6). In the lowest nutrient tower, algae at all depths appear to
be primarily limited by nutrients because the points representing resource conditions
are at low levels of nutrients While all at relatively high light levels. The algae at all
depths in the highest nutrient tower appear to be primarily limited by light because
the points representing resource conditions are at low levels of light while all depths
were at relatively high-nutrient levels. In Figure 3.4, biomass maxima were near the
bottom in the lowest nutrient treatment and at the surface in the highest nutrient
treatment so we see some support for our model-driven hypotheses. The towers appear
to be arrayed along a nutrient limited to light limited gradient but none are exactly
at the point of colimitation which is predicted by ESS theory for a DCM. Perhaps

this is the reason we did not observe a strong, persistent DCM in this study.

What limited growth overall? Our experiment may show scale-dependent limi-

107

 

tation. At the local level, nutrients were present in measurable concentrations in-
dicating that nutrients were never limiting. However, algae did move down in the
lowest nutrient treatments presumably to acquire more nutrients because they were
nutrient-limited. At the whole ecosystem level, more nutrients would always cause
more growth based on i) within an ecosystem- biomass was still increasing at day 50
in the highest nutrient treatment (Figure 3.4c) and ii) across ecosystems- biomass
exhibited a non—saturating relationship with nutrient treatment (Figure 3.7a). Light
was limiting at least locally in high-nutrient treatments based on vertical distributions
of biomass across towers and light levels below break-even levels toward the bottom

(Figure 3.10).

Klausmeier and Litchman (2001) also make other predictions regarding the re-
source conditions within the water column for a DCM. They predict that nutrients
should be at the break-even level, R*, above the thin layer and linearly increase below
it and that light immediately below the thin layer should be at the break-even level
1*. While direct support for this prediction is equivocal because we never observed
a well-defined DCM, light was below 1* for the highest nutrient treatment (Figure
3.40). However, this theoretical 1* value is derived from parameters that have large
confidence intervals (e.g. light half saturation constant, K I) and uncertainty in their
estimate (e.g. mortality, m) and assume constant physiology. Mortality was at least
the amount of media we withdrew to sample relative to the total volume of media
in a tower, however, mortality could be at least the levels commonly assumed in the
literature (0.1 d—l) but this is a difficult parameter to measure (Crumpton and Wet-
zel 1982). In addition, mortality likely changed over the course of the experiment, as
the biomass in most of the towers eventually declined. The cause of this mortality is

unknown but can be a common phenomenon in experiments (Fogg and Thake 1987).

Some results not related to previous predictions may be unanticipated. In Figure

3.5, the biomass in the surface layer was greater than the background in some towers

108

 

but these towers are not all high-nutrient towers as one might expect, nor are they all
low-nutrient towers. Furthermore, those towers that had higher biomass in the surface
layer than the background reached that transition at different times in the experiment.
In the lower nutrient towers (Figure 3.5b—d), the transition to high biomass in the
surface layer happened around day four but in higher nutrient towers (Figure 3.5f,g),
the transition occurred later, around day 12, and in the highest nutrient tower (Figure

3.5h), the transition did not occur until around day 45.

Interestingly, the proportion of biomass in a distinct surface layer appears posi-
tively related to nutrient treatment (Figure 3.8). This could be due to the greater
amount of biomass having a stronger effect on the resource environment and therefore
creating a sharper fitness gradient. All towers showed a spike in layer thickness early
in the experiment before generally thinning (Figure 3.9). It is interesting that layers
concentrated before they disappeared in the lower nutrient towers (Figure 3.9a—c),
rather than thickening due to the population spreading out because the layer loca-
tion has depleted resources. Consistently, the thinnest layer occurred in the highest
nutrient tower, perhaps because the light gradient was so sharp in that tower that
algae were tightly packed in the layer in an attempt to get enough light to persist
(Figure 3.9h).

At the beginning of the experiment, we imposed strong vertical heterogeneity.
Nevertheless, algae could live and grow at any location in every tower, i.e. this
species had a very large fundamental niche. However, through growth, aggregation,
and intraspecific competition by depletion of resources, algae reduced the locations
where they could grow in each tower, i.e. they created a realized niche confined
in space (for example Figure 3.4c). These niche construction processes shape the
environment for future generations of the algae in each tower (Laland et al. 1999,

Hastings et al. 2007).

Overall, there is mixed agreement between predictions from the full dynamic model

109

 

and experimental results (compare Figures 3.1-3.3 with Figures 3.4,3.6,3.7). We fo—
cused on qualitative support for predictions and it appears that most of the predic-
tions were upheld. Surface layers formed under predicted nutrient replete conditions
and appeared to be relatively more light limited. However, our predictions related
to a sub-surface layer formation (DCM or benthic layer) were not all fully supported

because we never observed a clearly defined sub-surface layer in any of the treatments.

There are several potential reasons we never observed a well-defined sub-surface
layer (i.e. a DCM): 1) Algae could not detect the resource gradients sufficiently to
respond. We expect this kind of layer to form at low to mid-level nutrient supply.
Under these conditions, algae quickly consume these nutrients and once the surface
is no longer the best place in the water column, they move down. However, the
nutrient gradient is small and may not be detectable to the algae at this point. The
algae are then left to wander on a fitness landscape that is relatively flat. There is
some field evidence that the genus we chose for our experiments, Chlamydomonas,
does not always show distinct vertical distributions even when other genera in the
water column do (Spaulding et al. 1994). 2) Because the range of nutrient levels
over which we predict a DCM to be the equilibrium strategy is narrow (Figure 3.7b),
we may have missed that range in parameter space with our treatments. 3) Algae
are actively migrating on a diurnal cycle or at random, as predicted to be a good
strategy in opposing resource gradients (Cullen and MacIntyre 1998). 4) Algae are
adjusting their light harvesting machinery with depth instead of moving to different
light conditions. There definitely is some variation in chlorophyll per cell with depth
in the towers (Figure A3a) but for towers where ‘a surface layer was present, the surface
did not have a different slope or intercept than the deep points in the relationship

with nutrient supply.

The models we employed consider constant stoichiometry. However, the physio—

logical and stoichiometry data indicate differences in cellular pigments and nutrients

110

between treatments and in some cases, with depth. The chlorophyll a per cell was
higher in higher nutrient towers (Figure 3.11a), which might be due to greater phos-
phorus availability if chlorophyll production was nutrient limited in towers but might
support the prediction that light competition is very important under high-nutrient
conditions so cells are making more chlorophyll. The chlorophyll azcarbon ratio mim-
ics this relationship so might also support this prediction (Figure 3.11b). Our values
of 0.001-0.019 are within range of Chl:C reported by others in the field and lab (Sharp
et al. 1980, Eppley et al. 1988, Fennel and Boss 2003).

The C:N decrease with increasing nutrient supply (Figure 3.11c) is somewhat
puzzling given that neither particulate carbon per cell nor particulate nitrogen per
cell was related to nutrient supply. However, the relationship is weak (R2 = 0.12)
and the C :N may be driven by the higher chlorophyll per cell in higher nutrient towers
because chlorophyll is known to have a significant nitrogen component (Sterner and
Elser 2002). Cellular phosphorus quota was greater in the deeper portion of the water
column than the surface for higher nutrient treatments (Figure 3.11d) which would
make sense if cells deeper in the water column are nutrient replete. The C:P and the
N :P ratios were greater in the surface and declined with increasing nutrient supply
for the high-nutrient treatments (Figure 3.11e,f). Increasing phosphorus supply could
decrease these ratios because cells have more phosphorus (Figure 3.11c) and carbon

per cell and nitrogen per cell were not related to nutrient treatment.

Our physiological and stoichiometric data shows that chlorophyll per cell varies
across nutrient treatments and phosphorus quota varies across nutrient treatments
and with depth. This complexity should be incorporated in future models. Models
that consider how chlorophyll and biomass with depth may not be perfectly correlated
have been developed (Fennel and Boss 2003) but predictions should be explored across
large environmental gradients, such as gradients in nutrient loading. Models with

variable stoichiometry (Grover 2009, Jaeger et al. 2010) have just scratched the

111

 

surface of possible ramifications for spatial distributions and our experimental results
indicates that more attention should be given to this area. However, modeling variable
stoichiometry in space can be challenging and we will have to rely on increasingly

complex model development (Grover 2009).

' More experiments should be conducted to test recent theory on stratified water
columns and multiple species competition. For example, inclusion of spatially varying
mixing can test theoretical predictions of the vertical distribution of phytoplankton
in stratified water columns (Mellard et al. Chapter 2). Experiments with multiple
species can test theoretical predictions of interspecific competition for nutrients and

light in spatially complex environments (Yoshiyama et al. 2009).

Although our experimental water columns are not a perfect replica of a lake or
other body of water, our results have implications for field data. We have shown that,
at least for surface layers, layer formation can be driven by plentiful nutrient supply
with motile algae moving to locations where conditions are best for growth. We have
shown this is due to the relative importance of nutrients and light under different
nutrient supplies and the influence of the algal population itself, through nutrient
uptake and self-shading. These results illustrate the plausibility of a mechanism
for surface bloom formation in bodies of water when nutrients are supplied only
from below: blooms can occur from nutrients diffusing from the bottom rather than
surface runoff or direct addition to the epilimnion. Some of the model predictions
were upheld, which may make it more likely that extensions of the model will be

useful in future analyses.

On the other hand, our towers may have real limitations as scale models of poorly—
mixed water columns and definitely have limited relevance for describing processes in
whole aquatic ecosystems (Carpenter 1996). Our towers may not be representative
of water columns in lakes for example because of their dimensions. Although we

attempted to scale down the physics (depth, light) in the experiment and model using

112

funk

dimensional analysis, the organisms were not scaled down. This means that even if
the 1.5 m towers can represent a 15 m water column, the biology of the organism in
the tower is unchanged and so the height of our towers could be too short to represent
the resource gradients that span many meters in water columns of lakes. Therefore,
just because competition in opposing nutrient and light gradients did not lead to a
clearly defined DCM does not mean that these processes cannot drive patterns in
real water columns of lakes. Field experiments are needed for further examination of
these processes.

In conclusion, the experiment qualitatively supports our conceptual and mathe-
matical models for spatial distributions of phytoplankton. We have shown that phy-
toplankton exhibit a fast behavioral response to resource gradients. Phytoplankton
grow at the depth they have selected, developing strong aggregations, and creating a
niche in resource space through impacts on their environment. Phytoplankton may
then modify their behavioral strategies as a consequence of these feedbacks and the

strategies of the other phytoplankton cells in the water column.

113

 

3.7 Appendix

114

 

3.7.1 Model

The full model includes spatially-explicit equations for biomass, b, nutrients, R, and
light, I in a one-dimensional water column where z is depth with the surface at z = 0

and the bottom at z = zb.

Change in biomass at depth 2 is the balance of growth, death, and passive and

active movement.

ab , 82b a 39
5; = m1n(fI(I(z,t)), fR(R(z, t))) -— m)b + D57 + 6—2. ['0 (a) b] (All

Phytoplankton do not leave or enter the water column, so boundary conditions are:

3b 09

Nutrients R are taken up by phytoplankton with a yield Y of biomass per unit nutrient

= 0 (A2)
z=0,zb

 

consumed, are mixed with eddy diffusion coefficient D, and are recycled from dead

phytoplankton with proportion e.

312 b 62R 0

‘37 = _7 min(fI(I(z, a), fR(R(z, t))) + 1252—2 + em? (A3)

Nutrients have no surface flux but diffuse into the water column from the sediments
where they have fixed concentration Rin at a rate proportional to the concentration

difference across the interface. The permeability of the interface is described by h.

6R 8R
3- : O and E = h(Rin — R(Zb)) (A4)
Z z=0 ~ z=zb

Light follows Lambert-Beer’s law, decreasing due to attenuation from biomass and

background turbidity (Kirk 1975a). The attenuation coefficient due to biomass is a

115

 

and due to background is abg'

— (abg2+f0z ab(Z,t)dZ)

[(2, t) = ine (A5)

Functions f [(1 ) and f R(R) are the potential growth rates as a function of the resource
I or R when that resource is limiting. We use the Michaelis—Menten form for the func—
tions in our numerical solutions, fI(I) = rI/(I + KI) and fR(R) = rR/(R + KR)
where r is the maximum growth rate and K I and K R are half-saturation constants
for light and nutrients, respectively. Our qualitative results, however, should hold for
other bounded, strictly increasing functions. Biomass is lost at density independent
rate m, which encompasses all sources of mortality. Net growth at depth 2 is only
possible if both I is greater than the break even light level, 1* = fI—1(m) and R is
greater than the break even nutrient concentration, R* = f§1(m) (Tilman 1982). A
turbulent eddy diffusion coefficient D describes passive movement. Active movement
is described by a taxis term (Okubo 1980). Phytoplankton behavior is governed by
simple rules. They move up if conditions immediately above are better than immedi-
ately below, move down if conditions immediately below are better than immediately
above, and do not move if conditions are worse immediately above and below. To
describe this behavior, we let phytoplankton movement depend on the gradient in
growth rate, 89/82, with velocity v (3%). We assume 2) to be an odd decreasing
function that approaches ’Umax as 89/82 approaches negative infinity (positive 11 is
upward), approaches —Umax as 89/82 approaches positive infinity, and 22(0) = 0.

The specific equation we use for v is v = ’Umax - g-g/ (3% + szim)-
Model analysis and parameterization

We simulated the full model with VODE (Brown et al. 1989) following Huisman
and Sommeijer (2002). To capture the same spatial resolution that we could measure

in the experiment, we set the number of bins to be the same as the number of

116

 

sampling ports in the experimental towers (n2 2 60). In addition, we employed the
Monsi-Saeki formulation (Monsi and Saeki 1953) for light limited growth within each
bin. We simulated the model over the same time course as the experiment (50 days)
with initial conditions approximating the same quantity and vertical distribution of
biomass (homogenized) and nutrients (linear gradient) as the initial conditions in the

experiment. We assume phosphorus to be the limiting nutrient in the model.

Parameters were measured independent of the experiment or back calculated from
the experiment (Table 3.1). The incoming light at the surface, Iin’ was measured as
the photosynthetically active radiation, PAR, just beneath the surface in a tower filled
with water before the experiment began. The values for a and abg were determined
by regressions of light on integrated biomass values for all towers and sampling times.
Specifically, [in was set to 43 and log (Tgfig) was regressed on integrated biomass.
The slope of this regression is a, the algal attenuation coefficient. The y-intercept
divided by 2b is abgv the background light attenuation. The nutrient concentration at
the sediments, Rim was the dissolved phosphorus concentration injected at the bot-
tom of the towers. The sediment-water column permeability, h, was calculated from
the equations of nutrient flux using the highest nutrient tower and a regression for the
portion of the experiment when a surface layer of algae was well-formed. The water
column depth, 2b, was measured before and during the experiment. Prior to the ex-
periment, the maximum growth rate, r, and the phosphorus half-saturation constant,
K R, was determined for the strain of Chlamydomonas used in the experiment by
fitting a growth-phosphorus curve to growth rates in different phosphorus treatments
(C. Steiner pers. comm.). Prior to the experiment, the light half-saturation constant,
K I, were determined for the strain of Chlamydomonas used in the experiment by fit-
ting a growth-irradiance curve to growth rates in different irradiance treatments (A.
Schwaderer pers. comm.): The mortality rate, m, was calculated to be the average

proportion of total media removed from the experiment in a day (20.0009 in Table

117

TPF"

 

3.1). The cellular phosphorus quota, 9, was calculated from particulate phosphorus
measurements at the end of the experiment by averaging this quota value across all

towers and sampling depths. The maximum swimming speed, V was taken from

swim,
Reynolds (1984) and represents an estimate of a theoretical maximum for all species.
The swimming speed half-saturation constant, szim’ was set to a value that gave
reasonable vertical distributions and smoothly running numerical simulations. The
diffusion coefficient, D, was estimated, based on previous tower experiments using a

passive tracer, to be the diffusion level required to homogenize the dye over measured

time periods.

118

 

 

 

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119

3.7 .2 Appendix figures

Figure 3.12. Biomass profiles for all towers at two time points: day 1 and day
50. Each profile has the best fit function using information criteria. Note that
for the three lowest nutrient supply towers (a, b, c) on day 50 the best function
was the line function. However, for all other towers on day 50, the exponential
function was the best function, indicating the presence of a surface layer. On

day 1, the exponential function was the best for all towers.

120

a) 5 pg PL"1

Day 1

Biomass [cells cm‘3]

Depth [m]

 

 

b) 10 pg P L-1

Day 1
Biomass [cells cm
10000

 

0.0
0.21
0.4g

0.6;

Depth [m]

0.8L
1.0L
1.21

1.41

 

 

10000 20000 30000

-3]
20000

 

Day 50
Biomass [cells cm‘3]
10000 20000
c

 

0.0

0.21

0.4 ~

1.21

1.4-

    

Day 50
Biomass [cells cm'

31
2000 4000 6000 800010000

 

0.61
0.8"—

1.01

 

# ....... fii: ........ ’-
.
b

 

Figure 3.12: Biomass profiles for all towers at two time points: day 1 and day 50.

121

c) 50 pg P L'1

 

 

 

 

 

 

 

  

 

 

 

Day 1 Day 50
Biomass [cells cm‘3] Biomass [cells cm'3]
20000 30002 0 10000 20000 30000 40000
0.
o
0.
F
l
E 0.6:
E l
g 0.8:
1.0;
. r"
1.22
r
l
1.4:
t
-1
d) 100 "g P L Day 1 Day 50
Biomass [cells cm‘3] Biomass [cells cm'3]
0 10000 20000 30000 40000 0 100000 200000
_ . , . . . . ........ 3.- . ................ -
o
O. . 0- o
o
0. ' 0.
"g 0.6:- 0
g i
5 0.87 0 .
1.0L 1
1.2: . 1
L o
1.4; o 1.
Figure 3.12 continued

122

e) 250 ug P 1:1

 

 

 

 

 

 

 

 

 

 

Day 1 Day 50
Biomass [cells cm‘3] Biomass [cells cm'3]
10000 20000 30000 40000 100000 200000
0.0? . . fl 0, .......................... t
I 0 C
0.23 0.2
I 0 I
0.41 ’ 0.4}
"g" 0.61 0.6:- L
is I . *1
g 0.8: 0.8:
1.0: o 1.0? . J I
: : 1
1.2' . 1.2:
1.4L ' 1.4:"
l 0 '
-l
f) 500 118 P L Day 1 Day 50
Biomass [cells cm‘3] Biomass [cells cm'3]
10000 30000 50000 200000 600000 1 X 106
a ................. O'- 0. . . .fl-
0
O. 0
o
0 0
E 0 0.
.5
3" o 0.
1 1
1. 1
1. 1

Figure 3.12 continued

123

-1
g) 1000 pg P L Day 1

Biomass [cells cm'3]

 

vva

Depth [m]

l.

-1
h) 5000 pg P L Day 1

Biomass [cells cm'3]
20000 40000 60000 80900

 

Depth [m]

 

 

Figure 3.12 continued

124

 

Day 50
Biomass [cells cm‘3]
200000 600000 1x 106

 

 

 

.7.
Day 50
Biomass [cells cm'3]
4 x 106 8 X 106
O.
0.
O.
0.

a) 5 pg P L'1
Chlorophyll 3 [pg L'l]
0 2 4 6 8 110 112

A

Depth [m]
'o
\)

-l.l:
T
-1.5. °

 

b)10ngL‘l
Chlorophyll a [pg L‘l]
0 1 2. 3 ‘1 5

 

c) 50 pg P L-1
Chlorophyll a [pg L'l]
0 5 [0 115 -20 25 30

 

55.5
qt»)

Depth [m]

-11:

 

-151 , '

d) 100 pg P L'1
Chlorophyll a [pg L"]

 

 

0 5.0 100 150‘ 200
.— -0.3: °
.5. .
5 -071 .
3 . .
Q -l.l~
-15: -

e) 250 ngL‘1
Chlorophyll a [pg L'l]
0 50 100 150 200 250

 

 

 

 

.— -0.3: .
E. . .
5. -O.71 .
8 « .
Q -l.l.
"1.51 o
0500 ngL-1 l
Chlorophyll a [pg L'l] :
0 200 400 600 800 1000 . 1
—. -0.3: -
E o
'5 ’07 o L,"
3 .
Q -l.1
-1.5: .

 

g) 1000 pg P L'1
Chlorophyll a [pg L"]
0 200 400 600 800‘

 

r—1'0.3:1 .
a 1 -
a -0 74 .
8 1 .
D -1.lJ
-l.54 -

 

h) 5000 pg P L‘1
Chlorophyll a [pg L’l]
0 2000 4000 6000 8000

 

Figure 3.13: Profiles of chlorophyll a at the end of the experiment for all towers.

   

Figure 3.14: Picture 1: Picture of experimental plankton towers.

126

Chapter 4

l s. vuln—

Community-wide phytoplankton

 

vertical distribution in stratified ;

temperate lakes

J arad P. Mellard
with
Mary A. Evans, Don R. Schoolmaster Jr., Kohei Yoshiyama, Elena Litchman, and

Christopher A. Klausmeier

4. 1 Abstract

Understanding spatial heterogeneity in ecological communities is a perennial task for
ecologists. Spatial patterns for some aquatic organisms are poorly known and the fac-
tors that determine them even less known. In particular, a plethora of phytoplankton
spatial distributions in the vertical dimension occur in nature. Both phytoplankton
total abundnce and community composition show patterns in the vertical dimension.

What drives patterns in vertical distributions of phytoplankton? The goals of our

127

study were first, to examine variation in phytoplankton community structure in lakes,
in particular phytoplankton vertical distributions, and second, to evaluate recent the-
oretical predictions across broad environmental gradients. Theoretical predictions
come from several models that predict the depth where algae should aggregate, what
limits their growth, amount of biomass in different locations of the water column, and
conditions for coexistence of multiple species within a lake. To test these predictions
and document variation in community structure with depth and across lakes, we con-
ducted a survey of 30 lakes in western Michigan (USA) throughout the stratified sea-
son. Lake survey results showed that for lakes with single sub-surface phytoplankton
biomass peaks, the vertical position of the peak was shallower at greater background
light attenuation and turbulent mixing but deeper in deeper water columns, as pre-
dicted by theory. Biomass in the deep layer increased with total phosphorus near
the bottom and biomass in the mixed layer increased with total phosphorus in the
mixed layer, as predicted by theory. Vertical distributions of phytoplankton were typ-
ically composed of multiple peaks of biomass. The number of peaks was related to the
amount of physical space available for peaks to form and the sharpness of the nutrient
and light gradients. Each peak in a lake exists at different nutrient and light levels,
which are negatively related to one another. Species compositions of phytoplankton
communities were structured in space, not only across broad environmental gradients
between lakes but also structured along the vertical axis within lakes. Communities
were more similar within than between lakes. Community similarity within lakes
likely arises due to different resources acting in opposition: light attenuation acts to
make communities more similar but the sharpness of the nutrient gradient acts to
make communities more dissimilar. Vertical niches could be filled by many different
taxonomic groups and species and was not consistent across lakes. Taxonomic groups
were related to environmental variables across lakes but some showed additional rela-

tionships with local resource conditions within lakes that makes predicting community

128

 

structure across lakes and with depth challenging. Species dominance changed along
the vertical dimension as well, particularly in deeper lakes. This study quantitatively
describes a variety of vertical distributions of phytoplankton communities occurring
across environmental gradients, characterizes them and their environments, and ex-
plicitly links the patterns to underlying mechanisms such as competition for multiple

resources, grazing, and physical mixing processes.

129

4.2 Introduction

Ecological communities exhibit pronounced spatial patterns. Populations are dis-
tributed variably in space, often relative to underlying spatial heterogeneity in re-
sources. The boundaries of a population in space and the abundance patterns within
those boundaries, may be set by tolerances to stressors and requirements for re-
sources (MacArthur 1972) as well as self-modification of the environment (Levins
1979). Species with different tolerances and requirements may competitively sort
themselves in space along these resource gradients as well as modify the environment
for others. Species sorting can create community-level patterns with resulting com-
position and diversity impacted by the spatial heterogeneity in resources (Levin 1976,

Stevens and Carson 2002).

Planktonic communities are responsible for much of the world’s primary produc-
tion and influence major biogeochemical cycles, ecosystem function, and fisheries
(Falkowski et al. 1998). Plankton live in a fluid environment, subject to water mo-
tion. Biological, chemical, and physical processes operating in bodies of water create
spatial heterogeneity (Reynolds 1984). Spatial heterogeneity adds to the problem of
understanding already complex ecological systems (Skellam 1951, MacArthur 1972,
Steele 1974, Levin 1994). In the aquatic environment, vertical spatial heterogeneity
comes in many forms, including: patchiness of populations (biological), turbulent

mixing gradients and light (physical), and nutrient gradients (chemical).

Phytoplankton vertical distributions can be extremely patchy. Fee (1976) showed
that primary production can vary at least three fold within a couple meters span in
the water column. Assuming primary production is proportional to chlorophyll a,
primary production within several meters in the water column may vary more than
2.5-fold in some lakes. Field et al. (1998) show that such a difference in primary

production is roughly equivalent to the difference between a desert and a tropical

130

“I; Ti!

 

rainforest!

Phytoplankton exhibit contrasting vertical distributions both between bodies of
water and through time within a body of water. They can be in high abundance in the
mixed layer or in pronounced surface blooms (Paerl 1988). Frequently phytoplankton
form a peak in abundance called a deep chlorophyll maximum, DCM, in the deep
poorly-mixed layer (Fee 1976). A DCM may be the global maximum of chlorophyll
a, or a local maximum, and it may have a single well-defined narrow peak, or a broad
hump (Camacho 2006). Part of the intrigue of DCMs is that they are found far from
the surface, away from the source of light and yet can be responsible for much of the
primary production within a lake (Fee 1976). If enough light reaches the bottom,
algae can also reach high abundances in a benthic layer, accessing nutrients entering

the water column from the sediments (Sand-Jensen and Borum 1991).

Vertical physical and chemical gradients further structure the environment of the
phytoplankton. Fluid mixing and turbulence in lakes are effects of multiple inter-
acting physical processes (wind shear, convective cooling, internal waves, seiches,
Langmuir circulation, inflow, etc. (Wetzel 1975). Often, the result of these processes
is temperature-driven density stratification, which can be characterized by the follow-
ing variables: turbulent (vertical) eddy diffusivity, D, and depth of the mixed layer,
2m. These variables are the exact parameters in many models (Chapter 2, Huisman
and Weissing 1994, Klausmeier and Litchman 2001, Diehl et al. 2002, Huisman et al.
2004) and can be used to summarize the physical conditions in lakes. Essential re-
sources such as nutrients and light are distributed heterogeneously and usually form
Opposing gradients, creating a dilemma for algae. Nutrients generally enter the water
column from the sediments but may also be supplied through horizontal advective
sources such as surface runoff or riverine inputs. Nutrient concentrations (Tilman
1982, Watson et a1. 1997) and nutrient ratios (Smith 1982, Tilman 1982), as well as

nutrient-to—light ratios (Smith 1986, Carney et al. 1988, Reynolds 1998), have been

131

 

 

shown to be important in determining phytoplankton community structure. Light is
attenuated exponentially with depth due to abiotic and biotic absorbance and scat-

tering according to Lambert-Beer’s law (Kirk 19750).

These complex biological and environmental gradients create a challenge for ecolo—
gists. For example, in this spatially complex environment, multiple resources interact
with behavioral movement of the algae, modification of the environment due to nu-
trient uptake and self-shading, and strategic adjustment due to the modified environ-
ment to determine vertical patchiness of populations that drives spatial heterogeneity.
Fee (1976) showed that there is often a significant phytoplankton population in a sin-
gle peak at or below the thermocline that can have important consequences for the
ecosystem processes operating throughout the water column, and called for systematic

investigations of the algal populations below the thermoclines in other lakes.

Vertical distributions of populations compose the community structure of the wa-
ter column. Populations interact with each other through many of the same mecha-
nisms that individuals interact, and through interspecific competition, to determine
community-wide patterns in phytoplankton vertical distribution. The result of these
processes is spatial heterogeneity within the community, which may explain the co-
existence of many species of phytoplankton (Hutchinson 1961). Recently, Longhi and
Beisner (2009) looked at how various environmental factors affect vertical distribution
of phytoplankton across lakes and regions. They found the global chlorophyll max-
imum to occur shallower in lakes with greater temperature variability, higher total
phosphorus in the mixed layer, and increasing light attenuation by dissolved organic
matter, (i.e., “color”). They also show that groups of phytoplankton with different
pigment compositions are distributed differently in the water column both by their
mean depth and their variation in depth. Perhaps the best evidence for community
spatial variation due to resource competition comes from Lake Tahoe. Through the

use of field patterns, transplant experiments, and measurements of demographic pro—

132

 

cesses and kinetics, Carney et al. (1988) convincingly showed that two species of
diatoms partitioned habitat in the vertical dimension. In addition, a more recent
study has Shown that, in limnocorrals, low levels of mixing in combination with deep
water columns allowed for vertical niche separation of different taxonomic groups of
algae (Jaeger et al. 2008).

Although these studies aid in our understanding of patterns of phytoplankton ver-
tical and community structure across environments, we contend that there is still a
lack of knowledge of how communities respond to, use, and divide the vertical dimen-
sion. Explicit tests of predictions from prior theory and measurements of parameters
for models of vertical distributions of phytoplankton are still missing. Also missing
are quantitative classifications of vertical distributions, along with fine scale measures
of turbulence, nutrients, and light. Detailed community analyses of species compo-
sition and diversity along the vertical dimension among diverse bodies of water are
necessary to test theoretical predictions. This study aims to remedy some of these
deficiencies in understanding determinants of vertical distributions of phytoplankton.
Anthropogenic stresses and predictions of widespread aquatic community reorganiza-
tion due to climate change (Schindler 1997) make it vital to measure and understand

the ecosystem- and community-level processes operating in bodies of water.

4.2.1 Predictions from previous theory:

I. Ecosystem (bulk properties of the community)

We have extended dynamic models of phytoplankton growing in well-mixed envi-
ronments (Huisman and Weissing 1994) and poorly mixed environments with oppos-
ing resource gradients (Klausmeier and Litchman 2001) to include spatially-varying
mixing conditions and multiple nutrient sources (Chapter 2). Our model predicts
the equilibrium spatial distribution of the phytoplankton as well as what limits their

growth. Eight distinct cases of phytoplankton vertical structure are possible. Popu-

133

 

lations here are considered to represent the bulk properties of the community. Our
model also predicts how the vertical distribution and biomass in different layers change

as a function of environmental parameters (Chapter 2).

Our analytical results provide specific predictions for how different environmen-
tal parameters affect vertical distribution and biomass. See Chapter 2 for a table,
further details, and methods used to generate these predictions. Increasing nutrient

concentration in the sediments, R should decrease the depth of the population

sed’
and increase deep layer biomass while increasing or having no effect on mixed layer
biomass. Increasing nutrient input to the mixed layer, RinMLl should decrease or
have no effect on the depth of the population and decrease or have no effect on deep
layer biomass while increasing or having no effect on mixed layer biomass. Increasing
background light attenuation, abg’ should decrease the depth of the population and
decrease or have no effect on deep layer and mixed layer biomass. Increasing mixed
layer depth, 2m, should have no effect on the depth of the population in the deep layer
and increase, decrease, or have no effect on the deep layer and mixed layer biomass.
Increasing water column depth, 2b, should increase the depth of the population and
decrease the deep layer biomass while decreasing or having no effect on mixed layer
biomass. Increasing turbulent diffusion, D, should decrease the depth of the popu-

lation and increase deep layer biomass while increasing or having no effect on mixed

layer biomass.
II. Community (biological variation)

Several models predict that species should segregate vertically according to nutri-
ent and light competitive abilities (Klausmeier 2000, Huisman et al. 2006, Yoshiyama
et al. 2009). Klausmeier (2000) predicts that for multiple species competition, the
better light competitor should reside under the better nutrient competitor in accor-
dance with resource ratio theory (Tilman 1982). Huisman et al. (2006) predict a

similar vertical zonation and show that vertical zonation patterns in the subtropi-

134

 

 

 

cal Pacific Ocean may be consistent with that prediction. Yoshiyama et al. (2009)
extend this previous work to analysis of multiple species competition in stratified
water columns and show that DCMS should attract one another in space due to the
feedbacks the DCMs have on resource conditions. Yoshiyama et al. (2009) also show
that the vertical zonation prediction from previous studies is complicated by envi-
ronmental conditions. For example, a good light competitor can reside under a good
nutrient competitor or it can take over the mixed layer, but these two competitive
outcomes can be disjunct along an environmental axis such that the good light com-
petitor is absent from the system for some area in environmental parameter space.
This complication, along with areas in parameter space with multiple stable states,

makes simple predictions difficult.

We conducted a lake survey to describe and better understand patterns in the
vertical distribution of phytoplankton. The goals were to determine the variation
in vertical distributions, characterize the distributions, and test model predictions
about the determinants of vertical distributions across broad environmental gradi-
ents. In addition, we aimed to measure the biological variation in the communities of
phytoplankton distributed along the vertical dimension within lakes and across en-
vironmental gradients between lakes. This biological variation comes in many forms
including community species diversity and composition, as well as broad taxonomic
groupings. We expect whole-lake and local environmental conditions to determine
the taxonomic turnover and resulting phytoplankton community structure for lakes

in the surveyed region.

Among the five questions we consider in the present study, questions 2) and 3)
have specific predictions from prior theory (Chapter 2) associated with them on how
environmental variables affect phytoplankton vertical structure. Questions 4) and
5) do not have specific predictions from prior theory associated with them, but for

those questions, we provide hypotheses that are constructed from theories of multiple

135

 

 

species competing for nutrients and light (Klausmeier 2000, Huisman et al. 2006,

Yoshiyama et al. 2009 and other general ecological studies.

The questions are the following: _

1)

2)

4)

What variation exists in vertical distributions of phytoplankton?

What drives this variation?

In a particular lake, A) Can a peak form in the deep layer? B) If a peak can
form in the deep layer, can a benthic layer form? C) What drives depth of
peaks?

What determines the amount of phytoplankton biomass?

Why do multiple peaks of phytoplankton biomass form and what determines

the number of peaks that form?

A) How can multiple peaks exist? H1: Multiple nutrient sources (Chapter
2). Sources such as riverine inputs of different densities, lateral intrusions, and
inputs from shear and other physical processes. H2: Multiple species with
nutrient—light tradeoff (Yoshiyama et al. 2009). Each peak is composed of a

different species from a tradeoff in competitive abilities for nutrients and light.

B) Is the number of peaks related to resource quantity and / or resource hetero-
geneity? H: Resource supply must be of sufficient quantity to sustain multiple
peaks but resource heterogeneity (Stevens and Carson 2002) increases number

of peaks.
How do phytoplankton communities change with depth and what drives these
changes?

A) Is species diversity greater in the surface mixed layer niche or DCM niche and

what explains diversity in these locations? H: The mixed layer provides greater

136

 

 

opportunities for coexistence (Huisman and Weissing 1995) because it has a

 

wider range of resource conditions than a DCM that exists at a single depth

and mixing may prevent competitive exclusion (Fléder and Sommer 1999).

B) Are communities more different within a lake or between lakes and what
explains differences in communities within lakes? H: Communities are more
different between lakes due to the large differences in environmental conditions
between lakes and the mixing that occurs within a lake but there are likely
differences in communities within lakes that are driven by habitat differentiation

in local conditions.

 

C) Do taxonomic groups or species found in the DCM differ from taxonomic
groups or species found in the mixed layer and why might they be differ—
ent? H: Some taxonomic groups are known for their associations with certain
vertical niches such as DCMs due to specific environmental conditions within
those niches but this could depend on whole-lake environmental characteristics

(Reynolds 1984).

4.3 Survey methods

4.3.1 Sampling in field

We conducted a lake survey of 30 lakes in western Michigan, sampling the lakes three
to five times in four distinct sampling campaigns during the stratified season from
May to October in 2007. We selected these lakes based on their similar geochemistry
but wide range of mixing depths, light attenuation, and total phosphorus levels.
At the deepest point in each lake, we obtained high spatial resolution (mm scale)
measurements of chlorophyll a fluorescence and physical conditions and collected

water samples at different locations throughout the water column in order to capture

137

chemical gradients.

We used casts from a microprofiling device (SCAMP, PME Carlsbad, CA) to mea-
sure a continuous high resolution temperature gradient, T(z), which we converted to
a temperature gradient spectrum so that we could obtain the turbulent kinetic energy
dissipation rate by fitting a Batchelor spectrum (Luketina and Imberger 2001). We
then calculated the vertical eddy diffusion coefficient, D(z) from energy dissipation
rate following Osborn (1980). Each cast also measured density, chlorophyll a fluo-
rescence, photosynthetically active radiation (PAR) with an attached LI-COR flat
sensor (LI-COR Biosciences, Lincoln, NE), and conductivity with depth. Three to
six casts were obtained per visit to a lake. These casts comprise what we will refer
to as a profile for a visit to a lake. We also took measurements of pH and oxygen
at 1 m intervals using a Hydrolab sonde (Loveland, CO). Integrated water samples
were collected with a tube sampler through the mixed layer and discrete depth water
samples were collected from pronounced fluorescence peaks (DCMs), 1 m above and
below each DCM, and 0.5 m above the sediments with a 10 cm diameter horizontal
van Dorn sampler. All water samples were immediately placed in a dark bottle and
taken to the lab for processing. We also took a vertical zooplankton net haul through-
out the water column during each lake sampling using a 0.3 m diameter, 80-micron

mesh net.

4.3.2 Laboratory measurements

All phytoplankton and chemical analyses were performed on the water samples from
the mixed layer and DCMs. Only chemical analyses were performed on the water
samples from distances above and below the DCMs and the samples 0.5 m above the
sediments.

Chemical analyses

Total phosphorus was measured by using persulfate digestion and then analyzing

138

 

 

 

colorimetrically on a Shimadzu spectrophotometer UV—240PC (Shimadzu Scientific
Instruments, Columbia, MD) at 880 nm. Samples for dissolved phosphorus and ni-
trogen were filtered through acid washed GF / F filters. Dissolved phosphorus (solu-
ble reactive phosphorus, SRP) was measured using the orthophosphate method on
Lachat Instruments Quick Chem 8500 (Lachat Instruments a Hach Co Brand, Love-
land, CO). Total nitrogen was measured after persulfate digestion (Bachmann and
Canfield 1996). Total nitrogen and dissolved nitrogen (nitrate) were measured by
second-derivative spectroscopy (Crumpton et al. 1992).

Phytoplankton analyses

Chlorophyll a was measured by filtering onto a 25 mm Whatman GF / B fil-
ter, which was extracted with 95 percent ethanol and measured fluorometrically
(Welschmeyer 1994). Chlorophyll a as measured in the lab was strongly correlated

with fluorescence measured in the field (Figure 4.1).

Samples for phytoplankton identification were poured into graduated cylinders,
preserved immediately using Lugols iodine, and allowed to settle for several days.
These condensed samples were used for identifying and enumerating species in Palmer
counting cells and settling chambers under compound and inverted microscopes, re-
spectively. Only data from a single sampling campaign, the September campaign,
were analyzed for community composition and diversity.

We counted individuals in random microscope fields until at least 400 individuals
were counted but a minimum of four fields when counting at 4OOX. The diameters of
chambers were also scanned for rare species and any species for which less than three
individuals were found before was recorded. Individuals were identified to species and
morphotype if possible but many could only be positively identified to genus while
some were only identified to class and a few were identified just as a morphological
description. We distinguished morphotypes based on whether individuals were a

colony (or part of a colony) and colony size. We will use the term species throughout

139

 

Chlorophyll (1 [pg 1:1]

 

 

 

 

Fluorescence

Figure 4.1: Relationship between chlorophyll a as measured in the laboratory with
standard protocols using ethanol extraction and on a laboratory fluorometer and
fluorescence as measured in the field using SCAMP built-in fluorometer for all lakes,
times, and samples (including mixed layer and discrete depths). Regression equation:

chlorophyll a = 23x fluorescence —O.55, P<0.001, Rid} = 0.58.
to describe the highest level of classification used for each individual counted. In
most cases, this classification represents a true species but in some cases it may just
be a distinct morphotype. Phytoplankton densities are reported as individuals per
mL, where individuals is generally number of single cells, number of cells in colonies
for countable cells, number of colonies for very small celled colonies, and number
of filaments for filamentous algae (see Appendix Table for what was considered an
individual for different species). We also measured length and width of 10 individuals
in each lake of the top two to five most abundant species.
Zooplankton analyses

Zooplankton samples were condensed and preserved with 95% ethanol. Later they

were identified to genus and enumerated under a dissecting scope using a counting

wheel to count approximately at least 200 individuals. Zooplankton densities were

140

 

 

 

calculated based on volume sampled in lakes. Densities were divided into three grazer
categories for analysis: Daphnia, other major zooplankton grazers (calanoid copepods,
Bosmina, Diapham'soma, and Cem'odaphnz’a), and other zooplankton (Demott 1982,

Sarnelle 2005).

4.3.3 Survey analysis

Ecosystem-level

To find peaks in chlorophyll a fluorescence, each cast was smoothed with a Savitzky-
Golay smoothing filter (Savitzky and Golay 1964). Savitzky-Golay smoothing filters
can do a better job of preserving peaks in data than other moving window smoothing
techniques because they approximate the underlying function within a window by
a higher order polynomial, rather than a constant (Press et al. 2001). We used a
window size of 50 data points, which corresponds to a 0.8 m window.

We found the following criteria to identify significant peaks in chlorophyll a flu—
orescence and match the depths we sampled in the field. The first derivative of the
smoothed profile was used to locate local maxima and minima and the second deriva-
tive was used to confirm the maxima. For a maximum to be called a peak, two other
criteria must be met: 1) in the region around a maximum bounded by a minimum on
each side, there must be a difference in the values of the first derivative of > 0.1, and
2) in the region around a maximum bounded by :t 1 / 2 window size, the standard
deviation in raw fluorescence values divided by the total standard deviation in raw
fluorescence values for the entire water column must be > 0.1. We also checked to
see if there was a benthic layer. In order for a benthic layer layer to be present,
the following criteria must be met: the first derivative of the smoothed profile has
to be increasing at the bottom and that rate of increase divided by the maximum
rate of increase for the whole profile had to be > 0.2. We used our multiple casts we

gathered during a visit to a lake as replicates to confirm the existence of a peak; that

141

 

is, there must have been peaks within 0.35 m of one another in at least two casts.
Those peak depths were then averaged across casts. We considered only peaks that

occurred below the mixed layer.

Environmental variables were calculated in the following ways. Water column
depth, 2b, was estimated in the field based on sonar readings and raw SCAMP casts.
Mixed layer depth, 2m, was calculated as the uppermost depth where dT / dz exceeded
1 degree C/m and then was averaged across casts of a lake during a visit. Background
light attenuation, abg, was calculated as total light attenuation minus chlorophyll
concentration (lab measurement) multiplied by a chlorophyll attenuation coefficient
of 0.01094 m2 mg—1 (Kirk 1975 b). Turbulent diffusion coefficient, D, was the average
log turbulent diffusion coefficient throughout the water column averaged across all

casts of a lake on the sampling date.

We loglO transformed all environmental variables as is commonly done when vari-
ables span several orders of magnitude. The environmental variables background
light attenuation, water column depth, total phosphorus in the mixed layer, mixed
layer depth, total phosphorus at the bottom, and turbulent diffusion coefficient were
checked for multicollinearity by regressing each environmental variable on all the other
environmental variables. Tolerance (the reciprocal of tolerance is variance inflation
factor) is calculated as 1-R2 and we used the common cut off criterion (Walker and
Maddan 2005) of any tolerance less than 0.25 to indicate multicollinearity. All of the

main environmental variables were within the tolerance limits.

For the statistical model of number of peaks, we used a different set of variables:
deep layer span calculated as zb -— zm, total phosphorus gradient in the deep layer
calculated as the absolute value of (total phosphorus at the bottom—total phosphorus
in the mixed layer) / (2b — zm), light gradient in the deep layer calculated as (light at
zm—light at 2b)/ (zb — zm), total phosphorus at the bottom, light at zm, and back-

ground attenuation. Total phosphorus at the bottom and total phosphorus gradient

142

 

in the deep layer are highly correlated, resulting in too low of a tolerance value to
be included in the same model together, as are light at 2m and light gradient in the

deep layer. Therefore, these variables were run in separate models.

Since each lake was sampled one to four times throughout the stratified season,
we added the covariate day-of-year into the models as a check for temporal effects to
determine whether sampling date should be explicitly modeled. Day-of-year was not
significant in any of the models presented. We also checked for temporal effects with
autocorrelation tests, autoregressive models, and residuals of variables at t + 1 vs t,
but no significant effects of time were detected (although there are only a few points
in time). Concluding that the environmental variables should absorb any temporal
effects, we pooled the data across the season. This is consistent with Wisconsin
studies that found only a small proportion of lakes sampled on one—five week intervals
showing autocorrelation and little effects of that autocorrelation in the statistical
results (Carpenter et al. 1989, Stow et al. 1998). Our discrete sampling campaigns
were separated by > 1 month intervals, which happens to coincide with the scale of

the greatest variation in primary production (Carpenter and Kitchell 1987).

We employed a multiple regression analysis, which included all environmental
variables for which we have theoretical predictions, as well as day-of-year in the model
to examine determinants of phytoplankton vertical distribution, biomass, and number
of peaks. We used the best model to indicate what environmental variables had a
significant impact on the biotic variable of interest. We found the best model using
two separate methods. 1) We put all variables into the model and then removed all
variables with P values > 0.05 and checked that the reduced model had a significantly
lower AIC than the full model. 2) We ran a backwards step-wise regression with all
variables included and used AIC values to reduce the model. In case of disagreement
between these methods (two cases of disagreement), we chose the model with the

lowest AIC to represent the best model (Burnham and Anderson 2002). Variables

143

 

 

 

from the best models are reported in the tables and figures. If a relationship appeared

quadratic, it was also checked for significant nonlinear terms but none were found.
Community-level

Shannon-Weiner (Weaver and Shannon 1949), Simpson’s (Simpson 1949), and
inverse Simpson’s diversity indices were calculated using species densities. We used t-
tests to test for differences in diversity between the mixed layer and main DCM, where
main DCM is the depth of the peak with the largest chlorophyll a fluorescence value.
To explain diversity across lakes, we used regressions with the same environmental
variables as in the ecosystem analyses with the addition of two zooplankton grazer
variables: 1) Daphnia density and 2) other major grazer density.

Detrended correspondence analysis (DCA) was conducted to examine the rela-
tionships of communities to one another (Legendre and Legendre 1998). DCA was
used instead of regular correspondance analysis (CA) because a CA plot exhibited an
arch (Legendre and Legendre 1998). DCA was also used to examine correlations of
environmental variables with community space. The Bray-Curtis dissimilarity index
was used on species densities to measure community similarities (Faith et al. 1987).
A Mantel statistic based on Pearson’s product-moment correlation and 999 permu-
tations was used to test for covarying dissimilarity indices (Legendre and Legendre

1998) between the mixed layer and main DCMs.

Phytoplankton were classified into seven major taxonomic groups (Watson et al.
1997): chrysophytes, cryptophytes, cyanobacteria, diatoms, dinoflagellates, euglenoids,
and greens. The dominant species was simply the species with the highest density
in a community. We present species densities that are > 5% of the total commu-
nity densities (typically summing up to 70 -— 80% of the total community) for each
community in the Appendix. Regressions for dissimilarity, taxonomic group relative
abundance, and dominance switches were run in a similar fashion to the ecosystem

models with the same model selection criteria and with all variables listed in the

144

 

 

captions of each table. Dissimilarity and taxonomic group relative abundance were
arcsine transformed for the regression analyses. Statistical analyses were performed
in M athematica v7 (Wolfram Research, Inc., Champaign, IL) and R v2.10 (The R

Foundation for Statistical Computing, Vienna, Austria).

4.4 Results

4.4.1 Ecosystem
4.4.1.1 Vertical distributions of phytoplankton

We observed considerable variation in phytoplankton distributions. In 104 profiles,
15 were not thermally stratified, and hence lacked a poorly—mixed deep layer where
a peak in chlorophyll a fluorescence could form. Peaks were identified in 86 of the
remaining 89 profiles with clearly defined deep layers. Many of the profiles had
multiple peaks: 39 profiles showed single peaks, but 17 showed double, 24 showed
triple, 5 showed quadruple, and 1 showed quintuplet peaks. The depth of the global
fluorescence maximum (largest fluorescence value in the water column), as well as all

peaks, occurred in different portions of the water column (Figure 4.2).

145

 

 

DD

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

V)

>. N - —
8 8 -1 o d __
8 m
g I— a
L: S - (>3 "1 “___ —
o A H [—1 8‘
W I I I l L: —
0 10 20 30 40 m,
Depth of global fluorescence maximum [m]
0.1 [—

9. - b __ 0.0 0.2 0.4 0.6 0.3 1.0
>‘ 3 _ Relative depth of global
3 o J — fluorescence maximum
0
:3 m
U"

.12 81
2 - K}. c _—
c. _ r - .. ._ o
I l I I 1 N. _ .—
o 10 20 30 40 a m _-* _
Depth of fluorescence peaks [m] g '-' . _
‘3' o
2 ._..
__ Ln

o C F In. [—

N - —l
g :3 .. o1
g, o __ 0T0 02 0.4 0.6 018 1'0
8 '— ‘ Relative depth of
u. fluorescence peaks

_ __l n H n

 

 

 

 

 

 

 

 

0 5
on;

10 2'0 :10 lo
Water column depth [m]

Figure 4.2: Depths of a) global fluorescence maximum, b) peaks in fluorescence,
and c) water column. Depths relative to water column depth of d) global fluorescence
maximum and e) peaks in fluorescence. Histograms include all lakes and times (n=104
for fluorescence maximum and water column and n=170 for all peaks).

146

4.4.1.2 Environmental parameters

The environmental parameters we measured in the survey lakes showed considerable
variation (Table 4.1). The total nitrogen to total phosphorus ratio in the mixed
layer showed significant variation (Figure 4.3a). However, overall, total nitrogen was

correlated with total phosphorus across all sampling depths (Figure 4.3b).

Table 4.1: Summary of major environmental variables

 

 

Minimum Mean Maximum
Water column depth [m] 1.9 9.95 35.50
Mixed layer depth [m] 1.27 3.06 17.58
Turbulent diffusion coefficient [no2 d’l] 1.22x10—11 6.20x10_5 7.581x10—4
Background attenuation coefficient [m_1] 0.18 0.77 3.24
Total phosphorus in mixed layer [pg P L—l] 4.01 19.18 107
Total phosphorus at bottom [pg P L‘l] 6.88 79.44 978

 

The existence of phosphorus gradients was indicated by comparing concentrations
of dissolved phosphorus 0.5 m above the bottom with concentrations in the mixed
layer. On average, the concentration in the mixed layer was 20 pg P L—1 lower than
the concentration 0.5 m above the bottom (Figure 4.4, paired t-test, t=2.27, P=0.013,
df=105). A nutrient gradient was not detected for dissolved nitrogen (paired t-test,
t=-2.09, P=0.98, df=70). , We used phosphorus as the focal limiting nutrient due to
the lack of a vertical gradient in nitrogen and the overall strong correlation of total

nitrogen and total phosphorus.

4.4.1.3 Vertical distributions across environmental gradients

To examine phytoplankton vertical structure across environmental gradients, we first
tested if algae formed a peak in the deep layer and in a benthic layer. We performed
a logistic regression of presence of a peak versus the light level at the bottom of
the mixed layer, but it was not significant. Together with the fact that there were

only a feW profiles that did not form a peak in the deep layer, there is a very high

147

 

Ll”

 

 

 

 

 

 

 

I . g
: fi- 0..
c> chd' ° '°
N - . o "o: .
z . ...00 "O.
*3 ca ' '3§3°‘ *1 r- '
*go ((3.1 .9 0.0%
1 .. ’:o'
H :. .Q.‘ .0.
o
2 - E :2 ‘ 4‘: ~
.0 o
O I
.7; -
O
._l 3, '° .

 

1T0 115 zfo 215 3:0
Loglo TP [pg total P L'l]

 

Frequency
1 0
l

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

I I I I l
0 50 100 150 200

N:P

Figure 4.3: Nitrogen and phosphorus relationships in the data. a) Molar N:P ratio
for total nitrogen and total phosphorus measured in the mixed layer (mean=115,
median=97, minimum=35, maximum=932). b) Relationship between loglO Total
nitrogen and loglO Total phosphorus for all lakes, times, and samples (including
mixed layer and discrete depths). Pearson’s correlation r=0.75, P <0.001, df=278).

probability that a peak can form in the deep layer in the lakes we sampled. However,
the probability that a benthic layer forms depended significantly on the light level
at the bottom of the water column (logistic regression, z statistic=3.57, P< 0.001,
Figure 4.5). Therefore, a deep layer peak is highly probable for given light conditions
but a benthic layer forms only if enough light reaches the sediments.

There is a high probability of a peak forming in the deep layer but what determines

the depth of these peaks? We focus on three main measures of vertical distribution of

148

 

 

._'T'

I

p.)

a. 2-

'0

d)

.2.

c

U)

.3

'0

on 14

:1.

l—J

5

o

'8.

m 0—

o

.1:

13..

o

0—4

8"

—-n _1_
-22

 

 

 

 

I T
0.5 m above bottom Mixed layer

Figure 4.4: Phosphorus gradient present in most lakes and times (paired t-test,
t=2.27, P=0.013, df=105). Note that in the plot, nutrient concentrations are log
scaled.

the phytoplankton: 1) depth of global maximum of chlorophyll a fluorescence in the
water column (most commonly used), 2) depths of peaks identified by fluorescence
profile analysis, 3) depth of a peak for lakes that only contain a single peak (a subset
of measure 2). The other measures of vertical distribution (average depth, average
depth in the deep layer, mean of peak depths, and maximum of peak depths) gave

very similar results to the global maximum of fluorescence measure.
Global maximum:

Depth of the global chlorophyll a fluorescence maximum was positively associated

149

 

1.0? 0000 o o. -0... 0.0 .

Benthic layer presence

 

 

-6 -4 -2 0 2 4
loglo light at bottom [pmol photons m'zs'l]

Figure 4.5: Logistic regression relating probability of a benthic layer forming to loglO
light at the bottom of the water column (2 statistic=3.57, P< 0.001).

with mixed layer depth and water column depth (Table 4.2), i.e. increasing mixed
layer or water column depth acts to move the peak deeper in the water column. Depth
of the global chlorophyll a fluorescence maximum was negatively associated with
background light attenuation and the turbulent diffusion coefficient, i.e. increasing

either of these two variables acts to move the peak shallower.

Table 4.2: Multiple linear regression results for depth of global fluorescence maximum
versus all environmental variables. Only relationships from the best model were
included in the table. The intercept was not significant (P< 0.05) so it was not
included in this table.

 

 

- 2
Coefficient (SE) t P-value Poverall R ad'L
Constant 0.2065 (0.1280) 1.613 0.1 < 0.001 0.39
loglo mixed layer depth 0.2722 (0.1013) 2.687 < 0.01
loglo water column depth 0.2192 (0.103) 2.129 0.036

loglo background light attenuation -0.3883 (0.1107) -3.509 < 0.001
logm turbulent diffusion coefficient -0.030 (0.0119) -2.532 0.013

 

All peaks:
Depths of all peaks were positively associated with mixed layer depth and water
column depth (Table 4.3), i.e. increasing mixed layer or water column depth acts to

move the peak deeper in the water column. Depths of all peaks were negatively associ-

150

 

ated with background light attenuation, i.e. increasing background light attenuation
acts to move the peak shallower.
Table 4.3: Multiple linear regression results for depths of fluorescence peaks versus

all environmental variables. Only relationships from the best model were included in
the table.

 

 

- 2
Coefficrent (SE) t P-value Poverall Radj.
Constant 04424 (0.0774) 5.719 < 0.001 < 0.001 0.35
loglo mixed layer depth 0.2532 (0.0544) 4.656 < 0.001
loglo water column depth 0.2115 (0.0802) 2.639 < 0.01

loglo background light attenuation -0.3186 (0.0819) -3.889 < 0.001

 

Single peaks:

The closest association of depth distribution with environmental variables occurs
in the lakes with only a single peak (Table 4.4). Single peak depth was positively
associated with mixed layer depth, i.e. increasing mixed layer depth acts to move
the peak deeper in the water column (Figure 4.6a, 4.7a). Single peak depth was also
positively associated with water column depth (Figure 4.6b, 4.7b). Single peak depth
was negatively associated with both background light attenuation (Figure 4.60, 4.7c)
and the turbulent diffusion coefficient (Figure 4.6d, 4.7d), i.e. increasing either of
these two variables acts to move the peak shallower. Single peak depth was positively
associated with total phosphorus in the mixed layer, i.e. was deeper with higher
nutrients (Figure 4.6e, 4.7e).

Table 4.4: Multiple linear regression results for depths of single fluorescence peaks

versus all environmental variables. Only relationships from the best model were
included in the table.

 

 

Coefficient (SE) t P-value Poveran Rgdj'
Constant -0.2800 (0.1354) -2.072 0.046 < 0.001 0.8
loglO mixed layer depth 0.3412 (0.0932) 3.663 < 0.001
loglO water column depth 0.4299 (0.0968) 4.441 < 0.001
loglo TP in mixed layer 0.1942 (0.0779) 2.494 0.018

loglO background light attenuation -0.4324 (0.1132) -3.821 < 0.001
loglO turbulent diffusion coefficient -0.0399 (0.0091) -4.403 < 0.001

 

151

 

Figure 4.6. Depth of peak of single peak lakes versus significant environmental
variables. a) Relationship with mixed layer depth. The line is not a fit for
the data, it is the depth of the mixed layer and denotes the upper limit of the
peak depth. b) Relationship with water column depth. The line is not a fit
for the data, it is the depth of the water column and denotes the lower limit of
the peak depth. c) Relationship with background attenuation. The line is not
a fit for the data, it is the Zmax depth and denotes a theoretical lower limit of
the peak depth and is calculated as log (ll‘IbegD' (1) Relationship with logm
turbulent diffusion coefficient. e) Relationship with total phosphorus in the

mixed layer.

152

Depth of algal peak [m] Depth of algal peak [111]

Depth of algal peak [m]

-6-4-20

-8

-12 -10

-6-4-20

-8

-12 -10

 

 

 

 

 

2 3 h 5 B 7

Mixed layer depth [m]

 

l

l

 

 

 

 

 

1

l

 

 

 

.0 6.5 1.0 1.5 2.0 2.5 10

Background light attenuation [in-1]

C

o 8 o o o
lo 20 30 40 5o 60

TP in mixed layer [pg P L'l]

-6—4-20

-8

L

-12 -10

-6 -4 -2 o

-8

-12 -10

 

l

l

 

 

 

4 16 8 10 12 14
Water column depth [m]

 

l

l

 

 

o 0 $ 0
o o e o 9
o o o o o ’
310 18 16 '4
loglo turbulent diffusion

coefficient [m2 d'l]

Figure 4.6: Depth of peak of single peak lakes versus environment.

153

 

 

 

 

Figure 4.7. The partial residual plots for the significant log10 transformed
variables in the model of depth of peak of single peak lakes versus significant
environmental variables. Note, these are the same variables as in Figure 4.6,
but these are the partial residual plots and so represent the true relationship
of the variable with peak depth. Lines are the slopes for the variables in the
table. In these plots, depth increases along the partial residual axes (larger

values are deeper).

154

Partial residuals Partial residuals

Partial residuals

 

 

1
o.-
O

l

0.2 0.3 0.4 0.5 0.6

 

l

 

 

 

 

 

 

 

 

 

   

 

 

 

 

 

 

 

3.- ° 3-
0.2 0.4 0.6 0.8 0.4 0.6 0.8 1.0 1.
loglo mixed layer depth [in] loglo water column depth [m]
cc
"1.
o .1
rs!
o '1
3 .
O.
o -
g .
(0:! ‘ 3 J 0 o o
-l).6 30.4 30.2 0.0 0.2 .4 Ylo 18 16 '4
loglo background light attenuation [m'l] loglo turbulent diffusion
coefficient [m2 d'l]
23 - e .

 

 

 

 

0.8 1.0 1.2 1.4 1.6 .8
loglo TP in mixed layer [pg P L'l]

Figure 4.7: Partial residual plots for the depth of peak of single peak lakes.

155

 

4.4.1.4 Biomass

Total biomass, as measured by in-situ chlorophyll a fluorescence integrated through-
out the water column, was positively associated with water column depth and back-
ground light attenuation (Table 4.5, Figure 4.8). Biomass in the deep layer, as mea-
sured by integrated fluorescence below the mixed layer, was positively associated with
water column depth and background light attenuation, and negatively associated with
mixed layer depth (Table 4.5, Figure 4.9). The mixed layer biomass, as measured by
integrated fluorescence in the mixed layer, was positively associated with mixed layer
depth, total phosphorus in the mixed layer, and background light attenuation (Table
4.5, Figure 4.10).

Table 4.5: Multiple linear regression results for integrated fluorescence (“biomass”)
versus all environmental variables. Only relationships from the best model were

 

included in the table.

 

 

Coefficrent (SE) t P-value Poverall fill-
Total biomass
Constant -0.3771 (0.0837) -4.506 < 0.001 < 0.001 0.6
loglo water column depth 0.8702 (0.1063) 8.187 < 0.001
loglO total phosphorus at bottom 0.05828 (0.04178) 1.395 0.167
loglo background light attenuation 0.84930 (0.11454) 7.415 < 0.001
Deep layer biomass
Constant -0.7321 (0.1152) -6.356 < 0.001 < 0.001 0.64
loglo water column depth 1.2291 (0.1422) 8.644 < 0.001
loglo mixed layer depth -0.4868 (0.0906) -5.370 < 0.001
loglo total phosphorus at bottom 0.08293 (0.05588) 1.484 0.142
loglo background light attenuation 0.7639 (0.1556) 4.908 < 0.001
Mixed layer biomass
Constant -0.7822 (0.1559) -5.017 < 0.001 < 0.001 0.85
loglo mixed layer depth 1.1360 (0.0835) 13.598 < 0.001
loglo total phosphorus in mixed layer 0.1923 (0.0976) 1.971 0.052
loglo background light attenuation 0.8956 (0.1189) 7.531 < 0.001
logm turbulent mixing ' 0.0148 (0.0097) 1.528 0.13

 

156

 

 

 

   

 

 

 

 

 

 

 

 

 

W
...:~ g b ° ,3
'3 - .0 °. 0' o . O"
'3 o. o . . .. . o . N
'8 .—1‘ ct . .0. o o- .,
3?. 1,“? , .
E 3,2 V .. . 0“ g .-
t: o. o. g . o .
:3 ° N
‘3‘ « '. o'.
o “3 '
o" .° . . . . . c." '. . . . . . ' . . . . .
0.4 0.6 0.8 1.0 1.2 1.4 -0.6-0.4-0.2 0.0 0.2 0.4 1.0 1.5 2.0 2.5 3.0
loglo water colurrm depth [m] loglO background light loglo TP at bottom

attenuation [m'l] [pg total P L'l]

Figure 4.8: Partial residual plots for total biomass (integrated fluorescence) versus
environmental variables in the best model.

4.4.1.5 Multiple peak coexistence

The light and nutrient conditions experienced by algae in the lakes were highly vari-
able both among lakes and within a lake. For example, the light level for the aver-
age depth of the deep layer algal biomass showed considerable variation (mean=19.6,
SE=4.29, minimum=0, maximum=352.80 pmol photons m—2s_1). Peaks exist along
a full range of light and phosphorus levels. A type II regression of log(light) on
log(dissolved phosphorus) at a peak showed a negative relationship that was highly
significant (RMA method, slope=-3.94, R2 = 0.15, P< 0.001, Figure 4.11).

4.4.1.6 Number of peaks

The number of peaks was determined by the amount of physical space in the deep
layer (Table 4.6, Fig. 4.12a) and the nutrient gradient (Fig. 4.12c). The data provide
some support that the light gradient also plays a role (Fig. 4.12b). All of these factors
are associated with an increased number of peaks (Table 4.6).

We could not test the relative importance of resource heterogeneity versus re-
source quantity (Stevens and Carson 2002) because TP at the bottom has too much

multicollinearity when in models with TP gradient in the deep layer (as does light at

157

 

_ ”ta" '-
aun~

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

N.
o-
'5 8-
1::
'8 N
2 of-
.73
a $-
1:.
‘0.
:3.
o °9 ° °
6- C?-
0.4 0.6 0.8 1.0 1.2 1.4 0.2 0.4 0.6 0.8 1.0 1.2
loglo water column depth [m] loglo mixed layer depth [m]
‘0.
° . . . . ~ . 2:.
‘12 0 ° 0
.3" o. .09’0 0° 2'
g N ° 0. .°°.‘oo o O
:2 O-r o f. o o'-
§ o X’HO/i N
rad-cum.“ 9°“ . . 8-
° 0 V
g N 0 . o °o O-
n- o. ° '
I O \o
V 0 on‘
95- oo
o‘ O
o. I
0'. o o
1.0 1.5 2.0 2.5 1.0 .06 30.4 30.2 0.0 (1.2 0.4
loglo TP at bottom [pg total P L‘l] loglo background light

attenuation [m' 1 ]

Figure 4.9: Partial residual plots for deep layer biomass (integrated fluorescence in
the deep layer) versus environmental variables in the best model.

Table 4.6: Multiple linear regression results for number of peaks versus the following
loglO transformed environmental variables: deep layer span, TP gradient in the deep
layer, light gradient in the deep layer, and background light attenuation; as well as
day-of-year. Only relationships from the best model were included in the table.

 

Coefficient (SE) t P-value Poverall Rgdj

loglo deep layer span 1.5280 (0.2692) 5.677 < 0.001 < 0.001 0.28
loglo TP gradient 0.3165 (0.1382) 2.290 0.02
long background light attenuation 0.9334 (0.5460) 1.709 0.09

 

 

158

 

 

Partial residuals

 

 

 

 

 

 

 

0'6 0'8 1’0 1'2 1'4 1.8 1.11
log 10 TP in mixed layer [pg total P L'l]

 

 

 

 

 

 

 

 

 

 

 

00. ° ° ° . 5r. d °° °
O" o-
?2 —:
o- 3.
T5 2- 1‘!
E *1 c?-
13.. 6,- v.
"1 c?-
O-
' “9.
s c..-
310 18 16 -'4 -0.6 30.4 30.2 0.0 0.2 0.4
loglo turbulent diffusion loglo background light
coefficient [m2 d'l] attenuation [m'l]

Figure 4.10: Partial residual plots for mixed layer biomass (integrated fluorescence in
the mixed layer) versus environmental variables in the best model.

the mixed layer and light gradient in the deep layer). However, when we replace the
gradients (vertical heterogeneity) in the above model with resource supplies (quanti—
ties), the best model to explain number of peaks becomes deep layer span and TP at
the bottom with all light variables being not significant. This indicates that for nu-
trients, either resource heterogeneity or resource quantity is important but we cannot

distinguish which is more important.

159

 

 

 

-

-2

-4

 

 

 

-6

 

I T I j j

52 31 0 l 2 3 4
loglo DP at peak [pg dissolved P L‘l]

loglo light at peak [pmol photons m‘zs‘l]

Figure 4.11: Type II regression of log light values at a peak versus log dissolved
phosphorus values at a peak.

 

 

 

 

a ‘ b ' 0 °
_g V1 Na N
a .. ~-
8 N
'3 ‘ ‘3‘
0% fi‘ T
a“ On N

0 l4 .

 

 

 

 

 

 

 

 

 

 

-l.0 -0.5 0:0 0:5 1:0 1.5 0.6-040.7010 0.2 0.4 -2 51 0 l
loglo deep layer span [m] loglo background light loglo TP gradient
attenuation [m' l] in deep layer
[pg total P L'1 m'l]

Figure 4.12: Partial residual plots for number of peaks versus environmental variables
in the best model.

4.4.2 Community
4.4.2.1 Species Diversity

Phytoplankton species richness varied from 13 to 54 (mean=28, SD29) species at

a depth. The mixed layer and the main DCM (peak with the largest chlorophyll

160

 

a fluorescence value) did not differ for any measure of diversity (species richness,
Shannon, Simpson’s, inverse Simpson’s, all paired and unpaired t-test P—values >
0.1). Mixed-layer Shannon diversity was positively associated with other major (non-
Daphm'a) grazers densities, background light attenuation, total phosphorus at the
bottom, and mixed layer depth and negatively associated with water column depth,
Daphnia densities, and total phosphorus in the mixed layer (Table 4.7). Shannon
diversity in the main DCM was positively associated with Daphnia density, total
phosphorus at the bottom, mixed layer depth, and the light level at the bottom
of the mixed layer and negatively associated with water column depth (Table 4.7).
Species richness in the mixed layer could be explained by a subset of the variables
that explained Shannon diversity in the mixed layer. Species richness in the main

DCM could not be explained by a significant model.

Table 4.7: Multiple linear regression results for Shannon diversity versus all environ-
mental variables in the best model. Environmental variables considered were the same
for the mixed layer and main DCM and included: turbulent mixing, water column
depth, Daphnia densities, other major grazers densities, background light attenua-
tion, total phosphorus at the bottom, total phosphorus in the mixed layer, and the
light level at the bottom of the mixed layer. Only relationships from the best model
were included in the table.

 

Coefficient (SE) t P-value Poverau 122

adj.
Mixed layer Shannon diversity
Constant -4.8339 (1.1753) -4.506 < 0.001 0.08 0.28

loglo water column depth -1.7529 (0.7137) -2.456 < 0.05
loglo Daphnia -0.4977 (0.1869) -2.663 < 0.05
loglo other major grazers 0.5670 (0.2994) 1.894 0.076
loglo background light attenuation 3.0862 (1.4315) 2.156 < 0.05
loglo total phosphorus at bottom 0.9239 (0.4075) 2.267 < 0.05
loglo total phosphorus in mixed layer -2.4828 (0.8995) -2.760 < 0.05
loglo mixed layer depth 1.6237 (0.6025) 2.695 < 0.05
Main DCM Shannon diversity
Constant -0.2867 (0.7898) -0.363 0.72 < 0.05 0.42
loglo water column depth 0.0684 (0.02459) -2.785 < 0.05
loglo Daphnia 0.0197 (0.0067) 2.924 < 0.05
loglo total phosphorus at bottom 0.0017 (0.00064) 2.709 < 0.05
loglo mixed layer depth 3.1778 (0.9393) 3.383 < 0.005
loglo light at bottom of mixed layer 0.6616 (0.2957) 2.237 < 0.05

 

161

 

 

 

4.4.2.2 Whole-community comparisons

Detrended correspondence analysis plot indicated variation between some communi-
ties while also showing conspicuous community overlap (Figure 4.13). For some of the
lakes, communities from different depths within a lake clustered in multidimensional
community space, indicating similarity within a lake. Furthermore, examination of
correlations between environmental variables and axes illustrated that communities
differentiated along several nutrient, light, and grazing axes.

The Bray-Curtis community dissimilarity index also showed that communities
within a lake (mean dissimilarity=0.57, SE=0.03, Fig. 4.14a) appear to be much
more similar to each other than communities across lakes (mean dissimilarity=0.84,
SE=0.003, Fig. 4.14b). Furthermore, both mixed layers and the main DCMs showed
a lot of dissimilarity across lakes (Fig. 4.14c and d respectively) indicating that within
each of these environments, the communities were not the same across lakes. Main
DCMS (mean dissimilarity=0.79, SE=0.01, minimum=0.25, maximum=0.996) appear
to be slightly more similar to one another on average than mixed layers (mean dis—
similarity=0.84, SE=0.009, minimum=0.09, maximum=1) and have a smaller range
in variation. In addition, main DCMs and mixed layers covary across lakes, meaning
that if a mixed layer community differs from all the other mixed layer communities,
the main DCM community will differ from all the other main DCM communities in
a similar fashion (Mantel test, 7' = 0.55, P<0.001, Fig. 4.14e). Dissimilarity between
paired samples of mixed layer and main DCM shows a large amount of variation

(mean dissimilarity=0.63, minimum=0, maximum=0.97, Fig. 4.14f).

162

 

0.4 0 0.4

 

 

   

 

 

 

1 l l
N
N
.2
X
< O
—.'— 5 °
5 v
“3— :
T i I I
-l 0 1 2

Axis I

Figure 4.13: Detrended correspondence analysis plot (DCA) of all communities (all
lakes and depths). Also plotted are environmental vectors for loglO transformed envi-
ronmental variables that did not overlap too strongly with another variable (excluded
turbulent mixing coefficient because it overlapped with abg and TP measured at the
depth of the sample because it overlapped with TP measured at the bottom). Other
variables and their scores (vectors scaled by correlation coefficient) for axis 1 and 2
respectively: DP is soluble reactive phosphorus (-0.24397522, 0.257411923) and light
is irradiance (0.02501621, 0.181052901) at the depth of the community sample, abg
is background light attenuation (—0.01306323, 0.341490988), TP(zb) is total phospho-
rus measured at the bottom (0.12299715, 0.387226041), Daphnia is Daphnia density
(0.10589080, 0.297177857), and Zoop is density of other major grazers (—0.13330044,
-0.008967929).

163

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

>» 2' o
O 00
5 oo
8- s
3 v
LL. O {—l I I I I O r——I1 I I I ' I
0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0
Within-lake dissimilarity Mixed layer dissimilarity
b o d
a s 2
5 o
8- 8 m
s m L
LL C [___1—1 I ’ I ’ I o [—'li—A—Iffi— I I I
0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 V
Across lakes dissimilarity Main DCM dissimilarity ‘
‘3- f
29
'1: °9
2 O‘
.... m __
E \o a" V '—
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g g- Paired mixed layer versus
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0'0 0'2 9.4 6.6 0T8 1'.0
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Figure 4.14: Frequency distributions for Bray-Curtis community dissimilarity indices
of different community samples. Dissimilarity is maximum at a value of 1. a) Dissim-
ilarity for samples taken within a lake. b) Across lake dissimilarity for communities.
c) Dissimilarity of mixed layer communities compared to other mixed layer commu-
nities. d) Dissimilarity of main DCM communities compared to other main DCM
communities. e) Correlation between dissimilarity of mixed layer communities (part
c) and dissimilarity of main DCM communities (part e). f) Dissimilarity between
paired mixed layer and main DCM samples for each lake.

The dissimilarity between communities in the mixed layer and main DCM could

 

164

best be explained by two environmental variables (Table 4.8): background light at-
tenuation appeared to make the communities more similar (Fig. 4.15a) and total
phosphorus at the bottom appeared to make the communities less similar (Fig. 4.15b)

although note that the overall model is not significant (P2015).

Table 4.8: Multiple linear regression results for dissimilarity versus the following loglo
environmental variables as indicated by the DCA to potentially play a role: TP at
the bottom, and abg’ Daphnia, and other major grazers. Only relationships from the
best model were included in the table. Note that TP at the bottom in the best model
could be replaced by TP gradient in the deep layer (P=0.05) but the model cannot
include both due to multicollinearity.

 

 

Coefficient (SE) t P-value Poverall R: (1L
loglO TP at the bottom 0.1892 (0.1287) 1.470 0.16 0.17 0.08
log10 abg -0.5218 (0.2879) -1.812 0.085

 

 

 

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0 2

0.0

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‘?

 

 

-0.6 -04 0.2 0'0 0'2 1'0 1'5 2'0 25 3:0
loglo background light attenuation [m'l] loglo TP at the bottom [micro g P L'l]

Figure 4.15: Partial residual plots for community dissimilarity between the mixed
layer and main DCM versus environmental variables in the best model.

4.4.2.3 Taxonomic group and species

DCMs were not all dominated by the same taxonomic group or genus (Appendix

Table). In fact, dominance by taxonomic group and genus shows as much variation

165

 

 

 

in DCMs as in the mixed layer. Thus, the DCM niche can be filled by a number of
different taxonomic groups and species.

Cyanobacteria appear to be the most abundant group across all lakes (Fig. 4.16).
Taxonomic group relative abundances showed some relationships with lake charac—
teristics across lakes (Fig. 4.16, Table 4.9). Chrysophytes increased with turbulent
mixing and decreased with mixed layer depth and Daphnia density. Cryptophytes
decreased with total phosphorus in the mixed layer. Cyanobacteria increased with
Daphnia density and appeared to decrease with other major grazers density. Diatoms
increased with other major grazers density and decreased with water column depth
and total phosphorus in the mixed layer. Dinoflagellates increased with background
light attenuation. Euglenoids decreased with other major grazers density. Greens

decreased with background light attenuation.

166

 

Figure 4.16. Relative abundance of taxonomic groups across lakes and with
depth within lakes for the 23 lakes from which multiple samples were taken
with depth. Each plot is a single lake and the communities from all the
depths sampled are arrayed in the vertical dimension of each according to
depth (surface is top and deepest depth is bottom). Plots are arrayed roughly
in 2 dimensional environmental space: Daphnia density increases along the
horizontal axis across lakes and background light attenuation increases along
the vertical axis across lakes. a) Pleasant, b) Lime, c) Gravel, (1) Little Long,
e) Big Glen, f) Baker, g) Donnell, h) Lawrence, i) Long, j) Gun, k)Fine, l)
Hogsett, m) Bristol, n) Baldwin, 0) Warner, p) Bassett, q) Cloverdale, r) Little

Mill, 8) Pine, t) Sherman, u) Hess, v) Brooks, w) Wintergreen.

167

 

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Table 4.9: Multiple linear regression results for relative abundance of taxonomic
groups versus all environmental variables in the best model. Environmental vari-
ables considered were: turbulent mixing, mixed layer depth, water column depth,
Daphnia densities, other major grazers densities, background light attenuation, total
phosphorus at the bottom, total phosphorus in the mixed layer.

 

 

Coefficient (SE) t P—value Poverall dej.

Chrysophytes
Constant 0.92238 (0.1662) 5.549 < 0001 < 0.001 0.38
loglO mixed layer depth -04061 (0.1217) -3.338 < 0.005
loglo turbulent mixing 0.0538 (0.0225) 2.397 < 0.05
loglo Daphnia -0.1976 (0.039) -5.068 < 0.001

Cryptophytes
Constant 0.2526 (0.03827) 6.60 < 0.001 < 0.01 0.09
loglo total phosphorus in mixed layer -0.0887 (0.0329) -2.698 < 0.01

Cyanobacteria
Constant 0.928 (0.04) 23.212 < 0.001 < 0.001 0.28
loglo Daphnia 0.2449 (0.0512) 4.787 < 0.001
loglo other major grazers -0.1002 (0.0545) -1.840 0.07

Diatoms
Constant 0.5617 (0.1012) 5.551 < 0.001 < 0.001 0.31
loglo water column depth ~0.1434 (0.059) ~2.430 < 0.05
loglO total phosphorus in mixed layer ~02666 (0.0537) -4.963 < 0.001
loglo other major grazers 0.0545 (0.023) 2.373 < 0.05

Dinoflagellatas
Constant 0.0433 (0.0054) 8.069 < 0.001 < 0.05 0.06
loglo background light attenuation 0.039 (0.0164) 2.371 < 0.05

Euglenoids
Constant 0.0326 (0.00505) 6.468 < 0.001 < 0.05 0.046
loglo other major grazers -0.01431 (0.00704) -2.031 < 0.05

Greens
Constant 0.2098 (0.0290) 7.229 < 0.001 < 0.05 0.05
loglo background light attenuation -01932 (0.0889) -2.173 < 0.05

 

Taxonomic group relative abundances appear to change significantly with depth

 

in some lakes but differed relatively little in other lakes (Fig. 4.16). Fig. 4.16 shows
that diatoms mostly decreased with depth, cryptophytes mostly increased with depth,
chrysophytes, cyanobacteria, and greens both increased and decreased with depth,

and other groups were roughly equal with depth across lakes. Analysis of how local

169

resource conditions correlated with relative abundance of taxonomic groups showed
that some groups have significant relationships with local resource conditions while
others showed no relationship (Table 4.10). Chrysophytes show a positive relationship
with light measured at the depth of the sample. Cyanobacteria show a negative
relationship with light measured at the depth of the sample. Diatoms show a positive
relationship with light measured at the depth of the sample and euglenoids show
a negative relationship with light measured at the depth of the sample. All other
taxonomic groups (cryptophytes, dinoflagellates, and greens) show no relationship
with local resource conditions.

Out of the 30 lakes sampled in September for community composition analyses,
23 had multiple depths sampled because those lakes were stratified and a DCM was
present. The identity of the dominant species switched between depths in the water
column in 15 of those 23 lakes, making a dominance switch a common occurrence
(Appendix Table). Dominance switches appear to be more likely in deeper lakes
(Table 4.11).

4.5 Discussion

4.5.1 Variation in phytoplankton vertical distributions

We established that there is considerable variation in phytoplankton vertical distri-
butions. Lakes varied in the depths of their chlorophyll a fluorescence peaks. In
addition, we found many lakes with multiple peaks, in agreement with Fee (1976),
who showed that usually a considerable amount of biomass exists in a peak below the
mixed layer.

Numerous hypotheses have been proposed to explain vertical distributions of phy-
toplankton, and in particular DCMs. However, we focused on several hypotheses

related to light, nutrients, and mixing: low turbulence and sufficient light penetra-

170

Table 4.10: Multiple linear regression results for relative abundance of taxonomic
groups versus local environmental variables in the best model. Environmental vari-
ables considered were: light at the sample depth and dissolved phosphorus at the
sample depth. For integrated mixed layer samples, the light level at the bottom of
the mixed layer was used as the light at the sample depth. NS indicates that the best
model was not significant (P< 0.1).

 

 

 

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- 2
Coeffic1ent (SE) t P—value Poverall R adj.

Chrysophytes
Constant 0.2185 (0.0654) 3.342 < 0.005 < 0.05 0.07
logm light 0.0977 (0.0398) 2.454 < 0.05
loglO dissolved phosphorus 0.1078 (0.071) 1.519 0.13

Cryptophytes
NS

Cyanobacteria
Constant 1.1303 (0.0773) 14.625 < 0.001 0.09 0.04
loglO light -0.0935 (0.0470) -1.988 0.05
loglo dissolved phosphorus -0.1254 (0.084) -1.494 0.14

Diatoms
Constant 0.0793 (0.0285) 2.778 < 0.01 < 0.05 0.056
loglo light 0.0419 (0.0186) 2.248 < 0.05

Dinoflagellates
NS

Euglenoids
Constant 0.04439 (0.007996) 5.552 < 0.001 < 0.05 0.08
loglo light —0.01364 (0.005217) -2.615 < 0.05

Greens
NS

 

tion are necessary for a DCM to persist (Fee 1976), while the light and nutrient
gradients may control the vertical position of the peak (Fee 1976, Klausmeier and
Litchman 2001). We considered how these hypotheses may contribute to not just
formation of DCMs but the variation in DCM vertical positions as well, and the over-
all variation in phytoplankton vertical distributions across environmental gradients.

Our model (Chapter 2) details how these hypothesized processes should work for a

171

 

Table 4.11: Logistic regression results for whether a lake switches identity of the
dominant species within the water column (by comparing all samples within a water
column) versus the following loglo environmental variables: water column depth,
mixed layer depth, turbulent mixing coefficient, background light attenuation, TP at
the bottom, and TP in the mixed layer. Only relationships from the best model were
included in the table.

 

Coefficient (SE) 2: P—value Poverall
Constant -5.772 (3.364) -1.716 0.086 0.15
loglO water column depth 6.381 (3.400) 1.877 0.06

 

 

particular algal physiology and provides specific predictions that we tested.

4.5.2 Depth of algae

Most of the profiles had peaks in the deep layer indicating that enough light pene-
trated to the deep layer for a peak to form. Consistent with our theoretical predic-
tions, our data show that light availability determines whether or not a peak forms

at the bottom (Figure 4.5).

When considering profiles with only a single peak, multiple regression models
explained much more of the variance (Rgdj. = 0.8) than the models of multiple peaks
(Rgdj. = 0.35) or the global maximum (Rgdj. = 0.39). In addition, more variables
predict peak depths for single peak profiles. For single peaks, five environmental
variables have significant effects, including total phosphorus. Fewer environmental
variables can explain the variation in algal distribution in profiles with multiple peaks

(three variables) or for the global maximum (four variables), and it appears that
nutrients are unimportant.

A statistical model that considers all of the multiple peaks, or ignores all but one,
has decreased predictive power for vertical distribution. This is likely because each
peak alters resource conditions for all the other peaks due to nutrient depletion and

shading. In addition, peaks can be composed of different species and interactions

172

 

 

between them may alter their vertical distribution. These modified distributions
based on species interactions are a common phenomenon, which may be driven by
habitat partitioning in the aquatic environment (Werner and Hall 1977, Werner et al.

1983, Leibold 1991) and especially among phytoplankton (Carney et al. 1988).

Relationships between depth of the single peaks and environmental variables gen-
erally agree with model predictions. Greater background light attenuation should
result in a shallower peak due to increased light limitation. Support for this predic-
tion is shown in Figure 4.70. As predicted, greater turbulent diffusion results in a a
shallower peak because the increases in turbulent diffusion may have increased nu-
trient flux from near the sediments to the biomass peak (Figure 4.7d). As predicted,
a deeper water column results in a deeper peak, likely because the nutrient source is
deeper (Figure 4.7b).

However, effects of two of the predictor variables differ in directionality from our
predictions. We predicted mixed layer depth to have no effect on depth of the peak,
however, depth of the peak was deeper with greater mixed layer depths. It is possible
that this result is more of an artifact of the definition of peaks (a peak in this analysis
must be below the mixed layer) but the global fluorescence maximum model also
shows that a deeper mixed layer depth results in a deeper peak (Table 4.2). Another
possibility is that peaks are composed of actively motile species that preferentially
seek lower turbulent mixing locations (Franks 2001, Incze et al. 2001) or species that

sink to fluid of equal density (Condie and Bormans 1997) below the mixed layer.

Additionally, total phosphorus in the mixed layer had a different effect on peak
depth than predicted. Peaks are deeper with increasing TP in the mixed layer. We
predicted increasing nutrient input to the mixed layer to move the depth of the peak
shallower because biomass in the mixed layer increases and shades the biomass in the
peak in the deep layer. However, there may be little mixed-layer biomass because

the biomass there is limited by another factor such as grazing or washout. In these

173

 

 

 

cases, excess nutrients may be available to the deep layer peak that is deeper and
hence closer to the nutrient source at the bottom than predicted because of the extra
mortality above it. More data is needed from other lakes to determine the robustness

of this unexpected pattern (next paragraph).

Although it is likely that different factors may have different relative importance
between lakes, a handful of environmental variables can explain much of the variation
in the single peak depth distribution. Other studies have shown similar variables to
be important. Barbiero and Tuchman (2001) show that light attenuation regulates
DCMs in the Laurentian Great Lakes. Longhi and Beisner (2009) also show shallower
peaks with greater background attenuation. However, they show the opposite trend
for TP in the mixed layer. In their data, the peak occurs shallower with more TP in
the mixed layer. Their result is also more similar to Lake Geneva, where a reduction
in phosphorus inputs to the surface led to a deepening of the depth of the DCM
(Anneville and Leboulanger 2001).

Other studies have shown factors other than what we considered here to be impor-
tant in determining depth distribution. Peaks have been shown to track the sulfide-
oxygen boundary (Gasol et al. 1992). Grazing can also shape or limit the upper
boundary of the peak and peaks have also been shown to track the silica gradient
(Barbiero and McN air 1996). Previous studies have also shown that the depth of the
peak roughly tracks the light level that is 1% of the surface irradiance. However, the
1% light level, and hence the depth of the 1% light level often used to delineate the
euphotic zone, can fluctuate significantly due to differences in surface irradiance and
processes operating within the water column so it is not clear why algae would follow

this light level (Banse 2004).

174

 

Eff—j

 

4.5.3 Amount and distribution of biomass

Total biomass can be determined by a number of factors (e.g. Lampert et al. 1986,
Schindler 1977, Diehl et al. 2002), but results support some model predictions. Total
biomass showed a positive relationship with water column depth (Figure 4.8a), more
likely the result of integrating biomass over the entire water column. Total biomass
showed a positive relationship with background light attenuation (Figure 4.8a) but we
predicted background light attenuation to decrease or have no effect on biomass. If it
merely had no effect, then a conclusion might be that biomass was never really light-
limited. However, because it increased, another explanation is needed. It is possible
that another variable, such as an essential or supplemental resource is correlated with

background attenuation that we did not consider in the model.

Deep layer biomass shows some predicted relationships with environmental vari-
ables. Biomass in the deep layer decreased with mixed layer depth (Figure 4%)
in line with model predictions, but it increased with water column depth (Figure
4.9b), which is opposite of what we predicted. Relationships with water column
depth and mixed layer depth could be an artifact, however, because they delineate
the boundaries for integrating deep layer biomass. Background light attenuation in-
creased deep layer biomass (Figure 4.9d) and we predicted it should have no effect
or decrease biomass but this could be for the same reasons background attenuation

impacted total biomass.

Mixed layer biomass followed many of the predicted relationships with environ-
mental variables. Biomass in the mixed layer increased with total phosphorus in the
mixed layer (Figure 4.10b). Biomass in the mixed layer increased with mixed layer
depth (Figure 4.10a), which we predicted it could do depending on the state of the
population, although this could be an artifact of integrating over the mixed layer

to calculate mixed layer depth. Background light attenuation increased mixed layer

175

 

biomass (Figure 4.9d) and we predicted it should have no effect or decrease it, but
once again, this could be for the same reasons background attenuation impacted total

biomass.

4.5.4 Multiple peaks and the environment

We frequently found multiple algal peaks within a water column. How can multiple
peaks exist? For a single species in opposing gradients of nutrients and light, theory
predicts a single best location in the water column (Klausmeier and Litchman 2001).
However, multiple peaks can be caused by multiple nutrient sources (Ch. 2), but for
this to be the case, all peaks but the deepest one must be nutrient limited. A plot
of light versus nutrient conditions at the peaks should yield little scatter along the
nutrient axis, resulting in a vertical regression line. However, a plot of light versus
nutrient conditions show a lot of variation in nutrient and light levels and exhibits
a strong negative relationship between the light and nutrient levels (Figure 4.11).
A nutrient-light competitive tradeoff has been proposed to explain coexistence of
species in well-mixed (Huisman and Weissing 1995), poorly-mixed (Huisman et al.
2006), and stratified environments (Yoshiyama et al. 2009). Some empirical evidence
exists for such a tradeoff (Carney et al. 1988, Strzepek and Harrison 2004, but see
Passarge et al. 2006) making its existence likely (Litchman and Klausmeier 2008).
The negative relationship between light and nutrient levels at peaks is consistent with
the hypothesis of a nutrient-light tradeoff in species that comprise the peaks. Our
community composition data demonstrated that indeed, separate peaks within a lake
are dominated by different species. We suggest that the changes in species dominance
between peaks are partly due to a tradeoff in competitive abilities for nutrients and
light.

We found that multiple peaks can be present simultaneously. The number of peaks

is determined by physical space, the strength of the light gradient, and the strength

176

 

of the nutrient gradient (Figure 4.12). The amount of physical space available for
peaks to form may be analogous to general species-area relationships (Smith et al.
2005), and likely there is some minimal amount of space required for multiple peaks
to exist. However, Yoshiyama et al. (2009) predict peaks to attract one another and
we have also observed multiple peaks within very small (< 1 m) depth spans. Two
measures of resource heterogeneity also acted to increase number of peaks, which is
consistent with the heterogeneity hypothesis of maintaining diversity (Stevens and
Carson 2002). Increasing background light attenuation, a measure of the strength of
the light gradient, also acts to increase the number of peaks. Increasing the change
in total phosphorus with depth in the deep layer also acts to increase the number
of peaks. However, this phosphorus gradient is correlated with phosphorus supply.
Phosphorus supply was significant in an alternative model, ultimately making it dif-
ficult to distinguish between the heterogeneity and energy hypothesis (Stevens and

Carson 2002) for nutrients.

4.5.5 Community

Somewhat surprisingly, species diversity did not differ within the water column even
though strong environmental gradients existed and the mixed layer and the DCM are
unique niches that are physically isolated from one another. To our knowledge, this
is the first study that compares phytoplankton species diversity at different depths
in a water column. Although diversity was not different between the mixed layer
and main DCM, the environmental variables that explain diversity differ between
these two locations. Both locations had significant variables that describe in—situ
conditions. For example, total phosphorus in the mixed layer affected mixed layer
diversity but not DCM diversity and light at the bottom of the mixed layer (supply
rate to deep layer) explained DCM diversity but not mixed layer diversity (Table 4.7).

Although it may be expected that communities within a lake are more similar to

177

 

one another than communities across lakes, with large landscape-level driven differ-
ences in environmental conditions between lakes, discrete depths within a lake were
often quite dissimilar to one another (Fig. 4.14a) relative to overall dissimilarity (Fig.
4.14b). Although a relatively small suite of species has been found in DCMs (Padisak
2004), we have shown that communities inhabiting the DCM niche are as dissimilar
from one another as communities in mixed layers (Fig. 4.14c,d). Keeping this in
mind, and that species diversity did not differ between the mixed layer and DCM,
it is perhaps not surprising that mixed layer and DCM communities varied similarly
across lakes (Fig. 4.14e). Two environmental variables, acting in opposition to one
another, may have been related to the dissimilarity between mixed layer and DCM
communities (Table 4.8, Fig. 4.15a,b). Although the overall model is not significant
(P > 0.05), the trends in this best model are worth discussing. For example, the
difference between light and nutrient effects indicates that light may be more impor-
tant for determining which community can exist in the deep layer while nutrients
may be abundant enough in the water column that they become an important axis

of community divergence.

Some taxonomic groups are known in particular for forming DCMs (e.g. flagel-
lates) and some groups are known in particular for growing in the mixed layer or
forming surface blooms (e.g. cyanobacteria, green algae) but we found these groups
in both niches (Fig. 4.16). Dominance of taxonomic groups varied as much in DCMs
as in the mixed layer. Often, a single taxonomic group dominated at all depths of a
lake. This result may indicate that our model that considers an aggregate community

may be a good approximation in some situations.

Across lakes, the relationships between taxonomic group relative abundance and
environmental variables (Table 4.9) mostly conform to understood patterns in tax-
onomic group abundances (Reynolds 1984). For example, cyanobacteria increased

with Daphnia abundance because they are not grazed as heavily by Daphnia as some

178

 

‘\ _—11v '3

other groups (Sarnelle 1992) and green algae decreased with background attenuation
because they often have a high light competitive strategy (Richardson et al. 1983,
Schwaderer et al. submitted). Some caution is warranted about concluding too much
from the taxonomic group abundance across lakes because lakes with more samples
are weighted heavier in the analyses. Nonetheless, because we are documenting the
across-lake and within-lake community structure, we considered all (sampled) depths
that have peaks in biomass. These results shed light on communities in the whole
lake (Longhi and Beisner 2009) rather than just the mixed layer (Duarte and Canfield
1992, Watson et al. 1997).

Taxonomic groups showed some correlation with local conditions of light and
dissolved phosphorus in a lake (Table 4.10). Although it does not fully explain the
vertical zonation observed (Fig. 4.16), there is indication that different taxonomic
groups have different requirements and impacts on their environment. Cyanobacteria
and euglenoids actually declined in the community with increasing light possibly due
to competition or a physiological or ecological tradeoff that allows them to grow in
low light conditions. Chrysophytes and diatoms increased in the community with
increasing light. Although the dissolved phosphorus term was not significant (P >
0.05) in any of the models, it was in the best model for two groups. The amount of
dissolved phosphorus may be a better measure of the impact on the resource levels,

rather than the requirements (Tilman 1982).

A single niche, such as the mixed layer or a DCM within a lake, is usually rather di-
verse in species richness but almost always heavily dominated by a single species. The
identity of that dominant species changed with depth in most of the lakes (Appendix
Table), begging the classic community ecology question, why do we find different

species across habitats?

We measured whether species were found in different habitats by whether the

dominance switched within the water column (mixed layer to DCM or DCM to DCM)

179

 

 

and showed that the only predictor of dominance switch was water column depth.
Water column depth can determine the number of peaks due to the effect it has on
the deep layer span, which was shown to be a significant predictor. Thus with more

peaks, the switch in dominance is more likely.

It is difficult to generalize too much about patterns in species abundances with
depth because of the large regional species pool, few samples with the same species
dominating, and whole lake and within lake interacting environmental factors. Nev-
ertheless, it appears that size changes with depth in some genera and that bigger
species tend to be deeper (Appendix Table). Bigger species may be poorer nutrient
competitors (Pasciak and Gavis 1974), have higher sinking rates (Vogel 1994), and/ or
be more resistant to grazing (Sarnelle 1992), resulting in size segregation within the
water column even if they are poorer light competitors (Finkel et al. 2004, Schwaderer
et al. submitted). It also appears that filamentous cyanobacteria are in greater abun-
dance at depth, which is likely because they are good light competitors (Schwaderer
et al. submitted). There appeared to be no real trend in evenness or diversity in
the mixed layer versus DCMs based on the dominant (> 5% of community) species,

either can be much greater than other (Appendix Table).

One final interesting result is that several species appear to exhibit a bimodal dis-
tribution within the water column. For example, a Chroococcus species was abundant
at a shallow depth, disappeared at a deeper depth, and then reappeared at an even
deeper depth in Lime lake and Fine lake. Theory predicts that for this to occur, either
the limiting environmental factor has to be the same in both locations or the species
must be phenotypically different in each location (simulation results not shown). It
is likely that some of these morphologically identical species are actually different
physiologically so our resolution of classification could not distinguish between these
cryptospecies or different strains of the same species. In such a case, closely related

Species may partition the vertical niche more than distantly related species, analagous

180

 

 

to divergent selection at the tips of a phylogenetic tree rather than deeper in the tree

(Losos et al. 2003).

4.5.6 Future work

Environmental filtering of phytoplankton between lakes and then phytoplankton sort-
ing within lakes may not exist in a strict hierarchy due to interactions with the scale
of taxonomic resolution. Scale is important (Levin 1992) for examining community
structure across landscapes of lakes and with depth within lakes. Species within
each taxonomic group we considered can be very different (Reynolds 1984), so these
broad taxonomic groups can overlap in niche space. This suggests that the division
of niche space across and within lakes can happen at the species level. Unfortunately,
species-specific environmental niche data is sparse, both in this study due to the large
regional species pool and turnover between lakes and depths, and in other studies,
so it is diflicult to describe species-level spatial distribution patterns let alone ascribe
these patterns to environmental conditions. To further complicate matters, environ-
mental conditions are mediated by the interactions of species themselves. Eiture
research should consider this sorting of different taxonomic resolutions at different
spatial scales in the environment (landscape versus within a lake) and with explicit
consideration of the feedbacks on the environment created by different phytoplank-
ton. This also highlights the importance of examining traits rather than taxonomic
classifications. A community aggregated light-competitive—ability trait was not re-
lated to light conditions for communities in this study (results not shown) but more
species-specific trait data are needed to examine relationships between phytoplankton

traits and the environment.

181

 

 

4.5.7 Further importance and conclusions

Nutrient concentration measured at the sediment interface was a better predictor for
many biotic variables than nutrient concentration measured in the mixed layer, as
indicated by presence and absence of these variables in the best models. Specifically,
total biomass and mixed layer diversity, as well as deep layer biotic variables such as
deep layer biomass, diversity and number of peaks had total phosphorus measured
at the bottom in their best models. Yet, most studies do not measure this variable,
rather, they measure total phosphorus at the surface. If a researcher is interested
in explaining population and community structure, the results of this study indicate
that nutrients at the bottom of the water column may be a better measure of potential
ecosystem processes. This highlights the importance of studying spatial coupling in
ecosystems, as some locations may be more tightly coupled with distant locations
than their local environment.

This study addresses crucial ideas in ecology, including, understanding and pre-
dicting spatial distributions of organisms, matching the strategies of the organisms
with their environments, and demonstrating how biological and physical components
of an ecosystem are coupled, using the plankton community as an example. Climate
change strongly affects physical processes operating in lakes in the Great Lakes region
(Kling et al. 2003) and worldwide (Fee et al. 1996, Schindler 1997, Livingstone 2003,
O’Reilly et al. 2003, Verburg et al. 2003). Understanding how physical processes
operating in lakes impact plankton communities is imperative to predict how future

climate change may alter freshwater ecosystems.

182

 

4.6 Appendix

183

 

Table 4.12: Appendix Table of dominant species for all samples. Shown are relative
abundances for species densities that are > 5% of the total community density of a
sample.

Lake Date Depthlm] Taxonomic Species Abund.
Brooks 19-Sep Integrated Cyanobacteria Chroococcus small (cells) 0.47
Cyanobacteria Aphanocapsa (small colony) 0.19
Diatom Cyclotella michiganiana (sm) 0.07
Green Oocystis (cells) 0.06
Brooks l9-Sep 3 Cyanobacteria Aphanocapsa (small colony) 0.43
Cyanobacteria Chroococcus small (cells) 0.22
Cyanobacteria Anabaena (cells) 0.06
Chrysophyte Chrysochromulina 0.06
Green Oocystis (cells) 0.05
Little Long 6-Sep Integrated Green Coccoid Green Sum 0.43
Diatom Cyclotella michiganiana (sm) 0.23
Cyanobacteria Aphanocapsa incerta 0.08
Green Green Flagellate 0.06
Little Long 6-Sep 4 Chrysophyte Chrysophyte ~5-7um 0.54
Diatom Cyclotella michiganiana (sm) 0.20

Cyanobacteria Aphanocapsa (small colony) 0.06

Little Long 6-Sep 8.5 Chrysophyte Chrysochromulina 0.25
Diatom Cyclotella michiganiana (sm) 0.17
Chrysophyte Chrysophyte ~5-7um 0.16
Cyanobacteria Chroococcus small (cells) 0.10
Cyanobacteria Aphanocapsa (small colony) 0.09
Green Oocystis (cells) 0.06
Big Fisher 26-Sep Integrated Cyanobacteria Chroococcus small (cells) 0.49
Dinoflagellate Dinoflagellate, most w/o shell: 0.10
Diatom Cyclotella michiganiana (sm) 0.08
Cyanobacteria Aphanocapsa incerta 0.07
Little Glen 26-Sep Integrated Chrysophyte Chrysochromulina 0.29
Cyanobacteria Chroococcus small (cells) 0.21
Cyanobacteria Aphanocapsa (small colony) 0.14
Cryptophyte Rhodomonas minuta 0.07
Unidentified Rod shaped cells 0.07

184

Table 4.12 continued
Lake Date Depthlm] Taxonomic

Little Fisher 26-Sep Integrated Chrysophyte
Diatom
Cyanobacteria
Cyanobacteria
Green

Warner 13-Sep Integrated Cyanobacteria
Cyanobacteria
Cyanobacteria

Warner 13-Sep 10.25 Cyanobacteria
Cyanobacteria
Chrysophyte
Cryptophyte
Cyanobacteria
Cryptophyte

Warner 13-Sep 11.75 Green
Cyanobacteria
Cyanobacteria

Pine l3-Sep Integrated Cyanobacteria
Chrysophyte

Cyanobacteria

Pine l3-Sep 9 Cyanobacteria
Cyanobacteria

Little Mill 5-Sep Integrated Cyanobacteria
Chrysophyte
Chrysophyte

Species
Chrysochromulina

Cyclotella michiganiana (sm)

Chroococcus med (cells)
Aphanocapsa (small colony)
Green F lagellate

Chroococcus small (cells)
Chroococcus med (cells)
Chroococcus large (cells)

Aphanocapsa (small colony)
Chroococcus small (cells)
Chrysochromulina
Rhodomonas minuta
Chroococcus med (cells)
Cryptomonas

Synechococcus
Pseudanabaena (cells)
Chroococcus small (cells)

Chroococcus small (cells)
Chrysochromulina
Aphanocapsa (small colony)

Chroococcus small (cells)
Aphanocapsa (small colony)

Chroococcus small (cells)
Chrysophyte ~5-7um
C hrysochromulina

Cyanobacteria Aphanocapsa (small colony)

Cryptophyte
Cyanobacteria

185

Rhodomonas minuta
Anabaena (cells)

Abund.

0.43
0.14
0.13
0.05
0.05

0.57
0.11
0.06

0.32
0.16
0.10
0.09
0.06
0.05

0.37
0.27
0.18

0.67
0.07
0.05

0.50
0.19

0.31
0.14
0.11
0.07
0.06
0.06

 

Table 4.12 continued

Lake
Little Mill

Big Glen

Big Glen

Shaw

Baldwin

Baldwin

Baldwin

Date

S-Sep 9

Depthlm] Taxonomic

Cyanobacteria
Green

Species
Chroococcus small (cells)
coccoid green clusters

Cyanobacteria Aphanocapsa (small colony)

Cyanobacteria
Cyanobacteria
Diatom

Chrysophyte

26-Sep Integrated Green

26-Sep 17

Cyanobacteria
Diatom
Chrysophyte
Cryptophyte

Chroococcus med (cells)
Pseudanabaena (strands)
F ragilaria 'crotonensis
Chrysochromulina

Coccoid Green <3um
Chroococcus small (cells)
Cyclotella michiganiana (sm)
Ochromonas

Rhodomonas minuta

Cyanobacteria Aphanocapsa incerta

Green
Cyanobacteria

Chrysophyte
Chrysophyte

Oocystis (cells)
Filamentous

Chrysochromulina
Chrysophyte ~5-7um

Cyanobacteria Aphanocapsa (small colony)

Green
Chrysophyte

Diatom
Cyanobacteria

12-Sep Integrated Cyanobacteria

Cyanobacteria
Cyanobacteria

Chrysophyte

21 -Sep Integrated Cyanobacteria

21-Sep 8

21-Sep 12.5

Chrysophyte

Oocystis (cells)
Ochromonas

Cyclotella comta (large)
Chroococcus small (cells)

Chroococcus small (cells)
Aphanocapsa (small colony)
Chroococcus med (cells)
Chrysochromulina

Chroococcus small (cells)
Chrysochromulina

Cyanobacteria Aphanocapsa (small colony)

Cyanobacteria

Chroococcus small (cells)

Cyanobacteria Aphanocapsa (small colony)

Cyanobacteria
Cyanobacteria
Cyanobacteria

186

Pseudanabaena (cells)
Chroococcus small (cells)
Aphanocapsa (small colony)

Abund.

0.23
0.16
0.06
0.06
0.06
0.05
0.05

0.15
0.14
0.13
0.09
0.08
0.08
0.07
0.05

0.23
0.20
0.08
0.07
0.06
0.06
0.05

0.64
0.07
0.06
0.05

0.67
0.06
0.05

0.65
0.07

0.62
0.18
0.07

Table 4.12 continued
Date

Lake

Wintergreen 4-Sep

Wintergreen 4-Sep

Wintergreen 4-Sep

Pleasant

Pleasant

Baker

Baker

Baker

0

3

4.25

Depthlm] Taxonomic

Cyanobacteria
Cyanobacteria

Cyanobacteria

Cyanobacteria
Cyanobacteria

5-Sep Integrated Chrysophyte

S-Sep

12-Sep

12-Sep

12-Sep

4.75

5.75

Cyanobacteria
Cyanobacteria
Green

Chrysophyte

Cyanobacteria

Chrysophyte

Cyanobacteria
Cyanobacteria

Cyanobacteria
Cyanobacteria
Cyanobacteria

Cyanobacteria
Cyanobacteria
Chrysophyte

Cyanobacteria
Cyanobacteria
Cyanobacteria

Cloverdale ll-Sep Integrated Cyanobacteria

Cloverdale “-Sep

4

Cyanobacteria
Cyanobacteria

Chrysophyte
Cyanobacteria

Cyanobacteria
Cyanobacteria

187

Species
Woronichinia # in colony
Woronichinia

Woronichinia

Worom'chinia
Woronichinia # in colony

Chrysophyte ~8um
Aphanocapsa (small colony)
Microcjystis (colony, cells)
Staurastrum

Chrysophyte ~8um
Aphanocapsa (small colony)
Chrysophyte ~5-7um in col.

Woronichinia # in colony
Woronichinia

Woronichim'a # in colony
Woronichinia
Aphanocapsa (small colony)

Woronichinia # in colony
Woronichinia

Chrysophyte ~S-7um
Merismopedia (small cells)
Aphanizemenon
Aphanocapsa (small colony)

Woronichinia

Aphanocapsa (small colony)
Woronichinia # in colony
Chrysophyte ~5-7um

Woronichinia # in colony
Woronichinia
A phanizomenon

Abund.
0.58
0.28

0.92

0.84
0.10

0.45
0.20
0.12
0.06

0.62
0.12
0.06

0.50
0.29

0.51
0.19
0.13

0.34
0.15
0.08
0.08
0.07
0.06

0.44
0.18
0.09
0.07

0.35
0.25
0.17

 

 

Table 4.12 continued

Lake

Date Depthlm] Taxonomic Species

Cloverdale ll-Sep 5 Cyanobacteria Aphanizomenon

Bassett

Bassett

Bassett

IIess

IIess

Lawrence

Lawrence

Cyanobacteria Microcystis (colony, cells)
Cyanobacteria Woronichinia
Cyanobacteria Aphanocapsa (small colony)

12-Sep Integrated Cyanobacteria Apham'zomenon
Cyanobacteria Planktolyngbya (straight)
Chrysophyte Chrysophyte ~<5 um

l2-Sep 6 Green Sphaerocystis (cells, colony)
Chrysophyte Chrysophyte ~<5 urn
Green C hlamydomonas

Cyanobacteria Aphanocapsa (small colony)
Unidentified long thin transparent rod
Cyanobacteria Aphanizomenon
Cyanobacteria Plankrothrix

12-Sep 7 Chrysophyte Chrysophyte ~<5 um
Unidentified long thin transparent rod
Cyanobacteria Cyanobium
Cyanobacteria Plankrothrix
Cryptophyte Rhodomonas minuta

19-Sep Integrated Cyanobacteria Aphanocapsa (small colony)
Cyanobacteria Chroococcus small (cells)
Cyanobacteria Planktolyngbya (straight)

19-Sep 5.5 Cyanobacteria Aphanocapsa (small colony)
Cyanobacteria Chroococcus small (cells)

4-Sep Integrated Cyanobacteria Woronichinia # in colony
Cyanobacteria Woronichinia
Chrysophyte Tribonema

Chrysophyte Chrysophyte ~5-7um

4-Sep 9.5 Cyanobacteria Aphanocapsa (small colony)

Chrysophyte Chrysophyte ~5-7um in colon:

188

Abund.

0.48
0.16
0.13
0.08

0.57
0.18
0.11

0.30
0.24
0.11
0.10
0.08
0.05
0.05

0.33
0.24
0.13
0.10
0.05

0.71
0.14
0.06

0.55
0.24

0.36
0.23
0.16
0.06

0.68
0.13

 

Table 4.12 continued
Date

Lake
Lawrence

Sherman

Sherman

Sherman

Long

Long

Long

4-Sep

Depthlm] Taxonomic
1 1.5

Cyanobacteria
Cyanobacteria
Cyanobacteria
Cyanobacteria
Cyanobacteria

lO-Sep Integrated Cyanobacteria

lO-Sep

lO-Sep

8

8.5

Green

Chrysophyte

Cyanobacteria
Green
Cyanobacteria
Chrysophyte

Cyanobacteria

Green
Green
Cyanobacteria
Cyanobacteria

Chrysophyte

12-Sep Integrated Cyanobacteria

12-Sep

12-Sep

7.5

8.5

Cyanobacteria
Cyanobacteria
Cyanobacteria

Cyanobacteria
Cyanobacteria
Cyanobacteria
Cyanobacteria
Cyanobacteria

Cyanobacteria

Cyanobacteria
Cyanobacteria

189

Species
Aphanocapsa large cells (001.)
Aphanocapsa (small colony)
C yanobacterium
Aphanocapsa large cells (cells
Arthrospira

Worom'chim'a # in colony
Sphaerocystis (cells, colony)
Chrysophyte ~<5 um

Worom'chinia # in colony
Sphaerocystis (unicells)
Aphanocapsa (small colony)
Chrysophyte ~<5 urn
Chroococcus small (cells)

Staurastrum
Sphaerocystis (unicells)
Woronichinia
Chroococcus small (cells)
Chrysophyte ~<5 um

Woronichinia # in colony
Aphanocapsa large cells (001.)
Woronichinia

Aphanocapsa (small colony)

Woronichinia # in colony
Aphanocapsa (small colony)
Chroococcus med (cells)
Chroococcus small (cells)
Woronichinia

Woronichinia # in colony
Aphanocapsa (small colony)
Chroococcus med (cells)

Abund.

0.43
0.14
0.14
0.12
0.05

0.50
0.16
0.06

0.61
0.12
0.06
0.05
0.05

0.30
0.15
0.13
0.10
0.05

0.30
0.27
0.10
0.05

0.41
0.25
0.11
0.08
0.07

0.44
0.25
0.09

 

Table 4.12 continued
Date

Lake
Lawrence

Sherman

Sherman

Sherman

Long

Long

Long

4-Sep

Depthlm] Taxonomic
1 1.5

Cyanobacteria
Cyanobacteria
Cyanobacteria
Cyanobacteria
Cyanobacteria

lO-Sep Integrated Cyanobacteria

lO-Sep

lO-Sep

8

8.5

Green

Chrysophyte

Cyanobacteria
Green
Cyanobacteria
Chrysophyte
Cyanobacteria

Green
Green
Cyanobacteria
Cyanobacteria

Chrysophyte

12-Sep Integrated Cyanobacteria

12-Sep

12-Sep

7.5

8.5

Cyanobacteria
Cyanobacteria
Cyanobacteria

Cyanobacteria
Cyanobacteria
Cyanobacteria
Cyanobacteria
Cyanobacteria

Cyanobacteria

Cyanobacteria
Cyanobacteria

189

Species
Aphanocapsa large cells (col.)
Aphanocapsa (small colony)
C yanobacterium
Aphanocapsa large cells (cells
Arthrospira

Woronichim'a # in colony
Sphaerocystis (cells, colony)
Chrysophyte ~<5 um

Woronichinia # in colony
Sphaerocystis (unicells)
Aphanocapsa (small colony)
Chrysophyte ~<5 um
Chroococcus small (cells)

Staurastrum
Sphaerocystis (unicells)
Woronichinia
Chroococcus small (cells)
Chrysophyte ~<5 urn

Woronichim'a # in colony
Aphanocapsa large cells (col.)
Woronichinia

Aphanocapsa (small colony)

Woronichinia # in colony
Aphanocapsa (small colony)
Chroococcus med (cells)
Chroococcus small (cells)
Woronichinia

Woronichinia # in colony
Aphanocapsa (small colony)
Chroococcus med (cells)

Abund.

0.43
0.14
0.14
0.12
0.05

0.50
0.16
0.06

0.61
0.12
0.06
0.05
0.05

0.30
0.15
0.13
0.10
0.05

0.30
0.27
0.10
0.05

0.41
0.25
0.11
0.08
0.07

0.44
0.25
0.09

 

Table 4.12 continued

Lake

Long

Lime

Lime

Lime

Lime

Fine

Date Depthlm] Taxonomic

Species

12-Sep 10.25 Cyanobacteria Aphanocapsa (small colony)

Cyanobacteria
Cyanobacteria
Cyanobacteria

Chroococcus small (cells)
Pseudanabaena (strands)
Chroococcus med (cells)

Cyanobacteria Arthrospira

l9-Sep Integrated Cyanobacteria
Chrysophyte
Chrysophyte
Unidentified
Chrysophyte

Cyanobacteria

l 9-Sep 2.5 Chrysophyte
Chrysophyte
Cyanobacteria
Cyanobacteria

19-Sep 5 Chrysophyte
Cyanobacteria
Cyanobacteria
Green
Chrysophyte
Cryptophyte

1 9-Sep 8 Cyanobacteria
Cyanobacteria
Cyanobacteria
Cyanobacteria
Green
Cyanobacteria

5-Sep Integrated Cyanobacteria
Cyanobacteria

Chroococcus small (cells)
Chrysophyte ~<5 um
Chrysophyte ~8um

small unicells (unclassifiable)
Chrysophyte ~5—7um
Gomphosphaeria (cells)

Chrysophyte ~8um
Chrysophyte ~<5 um
Gomphosphaeria (cells)
Aphanocapsa (small colony)

Chrysophyte ~<5 um
Aphanocapsa (small colony)
Gomphosphaeria (cells)
Diclyosphaerium (cells)
Chrysophyte ~5-7um
Cryptomonas

Chroococcus small (cells)
Gomphosphaeria (cells)
Pseudanabaena (strands)
Chroococcus med (cells)
Dictyosphaerium (cells)
Aphanocapsa (small colony)

Chroococcus small (cells)
Chroococcus med (cells)

Cyanobacteria Aphanocapsa (small colony)

Chrysophyte

Green

Chrysophyte ~<5 urn
Sphaerocystis (cells, colony)

Cyanobacteria Aphanothece (small colony)

190

Abund.

0.36
0.21
0.10
0.08
0.06

0.30
0.22
0.09
0.08
0.07
0.05

0.59
0.13
0.07
0.06

0.21
0.20
0.12
0.11
0.07
0.05

0.20
0.18
0.15
0.13
0.12
0.07

0.34
0.15
0.10
0.07
0.06
0.06

Table 4.12 continued

Lake Date Depthlm] Taxonomic Species Abund.
Fine S-Sep 6.5 Cyanobacteria Microcystis (colony, cells) 0.55
Cyanobacteria Aphanocapsa (small colony) 0.15

Cyanobacteria Aphanocapsa large cells (001.) 0.07

 

Fine 5-Sep 7.25 Cyanobacteria Aphanocapsa (small colony) 0.23
Cyanobacteria Microcystis (colony, cells) 0.15
Cyanobacteria Woronichinia # in colony 0.15
Cyanobacteria Aphanocapsa large cells (ml) 0.11
Cyanobacteria Chroococcus small (cells) 0.07
Bristol S-Sep Integrated Cyanobacteria Microcystis (colony, cells) 0.53
Cyanobacteria Aphanocapsa (small colony) 0.09
Cyanobacteria Woronichinia # in colony 0.09
Cyanobacteria Aphanocapsa large cells (001.) 0.06
Chrysophyte Chrysophyte ~<5 um 0.06
Bristol 5-Sep 8.5 Cyanobacteria Worom'chinia # in colony 0.42
Cyanobacteria Aphanocapsa (small colony) 0.14
Chrysophyte Chrysophyte ~<5 um 0.11
Chrysophyte Chrysophyte ~5-7um 0.05
Gun 24-Sep Integrated Cyanobacteria Aphanocapsa large cells (ml) 0.29
Cyanobacteria Aphanocapsa (small colony) 0.23
Chrysophyte Chrysophyte ~<5 um 0.18
Cyanobacteria Chroococcus small (cells) 0.07
Gun 24-Sep 6.5 Cyanobacteria Aphanocapsa (small colony) 0.24
Cyanobacteria Chroococcus small (cells) 0.20
Chrysophyte Chrysophyte ~<5 urn 0.16
Cyanobacteria Aphanocapsa large cells (ml) 0.12
Gun 24-Sep 13.5 Cyanobacteria Chlorogloea 0.22
Cyanobacteria C yanobacterium 0.21
Cyanobacteria Chroococcus small (cells) 0.18
Cyanobacteria Aphanocapsa (small colony) 0.12
Chrysophyte Chrysophyte ~<5 um 0.11
Cyanobacteria Chroococcus med (cells) 0.11

191

Table 4.12 continued

Lake Date Depthlm] Taxonomic Species Abund.
Hogsett 21-Sep Integrated Cyanobacteria Chroococcus small (cells) 0.46
Cyanobacteria Microcystis (medium) 0.37
Hogsett 21-Sep 6.75 Cyanobacteria Chroococcus small (cells) 0.37
Cyanobacteria Aphanocapsa (small colony) 0.16
Chrysophyte Chrysophyte ~<5 um 0.15
Cyanobacteria Microcystis (colony, cells) 0.05
Chrysophyte Chrysophyte ~5-7um 0.05
Hogsett 21-Sep 7.5 Cyanobacteria Aphanocapsa large cells (ml) 0.19
Cyanobacteria Chroococcus small (cells) 0.17
Chrysophyte Chrysophyte ~<5 um 0.15
Cyanobacteria Aphanocapsa (small colony) 0.13
Cyanobacteria Planktothrix 0.08
Cryptophyte Rhodomonas minuta 0.05
Swan l7-Sep Integrated Chrysophyte Chrysophyte ~<5 um 0.31
Cyanobacteria Apham'zomenon 0.25
Cyanobacteria Aphanocapsa (small colony) 0.18
Chrysophyte Chrysophyte ~5-7um 0.08
Cyanobacteria Planktolyngbya (straight) 0.05
Little Tom 17-Sep Integrated Chrysophyte Chrysochromulina 0.51
Cyanobacteria Aphanocapsa (small colony) 0.17
Cyanobacteria Chroococcus small (cells) 0.12
Spring 24-Sep Integrated Cyanobacteria Pseudanabaena (strands) 0.29
Chrysophyte Chrysochromulina 0.18
Cyanobacteria Planktolyngbya (straight) 0.08
Cyanobacteria Aphanocapsa (small colony) 0.07
Cyanobacteria Planktolyngbya (curved) 0.07
Donnell 21-Sep Integrated Cyanobacteria Chroococcus small (cells) 0.69
Chrysophyte Chrysochromulina 0.09
Cyanobacteria Aphanocapsa (small colony) 0.06
Donnell 21-Sep 4 Cyanobacteria Chroococcus small (cells) 0.71
Cyanobacteria Aphanocapsa (small colony) 0.09
Chrysophyte Chrysochromulina 0.08

192

 

Table 4.12 continued

Lake Date Depthlm] Taxonomic Species

Gravel 21-Sep Integrated Cyanobacteria Chroococcus small (cells)
Cyanobacteria Chroococcus large (cells)
Chrysophyte Chrysochromulina

Gravel 21-Sep 4.8 Cyanobacteria Chroococcus small (cells)

Cyanobacteria Chroococcus large (cells)
Chrysophyte Chrysochromulina

193

Abund.
0.44
0.24
0.13

0.42
0.31
0.05

Bibliography

194

Bibliography

Anneville, O. and Leboulanger, C. 2001. Long-term changes in the vertical distribu-
tion of phytoplankton biomass and primary production in Lake Geneva: a response

to the oligotrophication. Alti Associazione Italiana Oceanologia Limnologia 14:25—
35.

Arvola, L., Ojala, A., Barbosa, F., and Heaney, S. 1991. Migration behavior of 3
cryptophytes in relation to environmental gradients - an experimental approach.
British Phycological Journal 26:361—373.

Bachmann, R. W. and Canfield, D. E. 1996. Use of an alternative method for
monitoring total nitrogen concentrations in Florida lakes. Hydrobiologia 323:1—8.

Banse, K. 2004. Should we continue to use the 1% light depth convention for esti-
mating the compensation depth of phytoplankton for another 70 years? Limnology
& Oceanography Bulletin 13:49—52.

Barbiero, R. P. and McNair, C. M. 1996. The dynamics of vertical chlorophyll
distribution in an oligomesotrophic lake. Journal of Plankton Research 18:225-
237.

Barbiero, R. P. and Tuchman, M. L. 2001. Results from the US EPA’s biological open
water surveillance program of the Laurentian Great Lakes: II. Deep chlorophyll
maxima. Journal of Great Lakes Research 27:155—166.

Beckmann, A. and Hense, I. 2007. Beneath the surface: Characteristics of oceanic
ecosystems under weak mixing conditions - A theoretical investigation. Progress in
Oceanography 75:771—796.

Brown, J. H. 1984. On the relationship between abundance and distribution of
species. American Naturalist 124:255—279.

Brown, P. N., Byrne, G. D., and Hindmarsh, A. C. 1989. VODE— a Variable-coefficient
ODE Solver. SIAM Journal on Scientific & Statistical Computing 10:1038—1051.

Burnham, K. and Anderson, D., 2002. Model selection and multimodel inference: a
practical information-theoretic approach. Springer Science+Business Media, Inc.

Burrough, P. A. 1981. Fractal dimensions of landscapes and other environmental
data. Nature 294:240—242.

195

Camacho, A. 2006. On the occurrence and ecological features of deep chlorophyll
maxima (DCM) in Spanish stratified lakes. Limnetica 25:453—478.

Carney, H. J., Richerson, P. J ., Goldman, C. R., and Richards, R. C. 1988. Seasonal
phytoplankton demographic-processes and experiments on interspecific competi-
tion. Ecology 69:664—678. -

Carpenter, S. R. 1996. Microcosm experiments have limited relevance for community
and ecosystem ecology. Ecology 77:677-680.

Carpenter, S. R., Frost, T. M., Heisey, D., and Kratz, T. K. 1989. Randoomized inter-
vention analysis and the interpretation of whole-ecosystem experiments. Ecology
70:1142—1152.

Carpenter, S. R. and Kitchell, J. F. 1987. The temporal scale of variance in limnetic
primary production. American Naturalist 129:417—433.

Christensen, D. L., Carpenter, S. R., and Cottingham, K. L. 1995. Predicting chloro-
phyll vertical-distribution in response to epilimnetic nutrient enrichment in small
stratified lakes. Journal of Plankton Research 17:1461—1477.

Clegg, M., Maberly, S., and Jones, R. 2007 . Behavioral response as a predictor of
seasonal depth distribution and vertical niche separation in freshwater phytoplank-
tonic flagellates. Limnology & Oceanography 52:441—455.

Condie, S. A. and Bormans, M. 1997. The influence of density stratification on
particle settling, dispersion and population growth. Journal of Theoretical Biology
187:65—75.

Coon, T. G., Lopez, M., Richerson, P. J., Powell, T. M., and Goldman, C. R. 1987.
Summer dynamics of the deep chlorophyll maximum in Lake Tahoe. Journal of
Plankton Research 9:327—344.

Crumpton, W. G., Isenhart, T. M., and Mitchell, P. D. 1992. Nitrate and organic n
analyses with 2nd—derivative spectroscopy. Limnology And Oceanography 37:907—
913.

Crumpton, W. G. and Wetzel, R. G. 1982. Effects of differential growth and mor-
tality in the seasonal succession of phytoplankton populations in Lawrence Lake,
Michigan. Ecology 63:1729—1739.

Cullen, J. J. and MacIntyre, J. G., 1998. Physiological ecology of harmful algal
blooms, Chapter. Springer-Verlag, Berlin, Heidelberg.

Cullen, J. J ., Reid, F. M. H., and Stewart, E. 1982. Phytoplankton in the surface and
chlorophyll maximum off southern California in August, 1978. Journal of Plankton
Research 4:665—694.

196

 

Demott, W. R. 1982. Feeding selectivities and relative ingestion rates of daphnia and
bosmina. Limnology & Oceanography 27:518—527.

Depinto, J. V. and Verhoff, F. H. 1977. Nutrient regeneration from aerobic decom-
position of green-algae. Environmental Science & Technology 11:371-377.

Diehl, S. 2002. Phytoplankton, light, and nutrients in a gradient of mixing depths:
Theory. Ecology 83:386—398.

Diehl, S., Berger, 3., Ptacnik, R., and Wild, A. 2002.. Phytoplankton, light, and
nutrients in a gradient of mixing depths: Field experiments. Ecology 83:399—411.

Du, Y. and Hsu, S.-B. 2008. Concentration phenomena in a nonlocal quasi-linear
problem modelling phytoplankton II: Limiting profile. SIAM Journal on Mathe-
matical Analysis 40:1441-1470.

Duarte, C. M. and Canfield, D. E. 1992. Patterns in phytoplankton community
structure in florida lakes. Limnology & Oceanography 37:155—161.

Eppley, R. W., Swift, E., Redalje, D. G., Landry, M. R., and Haas, L. W. 1988.
Subsurface chlorophyll maximum in August-September 1985 in the climax area of
the North Pacific. Marine Ecology-Progress Series 42:289—301.

Faith, D. P., Minchin, P. R., and Belbin, L. 1987. Compositional dissimilarity as a
robust measure of ecological distance. Vegetatio 69:57—68.

Falkowski, P. G., Barber, R. T., and Smetacek, V. 1998. Biogeochemical controls
and feedbacks on ocean primary production. Science 281:200—206.

Fee, E. J. 1976. Vertical and seasonal distribution of chlorophyll in lakes of
Experimental-Lakes-Area, Northwestern Ontario implications for primary produc-
tion estimates. Limnology & Oceanography 21:767—783.

Fee, E. J., Hecky, R. E., Kasian, S. E. M., and Cruikshank, D. R. 1996. Effects
of lake size, water clarity, and climatic variability on mixing depths in Canadian
Shield lakes. Limnology & Oceanography 41:912—920.

Fennel, K. and Boss, E. 2003. Subsurface maxima of phytoplankton and chlorophyll:
steady-state solutions from a simple model. Limnology & Oceanography 48:1521—
1534.

Field, C. B., Behrenfeld, M. J., Randerson, J. T., and Falkowski, P. 1998. Pri-
mary production of the biosphere: Integrating terrestrial and oceanic components.
Science 281:237—240.

Finkel, Z. V., Irwin, A. J ., and Schofield, O. 2004. Resource limitation alters the 3/ 4
size scaling of metabolic rates in phytoplankton. Marine Ecology-Progress Series
273:269—279.

197

 

F léder, S. and Sommer, U. 1999. Diversity in planktonic communities: An experimen-
tal test of the intermediate disturbance hypothesis. Limnology & Oceanography
44:1114-1119.

Fogg, G. E. and Thake, B., 1987. Algal cultures and phytoplankton ecology. Univer-
sity of Wisconsin Press.

Franks, P. J. S. 1995. Thin-layers of phytoplankton — a model of formation by near-

inertial wave shear. Deep—Sea Research Part I-Oceanographic Research Papers
42:75—91.

Franks, P. J. S. 2001. Turbulence avoidance: An alternate explanation of turbulence-
enhanced ingestion rates in the field. Limnology & Oceanography 46:959~963.

Garside, C. 1985. The vertical-distribution of nitrate in open ocean surface-water.
Deep—Sea Research Part A- Oceanographic Research Papers 32:723-732.

Gasol, J. M., Garciacantizano, J ., Massana, R., Peters, F., Guerrero, R., and Pedros-
alio, C. 1991. Die] changes in the microstratification of the metalimnetic community
in Lake Ciso. Hydrobiologia 211:227—240.

Gasol, J. M., Guerrero, R., and Pedrosalio, C. 1992. Spatial and temporal dynamics
of a metalimnetic Cryptomonas peak. Journal of Plankton Research 14:1565—1579.

Gervais, F. 1998. Ecology of cryptophytes coexisting near a freshwater chemocline.
Freshwater Biologf 39:61—78.

Gonsiorczyk, T., Casper, P., and Koschel, R. 1998. Phosphorus-binding forms in
the sediment of an oligotrophic and an eutrophic hardwater lake of the Baltic lake
district (Germany). Water Science & Technology 37:51-58.

Gross, H. P., Wurtsbaugh, W. A., Luecke, C., and Budy, P. 1997. Fertilization of
an oligotrophic lake with a deep chlorophyll maximum: Predicting the effect on

primary productivity. Canadian Journal of Fisheries & Aquatic Sciences 5421177—
1189.

Grover, J. P. 2009. Is storage an adaptation to spatial variation in resource availabil-
ity? American Naturalist 173:E44—E61.

Guillard, R. 1975. Culture of phytoplankton for feeding marine invertebrates. Plenum
Pub Corp proceedings.

Hartmann, J., Kunimatsu, T., and Levy, J. K. 2008. The impact of Eurasian dust
storms and anthropogenic emissions on atmospheric nutrient deposition rates in
forested Japanese catchments and adjacent regional seas. Global & Planetary
Change 61:117-134.

198

Hastings, A., Byers, J. E., Crooks, J. A., Cuddington, K., Jones, C. G., Lambrinos,
J. G., Talley, T. S., and Wilson, W. G. 2007. Ecosystem engineering in space and
time. Ecology Letters 10:153—164.

Hays, G. C., Richardson, A. J ., and Robinson, C. 2005. Climate change and marine
plankton. Trends in Ecology & Evolution 20:337—344.

Hodges, B. A. and Rudnick, D. L. 2004. Simple models of steady deep maxima

in chlorophyll and biomass. Deep-Sea Research Part I- Oceanographic Research
Papers 512999—1015.

Holopainen, A. L., Niinioja, R., and Raméi, A. 2003. Seasonal succession, vertical

distribution and long term variation of phytoplankton communities in two shallow
forest lakes in eastern Finland. Hydrobiologia 506:237—245.

Huisman, J. 1999. Population dynamics of light-limited phytoplankton: Microcosm
experiments. Ecology 80:202—210.

Huisman, J., Arrayas, M., Ebert, U., and Sommeijer, B. 2002. How do sinking
Phytoplankton species manage to persist? American Naturalist 159:245—254.

Huisman, J ., Jonker, R. R., Zonneveld, C., and Weissing, F. J. 19990. Competition
for light between phytoplankton species: Experimental tests of mechanistic theory.
Ecology 80:211—222.

Huisman, J ., Sharples, J ., Stroom, J. M., Visser, P. M., Kardinaal, W. E. A., Verspa—
gen, J. M. H., and Sommeijer, B. 2004. Changes in turbulent mixing shift compe-
tition for light between phytoplankton species. Ecology 85:2960—2970.

Huisman, J. and Sommeijer, B. 2002. Maximal sustainable sinking velocity of phy-
toplankton. Marine Ecology-Progress Series 244239—48.

Huisman, J. and Sommeijer, B. 2002. Population dynamics of sinking phytoplank-
ton in light-limited environments: simulation techniques and critical parameters.
Journal of Sea Research 48:83-96.

Huisman, J., T hi, N. N. P., Karl, D. M., and Sommeijer, B. 2006. Reduced mixing
generates oscillations and chaos in the oceanic deep chlorophyll maximum. Nature
439:322—325.

Huisman, J ., van Oostveen, P., and Weissing, F. 19990. Species dynamics in phyto-
plankton blooms: Incomplete mixing and competition for light. American Natu-
ralist 154246—68.

Huisman, J., van Oostveen, P., and Weissing, F. J. 1999c. Critical depth and crit-
ical turbulence: Two different mechanisms for the development of phytoplankton
blooms. Limnology & Oceanography 44:1781—1787.

199

 

Huisman, J. and Weissing, F. J. 1994. Light-limited growth and competition for light
in well-mixed aquatic environments: an elementary model. Ecology 75:507—520.

Huisman, J. and Weissing, F. J. 1995. Competition for nutrients and light in a mixed
water column - a theoretical-analysis. American Naturalist 146:536—564.

Hutchinson, G. E., 1957. A Treatise on Limnology. John Wiley & Sons.

Hutchinson, G. E. 1961. The paradox of the plankton. American Naturalist 95:137—
145.

Incze, L. S., Hebert, D., Wolff, N., Oakey, N., and Dye, D. 2001. Changes in cope-
pod distributions associated with increased turbulence from wind stress. Marine
Ecology—Progress Series 213:229—240.

Jaeger, C. G., Diehl, S., and Emans, M. 2010. Physical determinants of phytoplankton
production, algal stoichiometry, and vertical nutrient fluxes. American Naturalist
175:E51—E104.

Jaeger, C. G., Diehl, S., and Schmidt, G. M. 2008. Influence of water-column depth
and mixing on phytoplankton biomass, community composition, and nutrients.
Limnology & Oceanography 53:2361—-2373.

Jtihnk, K. D., Huisman, J., Sharples, J., Sommeijer, B., Visser, P. M., and Stroom,
J. M. 2008. Summer heatwaves promote blooms of harmful cyanobacteria. Global
Change Biology 14:495—512.

Johnsen, G. H. and Jakobsen, P. J. 1987. The effect of food limitation on vertical
migration in Daphnia-Longispina. Limnology & Oceanography 32:873—880.

Karlsson, J., Bystrfim, P., Ask, J ., Ask, P., Persson, L., and Jansson, M. 2009. Light
limitation of nutrient—poor lake ecosystems. Nature 460:506—509.

Kirk, J. T. O. 1975a. Theoretical-analysis of contribution of algal cells to attenuation
of light within natural-waters. 1. General treatment of suspensions of pigmented
cells. New Phytologist 75:11-20.

Kirk, J. T. O. 1975b. Theoretical-analysis of contribution of algal cells to attenuation
of light within natural-waters. 2. spherical cells. New Phytologist 75:21-36.

Klausmeier, C. A. 1999. Regular and irregular patterns in semiarid vegetation.
Science 284:1826—1828.

Klausmeier, C. A., 2000. Ph.D. thesis, University of Minnesota.

Klausmeier, C. A. and Litchman, E. 2001. Algal games: The vertical distribution
of phytoplankton in poorly mixed water columns. Limnology & Oceanography
46:1998—2007.

200

 

Kling, G. W., Hayhoe, K., Johnson, L. B., Magnuson, J. J., Polasky, 8., Robinson,
S. K., Shuter, B. J., Wander, M. M., Wuebbles, D. J., Zak, D. R., Lindroth, R. L.,
Moser, S. C., and Wilson, M. L. 2003. Confronting climate change in the great lakes
region: impacts on our communities and ecosystems. Union of Concerned Scientists,
Cambridge, Massachusetts, and Ecological Society of America, Washington, DC .

Krause—Jensen, D. and Sand-Jensen, K. 1998. Light attenuation and photosynthesis
of aquatic plant communities. Limnology & Oceanography 43:396—407.

Kunz, T. J. and Diehl, S. 2003. Phytoplankton, light and nutrients along a gradient of

mixing depth: a field test of producer-resource theory. Heshwater Biology 48:1050—
1063.

Laland, K. N., Odling-Smee, F. J ., and Feldman, M. W. 1999. Evolutionary conse-
quences of niche construction and their implications for ecology. Proceedings Of
The National Academy Of Sciences Of The United States Of America 96:10242—
10247.

Lampert, W., Fleckner, W., Rai, H., and Taylor, B. E. 1986. Phytoplankton control
by grazing zooplankton - a study on the spring clear-water phase. Limnology &
Oceanography 31:478—490.

Lampert, W., McCauley, E., and Manly, B. F. J. 2003. Trade-offs in the vertical
distribution of zooplankton: ideal free distribution with costs? Proceedings of the
Royal Society of London Series B-Biological Sciences 270:765—773.

Legendre, P. and Legendre, L., 1998. Numerical Ecology. Elsevier Science B.V.

Leibold, M. A. 1990. Resources and predators can affect the vertical distributions of
zooplankton. Limnology & Oceanography 35:938—944.

Leibold, M. A. 1991. Trophic interactions and habitat segregation between competing
daphnia species. Oecologia 86:510—520.

Leibold, M. A., Holyoak, M., Mouquet, N., Amarasekare, P., Chase, J. M., Hoopes,
M. F., Holt, R. D., Shurin, J. B., Law, R., Tilman, D., Loreau, M., and Gonzalez,
A. 2004. The metacommunity concept: a framework for multi—scale community
ecology. Ecology Letters 72601—613.

Levin, S. A. 1976. Population dynamic-models in heterogeneous environments. An-
nual Review of Ecology and Systematics 7:287—310.

Levin, S. A. 1992. The problem of pattern and scale in ecology. Ecology 73:1943—1967.

Levin, S. A. 1994. Patchiness in marine and terrestrial systems - from individuals
to populations. Philosophical Transactions of the Royal Society of London Series
B—Biological Sciences 343:99—103.

201

 

Levins, R. 1979. Coexistence in a variable environment. American Naturalist 114:765—
783.

Lindholm, T. 1992. Ecological role of depth maxima of phytoplankton. Archiv fiir
Hydrobiologie-Beiheft Ergebnisse der Limnologie 35:33—45.

Litchman, E. and Klausmeier, C. A. 2008. Trait—Based Community Ecology of
Phytoplankton. Annual Review of Ecology, Evolution, and Systematics 39:615—
639.

Livingstone, D. M. 2003. Impact of secular climate change on the thermal structure
of a large temperate central European lake. Climate Change 57:205—225.

Longhi, M. L. and Beisner, B. E. 2009. Environmental factors controlling the vertical
distribution of phytoplankton in lakes. Journal of Plankton Research 31:1195—1207.

Loreau, M., Mouquet, N., and Gonzalez, A. 2003a. Biodiversity as spatial insurance
in heterogeneous landscapes. Proceedings Of The National Academy Of Sciences
Of The United States Of America 100:12765—12770.

Loreau, M., Mouquet, N., and Holt, R. D. 2003b. Meta-ecosystems: a theoretical
framework for a spatial ecosystem ecology. Ecology Letters 6:673—679.

Lorenzen, M. and Mitchell, R. 1973. Theoretical effects of artificial destratification
on algal production in impoundments. Environmental Science & Technology 7:939—
944.

Losos, J. B., Leal, M., Glor, R. E., de Queiroz, K., Hertz, P. E., Schettino, L. R.,
Lara, A. C., Jackman, T. R., and Larson, A. 2003. Niche lability in the evolution
of a Caribbean lizard community. Nature 424:542—545.

Lucas, L. V., Cloern, J. E., Koseff, J. R., Monismith, S. G., and Thompson, J. K.
1998. Does the sverdrup critical depth model explain bloom dynamics in estuaries?
Journal of Marine Research 56:375—415.

Luketina, D. and Imberger, R. 2001. Determining turbulent kinetic energy dissipation
from Batchelor curve fitting. Journal of Atmospheric and Oceanic Technology
18:100—113.

MacArthur, R., 1972. Geographical ecology: patterns in the distribution of species.
Harper & Row.

MacIntyre, S., Flynn, K. M., Jellison, R., and Romero, J. R. 1999. Boundary mixing
and nutrient fluxes in Mono Lake, California. Limnology & Oceanography 44:512—
529.

202

Magnuson, J. J., Webster, K. E., Assel, R. A., Bowser, C. J., Dillon, P. J., Eaton,
J. G., Evans, H. E., Fee, E. J., Hall, R. 1., Mortsch, L. R., Schindler, D. W.,
and Quinn, F. H. 1997. Potential effects of climate changes on aquatic systems:
Laurentian Great Lakes and Precambrian Shield Region. Hydrological Processes

11:825—871.

Mann, K. H. and Lazier, J. R. N ., 1996. Dynamics of marine ecosystems: biological-
physical interacting in the oceans. Blackwell Science.

Marsden, M. W. 1989. Lake restoration by reducing external phosphorus loading -
the influence of sediment phosphorus release. Freshwater Biology 21:139—162.

Mazumder, A., Taylor, W. D., McQueen, D. J., and Lean, D. R. S. 1990. Effects of
fish and plankton on lake temperature and mixing depth. Science 247:312—315.

McCann, K. S., Rasmussen, J. B., and Umbanhowar, J. 2005. The dynamics of
spatially coupled food webs. Ecology Letters 8:513—523.

Moll, R. A. and Stoermer, E. F. 1982. A hypothesis relating trophic status and
subsurface chlorophyll maxima of lakes. Archiv fiir Hydrobiologie 94:425—440.

Monsi, M. and Saeki, T. 1953. On the factor light in plant communities and its
importance for matter production. Japanese Journal of Botany 14:22—52.

Neff, J. C., Ballantyne, A. P., Farmer, G. L., Mahowald, N. M., Conroy, J. L., Landry,
C. C., Overpeck, J. T., Painter, T. H., Lawrence, C. R., and Reynolds, R. L. 2008.
Increasing eolian dust deposition in the western United States linked to human

activity. Nature Geoscience 1:189—195.

Okubo, A., 1980. Diffusion and ecological problems: mathematical models. Springer-
Verlag.

O’Reilly, C. M., Alin, S. R., Plisnier, P. D., Cohen, A. S., and McKee, B. A. 2003. Cli-
mate change decreases aquatic ecosystem productivity of Lake Tanganyika, Africa.
Nature 424:766—768.

Osborn, T. R. 1980. Estimates of the local-rate of vertical diffusion from dissipation
measurements. Journal of Physical Oceanography 10:83—89.

Padisak, J ., 2004. Phytoplankton, in The Lakes Handbook: Limnology and limnetic
ecology, Pages 251-308. Wiley-Blackwell.

Paerl, H. W. 1988. Nuisance phytoplankton blooms in coastal, estuarine, and inland
waters. Limnology & Oceanography 33:823—847.

Pannard, A., Bormans, M., Lefebvre, S., Claquin, P., and Lagadeuc, Y. 2007. Phy-
toplankton size distribution and community structure: influence of nutrient input
and sedimentary loss. Journal of Plankton Research 29:583—598.

203

 

 

Pasciak, W. J. and Gavis, J. 1974. Transport limitation of nutrient uptake in phyto-
plankton. Limnology and Oceanography 19:881—898.

Passarge, J., H01, 8., Escher, M., and Huisman, J. 2006. Competition for nutrients
and light: Stable coexistence, alternative stable states, or competitive exclusion?
Ecological Monographs 76:57—72.

Peeters, F., Straile, D., Lorke, A., and Ollinger, D. 2007. Turbulent mixing and phy-
toplankton spring bloom development in a deep lake. Limnology & Oceanography
52:286—298.

Peters, R. H. and Rigler, F. H. 1973. Phosphorus release by Daphnia. Limnology &
Oceanography 18:821—839.

Portielje, R. and Lijklema, L. 1999. Estimation of sediment-water exchange of solutes
in Lake Veluwe, the Netherlands. Water Research 33:279—285.

Press, W. H., Flannery, B. P., Teukolsky, S. A., and Vetterling, W. T., 2001. Numer-
ical recipes in Fortran 77: the art of scientific computing. Cambridge University
Press.

Ptacnik, R., Diehl, S., and Berger, S. 2003. Performance of sinking and nonsinking
phytoplankton taxa in a gradient of mixing depths. Limnology & Oceanography
48:1903—1912.

Reynolds, C. S., 1984. The ecology of freshwater phytoplankton. Cambridge Univer—
sity Press.

Reynolds, C. S. 1998. What factors influence the species composition of phytoplank-
ton in lakes of different trophic status? Hydrobiologia 370211-26.

Richardson, K., Beardall, J ., and Raven, J. A. 1983. Adaptation of unicellular algae
to irradiance- an analysis of strategies. New Phytologist 93:157—191.

Riley, G. A. 1942. The relationship of vertical turbulence and spring diatom flower-
ings. Journal of Marine Research 5:67-87.

Ross, O. N. and Sharples, J. 2007. Phytoplankton motility and the competition for
nutrients in the thermocline. Marine Ecology-Progress Series 347221—38.

Ryabov, A. B., Rudolf, L., and Blasius, B. 2009. Vertical distribution and compo-
sition of phytoplankton under the influence of an upper mixed layer. Journal of
Theoretical Biology .

Sand-Jensen, K. and Borum, J. 1991. Interactions among phytoplankton, periphyton,
and macrophytes in temperate freshwaters and estuaries. Aquatic Botany 41:137—
175.

204

Sarnelle, O. 1992. Nutrient enrichment and grazer effects on phytoplankton in lakes.
Ecology 73:551—560.

Sarnelle, O. 2005. Daphnia as keystone predators: effects on phytoplankton diversity
and grazing resistance. Journal of Plankton Research 27:1229—1238.

Savitzky, A. and Golay, M. J. E. 1964. Smoothing + differentiation of data by
simplified least squares procedures. Analytical Chemistry 36:1627—&.

Schindler, D. W. 1977. Evolution of phosphorus limitation in lakes. Science 195:260—
262.

Schindler, D. W. 1997. Widespread effects of climatic warming on freshwater ecosys-
tems in north america. Hydrological Processes 11:1043—1067.

Sharp, J. H., Perry, M. J ., Renger, E. H., and Eppley, R. W. 1980. Phytoplankton rate
processes in the oligotrophic waters of the Central North Pacific Ocean. Journal of
Plankton Research 2:335—353.

Sharpley, A., Daniel, T. C., Sims, J. T., and Pote, D. H. 1996. Determining envi-
ronmentally sound soil phosphorus levels. Journal of Soil & Water Conservation
51:160—166.

Simpson, E. H. 1949. Measurement of diversity. Nature 1632688.

Skellam, J. 1951. Random dispersal in theoretical populations. Biometrika 38:196-
218.

Smith, V. H. 1986. Light and nutrient effects on the relative biomass of blue-green
algae in lake phytoplankton. Canadian Journal of Fisheries & Aquatic Sciences
43:148—153.

Smith, V. H., Foster, B. L., Grover, J. P., Holt, R. D., Leibold, M. A., and deNoyelles,
F. 2005. Phytoplankton species richness scales consistently from laboratory micro-

cosms to the world’s oceans. Proceedings of The National Academy of Sciences of
The USA 102:4393—4396.

Smith, W. O. 1982. The relative importance of chlorophyll, dissolved and particulate
material, and sea-water to the vertical extinction of light. Estuarine Coastal and
Shelf Science 15:459—465.

Sommer, U. and Gliwicz, Z. M. 1986. Long-range vertical migration of Volvox in
tropical Lake Cahora Bassa (Mozambique). Limnology & Oceanography 31:650—
653. .

Spaulding, S. A., McKnight, D. M., Smith, R. L., and Dufford, R. 1994. Phyto—
plankton population—dynamics in perennially ice-covered Lake F‘ryxell, Antarctica.
Journal of Plankton Research 16:527—541.

205

Steele, J. 1974. Spatial heterogeneity and population stability. Nature 248:83.

Steele, J. H., 1978. Spatial pattern in plankton communities. NATO Conference Series
IV: Marine Sciences Vol. 3., Pages 1—20. Plenum Press, New York.

Sterner, R. W. and Elser, J. J ., 2002. Ecological stoichiometry: the biology of elements
from molecules to the biosphere. Princeton University Press, Princeton NJ.

Stevens, M. H. H. and Carson, W. P. 2002. Resource quantity, not resource hetero—
geneity, maintains plant diversity. Ecology Letters 52420—426.

Stow, C. A., Carpenter, S. R., Webster, K. E., and Frost, T. M. 1998. Long-term
environmental monitoring: Some perspectives from lakes. Ecological Complexity
8:269—276.

Strzepek, R. F. and Harrison, P. J. 2004. Photosynthetic architecture differs in coastal
and oceanic diatoms. Nature 431:689—692.

Suess, E. 1980. Particulate organic—carbon flux in the oceans - surface productivity
and oxygen utilization. Nature 288:260—263.

Sverdrup, H. U. 1953. On conditions for the vernal blooming of phytoplankton.
Journal du Conseil 18:287—295.

Tilman, D., 1982. Resource competition and community structure. Princeton Uni-
versity Press, Princeton NJ.

Tilman, D. and Kareiva, P. M., 1997. Spatial ecology: the role of space in population
dynamics and interspecific interactions. Princeton University Press, Princeton NJ.

Tittel, J., Bissinger, V., Zippel, B., Gaedke, U., Bell, E., Lorke, A., and Kamjunke,
N. 2003. Mixotrophs combine resource use to outcompete specialists: Implications
for aquatic food webs. Proceedings Of The National Academy Of Sciences Of The
United States Of America 100:12776—12781.

van de Koppel, J ., Gascoigne, J. C., Theraulaz, G., Rietkerk, M., Mooij, W. M., and
Herman, P. M. J. 2008. Experimental evidence for spatial self—organization and its
emergent effects in mussel bed ecosystems. Science 322:739—742.

Verburg, P., Hecky, R. E., and Kling, H. 2003. Ecological consequences of a century
of warming in Lake Tanganyika. Science 301:505—507.

Visser, P. M., Ibelings, B. W., vanderVeer, B., Koedood, J., and Mur, L. R. 1996.
Artificial mixing prevents nuisance blooms of the cyanobacterium Microcystis in
Lake Nieuwe Meer, the Netherlands. Freshwater Biology 36:435—450.

Vogel, S., 1994. Life in Moving Fluids. Princeton University Press, Princeton NJ.

206

 

Waite, A., Fisher, A., Thompson, P. A., and Harrison, P. J. 1997. Sinking rate ver-
sus cell volume relationships illuminate sinking rate control mechanisms in marine
diatoms. Marine Ecology-Progress Series 157:97—108.

Walker, J. T. and Maddan, S., 2005. Statistics in criminology and criminal justice:
analysis and interpretation. Jones & Bartlett Learning.

Watson, S. B., McCauley, E., and Downing, J. A. 1997. Patterns in phytoplankton
taxonomic composition across temperate lakes of differing nutrient status. Limnol-
ogy & Oceanography 42:487—495.

Weaver, W. and Shannon, C. E., 1949. The Mathematical Theory of Communication.
University of Illinois, Urbana, Illinois.

Welschmeyer, N. A. 1994. Fluorometric analysis of chlorophyll-a in the presence of
chlorophyll-b and pheopigments. Limnology & Oceanography 39:1985—1992.

Werner, E. E., Gilliam, J. E, Hall, D. J ., and Mittelbach, G. G. 1983. An experimental
test of the effects of predation risk on habitat use in fish. Ecology 64:1540—1548.

Werner, E. E. and Hall, D. J. 1977. Competition and habitat shift in 2 sunfishes
(Centrarchidae). Ecology 58:869—876.

Wetzel, R. G., 1975. Limnology. W.B. Saunders Company.

Williamson, C. E., Sanders, R. W., Moeller, R. E., and Stutzman, P. L. 1996.
Utilization of subsurface food resources for zooplankton reproduction: Implications
for diel vertical migration theory. Limnology & Oceanography 41:224—233.

Wiiest, A., Piepke, G., and Van Senden, D. C. 2000. Turbulent kinetic energy
balance as a tool for estimating vertical diffusivity in wind-forced stratified waters.
Limnology & Oceanography 45:1388—1400.

Yoshiyama, K., Mellard, J. P., Litchman, E., and Klausmeier, C. A. 2009. Phyto—
plankton competition for nutrients and light in a stratified water column. American
Naturalist 174:190—203.

Yoshiyama, K. and Nakajima, H. 2002. Catastrophic transition in vertical distri-
butions of phytoplankton: Alternative equilibria in a water column. Journal of
Theoretical Biology 216:397—408.

207