Appendix

POW calculation methods

INTRODUCTION

1.

This appendix provides a short introduction to the calculation of Pow. For further information the reader is referred to textbooks (1)(2).

2.

Calculated values of Pow are used for: — deciding which experimental method to use: Shake Flask method for log Pow between – 2 and 4 and HPLC method for log Pow between 0 and 6; — selecting conditions to be used in HPLC (reference substances, methanol/water ratio); — checking the plausibility of values obtained through experimental methods; — providing an estimate when experimental methods cannot be applied.

Principle of calculation methods

3.

The calculation methods suggested here are based on the theoretical fragmentation of the molecule into suitable substructures for which reliable log Pow increments are known. The log Pow is obtained by summing the fragment values and the correction terms for intramolecular interactions. Lists of fragment constants and correction terms are available (1)(2)(3)(4)(5)(6). Some are regularly updated (3).

Reliability of calculated values

4.

In general, the reliability of calculation methods decreases as the complexity of the substance under study increases. In the case of simple molecules of low molecular weight and with one or two functional groups, a deviation of 0,1 to 0,3 log Pow units between the results of the different fragmentation methods and the measured values can be expected. The margin of error will depend on the reliability of the fragment constants used, the ability to recognise intramolecular interactions (e.g. hydrogen bonds) and the correct use of correction terms. In the case of ionising substances the charge and degree of ionisation must be taken into consideration (10).

Fujita-Hansch π-method

5.

The hydrophobic substituent constant, π, originally introduced by Fujita et al. (7) is defined as: πX = log Pow (PhX) – log Pow (PhH) where PhX is an aromatic derivative and PhH the parent substance. e.g. πCl = log Pow (C6H5Cl) – log Pow (C6H6) = 2,84 – 2,13 = 0,71 The π-method is primarily of interest for aromatic substances. π-values for a large number of substituents are available (4)(5).

Rekker method

6.

Using the Rekker method (8) the log Pow value is calculated as: where ai is the number of times a given fragment occurs in the molecule and fi is the log Pow increment of the fragment. The interaction terms can be expressed as an integral multiple of one single constant Cm (so-called “magic constant”). The fragment constants fi and Cm have been determined from a list of 1 054 experimental Pow values of 825 substances using multiple regression analysis (6)(8). The determination of the interaction terms is carried out according to set rules (6)(8)(9).

Hansch-Leo method

7.

Using the Hansch and Leo method (4), the log Pow value is calculated as: where fi is a fragment constant, Fj a correction term (factor), ai and bj the corresponding frequency of occurence. Lists of atomic and group fragmental values and of correction terms Fj were derived by trial and error from experimental Pow values. The correction terms have been divided into several different classes (1)(4). Sofware packages have been developed to take into account all the rules and correction terms (3).

COMBINED METHOD

8.

The calculation of log Pow of complex molecules can be considerably improved, if the molecule is dissected into larger substructures for which reliable log Pow values are available, either from tables (3)(4) or by existing measurements. Such fragments (e.g. heterocycles, anthraquinone, azobenzene) can then be combined with the Hansch- π values or with Rekker or Leo fragment constants.

Remarks:

(i)	The calculation methods are only applicable to partly or fully ionised substances when the necessary correction factors are taken into account.

(ii)	If the existence of intramolecular hydrogen bonds can be assumed, the corresponding correction terms (approx. + 0,6 to + 1,0 log Pow units) must be added (1). Indications on the presence of such bonds can be obtained from stereo models or spectroscopic data.

(iii)

If several tautomeric forms are possible, the most likely form should be used as the basis of the calculation.

(iv)	The revisions of lists of fragment constants should be followed carefully.

LITERATURE ON CALCULATION METHODS

(1)

W.J. Lyman, W.F. Reehl and D.H. Rosenblatt (ed.). Handbook of Chemical Property Estimation Methods, McGraw-Hill, New York (1982).

(2)

W.J. Dunn, J.H. Block and R.S. Pearlman (ed.). Partition Coefficient, Determination and Estimation, Pergamon Press, Elmsford (New York) and Oxford (1986).

(3)

Pomona College, Medicinal Chemistry Project, Claremont, California 91711, USA, Log P Database and Med. Chem. Software (Program CLOGP-3).

(4)

C. Hansch and A.J. Leo. Substituent Constants for Correlation Analysis in Chemistry and Biology, John Wiley, New York (1979).

(5)

Leo, C. Hansch and D. Elkins. (1971) Partition coefficients and their uses. Chemical. Reviews. 71, 525.

(6)

R. F. Rekker, H. M. de Kort. (1979). The hydrophobic fragmental constant: An extension to a 1 000 data point set. Eur. J. Med. Chem. — Chim. Ther. 14, 479.

(7)

Toshio Fujita, Junkichi Iwasa & Corwin Hansch (1964). A New Substituent Constant, π, Derived from Partition Coefficients. J. Amer. Chem. Soc. 86, 5175.

(8)

R.F. Rekker. The Hydrophobic Fragmental Constant, Pharmacochemistry Library, Vol. 1, Elsevier, New York (1977).

(9)

C.V. Eadsforth and P. Moser. (1983). Assessment of Reverse Phase Chromatographic Methods for Determining Partition Coefficients. Chemosphere. 12, 1459.

(10)

R.A. Scherrer. ACS — Symposium Series 255, p. 225, American Chemical Society, Washington, D.C. (1984).

Appendix 1

Definitions

The following definitions and abbreviations are used for the purposes of this test method:

Biomass is the dry weight of living matter present in a population expressed in terms of a given volume; e.g., mg algae/litre test solution. Usually “biomass” is defined as a mass, but in this test this word is used to refer to mass per volume. Also in this test, surrogates for biomass, such as cell counts, fluorescence, etc. are typically measured and the use of the term “biomass” thus refers to these surrogate measures as well.

Chemical means a substance or mixture

Coefficient of variation is a dimensionless measure of the variability of a parameter, defined as the ratio of the standard deviation to the mean. This can also be expressed as a percent value. Mean coefficient of variation of average specific growth rate in replicate control cultures should be calculated as follows: 1. Calculate % CV of average specific growth rate out of the daily/section by section growth rates for the respective replicate; 2. Calculate the mean value out of all values calculated under point 1 to get the mean coefficient of variation of the daily/section by section specific growth rate in replicate control cultures.

ECx is the concentration of the test chemical dissolved in test medium that results in an x % (e.g. 50 %) reduction in growth of the test organism within a stated exposure period (to be mentioned explicitly if deviating from full or normal test duration). To unambiguously denote an EC value deriving from growth rate or yield the symbol “ErC” is used for growth rate and “EyC” is used for yield.

Growth medium is the complete synthetic culture medium in which test algae grow when exposed to the test chemical. The test chemical will normally be dissolved in the test medium.

Growth rate (average specific growth rate) is the logarithmic increase in biomass during the exposure period.

Lowest Observed Effect Concentration (LOEC) is the lowest tested concentration at which the chemical is observed to have a statistically significant reducing effect on growth (at p < 0,05) when compared with the control, within a given exposure time. However, all test concentrations above the LOEC must have a harmful effect equal to or greater than those observed at the LOEC. When these two conditions cannot be satisfied, a full explanation must be given for how the LOEC (and hence the NOEC) has been selected.

No Observed Effect Concentration (NOEC) is the test concentration immediately below the LOEC.

Response variable is a variable for the estimation of toxicity derived from any measured parameters describing biomass by different methods of calculation. For this test method growth rates and yield are response variables derived from measuring biomass directly or any of the surrogates mentioned.

Specific growth rate is a response variable defined as quotient of the difference of the natural logarithms of a parameter of observation (in this test method, biomass) and the respective time period

Test chemical means any substance or mixture tested using this test method.

Yield is the value of a measurement variable at the end of the exposure period minus the measurement variable's value at the start of the exposure period to express biomass increase during the test.

Appendix 2

Strains Shown to be Suitable for the Test

Green algae

Pseudokirchneriella subcapitata (formerly known as Selenastrum capricornutum), ATCC 22662, CCAP 278/4, 61.81 SAG

Desmodesmus subspicatus (formerly known as Scenedesmus subspicatus), 86.81 SAG

Diatoms

Navicula pelliculosa, UTEX 664

Cyanobacteria

Anabaena flos-aquae, UTEX 1444, ATCC 29413, CCAP 1403/13A

Synechococcus leopoliensis, UTEX 625, CCAP 1405/1

Sources of Strains

The strains recommended are available in unialgal cultures from the following collections (in alphabetical order):

ATCC: American Type Culture Collection 10801 University Boulevard Manassas, Virginia 20110-2209 USA

CCAP, Culture Collection of Algae and Protozoa Institute of Freshwater Ecology, Windermere Laboratory Far Sawrey, Amblerside Cumbria LA22 0LP UK

SAG: Collection of Algal Cultures Inst. Plant Physiology University of Göttingen Nikolausberger Weg 18 37073 Göttingen GERMANY

UTEX Culture Collection of Algae Section of Molecular, Cellular and Developmental Biology School of Biological Sciences the University of Texas at Austin Austin, Texas 78712 USA.

Appearance and characteristics of recommended species

	P. subcapitata	D. subspicatus	N. pelliculosa	A. flos-aquae	S. leopoliensis
Appearance	Curved, twisted single cells	Oval, mostly single cells	Rods	Chains of oval cells	Rods
Size (L × W) μm	8-14 × 2-3	7-15 × 3-12	7,1 × 3,7	4,5 × 3	6 × 1
Cell volume (μm3/cell)	40-60 (2)	60-80 (2)	40-50 (2)	30-40 (2)	2,5 (3)
Cell dry weight (mg/cell)	2-3 × 10- 8	3-4 × 10- 8	3-4 × 10- 8	1-2 × 10- 8	2-3 × 10- 9
Growth rate (4) (day- 1)	1,5 -1,7	1,2-1,5	1,4	1,1-1,4	2,0-2,4

Specific Recommendations on Culturing and Handling of Recommended Test Species

Pseudokirchneriella subcapitata and Desmodesmus subspicatus

These green algae are generally easy to maintain in various culture media. Information on suitable media is available from the culture collections. The cells are normally solitary, and cell density measurements can easily be performed using an electronic particle counter or microscope.

Anabaena flos-aquae

Various growth media may be used for keeping a stock culture. It is particularly important to avoid allowing the batch culture to go past log phase growth when renewing, recovery is difficult at this point.

Anabaena flos-aquae develops aggregates of nested chains of cells. The size of these aggregates may vary with culturing conditions. It may be necessary to break up these aggregates when microscope counting or an electronic particle counter is used for determination of biomass.

Sonication of sub-samples may be used to break up chains to reduce count variability. Longer sonication than required for breaking up chains into shorter lengths may destroy the cells. Sonication intensity and duration must be identical for each treatment.

Count enough fields on the hemocytometer (at least 400 cells) to help compensate for variability. This will improve reliability of microscopic density determinations.

An electronic particle counter can be used for determination of total cell volume of Anabaena after breaking up the cell chains by careful sonification. The sonification energy has to be adjusted to avoid disruption of the cells.

Use a vortex mixer or similar appropriate method to make sure the algae suspension used to inoculate test vessels is well mixed and homogeneous.

Test vessels should be placed on an orbital or reciprocate shaker table at about 150 revolutions per minute. Alternatively, intermittent agitation may be used to reduce the tendency of Anabaena to form clumps. If clumping occurs, care must be taken to achieve representative samples for biomass measurements. Vigorous agitation before sampling may be necessary to disintegrate algal clumps.

Synechococcus leopoliensis

Various growth media may be used for keeping a stock culture. Information on suitable media is available from the culture collections.

Synechococcus leopoliensis grows as solitary rod-shaped cells. The cells are very small, which complicates the use of microscope counting for biomass measurements. Electronic particle counters equipped for counting particles down to a size of approximately 1 μm are useful. In vitro fluorometric measurements are also applicable.

Navicula pelliculosa

Various growth media may be used for keeping a stock culture. Information on suitable media is available from the culture collections. Note that silicate is required in the medium.

Navicula pelliculosa may form aggregates under certain growth conditions. Due to production of lipids the algal cells sometimes tend to accumulate in the surface film. Under those circumstances special measures have to be taken when sub-samples are taken for biomass determination in order to obtain representative samples. Vigorous shaking, e.g. using a vortex mixer may be required.

Appendix 3

Growth Media

One of the following two growth media may be used:

—	OECD medium: Original medium of OECD TG 201, also according to ISO 8692

—	US. EPA medium AAP also according to ASTM.

When preparing these media, reagent or analytical-grade chemicals should be used and deionised water.

Composition of the AAP-medium (US. EPA) and the OECD TG 201 medium.

Component	AAP		OECD
	mg/l	mM	mg/l	mM
NaHCO3	15,0	0,179	50,0	0,595
NaNO3	25,5	0,300
NH4Cl			15,0	0,280
MgCl2·6(H2O)	12,16	0,0598	12,0	0,0590
CaCl2·2(H2O)	4,41	0,0300	18,0	0,122
MgSO4·7(H2O)	14,6	0,0592	15,0	0,0609
K2HPO4	1,044	0,00599
KH2PO4			1,60	0,00919
FeCl3·6(H2O)	0,160	0,000591	0,0640	0,000237
Na2EDTA·2(H2O)	0,300	0,000806	0,100	0,000269*
H3BO3	0,186	0,00300	0,185	0,00299
MnCl2·4(H2O)	0,415	0,00201	0,415	0,00210
ZnCl2	0,00327	0,000024	0,00300	0,0000220
CoCl2·6(H2O)	0,00143	0,000006	0,00150	0,00000630
Na2MoO4·2(H2O)	0,00726	0,000030	0,00700	0,0000289
CuCl2·2(H2O)	0,000012	0,00000007	0,00001	0,00000006
pH	7,5		8,1

The molar ratio of EDTA to iron slightly exceeds unity. This prevents iron precipitation and at the same time, chelation of heavy metal ions is minimised.

In test with the diatom Navicula pelliculosa both media must be supplemented with Na2SiO3 ·9H20 to obtain a concentration of 1,4 mg Si/l.

The pH of the medium is obtained at equilibrium between the carbonate system of the medium and the partial pressure of CO2 in atmospheric air. An approximate relationship between pH at 25 oC and the molar bicarbonate concentration is:

pHeq = 11,30 + log[HCO3]

With 15 mg NaHCO3/l, pHeq = 7,5 (U.S. EPA medium) and with 50 mg NaHCO3/l, pHeq = 8,1 (OECD medium).

Element composition of test media

Element	AAP	OECD
	mg/l	mg/l
C	2,144	7,148
N	4,202	3,927
P	0,186	0,285
K	0,469	0,459
Na	11,044	13,704
Ca	1,202	4,905
Mg	2,909	2,913
Fe	0,033	0,017
Mn	0,115	0,115

Preparation of OECD medium

Nutrient	Concentration in stock solution
Stock solution 1: macro nutrients
NH4Cl	1,5 g/l
MgCl2·6H2O	1,2 g/l
CaCl2·2H2O	1,8 g/l
MgSO4·7H2O	1,5 g/l
KH2PO4	0,16 g/l
Stock solution 2: iron
FeCl3·6H2O	64 mg/l
Na2EDTA·2H2O	100 mg/l
Stock solution 3: trace elements
H3BO3	185 mg/l
MnCl2·4H2O	415 mg/l
ZnCl2	3 mg/l
CoCl2·6H2O	1,5 mg/l
CuCl2·2H2O	0,01 mg/l
Na2MoO4·2H2O	7 mg/l
Stock solution 4: bicarbonate
NaHCO3	50 g/l
Na2SiO3·9H20

Sterilise the stock solutions by membrane filtration (mean pore diameter 0,2 μm) or by autoclaving (120 °C, 15 min). Store the solutions in the dark at 4 °C.

Do not autoclave stock solutions 2 and 4, but sterilise them by membrane filtration.

Prepare a growth medium by adding an appropriate volume of the stock solutions 1-4 to water:

Add to 500 ml of sterilised water: 10 ml of stock solution 1 1 ml of stock solution 2 1 ml of stock solution 3 1 ml of stock solution 4

Make up to 1 000 ml with sterilised water.

Allow sufficient time for equilibrating the medium with the atmospheric CO2, if necessary by bubbling with sterile, filtered air for some hours.

Preparation of U.S. EPA medium

1.

Add 1 ml of each stock solution in 2.1–2.7 to approximately 900 ml of deionised or distilled water and then dilute to 1 litre.

2.

Macronutrient stock solutions are made by dissolving the following into 500 ml of deionised or distilled water. Reagents 2.1, 2.2, 2.3, and 2.4 can be combined into one stock solution. 2.1 NaNO3 12,750 g. 2.2 MgCl2·6H2O 6,082 g. 2.3 CaCl2·2H2O 2,205 g. 2.4 Micronutrient Stock Solution(see 3). 2.5 MgSO4·7H2O 7,350 g. 2.6 K2HPO4 0,522 g. 2.7 NaHCO3 7,500 g. 2.8 Na2SiO3·9H2O See Note 1. Note 1: Use for diatom test species only. May be added directly (202,4 mg) or by way of stock solution to give 20 mg/l Si final concentration in medium.

3.

The micronutrient stock solution is made by dissolving the following into 500 ml of deionised or distilled water: 3.1 H3BO3 92,760 mg. 3.2 MnCl2·4H2O 207,690 mg. 3.3 ZnCl2 1,635 mg. 3.4 FeCl3·6H2O 79,880 mg. 3.5 CoCl2·6H2O 0,714 mg. 3.6 Na2MoO4·2H2O 3,630 mg. 3.7 CuCl2·2H2O 0,006 mg. 3.8 Na2EDTA·2H2O 150,000 mg. [Disodium (Ethylenedinitrilo) tetraacetate]. 3.9 Na2SeO4·5H2O 0,005 mg See Note 2. Note 2: Use only in medium for stock cultures of diatom species.

4.

Adjust pH to 7,5 ± 0,1 with 0,1 N or 1,0 N NaOH or HCl.

5.

Filter the media into a sterile container through either a 0,22 μm membrane filter if a particle counter is to be used or a 0,45 μm filter if a particle counter is not to be used.

6.

Store medium in the dark at approximately 4 °C until use.

Appendix 4

Example of a procedure for the culturing of algae

General observations

The purpose of culturing on the basis of the following procedure is to obtain algal cultures for toxicity tests.

Use suitable methods to ensure that the algal cultures are not infected with bacteria. Axenic cultures may be desirable but unialgal cultures must be established and used.

All operations must be carried out under sterile conditions in order to avoid contamination with bacteria and other algae.

Equipment and materials

See under test method: Apparatus.

Procedures for obtaining algal cultures

Preparation of nutrient solutions (media):

All nutrient salts of the medium are prepared as concentrated stock solutions and stored dark and cold. These solutions are sterilised by filtration or by autoclaving.

The medium is prepared by adding the correct amount of stock solution to sterile distilled water, taking care that no infection occurs. For solid medium 0,8 per cent of agar is added.

Stock culture:

The stock cultures are small algal cultures that are regularly transferred to fresh medium to act as initial test material. If the cultures are not used regularly they are streaked out on sloped agar tubes. These are transferred to fresh medium at least once every two months.

The stock cultures are grown in conical flasks containing the appropriate medium (volume about 100 ml). When the algae are incubated at 20 °C with continuous illumination, a weekly transfer is required.

During transfer an amount of “old” culture is transferred with sterile pipettes into a flask of fresh medium, so that with the fast-growing species the initial concentration is about 100 times smaller than in the old culture.

The growth rate of a species can be determined from the growth curve. If this is known, it is possible to estimate the density at which the culture should be transferred to new medium. This must be done before the culture reaches the death phase.

Pre-culture:

The pre-culture is intended to give an amount of algae suitable for the inoculation of test cultures. The pre-culture is incubated under the conditions of the test and used when still exponentially growing, normally after an incubation period of 2 to 4 days. When the algal cultures contain deformed or abnormal cells, they must be discarded.

Appendix 5

Data analysis by nonlinear regression

General considerations

The response in algal tests and other microbial growth tests — growth of biomass — is by nature a continuous or metric variable — a process rate if growth rate is used and its integral over time if biomass is selected. Both are referenced to the corresponding mean response of replicate non-exposed controls showing maximum response for the conditions imposed — with light and temperature as primary determining factors in the algal test. The system is distributed or homogenous and the biomass can be viewed as a continuum without consideration of individual cells. The variance distribution of the type of response for a such system relate solely to experimental factors (described typically by the log-normal or normal distributions of error). This is by contrast to typical bioassay responses with quantal data for which the tolerance (typically binomially distributed) of individual organisms are often assumed to be the dominant variance component. Control responses are here zero or background level.

In the uncomplicated situation, the normalised or relative response, r, decreases monotonically from 1 (zero inhibition) to 0 (100 per cent inhibition). Note, that all responses have an error associated and that apparent negative inhibitions can be calculated as a result of random error only.

Regression analysis

Models

A regression analysis aims at quantitatively describing the concentration response curve in the form of a mathematical regression function Y = f (C) or more frequently F(Z) where Z = log C. Used inversely C = f– 1 (Y) allows the calculation of, ECx figures, including the EC50, EC10 and EC20, and their 95 % confidence limits. Several simple mathematical functional forms have proved to successfully describe concentration — response relationships obtained in algal growth inhibition tests. Functions include for instance the logistic equation, the nonsymmetrical Weibul equation and the log normal distribution function, which are all sigmoid curves asymptotically approaching zero for C → 0 and one for C → infinity.

The use of continuous threshold function models (e.g. the Kooijman model “for inhibition of population growth” Kooijman et al. 1996) is a recently proposed or alternative to asymptotic models. This model assumes no effects at concentrations below a certain threshold EC0+ that is estimated by extrapolation of the response concentration relationship to intercept the concentration axis using a simple continuous function that is not differentiable in the starting point.

Note that the analysis can be a simple minimisation of sums of residual squares (assuming constant variance) or weighted squares if variance heterogeneity is compensated.

Procedure

The procedure can be outlined as follows: Select an appropriate functional equation, Y = f(C), and fit it to the data by non-linear regression. Use preferably the measurements from each individual flask rather than means of replicates, in order to extract as much information from the data as possible. If the variance is high, on the other hand, practical experience suggests that means of replicates may provide a more robust mathematical estimation less influenced by systematic errors in the data, than with each individual data point retained.

Plot the fitted curve and the measured data and examine whether the curve fit is appropriate. Analysis of residuals may be a particular helpful tool for this purpose. If the chosen functional relationship to fit the concentration response does not describe well the whole curve or some essential part of it, such as the response at low concentrations, choose another curve fit option — e.g., a non-symmetrical curve like the Weibul function instead of a symmetrical one. Negative inhibitions may be a problem with for instance the log — normal distribution function likewise demanding an alternative regression function. It is not recommended to assign a zero or small positive value to such negative values because this distorts the error distribution. It may be appropriate to make separate curve fits on parts of the curve such as the low inhibition part to estimate EClowx figures. Calculate from the fitted equation (by “inverse estimation”, C = f– 1(Y)), characteristic point estimates ECx's, and report as a minimum the EC50 and one or two EClow x estimates. Experience from practical testing has shown that the precision of the algal test normally allows a reasonably accurate estimation at the 10 % inhibition level if data points are sufficient — unless stimulation occurs at low concentrations as a confounding factor. The precision of an EC20 estimate is often considerably better than that of an EC10, because the EC20 is usually positioned on the approximately linear part of the central concentration response curve. Sometimes EC10 can be difficult to interpret because of growth stimulation. So while the EC10 is normally obtainable with a sufficient accuracy it is recommended to report always also the EC20.

Weighting factors

The experimental variance generally is not constant and typically includes a proportional component, and a weighted regression is therefore advantageously carried out routinely. Weighting factors for a such analysis are normally assumed inversely proportional to the variance:

Wi = 1/Var(ri)

Many regression programs allow the option of weighted regression analysis with weighting factors listed in a table. Conveniently weighting factors should be normalised by multiplying them by n/Σ wi (n is the number of datapoints) so their sum be one.

Normalising responses

Normalising by the mean control response gives some principle problems and gives rise to a rather complicated variance structure. Dividing the responses by the mean control response for obtaining the percentage of inhibition, one introduces an additional error caused by the error on the control mean. Unless this error is negligibly small, weighting factors in the regression and confidence limits must be corrected for the covariance with the control (Draper and Smith, 1981). Note that high precision on the estimated mean control response is important in order to minimise the overall variance for the relative response. This variance is as follows:

(Subscript i refers to concentration level i and subscript 0 to the controls)

Yi = Relative response = ri/r0 = 1 – I = f(Ci)

with a variance Var(Yi) = Var (ri/r0) ≅ (∂ Yi/∂ ri) · Var(ri) + ((∂ Yi/∂ r0)2 · Var(r0)

and since (∂ Yi/∂ ri) = 1/r0 and (∂ Y I/∂ r0) = ri/r0 2

with normally distributed data and mi and m0 replicates: Var(ri) = σ2/mi

the total variance of the relative response Yi thus becomes

Var(Yi) = σ2/(r0 2 · mi) + ri 2 · σ2/r0 4 · m0

The error on the control mean is inversely proportional to the square root of the number of control replicates averaged, and sometimes it can be justified to include historic data and in this way greatly reduce the error. An alternative procedure is not to normalise the data and fit the absolute responses including the control response data but introducing the control response value as an additional parameter to be fitted by non linear regression. With a usual 2 parameter regression equation, this method necessitates the fitting of 3 parameters, and therefore demands more data points than non-linear regression on data that are normalised using a pre-set control response.

Inverse confidence intervals

The calculation of non-linear regression confidence intervals by inverse estimation is rather complex and not an available standard option in ordinary statistical computer program packages. Approximate confidence limits may be obtained with standard non-linear regression programs with re-parameterisation (Bruce and Versteeg, 1992), which involves rewriting the mathematical equation with the desired point estimates, e.g. the EC10 and the EC50 as the parameters to be estimated. (Let the function be I = f (α, β, Concentration) and utilise the definition relationships f (α, β, EC10) = 0,1 and f (α, β, EC50 ) = 0,5 to substitute f (α, β, concentration ) with an equivalent function g( EC10, EC50, concentration).

A more direct calculation (Andersen et al, 1998) is performed by retaining the original equation and using a Taylor expansion around the means of ri and r0.

Recently “boot strap methods” have become popular. Such methods use the measured data and a random number generator directed frequent re-sampling to estimate an empirical variance distribution.

REFERENCES

Kooijman, S.A.L.M.; Hanstveit, A.O.; Nyholm, N. (1996): No-effect concentrations in algal growth inhibition tests. Water Research, 30, 1625-1632.

Draper, N.R. and Smith, H. (1981). Applied Regression Analysis, second edition. Wiley, New York.

Bruce, R..D. and Versteeg,, D.J. (1992). A Statistical Procedure for Modelling Continuous Ecotoxicity Data. Environ. Toxicol. Chem. 11, 1485-1494.

Andersen, J.S., Holst, H., Spliid, H., Andersen, H., Baun, A. & Nyholm, N. (1998). Continuous ecotoxicological data evaluated relative to a control response. Journal of Agricultural, Biological and Environmental Statistics, 3, 405-420.

Appendix 1

Definitions

The following definitions are applicable to this test method.

Chemical means a substance or a mixture.

ECx (Effect concentration for x % effect) is the concentration that causes an x % of an effect on test organisms within a given exposure period when compared with a control. For example, an EC50 is a concentration estimated to cause an effect on a test end point in 50 % of an exposed population over a defined exposure period.

NOEC (no observed effect concentration) is the test chemical concentration at which no effect is observed. In this test, the concentration corresponding to the NOEC, has no statistically significant effect (p < 0,05) within a given exposure period when compared with the control.

Test chemical means any substance or mixture tested using this test method.

Appendix 2

Fig. 1:   Examples for measuring unit

Key:

1 activated sludge 2 synthetic medium 3 test chemical 4 air 5 mixing vessel

6 magnetic stirrer 7 oxygen measuring cell 8 oxygen electrode 9 oxygen measuring instrument 10 recorder

Appendix 3

Fig. 2:   Example of measuring unit, using a BOD bottle

Key:

1	Test vessel
2	oxygen electrode
3	oxygen measuring instrument

Appendix 4

Fig. 3:   Example of inhibition curves

Key:

X	concentration of 3,5-dichlorophenol (mg/l)
Y	inhibition (%)
	inhibition heterotrophic respiration using a nitrifying sludge
	inhibition nitrification using a nitrifying sludge