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 Gorsevski 
ii

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. Fish diversity can be affected by changes to the 

characteristics of a river, including flow rates and suspended sediment 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 Environmental 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 USGS 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 into the symbolic regression. The symbolic regression created a 

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

variable was common among all four indices, but 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 suspended sediment. Suspended sediment variables 

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

regression was able to accurately predict the Margalef and Shannon 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. Enrique Gomezdelcampo, who has taught me not 

just how to program and write scientifically, 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 their 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 Geology 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 grammar and organizational issues in my papers. 

Thanks to Dennis Mishne and the rest of the Ohio 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 perspective 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 opportunity and pushing me to be the best I can. Thanks to my sister, 

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

night. Finally, thanks to my wife, 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 Using Symbolic Regression ..................... 74 
v

 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 Sediment 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 Calculated 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 Calculated 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 ............. 47 
vi

 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 Calculated 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 Index for Streamflow and Suspended 

Sediment .............................................................................. 74 

D-2 Tree Created for the Margalef 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 ............................................................................... 79 
vii

LIST OF FIGURES 

D-10 Tree Created for the Simpson Index 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 ............... 81 
viii

 LIST OF TABLES

Table Page 

1 Streamflow Variables Calculated From IHA 7 With Their 

Definitions .................................................................................... 23 

2 Suspended Sediment Variables Calculated From IHA 7 With 

Their Definitions ................................................................... 24 

3 Summary Table of Fish Data Used in This Study .............................. 25 

4 Average Temperature and Precipitation 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 For Creating Streamflow Statistics ............. 68 
ix

 LIST OF TABLES 

A-2 Parameters Used in the IHA For Creating Suspended Sediment 

Statistics .............................................................................. 69 

C-1 Streamflow Variables Calculated from IHA 7 and Then Ranked ............ 72 

C-2 Suspended Sediment Variables Calculated from IHA 7 and Then 

Ranked ............................................................................... 73 
x

 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 Created 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 Created 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 ................................................................... 43 
xi

 LIST OF EQUATIONS

15 Shannon Biodiversity Index for Evenness Created With 

Suspended Sediment ....................................................... 44 

16 Simpson Biodiversity Index Created With Streamflow and 

Suspended Sediment ....................................................... 47 

17 Simpson Biodiversity Index Created With Streamflow .............. 49 

18 Simpson Biodiversity Index Created With Suspended 

Sediment ..................................................................... 50 
1

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 spawning
2

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 et
3

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 of
4

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 with
5

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). Ecosystem
6

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 concentrated
7

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 Watershed
11

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 of
13

Figure 2. Map of the location of fish sampling locations and USGS gage 

station no. 04198000
14

 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 the
16

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

ni

N

ln

ni

N

(2)

Where N is the total number of individuals, ni 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

nini−1

N N −1

(4)
17

Where S is the number of species, N is the total number of organisms, and ni 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 the
19

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 occurs 
20

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 sediment 
23
24
25
26

Figure 4. Streamflow 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 (R2 =

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 (Shannon
29

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, R2 = 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 IBoth 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=QFall2∗QLPL2∗Q10 [QFall

2 ∗SS1minSS6∗QFall∗SS1min ]SS Reversal

−[SS Reversal−SS1Min∗QFall∗SS1minSS3]

QReversalSS9SS3maxSS min−SS LPL

[SS 6Q3min ]


30

Table 5. Streamflow and suspended sediment variables and the frequency of appearance in the

generated regression equations
31

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 fluxes
32

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=QLPL∗Q12 [Q1Min−Q4QLPL∗Q30max∗QFall][Q Max

2 ∗Q7∗

Q4

Q5

∗

Q1

Q5

]

Q Max

Q1



Q5

QLPL

Q1Q4Q7MaxQFall

 (8)

Where IQ 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, R2 = 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. A
33

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SS7SS Base2∗SS30Min SS9

SS8

SS30Min

]

−SS8−SS LPL−

SS Reversal

SS LPLSS30Min



 (9)

Where ISS 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, R2 =

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 SSBase and SSLPL 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 is
34

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 was 
35

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=SS30Min SS Min∗SS LPLQFallSS1

[SS LPLSS HPN ∗SS HPN∗SS9Q Min]QLPN (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, R2 = 0.75), but not as small as

any of the Margalef indices. The Shannon Index includes a component of species richness and a
37

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, SSLPL, 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=Q6Q Max

QHPN

QMaxQ3Q Min∗Q10

QFall∗QLPLQ3QLPN

 (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, R2 = 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 (QFall and Qmin) 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SS7SS LPN[SS Fall∗SS Reversal∗SS 11SS7

] (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, R2 = 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. The 
41

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.

EBoth=

SS LPNSS4

QHPLQLPL

QHPLQLPL2∗SS 122∗QLPN 

SS LPNSS4

(13)

Where EBoth 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, R2 = 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:

EQ=Q9−Q90Min QLPN[QLPLQ8∗QBase]∗QHPN∗QRise  (14)
44

Where EQ 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, R2

= 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. 

ESS=

SS 6

2∗SS11SS LPNSS30Min

SS30Max

2 ∗SS LPN SS30MinSS10SS LPN

(15)

Where ESS 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, R2 = 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=

Q102∗QFallQHPNSS 4

SS 30Min2∗QFallSS 4QHPN

QLPNSS LPNSS90MinQHPNQFallSS 4

SS 4QLPNSS LPNSS90Min

 (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 R2 = 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 R2 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=

Q3MinQFallQ12∗Q1Min 

Q1MinQFallQ7Min (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, R2 = 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. R2 does not

use an absolute value sign, thus subtracting as well as adding. This allows for R2 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SS5∗SS LPL∗SS3Min]−[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 R2 value for this entire study (abs error =

0.41, R2 = 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 the
53

Table 10. Summary of the best fit indices

Independent Origin Number of Depth Number of Absolute R

2

Variables Used Nodes Variables (observed-simulated)

IQ+SS Crossover 47 8 14 1.2 0.96

IQ 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

EQ+SS Crossover 23 7 6 0.33 0.58

EQ Crossover 15 6 8 0.67 0.44

ESS 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 is
54

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 fish
55

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

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APPENDICES
68

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 statistics
70

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 the
71

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 (R2 = 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 Regression
73
74

Appendix D

All Trees created using the Symbolic Regression

Figure D-1. Tree created for the Margalef Index for streamlow

and suspended sediment.
75

Figure D-2. Tree created for the Margalef Index for streamflow.
76

Figure D-3. Tree created for the Margalef Index for

suspended sediment.

Figure D-4. Tree created for the Shannon Index for streamflow

and suspended sediment.
77

Figure D-5. Tree created for the Shannon Index for

streamflow.

Figure D-6. Tree 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. Tree created for the Simpson Index for streamflow

and suspended sediment.
81

Figure D-11. Tree created for the Simpson Index for

streamflow.

Figure D-12. Tree created for the Simpson Index for

suspended sediment.