The added value of Bayesian inference for estimating biotransformation rates of organic contaminants in aquatic invertebrates

Toxicokinetic (TK) models refer to the process of contaminant bioaccumulation as a balance between rate of uptake from different sources (e.g., water or food), and rate of elimination via different processes such as excretion, growth and/or biotransformation. Biotransformation can considerably modify the fate of chemicals in an organism, especially their bioavailability, residence time, and toxicity. Invertebrate models generally neglect this process as they assume a low metabolic activity. However, some species such as Gammarus sp. amphipods are able to metabolize a vast range of organic compounds. Some recent TK models include biotransformation, but they prove limited for estimating related parameters by giving negative values and/or large uncertainties for biotransformation rate(s). Here we propose a generic TK model accounting for biotransformation using a Bayesian framework for simultaneously estimating the parameters. We illustrated the added value of our method by fitting this generic TK model to 22 published datasets of several benthic invertebrate species exposed to different chemicals. All parameters are estimated simultaneously for all datasets and showed narrow estimates. Furthermore, the median model predictions and their 95% credibility intervals showed that the model confidently fitted the data. In most cases the uncertainties around biotransformation rate(s) were reduced in comparison to the original studies. From a methodology standpoint, this paper reflects that Bayesian inference has real added value for simultaneously estimating all TK parameters for parent chemicals and their metabolite(s) based on all available data, while accounting for different types of data and the correlation between parameters. Bayesian inference was able to overcome the limits of previous methods, since no parameters were fixed and no irrelevant negative values were obtained. Moreover, the 95% credibility intervals around model predictions, which are core uncertainties for Environmental Risk Assessment, were easily acquired.