United States
            Environmental Protection
            Agency
             Office of Research
             Development
             Washington, DC 20460
EPA/600/R-03/106
 November 2003
SEPA
Interspecies Correlation
Estimations (ICE) for
Acute Toxicity to Aquatic
Organisms and Wildlife
            II.  User Manual and Software
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                                                   EPA/600/R-03/106
                                                     November 2003
Interspecies Correlation  Estimations
 (ICE) for Acute Toxicity To Aquatic
           Organisms and Wildlife

         II.  User Manual and  Software
                             By
              Amha Asfaw, Mark R. Ellersieck and Foster L. Mayer*
                    University of Missouri-Columbia
               College of Agriculture, Food and Natural Resources
                  Agricultural Experiment Station-Statistics
                       Columbia, MO 65211
                  *U.S. Environmental Protection Agency
                   Office of Research and Development
           National Health and Environmental Effects Research Laboratory
                        Gulf Ecology Division
                       Gulf Breeze, FL 32561
                  U.S. Environmental Protection Agency
                   Office of Research and Development
                    1200 Pennsylvania Avenue, N.W.
                       Washington, DC 20460
                                       /T~y Recycled/Recyclable
                                           Printed wrth vegetable-based ink on
                                           paper that contains a minimum of
                                           50% post-consumer libef content
                                           processed chlorine Iree

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                                          Notice
The U.S. Environmental Protection Agency through its Offices of Research and Development, Pesticide
Programs, Pollution Prevention and Toxics, and Water partially funded and collaborated in the research
described herein under EPA Project No. CR82827901 to University of Missouri-Columbia, College of
Agriculture, Food and  Natural  Resources,  Agricultural  Experiment Station-Statistics.   It has  been
subjected to the Agency's peer and administrative review and has been approved for publication as an
EPA document.  Mention of trade names or commercial  products does not constitute endorsement or
recommendation for use.

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                               Contents
List of Figures 	 ii
Abstract 	Ill
Introduction 	 1
      Data Base 	 1
      Software Language 	 2
Installing ICE  	  2
      System Requirements	  2
Using ICE in Windows 	  2
      Model Selection  	  3
ICE Application Windows 	  3
      ICE Windows 1 	  4
      ICE Windows 2 	  4
      Menu Bar	  6
            Print 	  6
            Back 	  6
            Options 	 6
            Help 	  6
Graphics 	  6
Exit  	  6
Software Development  	  8
      Model	  8
      Statistical Analyses and Equation Formation Procedures 	  8
Interpretation of Statistics 	 10
Acknowledgement 	12
References 	12
Quick References 	14

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                                    Figures




 Figure 1.     ICE window 1  	  4



 Figure2.     ICEwindow2  	  4



 Figures.     Menu bar 	  6



 Figure4.    Window  	  7



 Figures.    Data sets window 	  7



Figures.    Species versus species correlation  	  9



Figure 7.    Species versus genus correlation 	   9
                                    11

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                                            Abstract

Predictive lexicological models, including estimates of uncertainty, are necessary to address
probability-based ecological risk assessments.  A method and software (ICE) were developed for
estimating acute toxicity of chemicals to species, genera, and families when data are lacking.
Interspecies correlation models for acute toxicity (4082 models) were derived for 143 aquatic and
terrestrial organisms using Model II least squares regression, where both variables are independent
and subject to measurement error (log X2= a + b [log X,]).  Toxicity of a chemical to one species can
be predicted from toxicity to another species with known certainty. Correlations are generally best
within a taxonomic family, decreasing with increasing taxonomic distance. However, certain species
(e.g., rainbow trout) were found to be the most useful of all species for acute estimations among taxa,
including families.  Correlations for wildlife species  were not as good, in general, as those for aquatic
species, but routes of exposure are different - - oral or dietary versus respiratory, respectively.
                                              111

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                                      Introduction

Acute and chronic toxicity testing of several  species is required for protection of the numerous
species represented in environmental habitats.  Realistically, the number of species tested is
limited by test procedure, species availability, time and  expense.  Thus, environmental managers
must frequently perform risk analyses and make decisions regarding chemicals, mixtures, and
effluents for which even acute  data are minimal or do not exist.  This is of particular concern for
the protection of  endangered species that are unavailable to test, other species that have  not
been tested or are not feasible to test, and when minimal data sets exist for a chemical.

To address this  problem,  interspecies  correlations with selected organisms were conducted
relating acute toxicity of a chemical for  one  species that of another (Mayer et al. 1987, 2004).
The approach integrates  species sensitivity to  chemicals  with species taxonomic similarities
(physiology,  biochemistry) using correlation methodology.  This allows for estimation of acute
toxicity  of a  chemical to many species from toxicity values of only one or a  few species.
However, application of this methodology is  extremely time consuming without automation and
software.

This software program, Interspecies  Correlation  Estimation (ICE), described herein, allows  the
user to estimate acute toxicity for a species or higher taxa (genus, family) having no acute toxicity
data from a species having acute data.  ICE will, therefore, greatly enhance the use of probability-
based  risk assessments for chemicals  having minimal  data sets and will extend the utility of
quantitative structure-activity relationships QSAR  (Lipnick 1995), from one species (i.e., fathead
minnow, Pimephales promelas) to many species.   Also, if an acute toxicity test is  to  be
conducted, ICE can be used to more accurately identify the range of exposure concentrations
required. ICE is based on the Windows platform and is specifically designed for estimating acute
toxicity to aquatic and terrestrial organisms and  providing graphical and  tabular  presentation of
results.

Data Base

Three  data sets (aquatic, wildlife, wildlife  subacute) were  used for  correlation  analyses.   The
aquatic data set was a compilation of Mayer (1987), Mayer and Ellersieck  (1986),  ECOTOX (U.S.
Environmental Protection Agency 2002), and the  U.S.  Environmental Protection Agency's Office
of Pesticide  Programs (OPP) aquatic data (247 species,  661 chemicals, 4778 tests).  Data used
were based mainly on tests conducted with technical-grade chemicals, and water temperature,
pH, hardness, and  salinity generally conforming  to requirements of ASTM (2002).  Nominal or
measured concentrations (|ig/L) were based  on active  ingredients (>90%), with the exception of
metal salts, which were based on metal content.  The  data set was standardized additionally by
using only static  tests.   The  chemicals represent all major  pesticides, as well as numerous
industrial and inorganic chemicals. The aquatic data set was used to compare species, species
versus genera, and species versus families.  Two wildlife  sets, single oral dose or per os  (47
species, 316 chemicals, 893 tests) and 5-day dietary (19 species, 214 chemicals,  493 tests) were
analyzed.  The two data sets  consisted of  data from:  1)  acute per os tests with  data (mg
chemical/kg  of body weight) from Hudson et al. (1984), 2) 5-day dietary subacute tests with data
(mg chemical/kg dry weight of  diet) from Hill et al. (1975), and 3) the OPP data base of both  per
os and 5-day dietary tests.   Wildlife  data sets,  mainly  birds  and mammals, were partially
standardized  by using only tests with  technical-grade  chemicals.  No correlations could be
derived for wildlife species versus genera.  Detailed descriptions of the data sets  can be found in
Buckler et al. (2003) and Mayer et al. (2004).

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Software Language

The ICE software is based on a Windows platform and written in Visual Basic (Microsoft Visual
Basic 2000).  Subroutines (Fortran programs) in Visual Basic are required to call Fortran IMSL
routines necessary  in  certain  calculations (Compaq  Fortran, Visual Numeric  1999).   See
Software Development and Interpretation of Statistics for detailed methodology.

                                  Installing ICE


System Requirements
•   Operates on  Microsoft® Windows  95, 98, 2000,  NT and XP  (Windows® 98 or later is
    suggested).
•   Minimum 16MB RAM (64 MB or greater is suggested).
•   CPU speed of over 200  MHz is suggested; ICE will work with less, but is very slow acquiring
    equations.
•   6MB hard disk space.
•   Mouse or pointing device.
•   Printer (optional).

Remove any existing versions of ICE before installing the new one or malfunctions may occur.

To remove old ICE software:

1.       Double click My Computer.
2.       Double click Control Panel.
3.       Double click Add/Remove Programs.
4.       Click ICE.
5.       Click Delete or Change/Remove.
6.       Install new ICE software.

To install new ICE software:

1.       Place the ICE CD in the CD ROM drive.
2.       Click Start button.
3.       Select Run from the menu.
4.       Select Browse from the Run window.
5.       Select the drive letter associated with the CD drive from the Browse window (or ICE July
        17 2003) [D:]).
6.       Double-click Setup or D:\Setup.EXE file.
7       Click OK.
8.       Windows now walks you through the installation process.
9.       Following  installation, the  ICE program  can be accessed by clicking Start, Programs,
        and then ICE.  You can create an icon on the Desktop screen by placing the mouse
        pointer on the ICE icon, holding down the control button, and dragging the icon to desired
        location on the screen.

                            Using ICE in Windows

To start the program, double click the ICE icon and select a surrogate species for which you have
an acute value (ICE window 1, Fig. 1).  Select data sets in Options (See Options and Model
sections for available data sets).   Enter the  toxicity value  in /jg/L for aquaticspecies  (mg
chemical/kg of body weight  for wildlifespecies and wildlifefamily; mg chemical/kg dry  weight of

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diet for wildlifesubacute) where the value of 100 (default value) is the X row; press Enter. After a
surrogate species is chosen, a second list of species or taxa (X2) will appear for which you can
select and estimate the acute toxicity value (ICE window 2, Fig. 2).  Also at this time, the logo will
disappear and  be replaced with a  line graph and confidence limits.  Click on an X2  taxa to
estimate its acute toxicity value; additional X2  taxa may be selected from this window.  Click on
the Back command located in  the upper left corner to select another surrogate (X,) species; this
will produce a different listing of X2  species or taxa.  After choosing the X, and X2 species,  the
program lists statistics  and a graph; as you go from one X2 species  to  another, difference
statistics and graphics are produced  for that particular model.

Model Selection

The following is recommended  to provide the best confidence in the estimates made with the ICE
program:

1.     Use equations for species within the same genus or family.
2.     Use equations that have degrees of freedom (df) >3 (n> 5).
3.     Use equations that have a significant (p< 0.05) correlation (slope, b).
4.     If data for more than one potential surrogate species (X,) exists:
    a.   If n for surrogate, = n for surrogate2, use equation with the highest rvalue.
    b.   If n for surrogate! / n for surrogate2 use equation with smallest error mean square
        (EMS).
5.     If equations for species do not  exist in aquaticspecies or wildlifespecies, search for its
      genus or family in aquaticgenus, aquaticfamily, or wildlifefamily.  Generally, species within
      a genus or family will have more similar sensitivities to the same chemicals than more
      distantly related taxa.

                           ICE Application Windows

When first opened, the program will appear with the ICE logo to the right and a list of surrogate
species (X,) in the upper left box (Fig. 1). Scroll down to find the surrogate species of interest
and click on it. The screen will automatically go to ICE window 2 (Fig. 2); see following numbers
for explanation.

1.   List of species (X2) or taxa for which acute toxicity values can be estimated from a known
    surrogate species value (X,). Click on X2 species or taxa of interest. The  X2 species list
    changes depending on which surrogate species is chosen. If a specific surrogate and X2
    species or taxa have three or more chemicals in common, then a regression equation will be
    presented.

2.   Level of statistical Type 1 Error (a) used to determine specifice t values (e.g.,  1%, 5%, etc.)
    and confidence bands and may be changed in the Options window by user.

3.   Xt is the acute toxicity value associated with the surrogate species under the column Actual.
    The number to the right (under  the column Log-Base  10) is the same number, but the log
    base  10 (Iog10)  of that number.  The number 100 (default value) will first appear under  the
    Actual column. To change the  100 value to the acute value  of the surrogate species, click
    on the light green box and enter the surrogate species  acute value (ng/L for aquatic species
    [aquaticspecies, aguaticgenus,  aquaticfamily]; mg chemical/kg body weight [wildlifespecies,
    wildlifefamily] or mg chemical/kg  dry weight of diet [wildlifesubacute] for wildlife).

4.   X2 is the estimated acute value for species or taxa

5.   Upper and Lower confidence limits for the estimated acute toxicity value - Note the two sets
    of confidence limits listed; one  not associated with P  (pooled) and one associated with P
    The confidence limits not associated with P represent the confidence limits for that particular

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                           Figure 1. ICE window 1
                  Surrogate Spec*es

                          Figure 2. ICE window 2
                                                    Interspccles Corrvladon
                                                      18
                                                16
                                               —V
12
13


IS

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    species-species  (or  taxa) equation  (uncertainty due to model).   The  confidence limits
    associated  with  P represent  a pooled variance for  that surrogate species with all other
    species equations (uncertainty due to surrogacy).

6.  Surrogate Species (X,) is name of the selected surrogate species.

7.  Predicted Taxa (X2) is  name of the species or taxa for which acute  toxicity is being
    estimated.

8.  Degrees of freedom (df = n - 2) associated with each equation. The first df is based on the
    number of chemicals that X, and X2 have in common.  The second df (Pooled) represents the
    sum of df for that specific surrogate species and its equations among all other species.

9.  Intercept (a) is the Iog10  EC/LC/LD50 for the X2 species or taxa when the Iog10 value for the
    surrogate species (X2) is equal to 0.

10. Regression coefficient (Slope) or b represents the  Iog10 change  in X2 for every 1.0 Iog10
    change in X|.

11. Average value of predicted taxa is  the average acute toxicity value for X2 species  or taxa
    based on df + 2 (or n).

12. Error mean square (EMS) represents the variance associated with  the regression line. The
    Pooled value represents the sum of the error sum of squares associated with each equation
    divided by the pooled df.

13. Standard error of slope (SEB) is the standard error of the regression  coefficient (slope or
    b).

14. Correlation coefficient (r) is  the mutual linear association between X| and X2 species or
    taxa.

15. This window contains two t values (Calculated t value, Tabular t value) and the actual level
    of significance (Pr). The Calculated t value is a calculated  t statistic to test the significance
    of the relationship between X,  and X2.  It is calculated by dividing the slope by the standard
    error of the slope  (calculated t = b/SEB).  The Tabular t value is a two-tailed tabulated  t
    value from a standard t table.  If the  Calculated t value is  > Tabular t value, a significant
    relationship exists between the Xi  and X2 species (i.e., regression line is significantly different
    from 0).  A specific a level may be selected by changing the  % for a Type 1 error rate (see 2
    above) or the actual level of significance (Pr) may be used.

16. Graphic representation of the  regression line from the statistics (see 9-13 above),  with all
    values expressed as Iog-i0.
17. Curved lines represent confidence bands based on values for X2 species or taxa.  Two sets
    of confidence bands exist: solid and broken lines. The solid  lines are derived for that specific
    species to species/genus/family  equation  (uncertainty  due to  model) and broken  lines
    represent uncertainty due to surrogacy (see 5 and 12 above).

18. The horizontal line identifies the estimated Iog10 acute toxicity value where it crosses the X2
    axis.

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Menu Bar
The menu bar (Fig. 3) contains four commands: Print, Back, Options, and Help.

                                   Figure 3.  Menu bar
  Inleispeciei Acute Toxic** Cwidafan Models
Pnnt Bdck  Uptons Help
    Print - To print, click Print. There are two options:  1) click Single and the present screen is
    printed, or 2) click All and all equations associated with the surrogate species and the
    selected data set are printed.  Printing is accomplished on the default printer. If the printer
    supports zooming, the screen will be enlarged or reduced to fit in a landscape orientation. An
    alternative method of printing is to copy the screen displayed by simultaneously pressing ALT
    and Print Screen on the keyboard. This output can then be pasted to another program such
    as Microsoft" Word or Power Point, then printed from one of those programs.

    Back - Returns to ICE window 1  to select another surrogate species.
    Options - Allows setting program options (Fig. 4). The first option is choosing a data set.
    Data Sets (Common names) offers selection of data sets with species common name first
    followed by scientific name and Data Sets (Scientific names) provides the same data sets
    with species scientific name first followed by the common name. Click on the data set
    desired (Fig. 5), then Open (bottom right of window), followed by Select in the Options
    window. You can now work with the data set in the ICE program.  The default data set is
    aquatic species versus a variety of aquatic species (aquaticspecies). As described in the
    following Graphics section, the captions for the graph can be changed in the Options window.
    At the bottom center of the Options window is the significance level (a) in % for confidence
    bands and t tests; it can be changed here or at item 2 on the main screen.  The Select
    command will save all changes, and Cancel will only eliminate changes made while in the
    Options window. Changes made at the end of a session will  remain when the ICE program is
    started again. Click Default to return everything back to the default settings.
    Help - A narrative of the documentation. It is outlined according to major subjects. Print
    documentation by clicking on the subject and then clicking print.
                                      Graphics

Double click on the graph to fill the screen; double click again to return to the original size. The
graph can be manipulated by clicking on the Options command (upper left). Click on the
appropriate box in the Options window (Fig. 4) and type in desired caption changes for the X, and
X2 axes and the title. Then click on the Select command to install the changes. If the new
captions do not fit on the graph, click on each caption and drag to fit the allowable space. Click
Default to return all altered captions on the graph  back to default settings. To exit the Options
screen, click the upper right X on the Options window.

                                         Exit

To exit the ICE program, click the X in the upper right corner of the screen.

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Significance L«v«l
                                Figure 4.  Options window
                               |C \Pre0rani Fil«tUCE\iqu*ticsp«ci«i en
                                                                 « LA.I. L.b.l (Surrogat*)
                                                                 X2-AJII* L*b«
                              Figure 5.  Data sets window
         Look in.   _jlCE
                  _*] aquaticf arraty.cn
                  _•] aqu.aticgerius.cn
                  _*] 3quatic5pecies.cn
                  •lwilcllifefaiTiily.cn
                  •1 wildlifespecies.cn
                  _«] wildlif esubacute. en
                 Fife name
                 Files of type
                                                                                           JLJ2SJ
t file: comma tab or :pace delimited I  en I

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                            Software Development

Model

Interspecies correlations (Y = a + bX) were conducted using Model II least squares methodology
(Snedecor and Cochran  1 980) where both variables are random (both variables are independent
and subject to measurement error).  Different notations are used for model Y- a + bX(\.e., X2 = a
+ bXi), because  intertaxa toxicity comparisons are true correlations.  For that reason,  the
correlation coefficient r, a measure of the mutual linear association between two variables (X-\ and
X2), is used instead of the coefficient of determination r2 (the proportion of the variability of the
dependent variable Vthat is caused or explained by the independent variable X).

Slopes (b), intercepts (a), and other statistics were derived from the equation log X2 = a + £>(log
X), where X| equals the acute toxicity value for a surrogate species and  X2 equals the acute
toxicity value for another species (or genus or family).  Species with paired tests on three or more
chemicals were the minimum requirement for inclusion in  each analysis, although five or more are
recommended (Mayer and Ellersieck 1986).  When either of the paired species included more
than one acute value (EC, LC, or LD50), the geometric mean was  used (Fig. 6).  For genus and
family, a surrogate species was compared to all genera and families having acute  geometric
mean values for two or more individual species. These individual values were used for analyses
(i.e., a genus or family geometric mean was not used, Fig. 7). The surrogate species was not
included  in its own genus or family when those comparisons were made.  A rough estimate of
surrogate species/genus or surrogate species/family can be  made with aquaticspecies, with the
understanding that you are using only one species to represent a genus or family. In summary,
six equation data sets exist for ICE with aquaticspecies being the default data set for the software
program; they are:
1.  aquaticspecies - Aquatic species; 2914  models; 119 species versus  119 species; EC or
    LC50 in
2.  aquaticgenus - Aquatic species; 371 models; 96 species versus 14 genera; EC or LC50 in
    ng/L
3.  aquaticfamily - Aquatic species; 490 models; 1 02 species versus 1 3 families; EC or LC50 in
4.  wildlifespecies - Wildlife species; 278 models; 25 species versus 25 species; LD50  in mg
    chemical/kg of body weight
5.  wildlifefamily - Wildlife species;  61  models; 23  species  versus  5 families; LD50  in mg
    chemical/kg of body weight

6.  wildlifesubacute - Wildlife species; 14 models; 6 species versus 6 species; LC50  in mg
    chemical/kg dry weight of diet


Statistical Analyses and Equation Formation Procedures


All equations were generated  using SAS (1999). An algorithm was written to pair every species
with every other species (or genus or family) by common chemical. PROC GLM was then used
to calculate the regression equation of Iog10 predicted taxa = a + 6*log10 surrogate species  where
a = X2 intercept and b = regression coefficient (slope).
Another computer  procedure was written to capture the  necessary  statistics to generate the
equation for the data sets above. This is the same procedure to be used when data sets not


                                             8

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      Figure 6. Species versus species correlation.
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%  1.0
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                                   X2 = 0.319+ 0.828X,

                                        r = 0.974

                                        p<0.01
                  1.0          2.0           3.0

                  Fathead Minnow (log 96-h LC50)



       Figure 7. Species versus genus correlation.
                                                        4.0
o   4.0
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    1.0-
                                      = -0.194 + 1.

                                         r = 0.980

                                         p<0.01
                  1.0         2.0          3.0


                    Rainbow Trout (log 96-h LC50)
                                                      4.0

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included in ICE are of interest.  In order for ICE to be able to read data, the procedure performs
the following functions:

    1.  From the SAS  output, capture  the following parameters:  surrogate species  (X,) name,
       predicted species or  taxa  (X2)  name, sample  size,  intercept,  regression coefficient
       (slope),  predicted species  mean,  error mean  square,  standard error  of  the slope,
       correlation coefficient (r), and probability that slope is significant.
    2.  Enter  the  parameters in Microsoft® Excel  and save  them as  comma,  tab or space
       delimited files.  If space delimited  files are used, a data value can  not contain spaces. For
       this reason comma or  tab delimited files are preferred.
    3.  If more than one equation is  calculated, sort the file by X, and X2.

All equation data sets can be viewed in Microsoft* Excel or other spreadsheet software that can
read ASCII text files. All files supplied,  are comma delimited. The order  of the parameters is as
follows, which each letter representing a column in the spreadsheet.

A   =  Surrogate species (X,)
B   =  Predicted taxa (X2)
C   =  Sample size (n) for which each equation is based (df = n - 2)
D   =  Intercept (a)
E   =  Regression coefficient (slope b)
F   =  Average value of the predicted taxa
G   =  Error mean square (EMS)
H   =  Standard error of the regression coefficient (SEB)
I    =  Correlation coefficient (i)
J   -  Probability (Pr) that the slope is  not equal to 0

                           Interpretation of Statistics

The purpose of the ICE software is to estimate an acute toxicity value for an untested species or
taxa (X2) from an actual test value for the surrogate species (X,).  If a model for the X2 species
does not exist, an estimate may be made by using higher taxonomic levels (genus or family)
containing that X2 species.  The accuracy of the estimated value can be judged visually by the
closeness of the confidence bands to the regression line. The closer the confidence bands are to
the estimated  value, the higher the confidence in the estimate.   In certain cases, where the
correlation  may  be less than acceptable, the confidence in accuracy may be enhanced by the
correlative strength of the surrogate species selected.   This occurs when the confidence bands
for uncertainty due to surrogacy is smaller than the uncertainty due to the specific model.

ICE provides a  number  of other statistics  that estimate the accuracy of prediction.  The  first
statistic to evaluate is the significance of the correlation between XT and X2 or when slope (b) # 0
(see 15, Fig. 2). This is  accomplished by a t test and comparing the Calculated t value to the
Tabular t value or by using the actual  significance level (Pr).  If the Calculated t value is equal
to  or greater than the Tabular t value, then the correlation is significant  at the a level selected.
The Pr value should be < 0.05 for the correlation (slope,  b) to be significant. When the regression
coefficient (slope b) is close to 1.0,  chemicals affect the X, and X2 species in a similar fashion.
The Intercept (a) can be used to determine if chemicals are generally more or less toxic to one
species or taxa than another: negative  intercept,  the  X2 species or taxa are generally more
sensitive; positive intercept, the X) species are generally more sensitive.
                                             10

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The next statistic to assess is the Correlation coefficient (i).  The larger the r value and the
closer it is  to 1.0, the stronger the acute toxicity relationship is between the two taxa selected.
However, r can sometimes be misleading in that it can be very high, but the t-test statistic may
not show a significant relationship.  This most frequently occurs when the degrees of freedom (df)
are low and/or the slope is close to zero. We recommend that the degrees of freedom be at least
3 (or  n > 5) in order  to  increase confidence in the equations  (Mayer and  Ellersieck 1986).
However, all equations having degrees of freedom of > 1  (n > 3) were included, because many
species do  not have existing or acceptable data available.  These equations are intended to show
the relationship, based on the  available  data.    For further information on calculation  and
interpretation of linear regression analysis, see Ellersieck and LaPoint (1995).

Be aware that the prediction of sensitivity of one species from another by a regression equation is
not the same equation if reversed. This is why two different equations are needed. The only time
an equation can predict in either direction is if ? = 1.0.  The following is a proof to demonstrate.

Let:
 y = average value of Y
 x = average value of X
 y = predicted value Y
 x - predicted value of X
 Yc= substitute value of Y


The linear regression of Y on X with slope b:

 y=y + b(x-x)

 y = (y - bx ) + bx(y - intercept + slope [x])

Substitute a particular Y = Yc for y  and solve for* .

This is the predicted Xwhen Y - Yc

 x = (Yc-y +bx )/b = (Yc- y)/b+x                                (1)

The linear regression of Xon y with slope gr

 x=(x   gy) + gY (x  = intercept + slope [Y])
 x = (x  -gy)+gYc


Substitute g from r - Jbg  => g = r2 /b in the above equation.


 x = (x  -r2y/b) + r2Yc/b = (Yc-  y)rz/b + x                         (2)

Compare equation (1) and (2); the two will be equal only when r2 = 1.

If there is no variance around the  regression line, the error mean square will equal zero;  thus,  all
points will fit exactly on the regression line.  This is  the only time that r = 1.
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                               Acknowledgement

This project was sponsored  in part by the U.S. Environmental Protection Agency's Offices of
Research and Development, Pesticide Programs, Pollution Prevention and Toxics, and Water
under Cooperative Agreement CR82827901.  The authors wish to thank the many researchers
for  producing the acute and subacute toxicity values  over the years.  Also, thanks to Marcia
Nelson and Stephen Embry for technical  support on graphics,  and to Valerie Coseo,  Mary
Adkinson, and Debbie Scholes for manuscript preparation. Kathryn Gallagher, Brian Montague,
and Christine Russom provided  assistance in data acquistion  and Vic Camargo, Peggy Harris,
Linda Harwell, and Russ Ryder  contributed to data base management.  Peer review and beta
testing were contributed by M. Anderson, S. Belanger,  L. Burns, J. Camargo, C. Chancy, L.
Courtney, D. Dantin, S. Dyer, V. Engle, M. Faircloth, J. Harvey, S. Jordan, A. Kennedy, S. Kim, T.
Linton, K. Matsuzaki, R. Pepin, D. Rodier, M. Salazar, K. Solomon, K. Summers, T. Traas, C.
Walker, W.  Waller, and R. Wilhour.
                                    References

American Society for Testing and Materials. 2002.  Standard guide for conducting acute toxicity
tests on test materials with fishes, macroinvertebrates, and amphibians.  In Annual Book of ASTM
Standards, E729-96. Am. Soc. Test. Mater., West Conshohocken, PA.

Buckler, D.R.,  F.L. Mayer,  M.R. Ellersieck, and A. Asfaw.  2003.  Evaluation of minimum data
requirements for acute toxicity value extrapolation. U.S. Environmental Protection Agency Rept.
No. EPA/600/R-03/104, Washington, DC.

Compaq Fortran. 1999. Compaq Computer Corporation, Houston, TX.

Ellersieck, M.R. and T.W. LaPointe. 1995. Statistical analysis.  Pages 307-344. In G.M. Rand,
ed. Fundamentals of Aquatic Toxicology, 2nd Ed.  Taylor & Francis, Washington, DC.

Hill,  E.F.,  R.G. Heath, J.W.  Spann,  and J.D. Williams.   1975.   Lethal  dietary  toxicities of
environmental  pollutants to birds.  U.S. Fish and Wildlife Service  Special Scientific Rept. 191,
Washington, DC. 61 p.

Hudson, R.H.,  R.K.  Tucker, and M.A. Haegele.  1984.  Handbook of toxicity of pesticides to
wildlife.  U.S. Fish and Wildlife Service  Resource Publ. 153, Washington, DC. 90 p.

Lipnick, R.L.   1995.  Structure-activity relationships.   Pages  609-655.   In G.M. Rand, ed.
Fundamentals of Aquatic Toxicology, 2  Ed. Taylor & Francis, Washington, DC.

Mayer,  F.L.   1987.   Acute toxicity  handbook  of  chemicals  to  estuarine organisms.  U.S.
Environmental Protection Agency Rept. No. EPA/600/8-87/017, Gulf  Breeze, FL. 274  p.

Mayer, F.L. and M.R. Ellersieck.  1986. Manual of acute toxicity:  Interpretation and data base for
410 chemicals  and 66 species of freshwater animals.  U.S.  Fish and Wildlife Service Resource
Publ. 160, Washington, DC.  579 p.
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Mayer, F.L., C.H. Deans, and A.  G.  Smith.  1987   Inter-taxa correlations for toxicity to aquatic
organisms.  U.S. Environmental Protection Agency Rept. No. EPA/600/X-87/332, Gulf Breeze,
FL.  59 p.

Mayer, F.L., M.R. Ellersieck, and A. Asfaw. 2004.  Interspecies correlation estimations (ICE) for
acute toxicity  to aquatic organisms and  wildlife.   I  Technical  basis.   U.S.  Environmental
Protection Agency Rept. No. EPA/600/R-03/105, Washington, DC.

Microsoft Visual Basic 6.0 (SP5), Copyright 1987-2000, Microsoft Corporation, United States.

SAS Institute Inc.  1999. SAS/STAT®  User's Guide, Version 8.   SAS Institute Inc., Gary, SC.
3884 p.

Snedecor, G. W. and W. G. Cochran.  1980.  Statistical Methods,  7th ed.  Iowa State University
Press, Ames, IA. 507 p.

U.S. Environmental Protection Agency. 2002.  ECOTOX.  Release 2.0. Ecotoxicology Database
(www.epa.qov/ecotox), Duluth, MN.

Visual Numeric.   1999 Visual Numerics IML  Fortran 90 MP  Library, Version 4.01 for Microsoft
Windows.  Visual Numerics, Inc., Houston, TX.
                                             13

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                                 Quick Reference

1.   Installing ICE
       •   Insert disk into CD ROM drive
       •   Click Start button.
       •   Select Run from menu.
       •   Select Browse from the Run window.
       •   Select drive letter associated with CD Drive from the Browse window (or ICE July
           17, 2003 [D:]).
       •   Double Click Setup or D:\SETUP.EXE file.
       •   Click OK.
       •   Windows now walks you through installation process.
       •   Following installation, click Start, Programs, and then ICE; drag ICE icon to desired
           screen location.

2.   Using ICE
       •   Open ICE program.
       •   Select  data set  in Options (Data  Sets, select  data  set, Open, then  Select);
           aquaticspecies  =  aquatic  surrogate species vs. estimated species (aquaticgenus,
           species  vs. genus;  aquaticfamily,  species  vs. family), wildlifespecies =  wildlife
           surrogate species vs. estimated species (wildlifefamily, species vs. family; per os),
           wildlifesubacute = wildlife surrogate species vs. estimated species (dietary).
       •   Select Surrogate Species (X^) having an acute toxicity value.
       •   Enter surrogate species  acute  toxicity value  at  the  100  default  value (\ig/L  for
           aquaticspecies, aquaticgenus, aquaticfamily; mg/kg body weight for wildlifespecies
           and wildlifefamily;  mg/kg diet for wildlifesubacute).
       •   Select Predicted Taxa (X2)  to estimate acute toxicity.
       •   Select  Back in menu bar  to choose another surrogate species; select  Options to
           choose another data set.
       •   Select  Print then Single to print that  frame or All to  print all  correlations for the
           chosen surrogate  species within that data set.

3.   Choosing best correlations
       •   Use equations for surrogate and predicted taxa within same genus or family.
       •   Use equations having df > 3 (n> 5).
       •   Use equations having a significant (p < 0.05) correlation (slope, b).
       •   If data for more than one surrogate exists:
           n-i  = n2, use equation having highest rvalue
           n,  * n2, use equation having smallest error mean square value.
       •   If  equations for the species to  be  estimated do not  exist  in  aquaticspecies or
           wildlifespecies,  search for its genus  or family in aquaticgenus, aquaticfamily, or
           wildlifefamily.
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