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This is the supplementary information provided with the manuscript submitted in the journal Archives of Environmental Contamination and Toxicology with the same title.

Supplementary information linked to the paper in Environmental Science and Pollution Research entitled "A critical review of exposure and effect modelling approaches for ecological risk assessment of pesticides".

Supplementary information linked to the paper in Environmental Science and Pollution Research entitled "A critical review of modelling approaches for environmental risk assessment due to pesticides".

Providing reliable environmental quality standards (EQSs) is a challenging issue in environmental risk assessment (ERA). These EQSs are derived from toxicity endpoints estimated from dose-response models to identify and characterize the environmental hazard of chemical compounds such as those released by human activities. These toxicity endpoints include the classicalx% effect/lethal concentrations at a specific timet(EC/LC(x,t)) and the new multiplication factors applied to environmental exposure profiles leading tox% effect reduction at a specific timet(MF(x,t), or denotedLP(x,t) by the EFSA). However, classical dose-response models used to estimate toxicity endpoints have some weaknesses, such as their dependency on observation time points, which are likely to differ between species (e.g., experiment duration). Furthermore, real-world exposure profiles are rarely constant over time, which makes the use of classical dose-response models difficult and compromises the derivation ofMF(x,t). When dealing with survival or immobility toxicity test data, these issues can be overcome with the use of the general unified threshold model of survival (GUTS), a toxicokinetics-toxicodynamics (TKTD) model that provides an explicit framework to analyse both time- and concentration-dependent data sets as well as obtain a mechanistic derivation ofEC/LC(x,t) andMF(x,t) regardless of x and at any time t of interest. In addition, the assessment of a risk is inherently built upon probability distributions, such that the next critical step for ERA is to characterize the uncertainties of toxicity endpoints and, consequently, those of EQSs. With this perspective, we investigated the use of a Bayesian framework to obtain the uncertainties from the calibration process and to propagate them to model predictions, includingLC(x,t) andMF(x,t) derivations. We also explored the mathematical properties ofLC(x,t) andMF(x,t) as well as the impact of different experimental designs to provide some recommendations for a robust derivation of toxicity endpoints leading to reliable EQSs: avoid computingLC(x,t) andMF(x,t) for extremexvalues (0 or 100%), where uncertainty is maximal; computeMF(x,t) after a long period of time to take depuration time into account and test survival under few correlated and uncorrelated pulses of the contaminant in terms of depuration.

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