# Sample size in PNEC derivation

**Scott Dyer**

*Procter & Gamble, USA*

SSDs have been used to develop water quality criteria (e.g. PNECs) and other protective environmental concentrations (e.g. HC5). These criteria typically require large datasets (e.g. US EPA ambient water quality criteria utilize at least 8 acute toxicity values from several taxa spanning 3 trophic levels, fish, invertebrates and plants) of measured toxicity values. However, there has been a considerable debate regarding the minimum requirements for establishing protective concentrations, such as the HC5, within the scientific and regulatory communities. For organizations needing to establish these criteria, questions remain whether the addition of taxa into the SSD will greatly change the criterion. Is it possible that the addition of taxa will not change the HC5 and thereafter the PNEC? Is there a law of diminishing returns for expanding the number of taxa incorporated into an SSD? If so, then understanding factors that dictate the lack of need for additional taxa would result in appropriate PNECs without undo cost and time. To explore this question we developed 3 distributions, each assuming normality: 1) wide (toxicity values ranged 4 orders of magnitude); narrow (values ranged by 1 order of magnitude; and 3) mixed (sensitive taxa corresponded to 1/3 of the distribution and more tolerant taxa the remaining 2/3). In each distribution the numbers of taxa sampled were varied as well as the number of replicate tests/taxa. Monte-Carlo was used to sample each distribution 1000-times. The following conclusions were noted: 1) the spread of the HC5 values were proportional to magnitude of the spread of the toxicity data per distribution. For example, the 5^{th} percentile and 95^{th} percentiles of the range of HC5s from the wide distribution were 4-orders of magnitude apart. 2) Increasing the number of taxa sampled per distribution increasingly approximated the ‘true or ideal’ HC5. 3) There appeared to be a law of diminishing returns with increasing the number of taxa to approximate the ideal HC5. Approximately 10 taxa were sufficient to within a factor of 2 of the ideal HC5 for predicting any distribution. Considering this, discussion is warranted in the cost versus benefits of obtaining more taxa to derive an ideal HC5. While not presented, we also found the number of replicates per taxa did not significantly change the HC5, though they did narrow the range of HC5s. The common occurrence of a mixed distribution (e.g. algae more sensitive than invertebrates and fish) did not change the conclusions from the narrow and wide distributions. The authors recognize that this exercise was theoretically-based, however, the findings simplify future discussions regarding how many taxa are needed to obtain an HC5 to derive a PNEC.