Division 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:

${\mu }_{\mathrm{i-j}}=\frac{\ln X_j\mathrm{ – ln}{X}_i}{t_j{\mathrm{ – t}}_i}$ (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:

$$\%I_r=\frac{{\mu }_C\mathrm{ – }{\mu }_T}{\mu }C\mathrm{\times \; 100}$$

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.