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Conceived and designed the experiments: CS MS JS SB. Performed the experiments: CS. Analyzed the data: CS SB. Wrote the paper: CS MS JS SB.

The authors have declared that no competing interests exist.

In ecotoxicological and environmental studies

_{(area)} and r_{(num)}) were determined with a non-destructive image processing system.

To assess inter-experimental stability, 35 independent experiments were performed with 10 beakers each in the course of one year. We observed changes in growth rates by a factor of two over time. These did not correlate well with temperature or relative humidity in the growth chamber.

In order to assess intra-experimental stability, we analysed six systematic negative control experiments (nontoxicant tests) with 96 replicate beakers each. Evaluation showed that the chosen experimental set-up was stable and did not produce false positive results. The coefficient of variation was lower for r_{(area)} (2.99%) than for r_{(num)} (4.27%).

It is hypothesised that the variations in growth rates over time under controlled conditions are partly due to endogenic periodicities in

Members of the Lemnaceae family occur in standing and slowly flowing waters all over the world, except in arctic and antarctic regions

The methodological quality of a laboratory investigation depends amongst others on the uniformity of the experimental conditions as well as on the inclusion of a sufficient number of appropriate controls. Thus, close investigation of the entire experimental set-up prior to main experiments with test substances is recommended in guidelines for the

Though most _{(area)} and r_{(num)}) were calculated from the data obtained.

Our first aim was to assess inter-experimental stability, i.e. to determine natural variations or possible rhythmic changes in duckweed growth over time. We therefore analysed 35 independent experiments with 10 beakers of untreated

The second aim was to estimate intra-experimental stability. We thus analysed data of 96 test beakers of six full systematic negative control experiments (nontoxicant tests with pure moStM) each. The data were analysed in randomised groups of six beakers (‘pseudo-treatments’), since six replicates for the controls are recommended in guidelines for ecotoxicological tests with duckweeds

Furthermore, the variability of two calculation parameters, frond number-related growth rate (r_{(num)}) and area-related growth rate (r_{(area)}), were compared, frond number being the mandatory observation parameter in the guidelines mentioned above which must be combined with either frond area, dry weight, fresh weight or chlorophyll content as the second observation parameter.

Duckweed,

Cultivation medium was modified Steinberg medium (moStM), prepared according to the draft ISO/DIS 20079

Duckweed cultures were grown in a plant growth chamber (180×75×100 cm, made of an aluminium frame with glass walls covered with white paper, constructed by technicians from the Research Institute of Organic Agriculture) illuminated with fluorescent lights (143±3 µmol photons m^{−2} s^{−1} PAR, TL-D 36W/33-640, Philips, Zürich, Switzerland). Deviating from guidelines, where continuous illumination is required

Long term storage (solid stock-cultures): For long term storage the plants were maintained aseptically as stock-cultures in 100 ml Erlenmeyer flasks containing 50 ml of solid moStM with 1% (w/v) Bacto® dextrose (Difco, Detroit, USA) and 1% (w/v) bacteriological agar No. 1 (Oxoid, Basingstoke, Great Britain). Dextrose was added in order to detect a possible bacterial contamination of the cultures. After two weeks in the growth chamber these cultures were stored at 7°C in the dark for about a month, before some of the duckweed colonies were transferred to freshly prepared solid medium.

Adaptation (liquid stock-cultures): The method of keeping solid stock-cultures in the dark requires a thorough adaptation of the plants to liquid medium which takes several weeks. Here, about eight colonies were transferred aseptically from the solid stock-cultures into 500 ml Erlenmeyer flasks containing 150 ml of autoclaved moStM. These liquid stock-cultures were then cultured under normal experimental conditions in a second identical growth chamber for a period of at least four weeks before further use and their medium was changed weekly.

Pre-culture: Afterwards, duckweeds from the liquid stock-cultures were grown in two glass vessels with 1.8 L of moStM each in the second identical growth chamber for three to four weeks prior to the experiments in order to obtain large numbers of plants. Young, rapidly growing colonies from these pre-cultures were put into similar glass vessels with freshly prepared medium every week, covering less than one third of the surface at the beginning of the week. It was ensured that rapid, near-exponential growth was maintained and was not restricted e.g. due to space limitation or limited nutrient availability.

On the day when an experiment began, test specimens with a bright green colour without visible lesions, chlorosis or necrosis were selected from one vessel. They were sorted according to number of fronds of similar size (e.g. three fronds per colony or three large and one small frond per colony, respectively) and were put into petri dishes with medium until use. If necessary, any stipules connecting daughter fronds to the pouch of the mother frond were carefully separated without injuring the fronds. These young and healthy plants were used as inoculum for all test beakers.

Stock solutions of moStM (50-fold concentrated) were mixed together immediately before use

All measurements of frond area and number were obtained with an image processing system (Scanalyzer, duckweed analytic software, version 3)

After the initial measurement (day 0) each beaker was wrapped in black paper up to the surface of the test solution and put on black paper in the plant growth chamber in order to eliminate any diffused light from the side or the bottom. The light intensity at every location in the growth chamber had been measured previously. The beakers were placed in the growth chamber at places with similar light intensities at 5 cm distance to each other. Additionally, they were covered with watch-glasses (from the same manufacturing batch) to avoid excessive evaporation. Further measurements with the image processing system were taken on day 3, 5 and 7 of the experiment.

From the measured frond area and frond number the growth rate per day r [d^{−1}] was calculated for the total test period (day 0–7; average specific growth rate), and for four other time intervals (day 0–3, 3–5, 3–7, 5–7; segmented growth rates) according to the equation:_{t1} is the value of observation parameter at day t_{1}, x_{t2} is the value of observation parameter at day t_{2}, and t_{2}−t_{1} is the time period between x_{t1} and x_{t2} in days. The parameters used for statistical analysis were area-related growth rates (r_{(area)}) and frond number-related growth rates (r_{(num)}).

Annual variation in duckweed growth during 7 days was assessed in 35 experiments between January 2003 and January 2004. For this purpose untreated plants in 10 beakers with pure moStM were grown for one week, and frond area and frond number were assessed (see above). This study was part of a larger investigation on the effects of highly diluted substances on duckweed growth rate

The stability of the entire experimental set-up in the growth chamber was investigated in six independent systematic negative control experiments with pure moStM (full-size experiments with 100 beakers) performed at different points in time during the year. Four beakers out of 100 were eliminated by a random procedure in order to obtain 16 groups of six beakers (96 beakers in total), since the guidelines for the duckweed growth inhibition test

Data from the regular monitoring of duckweed growth rates were analysed using descriptive statistics and were illustrated graphically. Correlations with environmental parameters were calculated with nonparametric Spearman rank correlation.

From the systematic negative control experiments, data for a total of 576 beakers were obtained. Data from two beakers had to be excluded due to spilling. The experimental data were summarized using standard descriptive statistics. We calculated the variability of the average specific growth rates (day 0–7) for groups of six replicates as well as the variability of growth rate in time within one beaker. The latter was characterised by calculating the time-weighted section-by-section growth rate (day 0–3, 3–5 and 5–7) and the mean value of coefficients of variation (CV), according to the OECD guideline for freshwater algae and cyanobacteria growth inhibition test _{(area)} and r_{(num)} were evaluated for statistical significance based on analysis of variance (ANOVA) F tests, after checking the data for normal distribution with Shapiro-Wilk W Test and homogeneity of variance with Levene's Test. In a two-way analysis of variance the independent variables were experiment number and treatment (16 ‘pseudo-treatments’ with medium only) and the dependent variable was r_{(area)} or r_{(num)} (α = 5%), respectively. All analyses were carried out with the software STATISTICA version 6.0 (Stat Soft, Inc., Tulsa, OK, USA)

The variability of the absolute growth rates over time is illustrated graphically, displaying the data from all ten beakers individually for all 35 experiments analysed (^{−1} in early spring and 0.17 d^{−1} in autumn, whereas r_{(num)} varied between 0.36 d^{−1} and 0.15 d^{−1} respectively. In autumn the duckweed plants tended to have thicker fronds with a dark green colour. The variability between the ten replicates within each experiment was higher for the segmented growth rates compared to the average specific growth rates, especially at the beginning of the experiment (day 0–3) and for day 3–5 (data not shown).

Variations in area-related (r_{(area)}, A) and frond number-related (r_{(num)}, B) average specific growth rate (day 0–7) of

Correspondingly, the mean average specific growth rates (mean of all 10 beakers) varied by a factor of about two: 0.34 d^{−1} for r_{(area)} and 0.33 d^{−1} for r_{(num)} in spring and 0.18 d^{−1} and 0.17 d^{−1} in autumn respectively, though laboratory conditions remained fairly constant and did not show a similar pattern over time (_{(area)} and r_{(num)}) with day and night temperature and day and night relative humidity (RH) were calculated. Significant correlations were obtained with night temperature only (Spearman R = −0.418 for r_{(area)}, p = 0.012; and R = −0.518 for r_{(num)}, p = 0.001, respectively). Visual inspection of this correlation (

Average specific growth rates (day 0–7) of _{(area)}, r_{(num)}, mean maximal temperature (temp., day and night) and mean maximal relative humidity (RH, day and night) are plotted against the date of the experiment.

Six full-size negative control experiments were performed and evaluated (n = 96 beakers for each experiment). The mean values of the average specific growth rates (r_{(area)} and r_{(num)}) for all 16 groups of six replicates are shown in _{(area)} and r_{(num)} were similar in single experiments, and for the average of all six water control experiments the mean growth rate of r_{(area)} and r_{(num)} was nearly identical (r = ∼0.267 d^{−1}).The coefficient of variation (CV) for the average specific growth rates was 2.99% for r_{(area)} and 4.27% for r_{(num)}, averaging all six systematic negative control experiments. In general, the statistical variation was higher for r_{(num)} compared to r_{(area)}. This was also the case for all segmented growth rates (data not shown).

r_{(area)} |
n | mean | mean CI | mean SD | mean SE | mean CV[%] | min CV[%] | max CV[%] | |

−95% | +95% | ||||||||

exp. 1 | 16×6 | 0.303 | 0.295 | 0.310 | 0.007 | 0.003 | 2.41 | 1.06 | 4.71 |

exp. 2 | 16×6 | 0.274 | 0.265 | 0.282 | 0.008 | 0.003 | 2.81 | 1.41 | 4.96 |

exp. 3 | 16×6 | 0.233 | 0.223 | 0.242 | 0.009 | 0.004 | 3.95 | 1.90 | 5.82 |

exp. 4 | 16×6 | 0.244 | 0.235 | 0.253 | 0.008 | 0.003 | 3.37 | 1.23 | 4.93 |

exp. 5 | 16×6 | 0.286 | 0.276 | 0.295 | 0.009 | 0.004 | 3.13 | 1.76 | 4.63 |

exp. 6 | 16×6 | 0.265 | 0.258 | 0.271 | 0.006 | 0.002 | 2.30 | 0.91 | 4.04 |

exp. 1–6 | 6×16×6 | 0.267 | 0.259 | 0.276 | 0.008 | 0.003 | 2.99±0.62 |

r_{(num)} |
n | mean | mean CI | mean SD | mean SE | mean CV[%] | min CV[%] | max CV[%] | |

−95% | +95% | ||||||||

exp. 1 | 16×6 | 0.301 | 0.290 | 0.312 | 0.011 | 0.004 | 3.57 | 1.80 | 5.91 |

exp. 2 | 16×6 | 0.247 | 0.234 | 0.259 | 0.012 | 0.005 | 4.85 | 1.67 | 9.17 |

exp. 3 | 16×6 | 0.243 | 0.231 | 0.255 | 0.012 | 0.005 | 4.78 | 2.84 | 7.28 |

exp. 4 | 16×6 | 0.240 | 0.230 | 0.250 | 0.010 | 0.004 | 4.09 | 1.85 | 6.70 |

exp. 5 | 16×6 | 0.293 | 0.279 | 0.308 | 0.014 | 0.006 | 4.71 | 2.53 | 6.14 |

exp. 6 | 16×6 | 0.272 | 0.261 | 0.282 | 0.010 | 0.004 | 3.63 | 1.29 | 5.19 |

exp. 1–6 | 6×16×6 | 0.266 | 0.254 | 0.278 | 0.011 | 0.005 | 4.27±0.58 |

The variability of the growth rate calculated over section-by-section segmented growth rates (_{(area)} and 8.58±2.56% for r_{(num)}.

r_{(area)} |
n | mean | mean SD | mean CV[%] | min CV[%] | max CV[%] |

exp. 1 | 16×6 | 0.303 | 0.007 | 2.38 | 1.47 | 3.05 |

exp. 2 | 16×6 | 0.274 | 0.015 | 5.52 | 4.74 | 6.61 |

exp. 3 | 16×6 | 0.233 | 0.015 | 6.30 | 4.85 | 7.62 |

exp. 4 | 16×6 | 0.244 | 0.024 | 9.73 | 9.02 | 10.51 |

exp. 5 | 16×6 | 0.286 | 0.028 | 9.84 | 9.20 | 10.35 |

exp. 6 | 16×6 | 0.265 | 0.024 | 9.20 | 8.49 | 9.89 |

exp. 1–6 | 6×16×6 | 7.16±2.97 |

r_{(num)} |
n | mean | mean SD | mean CV[%] | min CV[%] | max CV[%] |

exp. 1 | 16×6 | 0.301 | 0.019 | 6.35 | 3.85 | 8.11 |

exp. 2 | 16×6 | 0.247 | 0.019 | 7.75 | 5.29 | 10.37 |

exp. 3 | 16×6 | 0.243 | 0.013 | 5.13 | 4.18 | 6.12 |

exp. 4 | 16×6 | 0.240 | 0.024 | 10.02 | 8.45 | 11.67 |

exp. 5 | 16×6 | 0.293 | 0.032 | 10.79 | 8.86 | 13.24 |

exp. 6 | 16×6 | 0.272 | 0.031 | 11.45 | 9.69 | 13.14 |

exp. 1–6 | 6×16×6 | 8.58±2.56 |

When comparing CVs of single experiments (

Analysis of variance (ANOVA) of the six systematic negative control experiments simultaneously assessed inter- and intra-experimental stability. The statistical analysis of the effects of the independent variables (factors) experiment number, treatment and their interaction on both growth rates yielded highly significant effects for the experiment number on r_{(area)} and r_{(num)} due to the variation in absolute growth rates between the six experiments (

0–7d | 0–3d | 3–5d | 3–7d | 5–7d | ||

r_{(area)} |
exp. no. | |||||

treatment | 0.660 | 0.258 | 0.970 | 0.986 | 0.419 | |

interaction | 0.131 | 0.209 | 0.212 | 0.099 | 0.649 | |

r_{(num)} |
exp. no. | |||||

treatment | 0.288 | 0.332 | 0.258 | 0.662 | 0.365 | |

interaction | 0.576 | 0.654 | 0.340 | 0.133 | 0.313 |

In this study the observed changes in area-related and frond number-related growth rates over about one year did not correlate well with changes of temperature and RH in the growth chamber (

The phenomenon of seasonally altered duckweed growth (under constant laboratory conditions) has also been observed elsewhere. Based on the number of fronds Wang

Given the fact that the absolute growth rates may vary by a factor of two in the course of a year, detailed investigations are needed to determine a possible relationship between absolute growth rates and the ecotoxicological sensitivity of ^{−1} is a sufficient validity criterion for all kinds of substances in

We furthermore compared the CVs of the different growth rates and calculation parameters. Both growth parameters determined in this study yielded similar average specific growth rates, but r_{(area)} had always lower CV values than r_{(num)}. This is most probably due to the fact that the area of fronds is a continuous variable, whilst the number of fronds increases discontinuously. Thus r_{(area)} seems to be a more stable parameter to measure the growth rate, whilst r_{(num)} remains important as basic parameter which is always accessible. These results confirm the findings of Cedergreen et al.

In our investigations, both average specific growth rates (r_{(area)} and r_{(num)}) measured did not always meet the single validity criterion of the test guidelines (0.275 d^{−1} ^{−1}

In order to empirically assess the hypothesis of altered sensitivity at different growth rates, evidence has to be provided that the used experimental set-up is stable, i.e. the experimental conditions do ensure a low variability within and between experiments, even at low growth rates. Therefore, two new validity criteria are proposed.

In our study, the observed CVs of both area-related and frond number-related average specific growth rates (2.99% and 4.27%, respectively) were small, indicating a good stability of the entire experimental set-up over the entire period of time, even at low growth rates. The values are in the same order of magnitude as those measured for six control replicates in an ISO _{(area)} and 4.19±2.48% (n = 68 tests) for r_{(num)} (in that analysis only valid tests with an average specific growth rate of r≥0.275 d^{−1} were included; M. Eberius, LemnaTec, Würselen, Germany, personal communication). It is therefore proposed that a maximum CV of the average specific growth rate between control replicates of 10% may be another useful and not too stringent validity criterion for

A further validity criterion already applied for the freshwater algae and cyanobacteria growth inhibition test

Both proposed complementary validity criteria should be confirmed for other

Additional information about the stability of an experimental set-up can be obtained by evaluation of statistical significance based on analysis of variance F tests of data from several systematic negative control experiments. With this type of analysis false positive results (that may occur due to uncontrolled variations within the experimental set-up) can be excluded with high certainty, if there is neither a significant ‘pseudo-treatment’ effect nor an interaction of ‘pseudo-treatment’ and experiment number. To document low variability of the test system may be of special importance, when low concentrations are to be tested, e.g. mixtures of single test substances which alone have no significant concentration effect

The authors wish to thank C. Schneider for laboratory assistance and P. Rossi, M. Eberius, V. Majewsky and T. Jaeger for valuable discussions. The authors are also grateful to E. Landolt for confirmation of the duckweed identity, K. Appenroth for genetical analysis, G. Ives for language revision, and two anonymous reviewers for helpful comments.