Division 2.2.1 Average specific growth rate

The average specific growth rate for a specific period is calculated as the logarithmic increase in the growth variables — rond numbers and one other measurement variable (total frond area, dry weight or fresh weight) — using the formula below for each replicate of control and treatments:

$${\mu }_{\mathrm{i-j}}=\frac{\mathrm{ln(}{N}_j\mathrm{) – ln(}{N}_i)}{t}$$

where:

— μ_i-j:

average specific growth rate from time i to j

— N_i:

measurement variable in the test or control vessel at time i

— N_j:

measurement variable in the test or control vessel at time j

— t:

time period from i to j

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

The average specific growth rate should be calculated for the entire test period (time ‘i’ in the above formula is the beginning of the test and time ‘j’ is the end of the test). For each test concentration and control, calculate a mean value for average specific growth rate along with the variance estimates. In addition, the section-by-section growth rate should be assessed in order to evaluate effects of the test substance occurring during the exposure period (e.g. by inspecting log-transformed growth curves). 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. In this case, a conservative approach would be to compare specific growth rates from treated cultures during the time period of maximum inhibition to those for controls during the same time period.

Percentage inhibition of growth rate (I_r) may then be calculated for each test concentration (treatment group) according to the following formula:

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

where:

— % I_r:

percentage inhibition in average specific growth rate

— μ_C:

mean value for μ in the control

— μ_T:

mean value for μ in the treatment group