Commission Regulation (EC) No 761/2009Show full title

ANNEX IV C.3. FRESHWATER ALGAE AND CYANOBACTERIA, GROWTH INHIBITION TEST

1. METHOD

This method is equivalent to OECD TG 201 (2006) (1).

1.1. INTRODUCTION

Testing Methods are periodically reviewed and updated in the light of scientific progress. Testing Method C.3 needed to be revised to include additional species and to meet the requirements for hazard assessment and classification of chemicals. The revision has been completed on the basis of extensive practical experience, scientific progress in the field of algal toxicity studies, and extensive regulatory use, which has occurred since the original adoption.

1.2. DEFINITIONS

The following definitions and abbreviations are used for the purposes of this Testing 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.

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 percentage value. The 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 of all the values calculated in point 1 to get the mean coefficient of variation of the daily/section-by-section specific growth rate in replicate control cultures.

EC_x : is the concentration of the test substance dissolved in the 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 the growth rate or from the yield, the symbols ‘E_rC’ and ‘E_yC’ are used respectively.

Growth medium: is the complete synthetic culture medium in which test algae grow when exposed to the test substance. The test substance 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 substance 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 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 the quotient of the difference of the natural logarithms of a parameter of observation (in this Testing Method, biomass) and the respective time period.

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.

1.3. APPLICABILITY OF THE TEST

This Testing Method is most easily applied to water-soluble substances which, under the conditions of the test, are likely to remain in the water. For testing of substances that are volatile, strongly adsorbing, coloured, having a low solubility in water or substances that may affect the availability of nutrients or minerals in the test medium, certain modifications of the described procedure may be required (e.g. closed system, conditioning of the test vessels). Guidance on some appropriate modifications is given in (2), (3) and (4).

1.4. PRINCIPLE OF THE TEST

The purpose of this test is to determine the effects of a substance on the growth of freshwater microalgae and/or cyanobacteria. Exponentially growing test organisms are exposed to the test substance in batch cultures over a period of normally 72 hours. In spite of the relatively brief test duration, effects over several generations can be assessed.

The system response is the reduction of growth in a series of algal cultures (test units) exposed to various concentrations of a test substance. The response is evaluated as a function of the exposure concentration in comparison with the average growth of replicate, unexposed control cultures. For full expression of the system response to toxic effects (optimal sensitivity), the cultures are allowed unrestricted exponential growth under sufficient nutrient conditions and continuous light for a sufficient period of time to measure reduction of the specific growth rate.

Growth and growth inhibition are quantified by measurements of the algal biomass as a function of time. Algal biomass is defined as the dry weight per volume, e.g. mg algae/litre test solution. However, dry weight is difficult to measure and therefore surrogate parameters are used. Of these surrogates, cell counts are most often used. Other surrogate parameters include cell volume, fluorescence, optical density, etc. A conversion factor between the measured surrogate parameter and biomass should be known.

The test endpoint is inhibition of growth, expressed as the logarithmic increase in biomass (average specific growth rate) during the exposure period. From the average specific growth rates recorded in a series of test solutions, the concentration bringing about a specified x % inhibition of growth rate (e.g. 50 %) is determined and expressed as the E_rC_x (e.g. E_rC₅₀).

For the application of this method within the EU regulatory framework, calculation of results should be based on an average specific growth rate for the reasons described in section 2.2 below. An additional response variable used in this Testing Method is yield, which may be needed to fulfil specific regulatory requirements in some countries. It is defined as biomass at the end of the exposure period minus the biomass at the start of the exposure period. From the yield recorded in a series of test solutions, the concentration bringing about a specified x % inhibition of yield (e.g. 50 %) is calculated and expressed as the E_yC_x (e.g. E_yC₅₀).

In addition, the lowest observed effect concentration (LOEC) and the no observed effect concentration (NOEC) may be statistically determined.

1.5. INFORMATION ON THE TEST SUBSTANCE

Information on the test substance, which may be useful in establishing the test conditions, includes the structural formula, purity, stability in light, stability under the conditions of the test, light absorption properties, pKa, and results of studies of transformation including biodegradability in water.

The water solubility, octanol water partition coefficient (P_ow) and the vapour pressure of the test substance should be known, and a validated method for the quantification of the substance in the test solutions with reported recovery efficiency and limit of detection should be available.

1.6. REFERENCE SUBSTANCE

Reference substance(s), such as 3,5-dichlorophenol used in the international ring test (4), may be tested as a means of checking the test procedure. Potassium dichromate can also be used as a reference substance for green algae. It is desirable to test a reference substance at least twice a year.

1.7. VALIDITY OF THE TEST

For the test to be valid, the following performance criteria should be met:

• The biomass in the control cultures should have increased exponentially by a factor of at least 16 within the 72-hour test period. This corresponds to a specific growth rate of 0,92 day^–1. For the most frequently used species, the growth rate is usually substantially higher (see Appendix 1). This criterion may not be met when species that grow slower than those listed in Appendix 1 are used. In this case, the test period should be extended to obtain at least a 16-fold growth in control cultures, while the growth has to be exponential throughout the test period. The test period may be shortened to at least 48 h to maintain unlimited exponential growth during the test, as long as the minimum multiplication factor of 16 is reached.

• The mean coefficient of variation for section-by-section specific growth rates (days 0-1, 1-2 and 2-3, for 72-hour tests) in the control cultures (see section 1.2 under ‘coefficient of variation’) must not exceed 35 %. See the second paragraph in section 2.2.1 for the calculation of section-by-section specific growth rate. This criterion applies to the mean value of coefficients of variation calculated for replicate control cultures.

• The coefficient of variation of average specific growth rates during the whole test period in replicate control cultures must not exceed 7 % in tests with Pseudokirchneriella subcapitata and Desmodesmus subspicatus. For other less frequently tested species, the value should not exceed 10 %.

1.8. DESCRIPTION OF THE METHOD

1.8.1. Apparatus

Test vessels and other apparatus, which will come into contact with the test solutions should be made entirely of glass or other chemically inert material. The items should be thoroughly washed to ensure that no organic or inorganic contaminants may interfere with the algal growth or composition of the test solutions.

The test vessels will normally be glass flasks of dimensions that allow a sufficient volume of culture for measurements during the test and a sufficient mass transfer of CO₂ from the atmosphere (see the second paragraph in section 1.8.9). Note that the liquid volume must be sufficient for analytical determinations (see the fifth paragraph in section 1.8.11).

In addition, some or all of the following equipment will be required:

• Culturing apparatus: a cabinet or chamber is recommended, in which the chosen incubation temperature can be maintained at ±2 °C.

• Light measurement instruments: it is important to note that the method of measurement of light intensity, and in particular the type of receptor (collector), will affect the measured value. Measurements should preferably be made using a spherical (4 π) receptor (which responds to direct and reflected light from all angles above and below the plane of measurement), or a 2 π receptor (which responds to light from all angles above the measurement plane).

• Apparatus to determine algal biomass. Cell count, which is the most frequently used surrogate parameter for algal biomass, may be made using an electronic particle counter, a microscope with counting chamber, or a flow cytometer. Other biomass surrogates can be measured using a flow cytometer, fluorimeter, spectrophotometer or colorimeter. A conversion factor relating cell count to dry weight is useful to calculate. In order to provide useful measurements at low biomass concentrations when using a spectrophotometer, it may be necessary to use cuvettes with a light path of at least 4 cm.

1.8.2. Test organisms

Several species of non-attached microalgae and cyanobacteria may be used. The strains listed in Appendix 1 have been shown to be suitable using the test procedure specified in this Testing Method.

If other species are used, the strain and/or origin should be reported. It has to be confirmed that exponential growth of the selected test alga can be maintained throughout the test period under the prevailing conditions.

1.8.3. Growth medium

Two alternative growth media, the OECD and the AAP medium, are recommended. The compositions of these media are shown in Appendix 2. Note that the initial pH value and the buffering capacity (regulating pH increase) of the two media are different. Therefore the results of the tests may be different depending on the medium used, particularly when testing ionising substances.

Modification of the growth media may be necessary for certain purposes, e.g. when testing metals and chelating agents or testing at different pH values. Use of a modified medium must be described in detail and justified (3)(4).

1.8.4. Initial biomass concentration

The initial biomass in the test cultures must be the same in all test cultures and sufficiently low to allow exponential growth throughout the incubation period without risk of nutrient depletion. The initial biomass should not exceed 0,5 mg/l as dry weight. The following initial cell concentrations are recommended:

Pseudokirchneriella subcapitata	5 × 103-104	cells/ml
Desmodesmus subspicatus	2-5 × 103	cells/ml
Navicula pelliculosa	104	cells/ml
Anabaena flos-aquae	104	cells/ml
Synechococcus leopoliensis	5 × 104-105	cells/ml

1.8.5. Concentrations of test substance

The concentration range in which effects are likely to occur may be determined on the basis of results from range-finding tests. For the final definitive test, at least five concentrations arranged in a geometric series with a factor not exceeding 3,2 should be selected. For test substances showing a flat concentration response curve, a higher factor may be justified. The concentration series should preferably cover the range causing 5-75 % inhibition of algal growth rate.

1.8.6. Replicates and controls

The test design should include three replicates at each test concentration. If determination of the NOEC is not required, the test design may be altered to increase the number of concentrations and reduce the number of replicates per concentration. The number of control replicates must be at least three, and ideally should be twice the number of replicates used for each test concentration.

A separate set of test solutions may be prepared for analytical determinations of test substance concentrations (see the fourth and sixth paragraphs in section 1.8.11).

When a solvent is used to solubilise the test substance, additional controls containing the solvent at the same concentration as used in the test cultures must be included in the test design.

1.8.7. Preparation of inoculum culture

In order to adapt the test alga to the test conditions and ensure that the algae are in the exponential growth phase when used to inoculate the test solutions, an inoculum culture in the test medium is prepared 2-4 days before start of the test. The algal biomass should be adjusted in order to allow exponential growth to prevail in the inoculum culture until the test starts. The inoculum culture shall be incubated under the same conditions as the test cultures. Measure the increase in biomass in the inoculum culture to ensure that growth is within the normal range for the test strain under the culturing conditions. An example of the procedure for algal culturing is described in Appendix 3. To avoid synchronous cell divisions during the test, a second propagation step of the inoculum culture may be required.

1.8.8. Preparation of test solutions

All test solutions must contain the same concentrations of growth medium and initial biomass of test algae. Test solutions of the chosen concentrations are usually prepared by mixing a stock solution of the test substance with growth medium and inoculum culture. Stock solutions are normally prepared by dissolving the substance in test medium.

Solvents, e.g. acetone, t-butyl alcohol and dimethyl formamide, may be used as carriers to add substances of low water solubility to the test medium (2)(3). The solvent concentration should not exceed 100 µl/l, and the same concentration of solvent should be added to all cultures (including controls) in the test series.

1.8.9. Incubation

Cap the test vessels with air-permeable stoppers. The vessels are shaken and placed in the culturing apparatus. During the test it is necessary to keep the algae in suspension and to facilitate transfer of CO₂. To this end, constant shaking or stirring should be used. The cultures should be maintained at a temperature in the range of 21 to 24 °C, controlled at ±2 °C. For species other than those listed in Appendix 1, e.g. tropical species, higher temperatures may be appropriate, providing that the validity criteria can be fulfilled. It is recommended to place the flasks randomly and to reposition them daily in the incubator.

The pH of the control medium should not increase by more than 1,5 units during the test. For metals and compounds that partly ionise at a pH around the test pH, it may be necessary to limit the pH drift to obtain reproducible and well defined results. A drift of < 0,5 pH units is technically feasible and can be achieved by ensuring an adequate CO₂ mass transfer rate from the surrounding air to the test solution, e.g. by increasing the shaking rate. Another possibility is to reduce the demand for CO₂ by reducing the initial biomass or the test duration.

The surface where the cultures are incubated should receive continuous, uniform fluorescent illumination e.g. of ‘cool-white’ or ‘daylight’ type. Strains of algae and cyanobacteria vary in their light requirements. The light intensity should be selected to suit the test organism used. For the recommended species of green algae, the light intensity at the level of the test solutions shall be selected from the range of 60-120 µE·m^–2·s^–1 when measured in the photosynthetically effective wavelength range of 400-700 nm using an appropriate receptor. Some species, in particular Anabaena flos-aquae, grow well at lower light intensities and may be damaged at high intensities. For such species an average light intensity in the range 40-60 µE·m^–2·s^–1 should be selected. (For light-measuring instruments calibrated in lux, an equivalent range of 4 440-8 880 lux for cool white light corresponds approximately to the recommended light intensity 60-120 µE·m^–2·s^–1). The light intensity shall not vary more than ±15 % from the average light intensity over the incubation area.

1.8.10. Test duration

The test duration is normally 72 hours. However, shorter or longer test durations may be used, provided that all validity criteria in section 1.7 can be met.

1.8.11. Measurements and analytical determinations

The algal biomass in each flask is determined at least daily during the test period. If measurements are made on small volumes removed from the test solution by pipette, these should not be replaced.

Measurement of biomass is done by manual cell counting by microscope or an electronic particle counter (by cell counts and/or biovolume). Alternative techniques, e.g. flow cytometry, in vitro or in vivo chlorophyll fluorescence (6)(7), or optical density can be used providing a satisfactory correlation with biomass can be demonstrated over the range of biomass occurring in the test.

The pH of the solutions shall be measured at the beginning and at the end of the test.

Provided an analytical procedure for determination of the test substance in the concentration range used is available, the test solutions should be analysed to verify the initial concentrations and maintenance of the exposure concentrations during the test.

Analysis of the concentration of the test substance at the start and end of the test of a low and high test concentration, and a concentration around the expected EC₅₀ may be sufficient where it is likely that exposure concentrations will vary less than 20 % from nominal values during the test. Analysis of all test concentrations at the start and end of the test is recommended where concentrations are unlikely to remain within 80-120 % of nominal. For volatile, unstable or strongly adsorbing test substances, additional sampling for analysis at 24 hour intervals during the exposure period is recommended in order to better define loss of the test substance. For these substances, extra replicates will be needed. In all cases, determination of test substance concentrations need only be performed on one replicate vessel at each test concentration (or on the contents of the vessels pooled by replicate).

Test media prepared specifically for analysis of exposure concentrations during the test should be treated identically to those used for testing, i.e. they should be inoculated with algae and incubated under identical conditions. If analysis of the dissolved test substance concentration is required, it may be necessary to separate algae from the medium. Separation should preferably be made by centrifugation at a low g-force, sufficient to settle the algae.

If there is evidence that the concentration of the substance being tested has been satisfactorily maintained within ±20 % of the nominal or measured initial concentration throughout the test, analysis of the results can be based on nominal or measured initial values. If the deviation from the nominal or measured initial concentration is greater than ±20 %, analysis of the results should be based on geometric mean concentration during exposure or on models describing the decline of the concentration of test substance (3)(8).

The alga growth inhibition test is a more dynamic test system than most other short-term aquatic toxicity tests. As a consequence, the actual exposure concentrations may be difficult to define, especially for adsorbing substances tested at low concentrations. In such cases, disappearance of the substance from solution by adsorption to the increasing algal biomass does not mean that it is lost from the test system. When the result of the test is analysed, it should be checked whether a decrease in concentration of the test substance in the course of the test is accompanied by a decrease in growth inhibition. If this is the case, application of a suitable model describing the decline of the concentration of test substance (8) may be considered. If not, it may be appropriate to base the analysis of the results on the initial (nominal or measured) concentrations.

1.8.12. Other observations

Microscopic observation should be performed to verify a normal and healthy appearance of the inoculum culture and to observe any abnormal appearance of the algae (as may be caused by exposure to the test substance) at the end of the test.

1.8.13. Limit test

Under some circumstances, e.g. when a preliminary test indicates that the test substance has no toxic effects at concentrations up to 100 mg·l^–1 or up to its limit of solubility in the test medium (whichever is the lower), a limit test involving a comparison of responses in a control group and one treatment group (100 mg·l^–1 or a concentration equal to the limit of solubility), may be undertaken. It is strongly recommended that this be supported by analysis of the exposure concentration. All previously described test conditions and validity criteria apply to a limit test, with the exception that the number of treatment replicates should be at least six. The response variables in the control and treatment group may be analysed using a statistical test to compare means, e.g. a Student'’t's t-test. If variances of the two groups are unequal, a t-test adjusted for unequal variances should be performed.

1.8.14. Modification for strongly coloured substances

The irradiation (light intensity) should be in the highest end of the range prescribed in this Testing Method: 120µE m-2 s-1 or higher.

The light path should be shortened by reduction of the volume of the test solutions (in the range of 5-25 ml).

Sufficient agitation (for example by moderate shaking) should be performed in order to obtain a high frequency of exposure of the algae to high irradiation at the surface of the culture.

2. DATA

2.1. PLOTTING GROWTH CURVES

The biomass in the test vessels may be expressed in units of the surrogate parameter used for measurement (e.g. cell number, fluorescence).

Tabulate the estimated biomass concentration in test cultures and controls together with the concentrations of test material and the times of measurement, recorded with a resolution of at least whole hours, to produce plots of growth curves. Both logarithmic scales and linear scales can be useful at this first stage, but logarithmic scales are mandatory and generally give a better presentation of variations in growth pattern during the test period. Note that exponential growth produces a straight line when plotted on a logarithmic scale, and that the inclination of the line (slope) indicates the specific growth rate.

Using the plots, examine whether control cultures grow exponentially at the expected rate throughout the test. Critically examine all data points and the appearance of the graphs, and check raw data and procedures for possible errors. Check in particular any data point that seems to deviate by a systematic error. If it is obvious that procedural mistakes can be identified and/or considered highly likely, the specific data point is marked as an outlier and not included in subsequent statistical analysis. (A zero algal concentration in one out of two or three replicate vessels may indicate the vessel was not inoculated correctly, or was improperly cleaned). Reasons for rejection of a data point as an outlier must be clearly stated in the test report. Accepted reasons are only (rare) procedural mistakes and not just bad precision. Statistical procedures for outlier identification are of limited use for this type of problem and cannot replace expert judgement. Outliers (marked as such) should preferably be retained among the data points shown in any subsequent graphical or tabular data presentation.

2.2. RESPONSE VARIABLES

The purpose of the test is to determine the effects of the test substance on the growth of algae. This Testing Method describes two response variables, as member countries have different preferences and regulatory needs. In order for the test results to be acceptable in all member countries, the effects should be evaluated using both response variables (a) and (b) described below.

(a)

Average specific growth rate: this response variable is calculated on the basis of the logarithmic increase of biomass during the test period, expressed per day.

(b)

Yield: this response variable is the biomass at the end of the test minus the starting biomass.

For the application of this method within the EU regulatory framework, calculation of results should be based on an average specific growth rate for the reasons described below. It should be noted that toxicity values calculated by using these two response variables are not comparable and this difference must be recognised when using the results of the test. EC_x values based upon average specific growth rate (E_rC_x) will generally be higher than results based upon yield (E_yC_x) if the test conditions of this Testing Method are adhered to, due to the mathematical basis of the respective approaches. This should not be interpreted as a difference in sensitivity between the two response variables, simply that the values are different mathematically. The concept of average specific growth rate is based on the general exponential growth pattern of algae in non-limited cultures, where toxicity is estimated on the basis of the effects on the growth rate, without being dependent on the absolute level of the specific growth rate of the control, on the slope of the concentration-response curve or on test duration. In contrast, results based upon the yield response variable are dependent upon all these other variables. E_yC_x is dependent on the specific growth rate of the algal species used in each test and on the maximum specific growth rate that can vary between species and even different algal strains. This response variable should not be used for comparing the sensitivity to toxicants among algal species or even different strains. While the use of average specific growth rate for estimating toxicity is scientifically preferred, toxicity estimates based on yield are also included in this Testing Method so as to satisfy current regulatory requirements in some countries.

2.2.1. Average growth rate

The average specific growth rate for a specific period is calculated as the logarithmic increase in biomass from the equation for each single vessel of controls and treatments:

(day^–1)

where:

µ _i-j:

is the average specific growth rate from time i to j;

X _i :

is the biomass at time i;

X _j :

is the biomass at time j.

For each treatment group and control group, calculate a mean value for growth rate along with variance estimates.

Calculate average specific growth rate over the entire test duration (normally days 0-3), using the nominally inoculated biomass as the starting value rather than a measured starting value, because in this way greater precision is normally obtained. If the equipment used for biomass measurement allows sufficiently precise determination of the low inoculum biomass (e.g. flow cytometer) then the measured initial biomass concentration can be used. Also assess the section-by-section growth rate, calculated as the specific growth rates for each day during the course of the test (days 0-1, 1-2 and 2-3) and examine whether the control growth rate remains constant (See validity criteria, section 1.7). A significantly lower specific growth rate on day one than the total average specific growth rate may indicate a lag phase. While a lag phase can be minimised and practically eliminated in control cultures by proper propagation of the pre-culture, a lag phase in exposed cultures may indicate recovery after initial toxic stress or reduced exposure due to loss of test substance (including sorption onto the algal biomass) after initial exposure. Hence the section-by-section growth rate may be assessed in order to evaluate effects of the test substance occurring during the exposure period. Substantial differences between the section-by-section growth rate and the average growth rate indicate deviation from constant exponential growth and that close examination of the growth curves is warranted.

Calculate the percent inhibition of growth rate for each treatment replicate from the equation:

where:

%I_r:

percent inhibition in average specific growth rate;

µ_C:

mean value for average specific growth rate (µ) in the control group;

µ_T:

average specific growth rate for the treatment replicate.

When solvents are used to prepare the test solutions, the solvent controls rather than the controls without solvents should be used in calculation of percent inhibition.

2.2.2. Yield

The yield is calculated as the biomass at the end of the test minus the starting biomass for each single vessel of controls and treatments. For each test concentration and control, calculate a mean value for the yield along with variance estimates. The percentage inhibition in yield (%I_y) may be calculated for each treatment replicate as follows:

where:

%I_y:

percentage inhibition of yield;

Y_C:

mean value for yield in the control group;

Y_T:

value for yield for the treatment replicate.

2.3. PLOTTING CONCENTRATION RESPONSE CURVE

Plot the percentage of inhibition against the logarithm of the test substance concentration and examine the plot closely, disregarding any such data point that was singled out as an outlier in the first phase. Fit a smooth line through the data points by eye or by computerised interpolation to get a first impression of the concentration response relationship, then proceed with a more detailed method, preferably a computerised statistical method. Depending on the intended usage of the data, the quality (precision) and amount of data, as well as the availability of data analysis tools, it may be decided (and sometimes well justified) to stop the data analysis at this stage and simply read the key figures EC₅₀ and EC₁₀ (and/or EC₂₀) from the eye fitted curve (also see section below on stimulatory effects). Valid reasons for not using a statistical method may include:

• data are not appropriate for computerised methods to produce any more reliable results than can be obtained by expert judgement — in such situations some computer programs may even fail to produce a reliable solution (iterations may not converge etc.),

• stimulatory growth responses cannot be handled adequately using available computer programs (see below).

2.4. STATISTICAL PROCEDURES

The aim is to obtain a quantitative concentration-response relationship by regression analysis. It is possible to use a weighted linear regression after having performed a linearising transformation of the response data — for instance into probit or logit or Weibull units (9), but non-linear regression procedures are preferred techniques that better handle unavoidable data irregularities and deviations from smooth distributions. Approaching either zero or total inhibition, such irregularities may be magnified by the transformation, interfering with the analysis (9). It should be noted that standard methods of analysis using probit, logit, or Weibull transforms are intended for use on quantal (e.g. mortality or survival) data, and must be modified to accommodate growth or biomass data. Specific procedures for determination of EC_x values from continuous data can be found in (10)(11) and (12). The use of non-linear regression analysis is further detailed in Appendix 4.

For each response variable to be analysed, use the concentration-response relationship to calculate point estimates of EC_x values. When possible, the 95 % confidence limits for each estimate should be determined. Goodness of fit of the response data to the regression model should be assessed either graphically or statistically. Regression analysis should be performed using individual replicate responses, not treatment group means. If, however, nonlinear curve fitting is difficult or fails because of too great a scatter in the data, the problem may be circumvented by performing the regression on group means as a practical way of reducing the influence of suspected outliers. Use of this option should be identified in the test report as a deviation from normal procedure because curve fits with individual replicates did not produce a good result.

EC₅₀ estimates and confidence limits may also be obtained using linear interpolation with bootstrapping (13), if available regression models/methods are unsuitable for the data.

For estimation of the LOEC and hence the NOEC, and for effects of the test substance on growth rate, it is necessary to compare treatment means using analysis of variance (ANOVA) techniques. The mean for each concentration must then be compared with the control mean using an appropriate multiple comparison or trend test method. Dunnett’s or Williams’ test may be useful (14)(15)(16)(17)(18). It is necessary to assess whether the ANOVA assumption of homogeneity of variance holds. This assessment may be performed graphically or by a formal test (18). Suitable tests are Levene’s or Bartlett’s. Failure to meet the assumption of homogeneity of variances can sometimes be corrected by logarithmic transformation of the data. If heterogeneity of variance is extreme and cannot be corrected by transformation, analysis by methods such as step-down Jonkheere trend tests should be considered. Additional guidance on determining the NOEC can be found in (12).

Recent scientific developments have led to a recommendation of abandoning the concept of NOEC and replacing it with regression based point estimates EC_x. An appropriate value for x has not been established for this algal test. A range of 10 to 20 % appears to be appropriate (depending on the response variable chosen), and preferably both the EC₁₀ and EC₂₀ should be reported.

2.5. GROWTH STIMULATION

Growth stimulation (negative inhibition) at low concentrations is sometimes observed. This can result from either hormesis (toxic stimulation) or from addition of stimulating growth factors with the test material to the minimal medium used. Note that the addition of inorganic nutrients should not have any direct effect because the test medium should maintain a surplus of nutrients throughout the test. Low dose stimulation can usually be ignored in EC₅₀ calculations unless it is extreme. However, if it is extreme, or an EC_x value for low x is to be calculated, special procedures may be needed. Deletion of stimulatory responses from the data analysis should be avoided if possible, and if available curve fitting software cannot accept minor stimulation, linear interpolation with bootstrapping can be used. If stimulation is extreme, use of a hormesis model may be considered (19).

2.6. NON-TOXIC GROWTH INHIBITION

Light absorbing test materials may give rise to a growth rate reduction because shading reduces the amount of available light. Such physical types of effects should be separated from toxic effects by modifying the test conditions and the former should be reported separately. Guidance may be found in (2) and (3).

3. REPORTING

3.1. TEST REPORT

The test report must include the following:

Test substance:

• physical nature and relevant physiochemical properties, including water solubility limit,

• chemical identification data, including purity.

Test species:

• the strain, supplier or source and the culture conditions used.

Test conditions:

• date of start of the test and its duration,

• description of test design: test vessels, culture volumes, biomass density at the beginning of the test,

• composition of the medium,

• test concentrations and replicates (e.g. number of replicates, number of test concentrations and geometric progression used),

• description of the preparation of test solutions, including use of solvents etc.,

• culturing apparatus,

• light intensity and quality (source, homogeneity),

• temperature,

• concentrations tested: the nominal test concentrations and any results of analyses to determine the concentration of the test substance in the test vessels. The recovery efficiency of the method and the limit of quantification in the test matrix should be reported,

• all deviations from this Testing Method,

• method for determination of biomass and evidence of correlation between the measured parameter and dry weight.

Results:

• pH values at the start and end of the test at all treatments,

• biomass for each flask at each measuring point and method for measuring biomass,

• growth curves (plot of biomass versus time),

• calculated response variables for each treatment replicate, with mean values and coefficient of variation for replicates,

• graphical presentation of the concentration/effect relationship,

• estimates of toxicity for response variables e.g. EC₅₀, EC₁₀, EC₂₀ and associated confidence intervals. If calculated, LOEC and NOEC and the statistical methods used for their determination,

• if ANOVA has been used, the size of the effect which can be detected (e.g. the least significant difference),

• any stimulation of growth found in any treatment,

• any other observed effects, e.g. morphological changes of the algae,

• discussion of the results, including any influence on the outcome of the test resulting from deviations from this Testing Method.

4. LITERATURE

(1)

OECD TG 201 (2006). Freshwater Alga and Cyanobacteria, Growth Inhibition Test.

(2)

ISO 1998: Water quality — Guidance for algal growth inhibition tests with poorly soluble materials, volatile compounds, metals and waster water. ISO/DIS 14442.

(3)

OECD 2000: Guidance Document on Aquatic Toxicity Testing of Difficult Substances and mixtures. Environmental Health and Safety Publications. Series on Testing and Assessment, no. 23.

(4)

ISO 1998: Water quality — Sampling — Part 16: General Guidance for Biotesting. ISO 5667-16.

(5)

ISO 1993: Water quality — Algal growth inhibition test. ISO 8692.

(6)

Mayer, P., Cuhel, R. and Nyholm, N. (1997). A simple in vitro fluorescence method for biomass measurements in algal growth inhibition tests. Water Research 31: 2525-2531.

(7)

Slovacey, R.E. and Hanna, P.J. In vivo fluorescence determinations of phytoplancton chlorophyll, Limnology & Oceanography 22,5 (1977), pp.919-925.

(8)

Simpson, S.L., Roland, M.G.E., Stauber, J.L. and Batley, G.E. (2003). Effect of declining toxicant concentrations on algal bioassay endpoints. Environ. Toxicol. Chem 22, 2073-2079.

(9)

Christensen, E.R., Nyholm, N. (1984): Ecotoxicological Assays with Algae: Weibull Dose-Response Curves. Env. Sci. Technol. 19, 713-718.

(10)

Nyholm, N. Sørensen, P.S., Kusk, K.O. and Christensen, E.R. (1992): Statistical treatment of data from microbial toxicity tests. Environ. Toxicol. Chem. 11, 157-167.

(11)

Bruce, R.D., and Versteeg, D.J. (1992). A statistical procedure for modelling continuous toxicity data. Env. Toxicol. Chem. 11:1485-1494.

(12)

OECD. (2004). Guidance Document on Statistical Analysis of Ecotoxicity Data.

(13)

Norberg-King T.J. (1988). An interpolation estimate for chronic toxicity: The ICp approach. National Effluent Toxicity Assessment Center Technical Report 05-88. USEPA, Duluth, MN.

(14)

Dunnett, C.W. (1955). A multiple comparisons procedure for comparing several treatments with a control. J. Amer. Statist. Assoc. 50: 1096-1121

(15)

Dunnett, C.W. (1964). New tables for multiple comparisons with a control. Biometrics 20: 482-491.

(16)

Williams, D.A. (1971). A test for differences between treatment means when several dose levels are compared with a zero dose control. Biometrics 27: 103-117.

(17)

Williams, D.A. (1972). The comparison of several dose levels with a zero dose control. Biometrics 28: 510-531.

(18)

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

(19)

Brain P. and Cousens R. (1989). An equation to describe dose-responses where there is stimulation of growth at low doses. Weed Research, 29, 93-96.

Appendix 1 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

  UNITED STATES

• CCAP, Culture Collection of Algae and Protozoa

  Institute of Freshwater Ecology,

  Windermere Laboratory

  Far Sawrey, Amblerside

  Cumbria

  LA22 0LP

  UNITED KINGDOM

• SAG: Collection of Algal Cultures

  Inst. Plant Physiology

  University of Göttingen

  Nicholausberger Weg 18

  3400 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

a Measured with electronic particle counter
b Calculated from size
c Most frequently observed growth rate in OECD medium at light intensity approx. 70 µE·m–2·s–1 and 21 °C
	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)	40-60a	60-80a	40-50a	30-40a	2,5b
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 ratec 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 2 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

a The molar ratio of EDTA to iron slightly exceed unity. This prevents iron precipitation and, at the same time, chelation of heavy metal ions is minimised.
Component	EPA		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	0,000269a
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

In the 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 °C and the molar bicarbonate concentration is:

PH_eq = 11,30 + log [HCO₃]

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

Element composition of test media

Element	EPA	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: macronutrients
NH4Cl MgCl2·6H2O CaCl2·2H2O MgSO4·7H2O KH2PO4	1,5 g·l–1 1,2 g·l–1 1,8 g·l–1 1,5 g·l–1 0,16 g·l–1
Stock solution 2: iron
FeCl3·6H2O Na2EDTA·2H2O	64 mg·l–1 100 mg·l–1
Stock solution 3: trace elements
H3BO3 MnCl2·4H2O ZnCl2 CoCl2·6H2O CuCl2·2H2O Na2MoO4·2H2O	185 mg·l–1 415 mg·l–1 3 mg·l–1 1,5 mg·l–1 0,01 mg·l–1 7 mg·l–1
Stock solution 4: bicarbonate
NaHCO3	50 g·l–1
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 AAP medium

A1.1.

Add 1 mL of each stock solution in A1.2.1-A1.2.7 to approximately 900 mL of deionised or distilled water and then dilute to 1 L.

A1.2.

Macronutrient stock solutions are made by dissolving the following into 500 mL of deionised or distilled water. Reagents A1.2.1, A1.2.2, A1.2.3, and A1.2.4 can be combined into one stock solution.

A1.2.1.

NaNO₃ —12,750 g.

A1.2.2.

MgCL₂·6H₂O—6,082 g.

A1.2.3.

CaCl₂·2H₂O—2,205 g.

A1.2.4.

Micronutrient Stock Solution—(see A1.3).

A1.2.5.

MgSO₄·7H₂O—7,350 g.

A1.2.6.

K₂HPO₄ —0,522 g.

A1.2.7.

NaHCO₃ —7,500 g.

A1.2.8.

Na₂SiO₃·9H₂O—See Note A1.1.

Note A1.1 — 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.

A1.3.

The micronutrient stock solution is made by dissolving the following into 500 mL of deionised or distilled water:

A1.3.1.

H₃BO₃ —92,760 mg.

A1.3.2.

MnCl₂·4H₂O–207,690 mg.

A1.3.3.

ZnCl₂ —1,635 mg.

A1.3.4.

FeCl₃·6H₂O—79,880 mg.

A1.3.5.

CoCl₂·6H₂O—0,714 mg.

A1.3.6.

Na₂MoO₄·2H₂O—3,630 mg.

A1.3.7.

CuCl₂·2H₂O—0,006 mg.

A1.3.8.

Na₂EDTA·2H₂O—150,000 mg.

[Disodium (Ethylenedinitrilo) tetraacetate].

A1.3.9.

Na₂SeO₄·5H₂O—0,005 mg See Note A1.2.

Note A1.2 — Use only in medium for stock cultures of diatom species.

A1.4.

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

A1.5.

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.

A1.6.

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

Appendix 3 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.

Suitable methods must be used 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 Testing 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 infections occur. For solid medium 0,8 % 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 4 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 such a system relates 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 is often assumed to be the dominant variance component. Control responses here are 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 associated error, 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 EC_x 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 non-symmetrical Weibul equation and the log normal distribution function, which are all sigmoid curves asymptotically approaching one for C → 0, and zero for C → infinity.

The use of continuous threshold function models (e.g. the Koyman 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. Preferably use the measurements from each individual flask rather than the mean values of the 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 the mean values of the 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 particularly helpful tool for this purpose. If the chosen functional relationship to fit the concentration response does not describe the whole curve or some essential part of it, such as the response at low concentrations well, 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 a 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 EC_{low x} figures. Calculate from the fitted equation (by ‘inverse estimation’, C = f^–1 (Y), characteristic point estimates EC_x’s, and report as a minimum the EC₅₀ and one or two EC_{low 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 also recommended to report always the EC₂₀.

Weighting factors

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

W_i = 1/Var(r_i)

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 w_i (n is the number of data points) so that their sum equals 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 (17). 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)

Y_i = Relative response = r_i/r₀ = 1 — I = f (C_i)

with a variance:

Var (Y_i) = Var (r_i/r₀) ≅ (∂Y_i / ∂ r_i)²·Var(r_i) + (∂ Y_i/ ∂ r₀)²·Var (r₀)

and since

(∂ Y_i/ ∂ r_i) = 1/r₀ and (∂ Y_i / ∂ r₀) = r_i/r₀ ²

with normally distributed data and m_i and m₀ replicates:

Var(r_i) = σ²/m_i

the total variance of the relative response, Y_i thus becomes:

Var(Y_i) = σ²/(r₀ ² m_i) + r_i 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 historical 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 r_i 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.

Literature

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

Bruce, R.D. and Versteeg, D.J.(1992) A Statistical Procedure for Modelling Continuous Ecotoxicity Data. Env. 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.