We revisit a classical method for ecological risk assessment, the Species Sensitivity Distribution (SSD) approach, in a Bayesian parametric and nonparametric framework.
SSD is a mandatory diagnostic required by environmental regulatory bodies from the European Union, the United States, Australia, China, among others. Yet, it is subject to much scientific criticism, notably concerning a historically debated parametric assumption for modelling species variability. Additional methodological flaws involve incomplete use of experimental data, often ignoring time-dependence, and poor uncertainty quantification. We demonstrate how to improve current methodoly in a number of ways using Bayesian parametric and nonparametric hierarchical models. In particular, we explain how to include censored data, time dependence and how to properly model uncertainty with the help of toxico-dynamic toxico-kinetic models. Next, tackling the problem using nonparametric mixture models, we show how to shed the classical parametric assumption and build a statistically sounder basis for SSD. The Bayesian nonparametric approach offers another advantage: the ability to deal with small datasets, typical in the field of ecological risk assessment. We use Normalised Random Measures with Independent Increments (NRMI) as the mixing measure because they offer a greater flexibility than the default prior in the field known as the Dirichlet process.
Indeed, NRMI induce a prior on the number of components in the mixture model that is less restrictive than the Dirichlet process. This feature is consistent with the fact that SSD practitioners do not usually have a strong prior belief on the number of components. We extend our mixture to censored data which are prevalent in ecotoxicology and we illustrate the advantage of the nonparametric SSD over the classical normal SSD and a kernel density estimate SSD on several real datasets.
We then perform a systematic comparison on simulated data, and finish by studying the clustering induced by the mixture model to examine patterns in species sensitivity.