Department of Mathematical Sciences, Durham University, UK
One approach to deriving the predicted no-effect concentration for a chemical is to use a species sensitivity distribution model to estimate the hazardous concentration affecting p% of species (HCp), where p is usually 5. Many questions have been raised about both principles and application of SSDs but the concept has nevertheless been found to be useful.
Analysis of a database of acute aquatic toxicity test results reveals several features which should be addressed by SSD methodology, including: (a) inter-species correlation; (b) tendencies of particular species to one or other end of the sensitivity distribution; and (c) inter-test variation. In earlier work (Dyer et al, 2006, Craig et al, 2012, Hickey et al, 2012), each issue has been addressed on its own. Addressing them collectively requires multivariate statistical modelling.
We present a Bayesian hierarchical model of variability and uncertainty for: (i) sensitivities of species to a chemical undergoing assessment and (ii) a database of relevant test results for other chemicals (Craig, 2013). Bayesian statistical methodology has several advantages over traditional non-Bayesian methodology which is intended primarily for analysing experimental data. It can incorporate data, expert judgements and results of meta-analyses. It provides a collective description of uncertainty for all components of a model, a coherent mechanism for revising uncertainty when additional data become available, and a decision-making framework.
Our model generalises the Aldenberg and Jaworska (2000) single randomly-sampled-chemical log-normal SSD model and addresses issues (a)-(c). It models inter-species correlation by building species tendencies and sensitivities hierarchically, based on the taxonomic classification of species. The taxonomic structure seems natural and enables a better description of the available data but means that it is necessary also to specify an eco-taxonomic scenario: the taxonomic structure of the community being protected by the HCp. The HCp is then scenario-specific, being the pth percentile of sensitivity to the chemical for species in the scenario. The model automatically delivers a quantitative assessment of uncertainty to accompany the HCp estimate.
The model is trained, using the same database as for the original data analysis, and is then ready for application to other chemicals. The trained model is available as software, known as hSSD, for application to test data for a new chemical in the user’s chosen eco-taxonomic scenario. The workshop included a demonstration of hSSD which is one of the methodologies used in the workshop case studies.
As an illustration, we applied the trained model to a chemical for which a substantial number of test data are available. For the eco-taxonomic scenario, we took the Kent river scenario that was developed for the workshop case studies. We highlighted the prediction from the model for the true sensitivity of each species in the scenario; the predictive uncertainty is high for species which are taxonomically distant from all tested species and low for tested species.