## INTRODUCTION

Modeling of species sensitivity distributions (SSD) is a well-established procedure for estimating the environmental risk of chemicals (Scott-Fordsmand and Damgaard 2006; Chen et al. 2010; Fox 2010). Species sensitivity distributions reflect sensitivity data for organisms to derive a hazard concentration (HCx%), for example the HC5 where 5% of the organisms are affected (95% protected) (Leeuwen and Vermeire 2007). For protective regulation, the 95% lower confidence limit of such an HC value is often used and combined with assessment factors to derive a predicted no effect concentration (PNEC) (Verdonck et al. 2001).

Species sensitivity distribution researchers are faced with challenges such as how effects on single species may be translated into effects on an ecosystem level (Scott-Fordsmand and Damgaard 2006; Kapustka 2008), and which SSD methodologies and concepts may be standardized (Wang et al. 2008). Numerous critical reviews have evaluated strengths and limitations of different methodologies (Power and McCarty 1997; Aldenberg and Jaworska 2000; Forbes and Calow 2002; Verdonck et al. 2003; van der Hoeven 2004; Jager et al. 2006).

One critical point is the model choice, especially the unknown—possibly unknowable—distributional form (Fox 2010). Newman et al. (2000) could not support a general use of theoretical distributions (log-normal SSDs) after comprehensively analyzing a large set of raw sensitivity information. For avoiding the use of theoretical distributions these authors (Newman et al. 2000, 2002) used bootstrap with resampling techniques (Jagoe and Newman 1997) to model 95% confidence intervals that represented on their lower sides conservative HC5 values. Verdonck et al. (2001) evaluated parametric and nonparametric bootstrapping, maximum likelihood estimation methods and Bayesian algorithms. The choice of a theoretical distribution was shown to be difficult when influencing the model output without overfitting the data: nonparametric models were observed to fit the data more efficiently, whereas parametric approaches showed smaller uncertainty bands. Grist et al. (2002) came to similar conclusions by asserting that nonparametric bootstrap computation (even when data-intensive) may ignore a prior distribution of raw biological responses, whereas parametric techniques require less data but may produce unrealistic assumptions on the distributional form.

A further question is: what constitutes a sufficient (limited) number and representative selection of tested species (organisms)? A thin data basis with a high variability of biological responses of organisms can be expected for emerging contaminants. Random selection is rare; organisms are often selected based on experimental manageability under laboratory conditions (van Straalen and van Leeuwen 2002). Van der Hoeven (2001) showed that even simple nonparametric techniques may produce acceptable SSD results. A method applicable from sample size 19 upward was presented to calculate an HC5 by ordering rough experimental data from high to low sensitivity. Wheeler et al. (2002) found stability of SSDs upward of 10 to 15 data points for log-normal and log-logistic models and concluded that considering variation in single species experiments would be a crucial step forward in studying species sensitivity.

Probabilistic distribution functions have also been used in risk assessment, to compare SSDs to exposure concentrations of the pollutants of concern. In Solomon et al. (2000), the intersection under either distribution (SSD and exposure concentration distribution [ECD]) is seen to represent the degree of risk. However, this is a simplification that ignores the distributional form above the mentioned intersection of both exposure and species sensitivity. Verdonk et al. (2003) used joint probability distributions for the exposure concentration (EC) and the species sensitivity (SS) that reflect the probability that EC exceeds SS. Their work focuses on theoretical (log-normal) curves for ECD and SSD. A numerical modeling procedure, for example based on the Monte-Carlo (MC) analysis, is not discussed. Such joint probability distribution methods were used on several occasions (Aldenberg et al. 2002; Zolezzi et al. 2005; Choi et al. 2009; Hayashi and Kashiwagi 2011).

In this article we propose an SSD alternative to cope with distinct variability and uncertainty (and small data sets) of raw information. Instead of considering one single deterministic (often averaged) toxic endpoint for each species, we probabilistically produce for all species their own sensitivity distributions, which, when taken together, comprise the generic SSD of a particular environmental compartment. Mathematical transformation of model input and output based on averaging (grouping) procedures and data fitting by means of theoretical distributions and a minimal amount of rough information does not occur. The distributional form is determined by the varying responses of the same organism to a particular pollutant, for example due to intra- and interlaboratory (field) variation and uncertainty. By leaving the prior model data unmodified, our stochastic and/or probabilistic concept assumes the input parameters distributed themselves, and considers the raw data size such as the sample of empirical values supplies.

To evaluate the performance of the model, we developed a series of simulations by using values from 2 case studies investigating the effects of triclosan on the aquatic environment. For the first simulation, the data were taken from Capdevielle et al. (2008); for the second simulation, the data were taken from Lyndall et al. (2010).

Additionally, we propose a numeric probabilistic risk estimation that links the modeled SSDs with the uncertainty and variability of environmental exposure conditions. In our work, risk combines the probability of both critical exposure concentrations and effects at relevant environmental concentrations. Such calculations are determined by the entire probability distributions (shape and areas) of EC and SS and thus are not focused on any intersections of both distributions. Risk probabilities are calculated and risk profiles graphically constructed for the aforementioned cases. Moreover, the method enabled us to calculate based on a standard SSD-based derivation procedure HC5 values and PNECs.