### Abstract

- Top of page
- Abstract
- INTRODUCTION
- MATERIALS AND METHODS
- RESULTS
- DISCUSSION
- Acknowledgements
- REFERENCES

This article presents a method of probabilistically computing species sensitivity distributions (SSD) that is well-suited to cope with distinct data scarcity and variability. First, a probability distribution that reflects the uncertainty and variability of sensitivity is modeled for each species considered. These single species sensitivity distributions are then combined to create an SSD for a particular ecosystem. A probabilistic estimation of the risk is carried out by combining the probability of critical environmental concentrations with the probability of organisms being impacted negatively by these concentrations. To evaluate the performance of the method, we developed SSD and risk calculations for the aquatic environment exposed to triclosan. The case studies showed that the probabilistic results reflect the empirical information well, and the method provides a valuable alternative or supplement to more traditional methods for calculating SSDs based on averaging raw data and/or on using theoretical distributional forms. A comparison and evaluation with single SSD values (5th-percentile [HC5]) revealed the robustness of the proposed method. Integr Environ Assess Manag 2013; 9: 79–86. © 2012 SETAC

### INTRODUCTION

- Top of page
- Abstract
- INTRODUCTION
- MATERIALS AND METHODS
- RESULTS
- DISCUSSION
- Acknowledgements
- REFERENCES

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.

### DISCUSSION

- Top of page
- Abstract
- INTRODUCTION
- MATERIALS AND METHODS
- RESULTS
- DISCUSSION
- Acknowledgements
- REFERENCES

The PSSD method allows all available empirical raw knowledge of the same type (mortality data, reproductive information, etc.) to be integrated into the SSD calculation procedure without any preliminary, possibly arbitrary, mathematical transformation of such model input. To assess the strengths and limitations of the model, it was therefore important to see how well the simulated distributions fitted the available empirical data. Second, we wanted to examine the degree to which the stochastic computations would enable us to depict realistically the border areas and extreme tails of joint species sensitivity distributions.

As is clearly visible in both case studies, the PSSD results reflect the experimental information well: the curves clearly follow single and averaged input values by considering to the same extent also intra species variation and extreme events. For species with several values for the same toxic endpoint, the geometric mean of these values is often considered (Slooff 1992). However, such means are not without their problems in handling environmental data. As has been mentioned early for biological and other populations (Finney 1941), and revisited for environmental concentrations (Parkhurst 1998), the use of geometric sample means as representatives of true means may bias (scale down) results. Although this problem was not too pronounced in the first triclosan study, and partially masked (second study) by the case specific and complex interplay of inter- and intraspecies statistical spread, we know that geometric means are by definition smaller than arithmetical ones, and therefore favor small values by automatically shifting the SSD curve to the left. Thus, unless it is a matter of eliminating high-concentration outliers, this can lead to an overinterpretation of experiments yielding very sensitive results and overprotection in risk management. The advantage of PSSD is that it avoids a priori such averaging procedures. Instead of elevating a single, albeit significant, piece of information for a particular species, a differentiated analysis of all available sensitivity data is carried out for each species. The uncertainty and/or variability of this data is considered by constructing sensitivity probability distributions for each species based on all the available empirical information. One important advantage of such an approach is therefore that these distributions may be continuously updated by integrating new empirical findings for species that had not been considered previously.

The stability of our nonparametric results can be seen to some extent when our first and second distributions are compared. No significant differences were observed between the curves that had been modeled based on 2 different groups of usable model input values. In contrast, the log-logistic distribution in the first comparative case (Capdevielle et al. 2008) deviated strongly from our curves in the concentration ranges of the SSD boundaries. In the second comparative study (Lyndall et al. 2010) bootstrapping was only used to calculate confidence intervals for possible hazard concentrations. No particular focus was given to improving the modeling of the extreme tails of the SSD. We performed a visual inspection and compared HC5 values, revealing stability for the PSSD results. Even when computed based on a weaker data basis (as in the first case study), the HC5 values modeled in this article are in the same range as the corresponding values derived from twice as much data in the second case study. The ranges of the 95% confidence intervals are even slightly smaller (see Table 1). This underlines the fact that the method may produce robust results even when performed on a small data basis. However, if low quality data is used, it will be difficult to see how far the results only reflect diversity in the species sensitivity caused by inappropriate design, performance and documentation of the toxicity experiments. Principles to consider in the assessment of data quality and relevance are, for example, given in technical guidance documents for deriving environmental quality criteria in the EU Water Framework Directive (EC 2011).

Contrasting effect probabilities with exposure probabilities allows risk to be quantified in a more highly differentiated way than simple risk quotients can achieve, for example using a PEC/PNEC approach (EC 2006). It is not necessary to compare a single uncertain exposure value with deterministic effect information that may be uncertain as well in its isolated form. However, such a definition should not be confused with mathematically unclear interpretations of risk such as the intersection of the distributions for exposure concentration and species sensitivity that is sometimes proposed (Solomon et al. 2000). It may be seen as an alternative method of numerical integration of critical exposure and effect curves in line with other numerical approaches critically analyzed and summarized in Verdonck et al. (2003).

Our risk probabilities indicate how often how many organisms are predicted to be affected: 100% risk means that 100% of the species will be exposed to critical concentrations all the time and at every position of a studied system (100% in time and space); 10% risk could, for example, mean that 50% of the organisms are at risk 20% of the time and locations, or vice versa. These examples show that a generally valid interpretation of such risk calculations is difficult, and that the results cover the probability, but not the acceptability, of risk. How acceptable a calculated risk is cannot be answered mathematically by deriving acceptability values from risk probabilities. This also holds true for the proposed complementary risk profiles that show more explicitly at which environmental concentrations risk should most likely be expected. However, a comparison of the risk profiles (magnitude and range of critical concentrations, as well as relative densities) of emerging chemicals with the profiles of well-known hazardous substances could provide an early insight into the acceptability of possible risks of new materials. However, this first requires that a risk profile database for well-known toxins be created. To assess the acceptability of risk, it would then be indispensable to have a risk assessor take a complementary view of the graphics behind the computations. Relative graphical representations in particular are informative when one is, for example, seeking peaks that may reflect short-term or geographically limited PEC extremes or small groups of highly sensitive species. Short-term extreme concentration events that destroy, for example, a whole fish population may be as disastrous as a slightly critical exposure of a large range of organisms over a long time period. For a distinction between spatial and temporal influence of such events or for the identification of highly sensitive organisms one must take out the raw data.