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The Species Sensitivity Distribution (SSD) is a key tool to assess the ecotoxicological threat of contaminant to biodiversity. It predicts safe concentrations for a contaminant in a community. Widely used, this approach suffers from several drawbacks: i)summarizing the sensitivity of each species by a single value entails a loss of valuable information about the other parameters characterizing the concentration-effect curves; ii)it does not propagate the uncertainty on the critical effect concentration into the SSD; iii)the hazardous concentration estimated with SSD only indicates the threat to biodiversity, without any insight about a global response of the community related to the measured endpoint. We revisited the current SSD approach to account for all the sources of variability and uncertainty into the prediction and to assess a global response for the community. For this purpose, we built a global hierarchical model including the concentration-response model together with the distribution law for the SSD. Working within a Bayesian framework, we were able to compute an SSD taking into account all the uncertainty from the original raw data. From model simulations, it is also possible to extract a quantitative indicator of a global response of the community to the contaminant. We applied this methodology to study the toxicity of 6 herbicides to benthic diatoms from Lake Geneva, measured from biomass reduction.

Censored data are seldom taken into account in Species Sensitivity Distribution (SSD) analysis. However, they are found in virtually every dataset and sometimes represent the better part of the data. Stringent recommendations on data quality often lead to discard a lot of this meaningful data, often resulting in datasets of reduced size, which lack representativeness of any realistic community. However, it is reasonably simple to include censored data into SSD by using an extension of the standard maximum likelihood method. In this paper, we detail this approach based on the use of the R-package \emph{fitdistrplus}, dedicated to the fit of parametric probability distributions. In particular, we introduce the new web-tool MOSAIC$\_$SSD to fit an SSD on datasets containing any kind of data, censored or not. MOSAIC$\_$SSD allows predicting any Hazardous Concentration (HC) and provides in addition bootstrap confidence intervals on the prediction. In the end, taking examples from published data, we illustrate the added value of including censored data in SSD., Comment: 26 pages, 2 figures

Reproduction data collected through standard bioassays are classically analyzed by regression in order to fit exposure-response curves and estimate ECx values (x% Effective Concentration). But regression is often misused on such data, ignoring statistical issues related to i) the special nature of reproduction data (count data), ii) a potential inter-replicate variability and iii) a possible concomitant mortality. This paper offers new insights in dealing with those issues. Concerning mortality, particular attention was paid not to waste any valuable data - by dropping all the replicates with mortality - or to bias ECx values. For that purpose we defined a new covariate summing the observation periods during which each individual contributes to the reproduction process. This covariate was then used to quantify reproduction - for each replicate at each concentration - as a number of offspring per individual-day. We formulated three exposure-response models differing by their stochastic part. Those models were fitted to four datasets and compared using a Bayesian framework. The individual-day unit proved to be a suitable approach to use all the available data and prevent bias in the estimation of ECx values. Furthermore, a non-classical negative-binomial model was shown to correctly describe the inter-replicate variability observed in the studied datasets.