CHANGES IN FISH DIVERSITY DUE TO HYDROLOGIC AND SUSPENDED SEDIMENT

VARIABILITY IN THE SANDUSKY RIVER, OHIO: A GENETIC PROGRAMMING APPROACH

LOUIS SANDERSON

A Thesis
Submitted to the Graduate College of Bowling Green State University in partial fulfillment of the requirements for the degree of

MASTERS OF SCIENCE

August 2009

Committee:
Enrique Gomezdelcampo, Advisor

James Evans

Peter Gorsevskiii

ABSTRACT

Enrique Gomezdelcampo, Advisor

There are numerous ways to measure the health of a riverine ecosystem, though fish

diversity is the most widely used measure. Fi sh diversity can be affected by changes to the

characteristics of a river, incl uding flow rates and suspended se diment concentration. Genetic

programming was used to create a symbolic regression to determine how four biodiversity

indices in fish were affected by variations in streamflow and suspended sediment. Fish data

collected by the Ohio Environmen tal Protection Agency and the Ohio Department of Natural

Resources spanning twelve years within 1952-2002 was used. Streamflow discharge rates and

suspended sediment concentrations at the US GS gage station 04198000 for the same time frame

as the fish data was used. The Indicators of Hydrologic Alteration software program was used

with the streamflow and suspended sediment data to generate different hydrologic and suspended

sediment variables for input in to the symbolic regression. Th e symbolic regression created a

best fit equation for each of the four biodiversit y indices. The results showed that no single

variable was common among all four indices, bu t groups of variables were common for all

indices. The fish of the Sandusky River have a large dependence on the magnitude and length of

high and low pulses of both streamflow and suspe nded sediment. Suspended sediment variables

were present more frequently in the best fit equations than flow variables. The symbolic

regression was able to accurate ly predict the Margalef and Sh annon Indices while the Simpson

Index and Shannon Index for Evenness predictions were less accurate. The better results for the

Margalef and Shannon Indices suggest that species richness is mostly influenced by changes in

streamflow and suspended sediment concentrations.iii

ACKNOWLEDGEMENT

I would like to thank my advisor, Dr. En rique Gomezdelcampo, who has taught me not

just how to program and write sc ientifically, but who has taught me how to view and analyze

data from a whole new perspective. I would also like to thank my committee members, Dr.

James Evans and Dr. Peter Gorsevski for all th eir helpful comments and suggestions throughout

my graduate school career. Thanks to Dr. Robert Vincent for giving me the research assistantship

which allowed me to come to graduate school.

Thanks to everyone in the Department of Ge ology at Bowling Green State University for

their time and commitment helping me become a better student and researcher. Thanks to the

Writing Center for helping me correct all the gr ammar and organizational issues in my papers.

Thanks to Dennis Mishne and the rest of the Oh io Environmental Protection Agency, as well as

the Ohio Department of Natural Resources for the fish data on the Sandusky River.

Thanks to all my friends who always helped put things in perspec tive and were always

there to help me through the rough times. Thanks to my parents, Dave and Sarah, for convincing

me that this was a great opportuni ty and pushing me to be the best I can. Thanks to my sister,

Meg, for always giving me somewh ere to go when I need to get away from all the work for a

night. Finally, thanks to my wi fe, Stephanie, for enduring the schedule I had to have to get

through graduate school, and for all the support you have given me over the past three years.iv

TABLE OF CONTENTS Page
INTRODUCTION

...................................................................................... 1
Literature Review

.................................................................... 1 Objective of This Study

.............................................................. 6
MATERIALS AND METHODS

...................................................... 9 Study Area

................................................................................ 9
Materials

................................................................................... 12
Methods

................................................................................... 15
RESULTS AND DISCUSSION

......................................................... 22 Indicators of Hydrologic Alteration

................................................ 22 Biodiversity Indices Results

......................................................... 28 Margalef Index

... ..................................................................... 29
Shannon Index

....................................................................... 34
Shannon Index for Evenness

....................................................... 40 Simpson Index

....................................................................... 47 All Biodiversity Indices

............................................................ 52
CONCLUSIONS

............................................................................... 57
REFERENCES

................................................................................ 59
APPENDICES

................................................................................ 67 Appendix A, Parameter Groups and Parameters For the IHA Runs

............. 68 Appendix B, Comparison of Both Gages on the Sandusky River

................. 70 Appendix C, Ranks of the IHA Variables Used in the Symbolic Regression

................................................................................ 72 Appendix D, All Trees Created Us ing Symbolic Regression

..................... 74v

LIST OF FIGURES

Figure Page

1 Map of the Location of the Sandusky River Watershed

...................... 10

2 Map of the Location of Fish Sampling Locations and USGS

Gage Station No. 04198000

...................................................... 13

3 Example of the Population Diversity of the Best Fit for the

Shannon Index

..................................................................... 20

4 Streamflow Vs. Suspended Sedime nt Concentration for the

Sandusky River Gage Near Fremont, OH

..................................... 26

5 The Three Symbolic Regression Equations for the Margalef Index

Versus the Field Data Calculated Margalef Index

........................... 35

6 Box Plot of the Margalef Index Ca lculated From Field Data and

The Three Regressed Margalef Indices

........................................ 36

7 The Three Symbolic Regression Equations for the Shannon Index

Versus the Field Data Calculated Shannon Index

........................... 41

8 Box Plot of the Shannon Index Ca lculated From Field Data and

The Three Regressed Shannon Indices

......................................... 42

9 The Three Symbolic Regression Equations for the Shannon Index For

Evenness Versus the Field Data Calculated Shannon Index For

Evenness

........................................................................... 46

10 Box Plot of the Shannon Index For Evenness Calculated From Field

Data and The Three Regressed Shannon Indices for Evenness

............. 47vi

LIST OF FIGURES

11 The Three Symbolic Regression Equations for the Simpson Index

Versus the Field Data Calculated Simpson Index

............................... 51

12 Box Plot of the Simpson Index Ca lculated From Field Data and

The Three Regressed Simpson Indices

............................................. 52

B-1 Comparison of the Streamflow of USGS Gage Number 04196500

And USGS Gage Number 0419800

.............................................. 70

D-1 Tree Created for the Margalef Inde x for Streamflow and Suspended

Sediment

.............................................................................. 74

D-2 Tree Created for the Margal ef Index for Streamflow

......................... 75

D-3 Tree Created for the Margalef Index for Suspended Sediment

.............. 76

D-4 Tree Created for the Shannon Index for Streamflow and Suspended

Sediment

............................................................................. 76

D-5 Tree Created for the Shannon Index for Streamflow

.......................... 77

D-6 Tree Created for the Shannon Index for Suspended Sediment

.............. 77

D-7 Tree Created for the Shannon Index for Evenness for Streamflow and

Suspended Sediment

................................................................ 78

D-8 Tree Created for the Shannon Index for Evenness for Streamflow

.......... 78

D-9 Tree Created for the Shannon Index for Evenness for Suspended

Sediment

............................................................................... 79vii

LIST OF FIGURES

D-10 Tree Created for the Simpson Inde x for Streamflow and Suspended

Sediment

.............................................................................. 80

D-11 Tree Created for the Simpson Index for Streamflow

........................... 81

D-12 Tree Created for the Shannon Index for Suspended Sediment

............... 81viii

LIST OF TABLES

Table Page

1 Streamflow Variables Calculat ed From IHA 7 With Their

Definitions

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

2 Suspended Sediment Variables Ca lculated From IHA 7 With

Their Definitions

................................................................... 24

3 Summary Table of Fish Data Used in This Study

.............................. 25

4 Average Temperature and Precipita tion for January and February

For All Years Containing Fish Data

.............................................. 28

5 Streamflow and Suspended Sediment Variables and the Frequency

Of Occurrence in Generated Regression Equations

............................. 30

6 Calculated and Regressed Margalef Indices for Each Year and for

The Three Sets

....................................................................... 35

7 Calculated and Regressed Shannon Indices for Each Year and for

The Three Sets

....................................................................... 41

8 Calculated and Regressed Shannon Indices for Evenness For Each

Year and for the Three Sets

......................................................... 46

9 Calculated and Regressed Simpson Indices for Each Year and for

The Three Sets

....................................................................... 51

10 Summary of the Best Fit Indices

.................................................. 53

A-1 Parameters Used in the IHA Fo r Creating Streamflow Statistics

............. 68ix

LIST OF TABLES

A-2 Parameters Used in the IHA Fo r Creating Suspended Sediment

Statistics

.............................................................................. 69

C-1 Streamflow Variables Calculated from IHA 7 and Then Ranked

............ 72

C-2 Suspended Sediment Variables Calc ulated from IHA 7 and Then

Ranked

............................................................................... 73x

LIST OF EQUATIONS

Equation Page

1 Margalef Biodiversity Index

................................................. 15

2 Shannon Biodiversity Index

.................................................. 16

3 Shannon Biodiversity Index for Evenness

............................... 16

4 Simpson Biodiversity Index

........................................................ 16

5 Inverse Simpson Biodiversity Index

....................................... 17

6 IHA Ranking

................................................................. 17

7 Margalef Biodiversity Index Cr eated With Streamflow and

Suspended Sediment

......................................................... 29

8 Margalef Biodiversity Index Created With Streamflow

................ 32

9 Margalef Biodiversity Index Created With Suspended

Sediment

....................................................................... 33

10 Shannon Biodiversity Index Created With Streamflow and

Suspended Sediment

......................................................... 36

11 Shannon Biodiversity Index Cr eated With Streamflow

................ 38

12 Shannon Biodiversity Index Created With Suspended

Sediment

...................................................................... 39

13 Shannon Biodiversity Index for Evenness Created With

Streamflow and Suspended Sediment

..................................... 42

14 Shannon Biodiversity Index for Evenness Created With

Streamflow

................................................................... 43xi

LIST OF EQUATIONS

15 Shannon Biodiversity Index for Evenness Created With

Suspended Sediment

....................................................... 44

16 Simpson Biodiversity Index Creat ed With Streamflow and

Suspended Sediment

....................................................... 47

17 Simpson Biodiversity Index Cr eated With Streamflow

.............. 49

18 Simpson Biodiversity Index Created With Suspended

Sediment

..................................................................... 501

INDTRODUCTION

Literature Review
Researchers have used numerous different measures of biodiversity to determine the true
health of an ecosystem (Fock et al ., 2002; Johnson and Hering, 2009; Qadir and Malik, 2009;
Xenopoulos and Lodge, 2006). Fish diversity has largely been used as the best measure of the
health of aquatic ecosystems, due to their sensitivity to subtle environmental changes such as
river stress (Karr, 1981; Qadir and Malik, 2009). This has led to the use of species richness
(Mellin et al., 2008; Xenopoulos and Lodge, 2006), common biodiversity indices (Qadir and
Malik, 2009; Johnson and Hering, 2009), and the attempted creation of new biodiversity indices
to better model ecosystem health (Campos and Fernando Isaza, 2009).
Fish need a wide variety of habitats, including large woody debris, boulders, pools, gravel
beds, and undercut banks (Piegay et al ., 2000). The habitats serve as important spawning
grounds and refuges (Schwartz and Herricks, 2005; Trautman, 1981). Fish habitat also includes
streamflow and suspended sediment. There has been a large amount of research conducted on
the importance of hydrologic variables and sedimentation of streams on fish habitat (Kemp et al.
, 1999; Suen and Herricks, 2006; Yang et al. , 2008).
Several studies have investigated how streamflows affect fish diversity (Bunn and
Arthington, 2002; Xenopoulos and Lodge, 2006). Schwartz and Herricks (2005) showed that
high streamflows are necessary in fish life cycles by measuring fish changes during flooding
events, as well as for the survival of juvenile fish which thrive in these conditions (Freeman et

al ., 2001). Grabowski and Isely (2007) showed that low streamflow events may be just as
important to fish diversity. They monitored the Robust Red-horse fish during the 2005 spawning2

season and discovered that almost half the nests created were left in areas with near-zero

streamflow conditions.
With both high and low streamflow events being shown to be important for fish diversity,
research is being conducted in the importance of the timing of the high and low streamflow

events. Yang et al . (2008) discovered that a major factor in fish diversity was the timing of the
low streamflows. By taking river habitat measurements along with fish collections and
comparing fish abundance with the different magnitudes and durations of streamflows, Jowett et

al . (2005) also discovered that timing of both low and high streamflow events were important to

fish in New Zealand.
While streamflows have been shown as important, it is not the only river condition
important to fish. Suspended sediment was measured near a gold mine in South America along
with fish diversity to determine how changes in sediment were impacting fish. Fish diversity
was significantly lower in the mine area due to the increased suspended sediment settling and
creating a uniform stream habitat. Suspended sediment results in a much higher turbidity (Mol
and Ouboter, 2003) which could result in a decrease in fish diversity (Trautman, 1981), and has
also been shown to damage fish gills and decrease growth rates in all stages of the fish life cycle
(Sutherland and Meyer, 2007).
Suspended sediment can affect fish in less direct ways as well. Turbidity has been shown
to decrease light penetration, which can have both negative and positive effects on fish
depending on the species (Collett et al ., 2008). Suspended sediment has been shown to have a
direct correlation to the amount of dissolved oxygen present in a river system (MacPherson et3

al ., 2007). Lower levels of dissolved oxygen can affect fish diversity negatively (McKinsey and
Chapman, 1998). Suspended sediment can be a transport for pollutants (Forstner, 2004).
Suspended sediment is often times increased by agriculture around a stream, for example,
when runoff carries large amount of sediment into the stream due to the reduction of plant
buffers around it (Goodwin et al ., 2003; Murphy et al ., 2007). Several studies have shown the
increase in suspended sediment may decrease fish diversity (Mol and Ouboter, 2003; Sutherland
and Meyer, 2007).
Suspended sediment is usually only measured as a single lethal threshold variable for all
fish (Vondracek, et al., 2003; Zimmerman et al., 2003) or a single value as a tolerance indicator
(Meador and Carlisle, 2007). This can provide many problems in determining negative impacts

on fish as a lethal threshold assumes that fish will not leave an area and then return. Also, there
is an assumption that there is an arbitrary level at which all species of fish are affected equally.
The difficulty in determining exact levels at which fish diversity is affected by changing
streamflows and suspended sediment has led to more advanced techniques being used. One of
these techniques is the use of neural networks. Neural networks are used due to their ability to
accurately show nonlinear relationships between abiotic/biotic characteristics and fish diversity
(Gutierrez-Estrada et al., 2008). Suryanarayana et al . (2008) discussed the use of Neural
Networks in predicting the abundance of fish as well. Kennard et al. (2007) used neural networks
and streamflow conditions to determine environmental factors influencing fish assemblages.
Neural networks are a form of machine learning where computers are given data which is
then used to by the computer to program itself. This concept has led to one of the newest
techniques, which is genetic programming. Very little research has been conducted in the use of4

genetic programming with fish diversity. Yang et al . (2008) compared genetic programming to
Principal Component Analysis and an autecology matrix to establish the accuracy of Genetic
Programming for determining hydrologic factors affecting fish. This study showed that Genetic
Programming could be an even better method for determining fish habitat than Principal
Component Analysis or autecology matrices.
Genetic programming (GP) is a form of machine learning based on the ideas of evolution.
GP can take the form of linear codes or graphs, but is most commonly associated with a treebased structure. GP works by first creating a training set from which the computer programs
learn, and then taking everything learned in the training set applying it to the test set (Koza,
1992).
GP starts with an initial population consisting of groups of random functions and variables
(also called terminals). Each group creates an initial algorithm, which is called a program. GP
then executes each of these individual programs with the input data. Each program is then
judged on a basis of fitness levels. Fitness is how well a program has learned to predict the
output from the inputs, and is most commonly measured as error (Koza, 1992). The best
program is defined as the computer program which creates the highest fitness values (Koza,
1992). Fitness values determine which programs may continue to the next generation. To move
to the next generation of the GP, there are three main avenues, all based on the idea of evolution.
The simplest form is reproduction. Here, a copy of the best program is included in the new
population which is created by GP (Surabhi Gaur, 2008). Another avenue taken to the next
generation is crossover. Here, two parent programs are selected. A random section of tree from
each parent is then selected. These two tree sections are swapped, creating two children with5

their trees comprised of both parents. These new children are then included in the new
populations if they create a better fitness value (Freitas, 2002). The final way GP evolves is
through the process of mutation. Here, a random point is selected within a single parent
program. This point is replaced by a randomly generated subtree containing the same limitations
(Koza, 1992). This new mutation is then included in the new population if fitness increases
(Freitas, 2002).
GP evaluates each solution for the best fitting measure. This fitting measure could be
determined by an amount of time, a certain payoff, or if a certain level of error is reached. Once
the predetermined number of generations has run, the GP terminates and the single best-so-far
individual is chosen as the end result of this run (Poli et al ., 2008; Yang et al . 2008). The bestso-far individual is the best computer program of any generation of the run (Koza, 1992).
Using GP, a symbolic regression can be created. A symbolic regression is a regression in
which the relationship of inputs and outputs does not have to be linear. This regression is guided
by error, where the smaller the error, the better the regression (Koza, 1992).
Biodiversity is one of the best measures of the true health of an ecosystem (Gaston and
Spicer, 1998). Biodiversity is a measure of how diverse an ecosystem is. Biodiversity is not just
a measure of the number of species, but depends on the kind and combination of all organisms
present (Maclaurin and Sterelny, 2008). Biodiversity can be split into three major categories:
species diversity, genetic diversity, and ecosystem diversity. Species diversity is simply the
count of the number of species and can be described as the size of the population, range of
species, or the variety of species (Becher, 1998). Genetic diversity is similar, but instead of
dealing with species, it deals with diversity in alleles and genes (Huston, 1994). Ecosystem6

diversity is the number of ecosystems present in an area. Ecosystem diversity can deal with
ecosystems which are next to each other or within one another (Becher, 1998).
Quantifying biodiversity is one of the most complicated aspects of biodiversity (Gaston and
Spicer, 1998). Many biodiversity indices have been created in an attempt to capture the diversity
of an ecosystem. These indices attempt to define biodiversity in many different ways, though
most indices use a combination of number of species and the degree of difference between those
species (Gaston and Spicer, 1998). Huston (1998) argued that it is absurd to expect one index to
characterize the diversity of an entire ecosystem, and said that the best way to characterize
biodiversity is through the use of numerous biodiversity indices. Even still, it is unlikely to ever
discover the “true” biodiversity of an ecosystem (Gaston and Spicer, 1998). The goal of using
multiple indices is to try to describe the diversity of an ecosystem as accurately as possible.

Objective of This Study
The Sandusky River, a tributary of Lake Erie, is a vital fish nursery for numerous species
of fish, both native and invasive. A number of studies in the Sandusky River and Lake Erie
region have focused on large fish species, and the walleye ( Stizostedion vitreum) in particular.
Walleye are one of the most important terminal predators in the region for sport and commercial
fishing (Mion et al ., 1998). Jones et al . (2003) studied the spawning habitat for walleye in the
Sandusky River and determined that it is potentially affected by the Ballville Dam near Fremont,
Ohio. The larval walleye fish survival are very highly associated with changes in streamflow,
though other factors may also affect them (Mion, et al., 1998). Not all studies have concentrated7

on the survival of walleye. Sharma and Jackson (2007) showed how water chemistry and
temperature affect all fish in northern Lake Erie.
While important as a fish nursery, the Sandusky River is also important for humans in
many ways. The Sandusky River attracts large numbers of tourists due to its excellent fishing
(Saxton 1977) and the native wildlife which can be viewed by both hiking along the river and
canoeing (Grob 1971). The river also serves as an important source of drinking water (Van
Tassel, 1929) and has even served as a source of hydroelectric power (Van Tassel, 1929; Clark,
1956).
The river contains four dams, with the Ballville Dam in Fremont, Ohio being the largest.
This dam is the source of much debate as to its effects on the Sandusky River ecosystem. While
many dams trap sediment and significantly reduce the amount of suspended sediment
downstream of the dam, the Ballville Dam traps less than five percent of the sediment (Evans et

al. , 2002). Most suspended sediment still streamflows downstream with its corresponding effect
on channel substrate (Mol and Ouboter, 2003). Increased sedimentation has changed portions of
the Sandusky River to a sandier substrate, ideal for invasive species such as the common carp
(Murphy et al ., 2007), while native fish rely on gravel substrates. The preservation of the native
fish species is important for both the ecology of the river and the economic benefits it provides.
The Ballville Dam may be affecting the genetic diversity along the Sandusky River. Lowhead dams may sometimes change the genotype between fish upstream and downstream creating
different subspecies of fish (Haponki et al ., 2007). For this study, subspecies are not considered,
as the fish data is not available at a subspecies level.8

This study uses a symbolic regression obtained through genetic programming to answer
two main questions about fish habitat in the Sandusky River: How does suspended sediment and
varying streamflows affect the fish of the Sandusky River? How are different biodiversity
indices affected by similar variations in streamflow and suspended sediment? This improves on
the work of Yang et al. (2008) by using suspended sediment concentrations as well as
streamflow data to determine parameters important to fish diversity. Multiple suspended
sediment variables are used to determine if varying levels of suspended sediment affect fish
diversity.
This study provides insight into the important streamflow and suspended sediment
variables with respect to fish biodiversity in the Sandusky River. It also serves as a comparison
of several indices of biodiversity.9

MATERIALS AND METHODS

Study Area
The Sandusky River is a 185 km (130 mi) long river emptying into the Sandusky Bay on
Lake Erie. The Sandusky Bay is located 13 km (8 mi) north of Fremont, Ohio (Figure 1). This
area is on the Eastern fringe of the eastern portion of the Great Plains, often called the Long
Grass region (ODNR, 1966). Sandusky Bay is the largest embayment on the south side of Lake
Erie (Baker, 1975). The entire Sandusky watershed is 3756 km2 (1,450 mi2), and largely
dominated by agricultural use (Baker, 1975) . The river drops from an elevation of 333 m (1,093
ft ) to 175 m (573 ft) (ODNR, 1965), which is approximately a drop of 0.76 m/km (4 ft/mi)
(Forsyth 1975).
The Sandusky River is located on the eastern flank of the Cincinnati Arch. This area is
dominated by carbonates eroded by the Wisconsin Glacier, causing the area to be very flat
(Forsyth, 1975). The retreat of the Wisconsin Glacier 14,000 years ago is the beginning of the
geologic history of the Sandusky River. This glacier went through a series of retreats and
recovery over the Ohio landscape over the course of 322 km (200 mi) and 4,000 years. As the
ice retreated, small streams began to extend northward over the land. These streams originally
flowed south due to glacial melt. The small streams eventually combined and created the
Sandusky River. While moving North, the glacier acted as a dam on the lake, allowing a
combination of the Maumee, Detroit, and Sandusky Rivers. As isostatic recovery occurred on
the Niagara outlet, the Maumee-Detroit-Sandusky River drowned, shortening this large river into
the three separate rivers that exist now. The Sandusky River continued to shorten until a state of
near-equilibrium was reached, leading to the current configuration of the river (Forsyth, 1975).10

Figure1. Map of the location of the Sandusky River Watershed11

The bedrock underlying the Sandusky Basin is mostly Silverman-Devonian carbonates
with some Devonian Shale and Mississippian sandstone. Due to the glacier, much of the
bedrock is covered with glacial till (Forsyth, 1975). This till sometimes is as deep as 41 m (135
ft) (ODNR, 1965). There are three main moraines located in this area. The Defiance Moraine is
the northern most moraine, and consists of low-rolling hills. The other two moraines are the Fort
Wayne Moraine, and the Wabash Moraine. These are similar to the Defiance End Moraine, but
are more complex due to the underlying sandstones which did not erode (Forsyth, 1975).
The river bottom is mostly alluvial deposits from the erosion of banks and the subsequent
settling of these materials. Much of the finer sediments remain in suspension until they reach
Lake Erie, where they are able to settle out. This suspension causes much of the river bottom to
be either gravel or muddy bottomed (Forsyth, 1975).
Currently, only minor geologic processes are being observed on the Sandusky River. The
main process is that of erosion, mainly caused by floods. There is some sedimentation occurring
from this erosion. River flooding and upland erosion are the final natural processes occurring on
this river. Some anthropogenic processes are also impacting the geology of the Sandusky River,
mainly due to rerouting for human uses and agricultural uses (Forsyth, 1975).
The Sandusky River contains four main dams on the river. These dams are the Ballville
Dam, Bacon's Dam, Ella Street Dam, and Mill Dam (Murphy et al. , 2007). The largest of these
dams is the Ballville Dam, which is located near Fremont, OH. It has been proposed by city
officials that this dam be torn down by the year 2013, opening up new spawning grounds for fish
(“Fremont,” 2009).12

The Sandusky River contains to USGS gage stations: gage no. 04198000 and gage no.
04196500. Gage no. 04198000 is located 5.6 km (3.5 mi) upstream of Fremont, OH at latitude
41°18'28" and longitude -83°09'32" (USGS, 2009a). This gage contains daily discharge data
from 1923-Present, and suspended sediment concentrations from 1950-2002. Gage no.
04196500 is located 3.2 km (3.0 mi) downstream of Upper Sandusky, OH at latitude 40°51''02"
and longitude 83°15'23" (USGS, 2009b). This gage contains daily streamflow discharge data
from 1921-Present, with no data present from 1936-1939 and 1981-2000. There is no suspended
sediment measurement at this gage station.

Materials
Fish data for this study came from two sources, the Ohio Environmental Protection
Agency (OEPA) and the Ohio Department of Natural Resources (ODNR). Streamflow and
suspended sediment data comes from the United States Geological Survey (USGS). Most of the
fish data used comes from the OEPA “fish inventory” (OEPA, 2008) . It consists of fish data
collected by electrofishing collected for all rivers in the state of Ohio. This data is first separated
by river basin, and then by individual river. This data ranged from 1976 until 2006 for all rivers
in the state of Ohio. All data on the Sandusky River was used here. This data consisted of dates

from 1979, 1981, 1988, 1990, 1999, 2000, 2001, and 2002. The fish were collected in different
reaches in all years of the study (Figure.2 ).
Two reports by the ODNR also provided fish data (Clark, 1956, Clark, 1993) . However,
only one report was used in this study. The second report had several perceived errors and was
not utilized. For example, when listing the fish species, the second report would list a total
number of fish collected, and then list all fish species with the percentage of the total number of13

Figure 2. Map of the location of fish sampling locations and USGS gage station no. 0419800014

individuals which were that species, but these percentages would not add up to 100%, and
sometimes they added up to 150%. The other perceived inaccuracy was related to the number of
white crappie. White crappie are hardly present in most years in the Sandusky River according
to the other fish data found. However, this second report had numbers as high as 6,933
individuals. The fish data from the ODNR report that was used utilized three different methods
for catching fish: test netting, seining, and surveying anglers (for bass) (Clark, 1956). Seining
was the most commonly used method. The ODNR data was collected from 1952 through 1955
and mostly near Fremont, Ohio, though some fish were collected further upstream.
Streamflow and suspended sediment data were obtained from the USGS gage number 04198000,
located on the Sandusky River near Fremont OH (Figure. 2). This gage has a large period of
record for both streamflow and suspended sediment. The second gage on this river (gage no.
04196500) contains little streamflow data for this time period and no suspended sediment data,

and therefore was not used with the fish data.
The Indicators of Hydraulic Alteration (IHA) is a software program designed by the
Nature Conservancy to determine important streamflow parameters for the environment (The
Nature Conservancy, 2007). IHA version 7 takes daily discharges from any USGS gage station
to derive relevant statistics for a river system. The statistics calculated can be divided into five
parameter groups: magnitude of monthly conditions, magnitude and duration of extreme water
conditions, timing of annual extreme water conditions, frequency and duration of high and low
pulses, and rate and frequency of water condition changes. IHA calculates 32 different statistics
of streamflow and 33 different statistics of suspended sediment that are relevant to fish

communities in streams and rivers.15

Since IHA only calculates statistics for the different variables it , can also be used to
compute the statistics for suspended sediment. These were classified into five parameter groups
for suspended sediment: magnitude of monthly conditions, magnitude and duration of extreme
suspended sediment conditions, timing of annual extreme suspended sediment conditions,
frequency and duration of high and low sediment pulses, and rate and frequency of suspended
sediment condition changes.

Methods
Four different biodiversity indices were used as a measure of fish diversity. They were
chosen due to the different components that they measure. These four indices are the Simpson
Index, the Shannon Index, the Shannon Index for Evenness, and the Margalef Index.
The Margalef Index (I) is an index that measures diversity based on species richness, so it

is similar to the Shannon Index. This index differs from the Shannon Index, however, in that it
does not take into account the number of individuals per species. For this reason, it is sometimes
considered a measure of species richness as opposed to a biodiversity index. This index is
calculated using the equation:

I = S

− 1 ln  N  (1)

Where S is the total number of species and N is the total number of individuals.
The Shannon Index (H') is another widely used diversity index. This index is based on
species richness as well, though it also uses the number of individuals. This index measures the
average degree of uncertainty in predicting the identity of a species chosen at random. As the16

number of species increase and the distribution among the species becomes similar, the
likelihood of predicting the identity of the species chosen becomes less likely, thus enlarging the
diversity index. The maximum H' is usually reached between 1.5 and 3.5 ( Zak and Willig

. , 2004). The equation for this index is:

H ' = 

## ∑

i = 1 S n i N ln n i N (2)

Where N is the total number of individuals, n i is the number of individuals in species i, and
S is the total number of species.

The Shannon Index is often times calculated as an evenness index. An evenness index
calculates the relative abundance of individuals among each species. The Shannon Index for
Evenness ( E ) measures the evenness of the species present by taking the Shannon Index and
dividing it by the maximum Shannon Index. E is a measure of the degree to which a particular
community compares to the maximum diversity possible, eliminating the species richness aspect
of the Shannon Index (Zak and Willig, 2004). The equation is represented by:

E = H ' ln  S  (3)

Where H' is the previously calculated Shannon Index, and S is the total number of species.
Finally, the Simpson Biodiversity Index (D) is considered a dominance index because it
can be strongly influenced by the most abundant species. This index is widely used and contains
a very low sensitivity to sample size ( Zak and Willig , 2004). The Simpson Index is the
probability that any single species will be from two different species. This index equation is:

D = 

## ∑

i = 1 S
n i  n i − 1 

N  N

− 1  (4)17

Where S is the number of species, N is the total number of organisms, and n i is the number
of individuals in species i. This index shows greater diversity as the numbers get smaller. To
correct this, the Simpson Index was simply changed to:

D ' = 1

− D (5)

Where D is the Simpson Index calculated above, and D' is the new Simpson Index created
so that as diversity increases, the indices increase. This makes reading the indices easier to

understand.
IHA 7 was used to create the 32 IHA's for the Sandusky River streamflow. For
streamflow, zero flow days were omitted because there were no instances of zero flow days
occurring in any year. This same program was used to calculate the different statistical
parameters for suspended sediment. Zero suspended sediment days were included here because
there were days which did not have suspended sediment concentration. With some of the
concentration days being very low, it is possible that not enough suspended sediment was
transported by streamflow to be detected by the meter present. This could also be due to
rounding by the suspended sediment gage. Due to the large size of some numbers as opposed to
others, these numbers were normalized to compensate the effects of magnitude. The IHA's were
sorted based on each variable and ranked from one through twelve, and then normalized using
the following equation:

IHA = r

− 1 R

− 1 (6)18

Where r is the ranked number for that specific year and R is the highest ranking which
occurs (in this case, it is twelve for each variable). These were then input as the independent
variables (or terminals) in the Genetic Program.
MATLAB (version 7.7) and the GP Lab toolbox were used to create a symbolic regression
generated by genetic programming. MATLAB is a high level computing language for algorithm
development containing powerful commands which allow the creation for both 2D and 3D
graphics (Mathworks, 2008). MATLAB contains about 25 toolboxes, including a toolbox
designated for Genetic Programming, called GP Lab (Part-Enander and Sjoberg, 1999; Silva,
2007).
To set the symbolic regression terminals, functions, and fitness need to be defined. The
terminals are set as the independent and dependent variables calculated above. The functions are
simply the mathematical operators which are being used. In this case, addition, subtraction,
division, and multiplication were selected. Finally, fitness is calculated here as the absolute
difference between the expected outputs and the value returned in the program. The lower the
fitness value, the similar the calculated and regressed indices, and therefore the better the fitness.
The next step in the symbolic regression is determining how the genetic tree will grow. A
ramped half-and-half system is used for the growing method. This allows for both the full and
growth methods of tree reproduction. The full method has a fixed length for which the genetic
tree can grow, while the growth method allows the genetic tree to grow at an infinite rate (Koza,
1992). The ramped half and half method creates an equal number of trees using depths from two
to the maximum depth. This method is suggested as the best method as it allows for the19

positives from both the growth and full methods to be utilized (Koza, 1992). Generations are
how many generations of children are created in the structure from the parents. For this study, a
maximum of 25 generations was selected. This number of generations is appropriate as the
diversity of the populations dwindle to near zero by this time in all cases (Figure. 3). Also, the
initial population needs to be determined. This is how many randomly generated programs are
used to start the symbolic regression. For this study, the initial population is set to 1,000 as
suggested by Yang et al. (2008). The crossover and mutation rates also need to be established.
The crossover rate is the probability that two different programs (equation) will be selected and
sub-trees from each selected individual will be swapped. The mutation rate is the probability
that a single program (equation) is selected, and that a randomly generated sub-tree will be

substituted in for a sub-tree in the selected individual. Crossover was set to a rate 0.9, while

mutation was set at a rate of 0.1, as suggested by Koza (1992).
For the sampling method, a tournament style was selected. In this style, two programs are
randomly selected to mate. The program which has the higher fitness wins the tournament and
moves on to mate. This method is the most common method used in genetic programming
(Koza, 1992). Survival is based on the concept of total elitism. All parents and children are
ordered by greatest fitness, with the most fit being selected to move on, regardless of being a
parent or child. This method was used to ensure that the best individuals are the ones always
mating. The population size surviving is the same as the initial population size.
One final aspect of the symbolic regression is the stop conditions. Stop conditions stop the
regression once a certain fitness level or size are reached before the end of the generations. This
symbolic regression in this study contains no stop conditions, meaning stoppage only occurs20

Figure 3. Example of the the population diversity of the best fit

for the Shannon Index (H').

when 25 generations are reached. A population diversity is also calculated to ensure that no
single parameter is dominating the genetic program. Population diversity is how different all the
programs in a given generation are from each other. Once a diversity gets low, this signifies that
most the population contains the same program, therefore crossovers can not produce new,
unique individuals. Thus only mutation has a chance of improving the fitness.
Results are then produced into graphs. A graph of the tree structure shows how the tree is
built out among generations for the best fit individual. A complexity graph shows the
progression of the number of nodes and depth of the best fit individual, as well as the maximum
nodes and depth created. A diversity graph ensures that diversity has leveled when generation 25
is achieved. A box plot shows any outliers which may be a potential problem. Finally, a graph
of observed vs simulated is produced to determine how the symbolic regression fits the observed
diversity indices.21

This process was repeated twenty five times for each index. The results from each best fit
equation was recorded to determine the likelihood of each variable occurring in a run. After
being run for each index using both the streamflow and suspended sediment variables, the same
process was carried out just for streamflow variables and then just for suspended sediment
variables. This allowed a comparison of how the results from the combination of both
streamflow and suspended sediment were related to results for just streamflow and just
suspended sediment.
Multicollinearity is a major problem which can occur in regression models in which
multiple variables are highly correlated with each other. If this is happening, fitness may be
portray the regression as fitting the observed data at a much higher rate than it actually is. Very
little research has been conducted in how multicollinearity affects symbolic regressions, but the
limited research has shown that symbolic regressions do not present high levels of
multicollinearity, even when linear regressions are obtained (Castillo et al. , 2005).22

RESULTS AND DISCUSSION

Indicators of Hydrologic Alteration
Tables 1 and 2 show the IHA variables for streamflow and suspended sediment
respectively. Table 3 shows a summary table of all fish data used. The highest streamflow for a
single year was 1990, followed by 1981. The year 1990 contained the least number of low pulse
events, while having the most high pulse events. The year 1981 contained the second least low
pulse days, and the third most high pulse days. The least streamflow occurred in 1953 and 1954.
The year 1954 contained the most low pulse days and the second least high pulse days. The year
1953 had the third most low pulse days and the least high pulse days. As expected, the day of
the year with minimum streamflow generally occurred between July and September and the day
of the year for maximum streamflow generally occurred sometime between December and
March. In the Midwest, summer is the driest time of year, and spring is the time of snow melt
and seasonal rains. However, in 1953 and 1981 the maximum streamflow occurred in early
summer. In 1953, May had an abnormally high median streamflow when compared to other
years, while 1981 had an extremely high median streamflow in June.
The highest suspended sediment concentration occurred in 1981 and 1990. In 1990, there
were no low suspended sediment pulse days, but it had the second most high suspended sediment
pulse days at 22. The year 1981 had the fifth least low suspended sediment pulse days, and the
fourth most high suspended sediment pulse days. Suspended sediment low concentration days
occurred from August through December. The maximum day of suspended sediment
concentration occurred throughout the entire year.
Figure 4 shows a comparison of streamflow discharge to suspended sediment23242526

Figure 4 . S treamflow vs suspended sediment concentration for the Sandusky River gage near

Fremont, Ohio.

concentrations for the Sandusky River near Fremont Ohio gaging station. As expected,
streamflow and suspended sediment concentration are correlated in the Sandusky River (R 2 =
0.73). Higher streamflow discharges are able to carry larger sediments as well as smaller,
leading to larger concentrations of sediment in suspension when the discharge rates are higher,
and less concentrations when discharges are smaller. Similar results have been found by NadalRomero et al. (2008) in the Mediterranean area and Jugaru Tiron et al. (2009) on the Danube

River.27

The IHA results for suspended sediment were different from the maximum and minimum
streamflow dates in Table 2. The high streamflow rates in the colder months could be due to
snow melt from the warmer winter temperatures, and if this is the case, the ground may not have
thawed yet, having very little suspended sediment to be carried with these high streamflows.
Most sediment is frozen during the winter, leading to little suspended sediment in the winter
months. However, there are some years (1952, 1953, and 1979) where the January suspended
sediment was actually higher than in the following month. These three years correspond with the
years in which streamflow was also much higher in January than the following month of
February
Temperature and precipitation data from the National Climatic Data Center for the entire
state of Ohio was used to determine how these years may have been different (NCDC, 2009).
Table 4 shows data for temperature and precipitation for January and February for the entire state
of Ohio. Only four years had average temperatures above freezing in January (1952, 1953, 1990
and 2002). Snow in these years was probably melting, as well as the ground thawing during
January. Also, 1952 and 1953 had the highest and third highest precipitation totals in January,
respectively. The amount of precipitation for these two years decreased markedly in February.
The high temperatures along with the higher precipitation could lead to the increases of both
streamflow and suspended sediment in January. The year 1990 had a significantly high
temperature for January as well as a large precipitation, in fact, it had the second largest
discharge for the month of January. However, 1990 had a large increase in precipitation in
February, leading to February having a larger discharge than January. The year 2002 was the
only other year that the temperature averaged above freezing for January. This year however,28

Table 4. Average temperature and precipitation for January and February

for all years containing fish data

Year January Average February Average January Average February Average Temperature (°C) Temperature (°C) Precipitation (mm) Precipitation (mm)
1952 0.89 0.83 130 57
1953 1.1 1.3 97 31
1954 -1.0 2.9 65 41
1955 -2.6 -0.56 44 90
1979 -6.3 -7.8 93 70
1980 -2.5 -4.7 39 32
1988 -3.8 -2.3 37 85
1990 2.5 2.5 60 110
1999 -1.9 1.6 110 68
2000 -3.1 2.0 67 84
2001 -2.6 1.2 33 41
2002 1.2 1.8 55 43

did not have a large discharge, but in December, 2001, the average temperature was 3.3 ° C (38.0

° F). The most likely scenario is that most snow melted and thawing occurred in the previous
month, leaving little to no snow to melt in January. Finally, in 1979 the temperature in January
was below freezing but there was a large amount of precipitation in this month. This increase in
precipitation could probably be the reason for the increased streamflow and suspended sediment
in January.

Biodiversity Indices Results
Four biodiversity indices were calculated here. They were the Margalef Index, Shannon
Index, Shannon Index for Evenness, and the Simpson Index. These four indices measure
biodiversity using either species richness (Margalef and Shannon Indices), evenness (Shannon29

Index for Evenness), or dominance (Simpson Index). The results using these four indices are

listed below.
Margalef Index
The Margalef Index had the best correlation between the biodiversity index calculated
from the fish data and the index created by the symbolic regression for all the biodiversity
indices. The Margalef Index was first run with both streamflow and suspended sediment as the
independents variables. Each run created an index tree representing the best fit equation as a tree

from which crossovers and mutations occurred . The tree is the end result of the symbolic
regression. All the trees are located in Appendix D. The best single run for streamflow and
suspended sediment together resulted in the symbolic regression equation 7. The run contained
the lowest error of the 25 total runs for both streamflow and suspended sediment. This equation
produced small error values (abs error = 1.2, R 2 = 0.96), indicating that these variables are able to
explain a large percentage of the variability in the Margalef Diversity Index for the Sandusky

River.

(7)

Where I Both is the Margalef index created using the symbolic regression for both
streamflow and suspended sediment, and all variables are defined by Table 5.
Table 5 also shows the frequency with which each variable occurred during the 25 runs.
multiple variables of streamflow and suspended sediment make up the regression for the I Both =  Q Fall   2 ∗ Q LPL    2 ∗ Q 10   [  Q Fall 2 ∗ SS 1min   SS 6 ∗ Q Fall ∗ SS 1min ]  SS Reversal 

−  [  SS Reversal − SS 1Min  ∗  Q Fall ∗ SS 1min  SS 3  ] Q Reversal  SS 9  SS 3max  SS min − SS LPL [ SS 6  Q 3min ] 30

Table 5. Streamflow and s uspended sediment variables and the frequency of appearance in the generated regression equations31

Table 5 Continued

Margalef Index. However, it appears that the length of suspended sediment pulses is a major
factor as it is present in the best equation, and occurred in 28% of all 25 runs (Table 5). The
regression equation along with data present in Table 2 shows that the shorter the low pulse of
suspended sediment, the higher the Margalef Index. It is widely known that large amounts of
suspended sediment can be harmful to many fish species (Bunt et al. , 2004; Mol and Ouboter,
2003; Sutherland and Meyer, 2007 ). However, it appears that fish in the Sandusky River are
negatively affected by extended periods of very low suspended sediment levels. One explanation
for this may be that fish prefer some level of suspended sediment to hide from predators. It was
shown by Turesson and Bronmark (2007) that prey fish may behave differently in turbid water
which makes them less likely to encounter predators. Furthermore, riverine fish species are
better adapted to living with suspended sediment than lake fish (Bunt et al. , 2004), so perhaps
these fish actually prefer the benefits of some suspended sediment as opposed to none.
The only variable which occurred greater than 50% of the time for the Margalef Index was
the number of suspended sediment reversals. This variable is also present in the best fit
equation, which may suggest that it has the largest impact on the Margalef Diversity Index. Bunt

et al. (2004) showed that fish adapts to levels of suspended sediment, but if there are large fluxes32

of suspended sediment, it is possible that the variability prevents fish from adapting and thus
many species do not survive.
The Margalef Diversity Index was then regressed using only streamflow variables as
independent variables. The best symbolic regression run using only streamflow generated
equation 8.

I Q =  Q LPL ∗ Q 12   [  Q 1Min − Q 4  Q LPL  ∗ Q 30max ∗ Q Fall ]  [ Q Max 2 ∗ Q 7 ∗  Q 4 Q 5  ∗  Q 1 Q 5  ]

 Q Max Q 1  Q 5 Q LPL  Q 1  Q 4  Q 7Max  Q Fall (8)

Where I Q is the Margalef Index created using the symbolic regression with streamflow
variables as the only independent variables as defined in Table 5. Equation 8 also has very small
error values (abs error = 1.44, R 2 = 0.88), although not as small as the regression using both flow
and suspended sediment.
Many of the flow values observed in the Margalef Index for flow are not actually present
in the index equation for both flow and suspended sediment. This could be for a variety of
reasons. It is possible that variables used by equations 7 and 8, while being different, may
represent similar changes in river conditions. For example, perhaps flow reversals used in
equation 7 is accounting for the the flow in April and flow in May being used in equation 8 due
to reversals in flow from April to May. Another possible explanation is that the symbolic
regression creates the best fit algorithm while using the least possible variables. Many of these
flow variables may not increase fitness to a level which necessitated an addition to the algorithm.
Along with this, the regression can only use 1000 equations (programs) for each generation. A33

program containing these variables may just never have been found using the initial random
population which passed the criteria to continue to the next generation. A final explanation
could be that the Margalef Index for flow had a larger error than the Margalef Index for flow and
suspended sediment. A mutation or a crossover point changing could lead to the error becoming
less, and the variables contained in equation 8 more closely resembling the flow variables seen in
equation 7.
A Margalef Index was also created using just suspended sediment variables. Equation 9
shows the symbolic regression equation created using only suspended sediment.

I SS = [  2 ∗ SS LPL   SS 7  SS Base   2 ∗ SS 30Min   SS 9  SS 8 SS 30Min ]

−  SS 8 − SS LPL − SS Reversal

SS LPL  SS 30Min  (9)

Where I SS is the Margalef Index regressed using only suspended sediment, and the variables

are described in Table 5.
While the errors when using only suspended sediment are still small (abs error = 1.9, R 2 =
0.87), they are larger than the ones from equations 7 and 8. Again, the suspended sediment
variables in equation 9 are different from the suspended sediment variables in equation 7.
However, these variables do appear to more closely resemble the variables in equation 7 than the
variables in equation 8. Both SS Base and SS LPL are in equations 7 and 9. Also, the median flow
for July, August, and September are used in equation 9. In equation 7, the variables using
median suspended sediment are for the months June and September. It could be that June is34

close enough to July that it was able to be used here, while the suspended sediment in September
may do well enough to be used in place of having a variable for August as well.
The symbolic regression was able to closely estimate the Margalef Diversity Index, even
when using only streamflow or only suspended sediment as the independent variables (Table 6).
Figure 5 shows that all three regression equations are very highly correlated. Figure 6 shows that
the three regression equations were able to reproduce the median and variability of the field data.
The Margalef Index is considered a measure of species richness, and species richness in
the Sandusky River is relatively high. Accounting for just species richness has the ability to
show how a species is truly reacting to different factors. For instance, an individual fish may
leave a location without having anything to do with the physical factors present in the river, but
because the area does not have enough females for spawning, or because they are chased away
by a predator. By not accounting for individuals in the Margalef Index, all of an entire species
could have to leave for reasons not attributed to physical factors in the river, which is highly
unlikely.
Both streamflow and suspended sediment are responsible for nearly all the variation in the
Margalef Diversity Index in the Sandusky River. Different variables of suspended sediment and
streamflow are accounting for nearly all the changes in species richness present in the Sandusky

River.

Shannon Index
The Shannon Index is another biodiversity index based on species richness. This index
also provided good results when regressed with flow and suspended sediment. This index was35

Table 6. Calculated and regressed Margalef Indices for each year and for the three sets.

Year Calculated I Regressed I

with Flow + SS Regressed I

with Flow Regressed I

with SS 1952 4.35 4.35 4.34 4.51 1953 4.52 4.53 4.49 4.26 1954 4.5 4.51 4.54 4.54 1955 3.89 3.84 3.90 3.87 1979 4.26 4.21 4.22 4.19 1981 5.39 5.66 5.61 5.40 1988 5.75 5.70 5.79 5.71 1990 5.01 4.90 5.01 5.36 1999 4.44 4.51 4.45 5.00 2000 3.75 3.37 4.13 3.71 2001 4.69 4.82 4.22 4.54 2002 4.4 4.42 4.22 4.59

Figure 5. The three symbolic regression equations for the Margalef Index

versus the field data calculated Margalef Index.36

Figure 6. Box plot of the Margalef Index calculated from the field data and the

three regressed Margalef Indices.

also run for both flow and suspended sediment combined, and then for flow and suspended
sediment separately. Equation 10 is the symbolic regression equation for the Shannon Index
using streamflow and suspended sediment variables.

H ' Both = SS 30Min   SS Min ∗ SS LPL   Q Fall  SS 1  [  SS LPL  SS HPN  ∗ SS HPN ∗  SS 9  Q Min  ]  Q LPN (10)

Where H' Both is the Shannon Index regressed using flow and suspended sediment as the
independent variables, and all variables are explained in Table 5.
This equation has relatively small errors (abs error = 1.3, R 2 = 0.75), but not as small as
any of the Margalef indices. The Shannon Index includes a component of species richness and a37

component of the number of individuals. This last component makes this index more sensitive to
the migrations or location of each individual.
Two variables in equation 10 may necessitate further explanation, although the first

variable, SS LPL , was explained in the Margalef Index section, and once again had a frequency
occurrence of 28% (Table 5). The second variable is the median suspended sediment in January.
It is important to note that while this variable does appear in the best fit equation, it only
occurred in 16% of all runs (Table 5). Typically, there is snow on the ground in January and the
streamflow and suspended sediment concentrations are low. Also, no fish samples were taken in
this month. This variable seems to be more important as an indicator of how the river and area
as a whole will act throughout the entire year. Fish diversity in general increases as suspended
sediment in January increases, which could indicate an earlier flushing of spawning grounds,
creating more suitable spawning habitat earlier than without this January flush (Acornley and
Sear, 1999). This is important as it allows fish species such as walleye to spawn earlier. Walleye
spawn between early April and mid May, and it has been shown by Mion et al. (1998) that the
earlier the spawning of walleye, the more likely the juveniles will survive. However, 1952 has
the lowest fish diversity, yet the highest suspended sediment level for January. This is most
likely due to the fact that too much sediment is flowing here, which negatively impacted the type
of river bottom in the following months. The median suspended sediment concentration for
January in 1952 was 100 to 1000 times higher than any other January in this study, and the third
highest month seen in all the data (Table 2).38

The most common variable in the 25 runs was the streamflow fall rate, occurring 52 % of
the time (Table 5). This variable was also present in the best fit equation, which shows that it
may be the most important one when measuring fish diversity using the Shannon Index.
The Shannon Index was next run using flow as the only independent variable. Equation 11
shows the symbolic regression for the Shannon Index using only streamflow.

H ' Q = Q 6  Q Max  Q HPN

Q Max  Q 3   Q Min ∗ Q 10    Q Fall ∗ Q LPL   Q 3  Q LPN (11)

Where H' Q is the Shannon Index regressed with flow as the only independent variable, and
all variables are explained in Table 5. Equation 11 had the largest errors of the three
Shannon Index regressions (abs error = 1.5, R 2 = 0.60). It may be that flow is not having a large
impact on fish diversity when the measure of diversity is the Shannon Index. In equation 10,
only two streamflow variables (Q Fall and Q min ) are used to create the regression, which are both
included in equation 11. The levels of streamflow seem to have little importance when
calculating the Shannon Index for the fish of the Sandusky River. It also shows the importance
of suspended sediment in the Shannon Index. Streamflow for March, which is used in the
regression, occurs when no fish data was collected. It appears that higher flows in March leads
to a higher Shannon Index. One reason for this may be that the higher flow creates many of the
pools and riffles for spawning later in the year. Another explanation may be that this is simply
because this Shannon Index for flow is simply not predicting well.
Finally, a Shannon Index was regressed using only suspended sediment as the independent
variable. The symbolic regression equation for the best fit is equation 12.39

H ' SS = SS 11  SS 8  SS LPL  SS 7  SS LPN  [ SS Fall ∗ SS Reversal ∗  SS 11  SS 7  ] (12)

Where H' SS is the Shannon Index created using a symbolic regression with suspended
sediment concentration only, and all variables are shown in Table 5.
The errors here are relatively small, and in fact, almost identical to the errors of equation
10 (abs error = 1.4, R 2 = 0.75). The results show that for a diversity calculation of the Shannon
Index, suspended sediment variables seem to be more important than streamflow variables.
However, like with the Margalef Index, the variables created using only suspended sediment as
the independent variables are different from those used when calculating the Shannon Index
using both streamflow and suspended sediment as independent variables. A similar reasoning as
the one for the Margalef Index can explain some of this discrepancies. However, the fall rate of
suspended sediment is one variable which is not present in equation 10. It is likely that this
variable is not used in equation 10 because equation 10 already contains the variable of fall rate
for streamflow. Flow fall rate and suspended sediment fall rate appear to be similar. Therefore,
one of these two variables can be used in place of both variables. This could also be an
indication that multicollinearity may not be a problem in this particular study.
Suspended sediment for November is another median month variable which does not have
any actual fish data for that month. This may be an indicator that streamflows and suspended
sediment were carried later into the season than normal, which would include October (the last
month of sampling). The higher values of suspended sediment do appear to correlate with higher
Shannon Indices, meaning that this is a possibility.40

The symbolic regression Shannon Index, while not performing as well as the Margalef
Index on all levels, still performed very well, having values very similar to those calculated from
the fish data (Table 7). Figure 7 shows a comparison of all three Shanon Indices
using symbolic regressions. The suspended sediment index and the flow and suspended
sediment index both did a much better job of predicting the Shannon Index than the index using
only streamflow.
Figure 8 shows the box plot of all three Shannon Indices from regressions, as well as the
Shannon Index calculated from the fish data. All three regressed indices appear to have some
similarities to the calculated index. However, the Shannon Index for flow and suspended
sediment has a slightly higher variability in the interquartile range than the field data The other
two regressions have a similar interquartile range variability, but the whiskers are much shorter,
and both show the presence of an outlier year (1952) This outlier is most likely the result of the
higher error created for this regressed index.
This index, like the Shannon index using only flow, also had a value at 1952 which was very far
The changes in the number of individuals may be less related to changes in flow and
suspended sediment than changes in species richness, which is much closely related to changes
in flow and suspended sediment.

Shannon Index for Evenness
This index was chosen as the only index representing evenness. An evenness index is an
index which accounts for the relative abundance of each species in a particular ecosystem. The41

Table 7. Calculated and regressed Shannon Indices for each year and for the three sets.

Year Calculated

H' Regressed H' with Flow + SS Regressed H' with Flow Regressed H' with

SS 1952 2.13 2.10 1.86 1.90 1953 2.54 2.40 2.89 2.52 1954 2.50 2.79 2.50 2.37 1955 2.66 2.64 2.56 2.91 1979 2.54 2.41 2.76 2.68 1981 2.77 2.58 2.81 2.80 1988 2.84 2.77 2.58 2.80 1990 2.87 3.04 2.87 2.82 1999 2.81 2.76 2.76 2.80 2000 2.74 2.85 2.77 2.62 2001 3.04 3.07 2.88 2.80 2002 2.61 2.66 2.62 2.50

Figure 7. The three symbolic regression equations for the Shannon Index

versus the field data calculated Shannon Index.42

Figure 8. Box plot of the Shannon Index calculated from the field data and the

three regressed Shannon Indices.

Shannon Index for Evenness was first calculated using both flow and suspended sediment
variables. Equation 13 shows the symbolic regression for this index.

E Both = SS LPN  SS 4

Q HPL  Q LPL Q HPL  Q LPL   2 ∗ SS 12    2 ∗ Q LPN   SS LPN  SS 4 (13)

Where E Both is the Shannon Index for Evenness using flow and suspended sediment as
independent variables. The variables are described in Table 5.
The regression index provided relatively good results for the Shannon Index for Evenness
(abs error = 0.33, R 2 = 0.58). Once again, a variable for the month of December was selected.43

This is most likely an indicator of increased suspended sediment throughout the year. It could be
an indicator of next year's suspended sediment as well, but when comparing year to year,
December appears to be much less related to the next year's suspended sediment levels than to
the suspended sediment levels seen in the year that December falls in. Most likely, it is just an
abnormality as this variable was only selected in the best fit run.
While the number of low pulse days of suspended sediment occurred in 56% of runs, it
was not the highest occurrence. Median suspended sediment concentration for June occurred
92% of the time (Table 4). This is the highest percentage of frequency for any variable in an
index. It may be an artifact as symbolic regression is not able to advance generations if the
numerical values are close together, as is the case for the Shannon Index for Evenness.
Suspended sediment in June may have provided the increase in diversity values for an
advancement in the generations to occur. It is also possible that the suspended sediment at the
beginning of summer, which is hatching time for fish, is extremely important to the relative
abundance of each species, but not for species richness. This would result in suspended
sediment in June being extremely high for the Shannon Index for Evenness and much lower for
the Margalef and Shannon Indices as it is the case in this study.
The Shannon Index for Evenness was next calculated using just streamflow variables.
The equation created using the symbolic regression is:

E Q =  Q 9 − Q 90Min   Q LPN   [ Q LPL   Q 8 ∗ QBase  ] ∗ Q HPN ∗ Q Rise  (14)44

Where E Q is the Shannon Index for Evenness using only streamflow variables, and the

variables are defined in Table 5.
This index did not predict the Shannon Index for Evenness very well (abs error = 0.67, R 2

= 0.44). Equation 14 contains very different variables from those presented in equation 13. The
reasons are most likely similar to those presented in the other diversity indices. However, one
difference is that in equation 14, there are two months for streamflow (September and August)
which have no immediately evident correspondent variable in equation 13. This could signify
that the best fit individual using both streamflow and suspended sediment may not have been
reached. However, getting to this best fit may require a very large number of variables, which
may not substantially increase the error value to warrant inclusion. Like in other cases, the error
for the Shannon Index for Evenness using only streamflow variables is rather large, so it could
be that as error improved for this index, these variables would be replaced with better fitting

variables.
The third Shannon Index for Evenness regression equation used only suspended sediment
variables as independent variables. Equation 15 describes this regression.

E SS =  SS 6 2 ∗ SS 11   SS LPN  SS 30Min  SS 30Max 2 ∗ SS LPN   SS 30Min  SS 10  SS LPN (15)

Where E SS is the Shannon Index for Evenness using suspended sediment variables only.

The variables are described in Table 5.
This regression equation performed better than equation 13 ( abs error = 0.55, R 2 = 0.53).
Three of the suspended sediment variables found in equation 15 are not present in equation 13.45

This leads to the conclusion that the best fit equation was most likely not yet discovered, much
like the findings using the Shannon Index for Evenness using only streamflow variables.
Overall, all indices do fall into the range of values for a Shannon Index of Evenness (Table
8). Figure 9 shows that while the regressed indices do fall between zero and one as they should,
the regressed indices are still inaccurate at determining the Shannon Index for Evenness. The
major reason for the increase in error is that by calculating the evenness index, the component of
species richness is taken out. Species richness has been shown by both the Margalef Index and
the Shannon Index to be highly correlated to changes in suspended sediment and streamflow
variables. By removing the component of species richness, the error values increase. This is
further evidence that species richness is best indicated by streamflow and suspended sediment.
The box plot for the Shannon Index for Evenness is shown in Figure 10. It appears that the
Shanon Index for Evenness using both flow and suspended sediment had a similar median,
interquartile, and whisker fit with respect to the calculated data. The symbolic regression
includes most of the variability found in the field data. The box plot of the Shannon Index for
Evenness using just streamflow variables has larger variability and asymmetric whiskers when
compared with the field data. The Shannon Index for Evenness using only suspended sediment
variables had the closest median to the median of the calculated data. However, the interquartile
range and whiskers are larger.
With the Shannon Index for Evenness, the component of species richness is removed. As
shown by the Margalef and Shannon Indices, streamflow and suspended sediment variables
appear to do a very good job of simulating species richness, thus accounting for the larger
regression errors in the Shannon Index for Evenness.46

Table 8. Calculated and regressed Shannon Indices for Evenness

for each year and for the three sets.

Year Calculated E Regressed E with Flow + SS Regressed E with

Flow Regressed E with

SS 1952 0.60 0.60 0.64 0.59 1953 0.70 0.71 0.55 0.76 1954 0.70 0.83 0.80 0.65 1955 0.77 0.75 0.82 0.75 1979 0.70 0.74 0.71 0.68 1981 0.74 0.74 0.70 0.74 1988 0.71 0.69 0.59 0.82 1990 0.74 0.75 0.73 0.74 1999 0.78 0.76 0.69 0.75 2000 0.86 0.87 0.84 0.96 2001 0.80 0.80 0.82 0.66 2002 0.83 0.76 0.81 0.82

Figure 9. The three symbolic regression equations for the Shannon Index for Evenness

versus the field data calculated Shannon Index for Evenness.47

Figure 10. Box plot of the Shannon Index for Evenness calculated from the field data and the

three regressed Shannon Indices for Evenness.

Simpson Index
The symbolic regressions for the Simpson Index did not predicted well. This index is not
based on species richness, it is based on dominance, which means that it has a very low
sensitivity to rare species. Another possible reason for its lack of predictive power is that 1952
was an outlier for the Simpson Index calculated from the fish data.
The first Simpson Index was run with both streamflow and suspended sediment input as
the independent variables. Equation 16 is the symbolic regression equation for this index.

D ' Both = Q 10   2 ∗ Q Fall   Q HPN  SS 4

SS 30Min   2 ∗ Q Fall   SS 4  Q HPN Q LPN  SS LPN  SS 90Min  Q HPN  Q Fall  SS 4  SS 4  Q LPN  SS LPN  SS 90Min (16)48

Where D' Both is the Simpson Index regressed with suspended sediment and streamflow as
the independent variables. The variables are described Table 5.
This regression equation has a large error with respect to the Simpson Index (abs error =

0.38 R 2 = 0.33). This could be due to the outlier created for 1952. This outlier was removed and
a new regression was run. However, due to how similar the values of the Simpson Index are, the
symbolic regression was never able to create trees of multiple depth and nodes using the ramped

half-and-half method. Thus, the outlier was included in this data.
The year 1955 appears to be the major source of the error in this regression. When the data
for the year 1955 is removed from the table, the R 2 increases to 0.70 from 0.34. This indicates
that 1955 is causing a large amount of the error seen in this equation.
This index is dominated by the most abundant species, which can affect diversity
calculations when there are very dominant species (Jayalakshmy and Rao, 2006). This is most
likely what caused the outlier in 1952 and the trouble in regressing the Simpson Index as there
are some species which have numbers of individuals nearing the thousands while many other
species have only a few individuals (Table 3). These large numbers of individuals can skew the
data and lead to outliers in the data and the problem in the creation of this index as shown in
Figure 11.
The variable which occurred most frequently was the fall rate of streamflow. Its frequency
of occurrence was 60%, and it was also present in the best fit equation. It is likely that this
variable is very important for the Simpson Index, even though the fits are not as good as for the

other indices.49

The Simpson Index symbolic regression was also run with streamflow as the only
independent variables. Equation 17 shows the results of the symbolic regression.

D ' Q = Q 3Min  Q Fall   Q 12 ∗ Q 1Min 

Q 1Min  Q Fall  Q 7Min (17)

Where D' Q is the Simpson Index regressed with with only streamflow as the independent

variables. The variables are described in Table 5.
This index had the smallest number of variables from all other indices in this study. This
regression equation had a larger absolute error than that of equation 16, but a significantly better

R 2 value (abs error = 0.52, R 2 = 0.41). This is believed to have occurred due to the problems
with the outlier in the calculated Simpson Index. This is most likely due to the way error is
calculated. Here, by taking the absolute values of error, all error is added together. R 2 does not
use an absolute value sign, thus subtracting as well as adding. This allows for R 2 to show more
accurately how the calculated and regressed indices are related.
Only one of the streamflow variables from the Simpson Index using streamflow is also in
the Simpson Index equation using streamflow and suspended sediment. It is possible that the
streamflow values in equation 17 could be represented in the suspended sediment variables in
equation 16. However, it is more likely that the lack of similar variables is simply a product of
the fact that neither equation accurately showed the changes in the Simpson Index.
The Simpson Index regressed using suspended sediment as the independent variable had
the lowest R2 of all the indices in this study. The equation created for this index is:50

D ' SS = [ SS HPN  SS LPN   SS 5 ∗ SS LPL ∗ SS 3Min  ]

− [  SS 2  SS HPN  ∗ SS LPN ∗ SS HPN ] (18)

Where D' SS is the Simpson Index created using the symbolic regression with suspended
sediment independent variables. The variables are described in Table 5.
This regression equation index had the lowest R 2 value for this entire study (abs error =

0.41, R 2 = 0.25). However, it had a better absolute value error than that of equation 16. This is
probably the product of equation 17 having both positive and negative values for error, while the
equation 18 regressed values are mostly much higher than the calculated values.
Table 9 shows the results from the three regressions as well as the calculated Simpson
Index. It can be seen that there are numerous times in which an index of 1.0, or a perfect
diversity is calculated, which is incorrect here. When looking at Figure 11, it can be seen that
the regressed Simpson Indicies were extremely inaccurate.
The box plot of the Simpson Index is shown in Figure 12. The Simpson Index created
using streamflow and suspended sediment has a median very close in value to the field data.
However, the interquartile range and whiskers are much larger, and it has an outlier in 1955,
whereas the field data outlier is in 1952. The other two box plots in figure 12 are different in all
categories (median, interquartile range, and whiskers).
It was expected that the Simpson Index would be the worst indicator of diversity due to the
dominance which some fish species have each year. It shows how much influence dominance
can have on the Simpson Index, and the importance of using multiple biodiversity indices. If
only this index was used, it would be thought that streamflow and suspended sediment have very
little influence on the fish diversity in the Sandusky River.51

Table 9. Calculated and regressed Simpson Indices for each year and for the three sets.

Year Calculated

D' Regressed D'

with Flow + SS Regressed D'

with Flow Regressed D'

with SS 1952 0.79 0.79 0.76 0.84 1953 0.88 0.85 0.88 0.87 1954 0.87 0.90 0.87 0.87 1955 0.91 0.75 0.88 0.86 1979 0.89 0.89 0.87 0.87 1981 0.91 0.94 0.96 0.92 1988 0.91 0.91 1.0 0.98 1990 0.92 1.0 1.0 0.91 1999 0.92 0.91 0.85 0.93 2000 0.92 0.91 0.84 0.88 2001 0.94 0.94 0.93 0.90 2002 0.90 0.92 0.84 1.0

Figure 11. The three symbolic regression equations for the Simpson Index

versus the field data calculated Simpson Index.52

Figure 12. Box plot of the Simpson Index calculated from the field data and the

three regressed Simpson Indices.

All Biodiversity Indices
Table 10 shows a comparison of all created indices using streamflow and suspended
sediment, only streamflow, and only suspended sediment as the independent variables. All best
fit equations were created as a result of crossover except for the Simpson Index using only

streamflow, which used mutation.
Most of the indices calculated the years as having the same basic order. For example, the
Simpson index shows 1953 as the second lowest diversity year, while the Shannon index and the
Shannon Index for Evenness both show this year as third worst (Table 10). The one exception to
this is the Margalef Index, which shows 1953 as the fifth best year. This is most likely the53

Table 10. Summary of the best fit indices

Independent Origin Number of Depth Number of Absolute R 2

Variables Used Nodes Variables (observed-simulated) I Q+SS Crossover 47 8 14 1.2 0.96 I Q Crossover 43 8 12 1.4 0.88 I SS Crossover 27 6 7 1.9 0.87 H' Q+SS Crossover 21 6 8 1.3 0.75 H' Q Crossover 21 7 10 1.5 0.60 H' SS Crossover 17 6 7 1.4 0.75 D' Q+SS Crossover 39 8 8 0.38 0.33 D' Q Mutation 7 13 5 0.52 0.41 D' SS Crossover 5 17 6 0.41 0.25 E Q+SS Crossover 23 7 6 0.33 0.58 E Q Crossover 15 6 8 0.67 0.44
E SS Crossover 6 21 6 0.55 0.53

case due to the fact that this is the one index which does not account for the number of

individuals.
As one of the objectives was to compare how streamflow and suspended sediment affect
fish diversity, all equations and indices referred to from now on will be referring to equations
created using both streamflow and suspended sediment as the independent variables.
Overall, there were no variables which were present in the best fit equation for all four
indices. However, the number of low pulse streamflow days was present in the best fits of the
Shannon Index, the Simpson Index, and the Shannon Index for Evenness. The presence of this
variable in three of the indices suggests that the number of low pulse streamflow days is an
important variable to monitor for the health of the overall fish population in the area. For all
three indices, as the number of low pulse days increases, so do those diversity indices. This is54

believed to be the case here because lower river discharges allow for more fish from tributaries
along the Sandusky River to enter the stream without fear of getting swept away, which would
be particularly true for juvenile populations. Isely (2007) confirmed this situation when studying
the breeding population of the Robust Red-Horse.
Also, while only appearing in two of the best fit equations, the fall rate of streamflow is
present in many runs for all four indices, with the lowest frequency of occurrence (36%) being
the Margalef Index. This may indicate that this variable could also be very important to the
overall diversity of the Sandusky River.
At least one of the variables dealing with the the magnitude and duration of extreme water
conditions were included in each biodiversity index created by the symbolic regression,
although a common single variable was not included in all indices. Both streamflow and
suspended sediment followed a general pattern that higher minimum streamflow discharges and
lower maximum streamflow discharges provided higher index values, thus, better indications of
diversity. These results of low and high streamflow initially appear to go against the findings of

Freeman et al. (2001) who found that periods of high streamflow are needed for some juvenile
fish, and Taylor et al. (2008) who discovered that increased minimum streamflows have a
negative impact on fish diversity. However, the streamflow measured here is not elevated
streamflows, it is extremely high and low streamflows. Therefore, it could be that high
streamflows are not affecting the fish, but extreme high streamflows are negatively impacting
fish diversity. This is especially true of the suspended sediment concentration, as multiple
studies have shown that increased suspended sediment conditions can lead to damage to the fish55

and ultimately to death (Mion et al. , 1998; Mol and Ouboter, 2003 ;Sutherland and Meyer,
2007).
Another common factor among all indices were pulse conditions. These included the high
pulse number and length as well as the low pulse number and length. It appears that the shorter
the length of low pulses for both streamflow and suspended sediment, the higher the diversity
index for all four indices. Prey fish behave differently in turbid streamflows by changing
behaviors such as schooling patterns, making them harder for predators to catch than in clear
waters (Turesson and Brunmark, 2007). Also, less suspended sediment transport could result in
more fine sediments overtopping spawning grounds. This would lead to a negative impact on
fish populations (D'Ambrosio et al. , 2009; Onoda et al ., 2009). More interesting are the high
pulses. The more high pulse days, the higher the fish diversity. However, the longer these high
pulses of suspended sediment and streamflow last, the less the fish diversity One assumption
would be that a larger number of days of suspended sediment pulses would kill fish species.

However, Bunt et al . (2004) showed that riverine fish species adapt to elevated suspended
sediment levels within 60 minutes. So it is possible that short pulses of suspended sediment do
not affect the fish in the Sandusky River, but prolonged exposure could end up destroying gills
and killing fish. Schwartz and Herricks (2005) showed that many times fish rely on high
streamflow pulses to inhabit vegetated point bars along the banks of rivers for refuge and to
create pool-riffle structure. Perhaps predator and prey live extremely close together in these
point bars, so the longer fish must inhabit these areas to avoid the high streamflows of the floods,
the more susceptible they are to predation.56

Overall, it appears that suspended sediment has a very large impact on fish diversity in the
Sandusky River. In fact, a suspended sediment variable showed up in one of the four best fit
regressed biodiversity indices 34 times, compared to just 29 by streamflow variables. This
indicates that suspended sediment concentrations may be more important to the diversity of the
Sandusky River than streamflow levels.
Biodiversity indices calculated using different concepts (species richness, evenness, and
dominance) have several similar variables. While no single variable was present throughout the
entire study, many similar variables (such as pulse variables) were common throughout, and
many single variables did show up for in at least two diversity indices. This shows that
calculating values for multiple biodiversity indices can help in determining the most important
levels of streamflow and suspended sediment in maintaining river diversity of fish species.57

CONCLUSIONS
The results of this study suggest that the main factors influencing species richness in the
Sandusky River are different variables of streamflow and suspended sediment. Both the
Margalef Index and the Shannon Index created by regressing streamflow and suspended
sediment variables were able to very accurately predict the Margalef Index and Shannon Index
calculated from the fish data. Since these indices are based on species richness, this may indicate
that species richness is dependent mainly on streamflow and suspended sediment in the
Sandusky River.
Suspended sediment is as important, if not more important, than streamflow to fish
diversity in the Sandusky River. Both high and low suspended sediment concentration levels
were shown to negatively affect fish diversity. Therefore, it is important that suspended
sediment concentrations are kept not just from increasing to high levels for optimal fish
diversity, but also from decreasing to lower levels.
Finally, there are two categories which are most influential on fish diversity in the
Sandusky River. The first category concerns the timing and magnitude of the high and lows for
both streamflow and suspended sediment concentrations. The second category uses the
magnitude and length of pulse events for streamflow and suspended sediment. These variables
should be accounted for when decisions on the river are made to ensure that fish diversity is
maintained for the health of the ecosystem.
There are other variables which may influence fish diversity in the Sandusky River such
as pollutant and nutrients. There also may be a significant difference in how native fish respond
to increased levels of streamflow and suspended sediment when compared to the reaction of non-58

native fish. Future research should include the use of pollution and nutrient variables to build on
this research, as well as determining how both native and non-native fish are influenced by the
variables used in this study.
Genetic Programming was able to determine the factors influencing fish diversity in the
Sandusky River. The ability of symbolic regressions to determine non-linear relationships can
be very important to riverine ecosystems as these ecosystems are complex and often do not
follow linear trends. Genetic programming and symbolic regressions are useful tools for
understanding riverine ecosystems.
This study improved our understanding on how fish diversity is affected by streamflow
and suspended sediment on the Sandusky River. The equations developed here may be used in
future research for predictions over temporal scales. It also highlights the need for a
standardized method of fish sampling. The inconsistant location and methods for fish sampling
made the interpretation of results extremely difficult. Hopefully, future fish data collection will
center on predetermined locations and occur in consecutive years, which will allow for more

definite conclusions to be reached on human and natural effects on fish.
There are plans for removing the Ballville Dam in the near future. The dam currently is
trapping little suspended sediment. However, with the removal of the dam there is going to be
new sediment sources for some time that may affect the stream reaches downstream from it. If
these new sources are not handled correctly, there may be a significant loss of fish diversity on
the Sandusky River.59

REFERENCES

Acornley, R.M. and Sear, D.A. (1999). Sedimentation Transport and Siltation of Brown Trout (Salmo Trutta L.) Spawning Gravels in Chalk Streams. Hydrological Processes , 13(3), 447-158.

Baker, D.B. Introduction to the Sandusky River Basin (1975). In , David B. Baker, William B. Jackson, And Bayliss L. Prater, eds. Proceedings, Sandusky River Basin Symposium , May 2-3, 1975, Tiffin
, Ohio . Sponsored by Heidelberg College, [and] Bowling Green State University. Washington, D.C.: International Reference Group on Great Lakes Pollution from Land Use Activities, International Joint Commission, United States Environmental Protection Agency.

Becher, Anne (1998). Biodiversity

. Santa Barbara, Ca: ABC-CLIO Ltd.

Bunn, Stuart E. and Arthington, Angela H. (2002). Basic Principles and Ecological Consequences of Altered Flow Regimes for Aquatic Biodiversity. Environmental Management , 30(4), 492-507.

Bunt, Christopher M., Cooke, Steven J., Schreer, Jason F., Philipp, David P. (2004). Effects of Incremental Increases in Silt Load on the Cardiovascular Performance of Riverine and Lacustrine Rock Bass, Ambloplites Rupestris. Environmental Pollution , 128(3), 437-444.

Campos, Diogense and Fernando Isaza, Jose (2009). A Geometrical Index for Measuring Species Diversity. Ecological Indicators , 9(4), 651-658.

Castillo, Flor, Kordon, Arthur, Sweeny, Jeff, and Zirk, Wayne (2005). In Una-May O’Reilly, Tina Yu, Rick Riolo, and Bill Worzel, eds. Genetic Programming Theory and Practice II

. New York: Springer.

Clark, C. F. (1956). Sandusky River Report . Columbus, OH: Ohio Division of Wildlife.

Clark, C. F. (1993). Fishes of the Sandusky River Basin . Columbus, OH: Ohio Division of Wildlife.60

Collett, Paul D., Vine, Niall G., and Kaiser, Horst (2008). The Effect of Light Intensity on Growth of Juvenile Dusky Kob Argyrosomus Japonicus (Temminck & Schlegel 1843). Aquaculture Research , 39(5), 526-531.

D’Ambrosio, Jessica, Williams, Lance, Witter, Jonathon, and Ward, Andy (2009). Effects of Geomorphology, Habitat, and Spatial Location on Fish Assemblages in a Watershed in Ohio, USA. Environmental Monitoring and Assessment , 148(1-4), 325-341.

Evans, J. E., Levine, N. S., Roberts, S. J., Gottgens, J. F., and Newman, D. M. (2002). Assessment Using GIS and Sediment Routing of the Proposed Removal of Ballville Dam, Sandusky River, Ohio. Journal of the American Water Resources Association, 36(6), 1549-1565.

Fock, H., Uiblein, F., Koster, F., and von Westernhagen, H. (2001) Biodiversity and Species— Environment Relationships of the Demersal Fish Assemblage at the Great Meteor Seamount (Subtropical NE Atlantic), sampled by Different Trawls. Marine Biology
, 141(1), 185-199.

Forstner, Ulrich (2004). Sediment Dynamics and Pollutant Mobility in Rivers: An Interdisciplinary Approach. Lakes and Reservoirs: Research and Management , 9, 25-40.

Forsyth, J.L. The Geological Setting of the Sandusky River Basin(1975). In , David B. Baker, William B. Jackson, And Bayliss L. Prater, eds. Proceedings, Sandusky River Basin Symposium , May 2-3, 1975, Tiffin
, Ohio . Sponsored by Heidelberg College, [and] Bowling Green State University. Washington D.C.: International Reference Group on Great Lakes Pollution from Land Use Activities, International Joint Commission, United States Environmental Protection Agency.

Fremont Officials Want to Raze Dam. (2009, February 9). The Toledo Blade, http://www.toledoblade.com/apps/pbcs.dll/article?AID=/20090209/NEWS16/902090283.

Freeman, M. A., Bowen, Z. H., Bovee, K. D., and Irwin, E. R. (2001). Flow and habitat Effects of Juvenile Fish Abundance in Natural and Altered Flow Regimes. Ecological Applications, 11(1), 179-190.

Freitas, Alex A. (2002). Data Mining and Knowledge Discovery With Evolutionary Algorithms

. New York, NY: Springer.61

Gaston, Kevin J. and Spicer, John I. (1998). Biodiversity: An Introduction

. Oxford: Blackwell Science Ltd.

Grabowsk, Timothy B. and Isely, Jeffrey J. (2007). Effects of Flow Fluctiations on the Spawning Habitat of a Riverine Fish. Southeastern Naturalist , 6(2), 471-478.

Grob, Ray (1971). Down the Sandusky

. Sandusky, OH: Sandusky River Committee of the Sandusky County Chamber of Commerce.

Goodwin, Tracey H., Young, Andrew R., Holmes, Mathew G.R., Old, Gareth H., Hewitt, Ned, Leeks, G.J., et al. (2003). The Temporal and Spatial Veriability of Sediment Transport and Yields Within the Bradford Beck Catchment, West Yorkshire. The Science of the Total Environment , 314-316, 475-494.

Gutierrez-Estrada, J.C., Vasconcelos, R., and Costa, M.J. (2008). Estimating Fish Community Diversity from Environmental Features in the Tagus Estuary (Portugal): Multiple Linear Regression and Artificial Neural Network Approaches. Journal of Applied Ichthyology
, 24(2), 150-162.

Haponski, Amanda E., Marth, Thomas A., and Sepien, Carol A. (2007). Genetic Divergence Across a Low-Head Dam: A Preliminary Analysis Using Logperch and Greenside Darters. Journal of Great Lakes Research, 33 (Special Issue 2), 117-126.

Huston, Michael A. (1994). Biological Diversity: The Coexistence of Species on Changing Landscapes. Cambridge: Cambridge University Press.

Johnson, Richard K. and Hering, Daniel (2009). Response of Taxonomic Groups in Streams to Gradients in Resource and Habitat Characteristics. Journal of Applied Ecology , 46(1), 175-186.

Jones,Michael L., Netto, John K., Stockwell, Jason D., and Mion, Joseph B. (2003). Does the Value of Newly Accessible Spawning Habitat for Walleye (Stizostedion Vitreum) Depend on its Location Relative to Nursery Habitats? Canadian Journal for Fisheries and Aquatic Sciences , 60(12), 1527-1538.

Jowett, I. G., Richardson, J., and Bonnett, M.L. (2005). Relationship Between Flow Regime and Fish Abundances in a Gravel-Bed River, New Zealand. Journal of Fish Biology , 66(55), 1419-1436.62

Jugaru Tiron, Laura, Le Coz, Jerome, Provansal, Mireille, Panin, Nicolae, and Raccasi, Guillaume (2009). Flow and Sediment Processes in a Cutoff Meander of the Danube Delta During Episodic Flooding. Geomorphology , 106(3-4), 186-197.

Karr, J.R., (1981). Assessment of Biotic Integrity Using Fish Communities. Fisheries , 6(6), 21-27.

Kemp, J. L., Harper, D. M., and Crosa, G. A. (1999). Use of 'Functional Habitats' to Link Ecology With Morphology and Hydrology in River Rehabilitation. Aquatic Conservation: Marine and Freshwater Ecosystems , 9(1), 159-178.

Kennard, Mark J., Olden, Julian D., Arthington, Angela H., Pusey, Bradley J., and Poff, N. Leroy (2007). Multiscale Effects of Flow Regime and Habitat and Their Interaction on Fish Assemblage Structure in Eastern Australia. Canadian Journal of Fisheries and Aquatic Sciences , 64(10), 1346-1359

Koza, John R (1992). Genetic Programming on the Programming of Computers by Means of Natural Selection. Cambridge, MA: MIT Press.

Maclaurin, James and Sterelny, Kim (2008). What is Biodiversity? Chicago, IL: The University of Chicago Press.

MacPherson, Tara, Cahoon, Lawrence, and Mallin, Michael (2007). Water Column Oxygen Demand and Sediment Oxygen Flux: Patterns of Oxygen Depletion in Tidal Creeks. Hydrobiologia, 586(1), 235-248.

Mathworks Inc. (2008). MATLAB

. Computer Software Version 7.7, Natick MA, Mathworks Inc.

McKinsey, Deborah M. and Chapman, Lauren J. (1998). Dissolved Oxygen and Fish Distribution in a Florida Spring. Environmental Biology of Fishes , 53(2), 211-223.

Meador, Michael R and Carlisle, Daren M. (2006). Quantifying Tolerance Indicator Values for Common Stream Fish Species of the United States. Ecological Indicators , 7, 329-338.

Mellin, C., Ferraris, J., Galzin, R., Harmelin-Viven, M., Kulbicki, M., and de Loma, T. Lison (2008). Natural and Anthropogenic Influences on the Diversity Structure of Reef Fish63

Communities in the Tuamotu Archipelago (French Polynesia). Ecological Modelling
, 218(1-2), 182-187.

Mion, Joseph B., Stein, Roy A., and Marschall, Elizabeth A. (1998). River Dishcarge Drives Survival of Larval Walleye. Ecological Applications , 8(1), 88-103.

Mol, J. H., and Ouboter, P. E. (2004). Downstream Effects of Erosion From Small-Scale Gold Mining on the Instream Habitat and Fish Community of a Small Neotropical Rainforest Stream. Conservation Biology, 18(1), 201-214.

Murphy, Ryan P., Gomezdelcampo, Enrique, and Evans, James E. (2007). Using Pre-existing Channel Substrate to Determine the Effectiveness of Best Management Practices, Sandusky River, Ohio. Journal of Great Lakes Research , 33 (SI2), 167-281.

Nadal-Romero, E., Latron, J., Marti-Bono, C., and Regues, D. (2008). Temporal Distribution of Suspended Sediment Transport in a Humid Mediterranean Badland Area: The Araguas Catchment, Central Pyrenees. Geomorphology , 97, 601-616.

NCDC [National Climatic Data Center] (2009). Division of National Oceanic and Atmospheric Administration. Ohio Climate Summary,

. http://www.ncdc.noaa.gov/oa/climate/research/cag3/oh.html

.

ODNR [Ohio Department of Natural Resources] (1965). Water Inventory of the Portage and Sandusky River Basins and Adjacent Lake Erie Tributary Areas, OH, ODNR Report 20.

OEPA [Ohio Environmental Protection Agency] (2008). Fish Survey Database, Columbus, OH.

Onoda, Yukio, Maruyama, Atsushi, Kohmatsu, Yukihiro, and Yuma, Masahide (2009). The Relative Importance of Substrate Conditions as Microhabitat Determinants of a Riverine Benthic Goby, Rhinogobius Sp. OT (Orange Form) in Runs. Limnology , 10(1), 57-61.

Part-Enander, Eva and Sjoberg, Anders (1999). MATLAB 5 Handbook. Harlow England: Prentice Hall.

Piegay, H., Thevenet, A., Kondolf, G. M., and Landon, N. (2000). Physical and Human Factors Influencing Potential Fish Habitat Distribution Along a Mountain River, France. Geografiska Annaler, 82 A(1), 121-136.64

Poli, Ricardo, Langdon, William B., and McPhee, Nicholas F (2008).A Field Guide to Genetic Programming. Published via http://lulu.com and freely available at http://www.gp-fieldguide.org.uk

.

Qadir, Abdul and Malik, Riffat Naseem (2009). Assessment of an Index of Biological Integrity (IBI) to Quantify the Quality of Two Tributaries of River Chenab, Sialkot, Pakistan. Hydrobiologia , 621 (1), 127-153.

Saxton, J. M. (1977). A Study of the Recreational Aspects of the 1976 Walleye Spawn in the Sandusky River at Freemont, OH. Thesis 3242 , 1-86.

Schwartz, J. S. and Herricks, E. E. (2005). Fish Use of Stage-Specific Fluvial Habitats as Refuge Patches During a Flood in a Low-Gradient Illinois Stream. Canadian Journal of Fisheries & Aquatic Sciences , 62(7), 1540-1552.

Sharma, Sapna and Jackson, Donald A. (2007). Fish Assemblages and Environmental Conditions in the Lower Reaches of Northeastern Lake Tributaries. Journal of Great Lakes Research , 33 (1), 15-27.

Silva, Sara (2007). GPLAB: A Genetic Programming Toolbox for MATLAB. Computer Software Version 3, Portugal.

Suen, J., and Herricks, E. (2006). Investigating the Causes of Fish Community Change in the Dahan River (Taiwan) Using an Autecology Matrix. Hydrobiologia, 568(1), 317-330.

Surabhi Gaur, M.C. Deo (2008). Real-Time Wave Forecasting Using Genetic Programming. Ocean Engineering , 35, 1166-1172.

Suryanarayana, Iragavarapu, Braibanti, Antonio, Sambasiva Rao, Rupenaguntla, Ramam, Veluri Anantha, Sudarsan, Duvvuri, & Nageswara Rao, Gollapalli (2008). Neural Networks in Fisheries Research. Fisheries Research , 92, 115-139.

Sutherland, Andrew B. and Meyer, Judy L. (2007). Effects of Increased Suspended Sediment on Growth Rate and Gill Condition of Two Southern Appalachian Minnows. Environmental Biology of Fishes , 80 (4), 389-403.65

Taylor, Christopher M., Millican, Daniel S., Roberts, Matt E., and Slack, William T. (2008). Long-Term Change to Fish Assemblages and the Flow Regime in a Southeastern U.S. River System After Extensive Aquatic Ecosystem Fragmentation. Ecography , 31, 787-797.

The Nature Conservancy (2007). Indicators of Hydrologic Alteration

. Computer Software Version 7, Arlington VA.

Trautman, M. B. (1981). The Fishes of Ohio . Columbus, OH: Ohio State University Press.

Turesson, Hakan and Bronmark, Christer (2007). Predator-Prey Encounter Rates in Freshwater Piscivores: Effects of Prey Density and Water Transparency. Oecologia , 153, 281-290.

Van Tassel, Charles Sumner (1929). Story of the Maumee Valley, Toledo, and the Sandusky Region

. Chicago, IL: S.J Clarke.

Vondracek, Bruce; Zimmerman, Julie K. H.; and Westra, John V. (2003). Setting an Effective TMDL: Sediment Loading and Effects of Suspended Sediment on Fish. Journal of the American Water Resources Association , 39 (5), 1005-1015.

Xenopoulos, Marguerite A. and Lodge, David M. (2006). Going With the Flow: Using SpeciesDischarge Relationships to Forecast Losses in Fish Biodiversity. Ecology , 87(8), 1907-1914.
USGS (U.S. Geological Survey, 2009a). Streamflow Data: Sandusky River at Station 04198000. Available at waterdata.usgs.gov/nwis/uv?04198000

. Accessed on January 23, 2009.
USGS. (U.S. Geological Survey), 200(b. Streamflow Data: Sandusky River at Station 04198000. Available at waterdata.usgs.gov/nwis/uv?04198000

. Accessed on March 17, 2009.
Yang, Yi-Chen E., Cai, Ximing, & Herricks, Edwin E (2008). Identification of Hydrologic Indicators Related to Fish Diversity and Abundance: A Data Mining Approach for Fish Community Analysis. Water Resources Research , 44, W04412. Doi: 10.1029/2006WR005764.
Zak, John C. and Willig, Michael R. (2004). In , Gregory M. Mueller, Gerald F. Bills, and Mercedes S. Foster, eds. Bidoiversity of Fungi: Inventory and Monitoring Methods. Burlington, MA: Elsevier Academic Press66

Zimmerman, Julie K.H.; Vondracek, Bruce; and Westra, John (2003). Agricultural Land Use Effects on Sediment Loading and Fish Assemblages in Two Minnesota (USA) Watersheds. Environmental Management, 32 (1), 93-105.67

APPENDICES68

Appendix A

Parameter Groups and Parameters for the IHA Runs
Table A-1. Parameters used in the IHA for creating

streamflow statistics.69

Table A-2. Parameters and groups used to create

suspended sediment statistics70

Appendix B

Comparison of both gages on the Sandusky River

Figure B-1. Comparison of the streamflow of USGS gage number

04196500 and USGS gage number 0419800

The Sandusky River has two USGS gage stations along its course. The first is USGS gage
number 04198000, which is the gage located just upstream of Fremont, OH, and is the gage used
in this study. The second is USGS gage number 04196500, which is located upstream of the
gage used in this study ( Lat 40°51''02", Long -83°15'23"). This gage has no data on suspended
sediment at any time, and is also missing discharge data from 1981-2000, which is why this gage
was not used in this study. However, this gage was used to determine if the streamflow of the
Sandusky River changes uniformly for the entire river by comparing its streamflow with the71

streamflow from USGS gage number 04198000 from 1952-2002 (minus the 20 years which were
missing for gage number 04196500).
The results here show that the streamflows from both gages are similar (R 2 = 0.79). This
justifies that fish data from the whole river can be used in this study, as the streamflows are
changing at approximately the same rate throughout the entire river. Taking this along with the
data from from Figure 4, which shows a high correlation between suspended sediment
concentrations and streamflow, it is acceptable to use streamflow and suspended sediment data
from only gage 04198000 for the fish data for the entire Sandusky River.72

Appendix C

Ranks of the IHA Variables used in the Symbolic Regression7374

Appendix D

All Trees created using the Symbolic Regression

F igure D-1. Tree created for the Margalef Index for streamlow

and suspended sediment.75

Figure D-2. T ree created for the Margalef Index for stream flow.76

Figure D-3. T ree created for the Margalef Index for

suspended sediment.

Figure D-4. T ree created for the Shannon Index for streamflow

and suspended sediment.77

Figure D-5. T ree created for the Shannon Index for

streamflow.

Figure D-6. T ree created for the Shannon Index for

suspended sediment.78

Figure D-7. Tree created for the Shannon Index for Evenness for

streamflow and suspended sediment.

Figure D-8. Tree created for the Shannon Index for Evenness for streamflow.79

Figure D-9. Tree created for the Shannon Index for Evenness for

suspended sediment.80

Figure D-10. T ree created for the Simpson Index for streamflow

and suspended sediment.81

Figure D-11. T ree created for the Simpson Index for

streamflow.

Figure D-12. T ree created for the Simpson Index for

suspended sediment.