A probabilistic method for species sensitivity distributions taking into account the inherent uncertainty and variability of effects to estimate environmental risk


  • Fadri Gottschalk,

    1. Empa-Swiss Federal Laboratories for Materials Science and Technology, Technology and Society Laboratory, Lerchenfeldstrasse 5, CH-9014 St Gallen, Switzerland
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  • Bernd Nowack

    Corresponding author
    1. Empa-Swiss Federal Laboratories for Materials Science and Technology, Technology and Society Laboratory, Lerchenfeldstrasse 5, CH-9014 St Gallen, Switzerland
    • Empa-Swiss Federal Laboratories for Materials Science and Technology, Technology and Society Laboratory, Lerchenfeldstrasse 5, CH-9014 St Gallen, Switzerland
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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


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.


Species sensitivity modeling

By means of MC calculations, the sensitivity of individual species to potential pollutants is estimated and the sensitivity information is combined into a probabilistic species sensitivity distribution (PSSD). The MC routines are formalized and conducted in R (R Development Core Team 2008). First, available experimental toxic endpoints are collected for a particular system. Literature data is often presented as the ECx (concentration affecting x% of organisms), the ICx% (x% inhibition concentration), the LCx% (concentration that is lethal to x% of a population), the no observed effect concentration (NOEC), or lowest observed effect concentrations (LOEC). Species sensitivity analysis can be carried out with all kinds of inhibition, effect, and NOECs depending on the guidelines applied. The uncertainty and/or variability of such endpoints for each single species are considered by lumping together all available values of a chosen endpoint for a particular species into a single probability density function (PDF). Such a transformation of deterministic data into probabilistic information is done by computing in a sequence of intervals and based on MC routines PDFs that are formed and bounded by the available raw endpoints.

As shown in Figure 1Ai for species with only one single toxicological endpoint (V1) in the literature, a triangular PDF may be calculated around this value by considering a coefficient of variation (CV) for the smallest and the highest expected sensitivity. Whenever such variation is not indicated in the literature, a range of uncertainty and/or variability has to be assumed. In this study, for single endpoints and for boundary values of compound distributions, a CV of 30% was used. Such a CV represents roughly the mean within-laboratory variation reported for chronic endpoints in US guidelines (USEPA 2000). However, the use of higher or lower CVs adapted to other test conditions can be considered (USEPA 2000). In cases where 2 empirical toxic endpoints are available for an individual species, a trapezoidal distribution is computed. Such a trapezium may be constructed based on a uniform distribution bounded by the 2 endpoints and complemented on each side with a triangular distribution determined by the CVs used (Figure 1Aii). For species with several toxic values, the lowest value found and the next highest value constitute the border of the first interval (uniform distribution), followed by the second lowest and the third lowest value (Figure 1Aiii). Consequently, in cases with n toxicological endpoints n − 1 intervals may be defined.

Figure 1.

Procedure for modeling probabilistic species sensitivity distributions (PSSD). (A) (i) For species having only one single toxic value (V1) a triangular probability density function (PDF) is modeled around this value by considering a range of uncertainty and/or variation (V1* to V1**); cases (ii) to (iii) show how to construct such PDFs for 2 and 3 usable toxic endpoints. The same procedure is used for all other quantities of endpoints. (B) Sample derivation of 1 single PDF* that combines individual PDFs into a generic one representing the probability distribution of the sensitivity of an individual species. This PDF is used in (C), among others, to model the PSSD for a particular environmental compartment.

In a second step (Figure 1B), these individual PDFs are combined into a generic PDF that represents the probability distribution of the sensitivity of an individual species. The stochastic algorithm randomly considers an equal number of values (10 000 in this work) from all the individual PDFs and unifies them in a generic probability distribution for one individual organism. This distribution is then used (Figure 1C) among others from all other species to compute the total PSSD for a corresponding environmental compartment. This last computation step is based on the same MC routine as the previous one. If individual species are overrepresented (e.g., a high number of toxicity values per species compared to the total number of toxicity values) in the collection of endpoints, this last modeling step may be modified by first producing individual probability distributions for taxonomic groups that are then combined to a total PSSD. With reference to strict European requirements (ECHA 2008), a reliable SSD should be based on at least 10 species by covering 8 taxonomic groups at a minimum. Other guidelines set limits for (parametric) SDD modeling if 5 chronic endpoints are unavailable (TenBrook et al. 2010).

Performance of the method

To demonstrate the robustness and applicability of the approach, 2 case studies for triclosan in surface water were carried out by using previously compiled data and comparing our results to the corresponding published SSDs (Capdevielle et al. 2008; Lyndall et al. 2010). Triclosan is a biocide and is mostly released into the aquatic environment via wastewater treatment effluents (Orvos et al. 2002). To preserve the comparability of the results, we fed our PSSD model with the same raw data that had been used to construct SSDs in Capdevielle et al. (2008) and Lyndall et al. (2010). The 23 endpoints (NOEC, EC10, EC20, EC25, as well as IC25 values) collected in Table 1 of Capdevielle et al. (2008) were used in case study 1. These untreated chronic endpoints were allocated to 14 species ranging from a 0.53 µg/L NOEC (Scenedesmus subspicatus) to a 290 µg/L IC25 (Oryzias latipes). For the second case study based on 33 species, we used the endpoints (NOEC, EC10, EC25, EC50, IC25, as well as LC25 values) in Table 5 in Lyndall et al. (2010) that contained the endpoints of the first case and 23 new results. Forty-six chronic toxic endpoints, ranging from 0.2 µg/L (Pseudokirchneriella subcapitata) to 440 µg/L (Chironomus riparius) (both NOECs), were linked to 29 sensitivity distributions for individual species. To maintain the comparability with (Lyndall et al. 2010), the second PSSD was not strictly based on single species, but in some cases also on combined data for the same genus.

Risk estimation

Risk is defined in our article as the product of the probability of critical environmental concentrations and the probability of an organism in a particular environmental compartment (fraction of organisms) being impacted negatively by such concentrations. The mean and low flow predicted environmental concentrations (PEC) of triclosan in US surface waters (recomputed by means of data provided by Anderson et al. [2004]) were used as environmental concentrations. The risk is then calculated as follows:

equation image(1)

This calculation provides the probability of the so-defined environmental risk. The extreme values used in the equation were taken from the discrete probability distributions returned by the MC calculations. One hundred percent risk would mean that the whole PEC graph overlapped the PSSD graph, 0% that all PEC values were smaller than the lowest possible sensitivity value. If the species sensitivity metric only reflects values considered unlikely to produce an adverse effect, the expected value of the equation represents a hazard rather than a risk. Consistent use of toxicity reference values is clarified in Allard et al. (2010), as is the distinction between screening, risk assessment, and quantitative uncertainty analysis in Hope (2009). The necessity of including socioeconomic and cultural processes on ecological systems in risk assessment is discussed in Kapustka et al. (2010).

Risk profiles for a potential contaminant reflect the risk of such a material at different (evenly distributed and grouped) environmental concentrations. These computations combine the probability of achieving certain toxicant concentrations in the environment with the probability of observing negative effects at these concentrations. Such probabilities are represented by the relative frequencies for both exposure and effects at different (selected) environmental concentrations. The risk profile is computed by multiplying each selected relative density of the PEC distribution with its counterpart of the PSSD:

equation image(2)

Zero risk is returned from the MC simulations whenever either the predicted negative effects were observed at unrealistic high toxicant concentrations or the predicted toxicant concentrations were shown to be harmless for organisms in the environment.


Sensitivity distributions

In the first case study, 23 toxicity values were used for running simulations of PSSDs for triclosan and organisms in aquatic environments. Single organism sensitivity distributions were modeled by considering 4, 3, 2, or 1 single toxic endpoint and/or endpoints. These 14 probability distributions were combined to create the aquatic PSSD shown in Figure 2A. For comparison, the raw sensitivity data used are shown in empty circles; the geometric mean for one species is shown as black circles. The SSD curve proposed by Capdevielle et al. (2008) is shown as a black line. The second case study contained twice as many endpoints (46), representing 29 individual species. The resulting PSSD curve is shown in Figure 2B together with the raw data used in Lyndall et al. (2010). The PSSDs clearly follow the raw information; this also applies to extreme empirical events that are crucial to the risk estimation. It was possible to produce extreme tail probabilities by considering all extreme endpoints as given in the raw database without any need to average them before feeding the model, and by computing CVs for minimal and maximal endpoints.

Figure 2.

Probabilistic species sensitivity distribution (PSSD) for triclosan in surface water (red curves) compared with the raw sensitivity data used (empty circles) from (A) Capdevielle et al. (2008) and (B) Lyndall et al. (2010). In (A) the PSSD is also compared with a log-logistic nonlinear regression (black curve) recomputed as shown in the aforementioned comparative study (Capdevielle et al. 2008).

Although the calculation of HC5 values is not central in the PSSD approach, it may be estimated if desired. A comparison of median HC5 values reveals that our HC5 (0.63 µg/L) is less than half that of the corresponding value (1.55 µg/L) taken from Capdevielle et al. (2008) and in the same range as the 0.8 µg/L HC5 of the follow-up work (Lyndall et al. 2010). Our second median HC5 value of 0.66 µg/L (Table 1) equals our first one almost exactly and was again close to the one given in Lyndall et al. (2010). Both factors—visual inspection of the 2 PSSDs (Figure 2A and B) and the comparison of the HC5 values (Table 1)—are indicative of the robustness of the proposed SSD approach. However, the different methods applied might have a stronger influence on the HC5 values than the different sizes of the used data sets.

Table 1. HC5 (concentrations where 5% of the species included are affected) values for triclosan derived from different SSD models
Case studySSD modelMedian HC5 in µg/L (95% lower CI)Percentage of toxic endpoints <HC5Total toxic endpointsSource
  1. CI = confidence interval; PSSD = probabilistic species sensitivity distribution; SSD = species sensitivity distribution.


Log-logistic (Versteeg et al. 1999)


Capdevielle et al. 2008

 Nonparametric PSSD0.63 (0.49)423This work

Nonparametric (bootstrap) (Newman et al. 2000)

0.8 (0.5)1146

Lyndall et al. 2010

 Nonparametric PSSD0.66 (0.54)746This work

Risk estimation

PEC distributions of triclosan in surface water were compared to the species sensitivity distributions. Figure 3A shows the PSSD (see Figure 2A) modeled in the first case study with mean and low flow PECs for triclosan in US surface waters recomputed by means of data provided by Anderson et al. (2004). The overlapping areas of PECs and effect concentrations (PSSD) show the degree of risk. Risk is defined as the product of the probability of critical concentrations (higher than the smallest no observed effect concentration produced) and the probability of an organism being exposed to such concentrations. Using the PSSD of the first case study, 0.1% risk is predicted for mean flow conditions and 3.3% risk for low flow water levels.

Figure 3.

Probabilistic species sensitivity distribution (PSSD) for triclosan in surface water computed in relative form based on data collected (A) in Capdevielle et al. (2008) and (B) in Lyndall et al. (2010) compared with mean and low flow predicted environmental concentrations (PEC) of triclosan in US surface waters (recomputed by means of data provided by Anderson et al. [2004]). The extent of overlapping of PECs and sensitive concentrations (PSSD) shows the degree of risk.

We also used the same PEC scenarios for a comparison with the SSD results (see Figure 2B) of our second case study. As shown in Figure 3B, again almost only low flow PECs exceed critical sensitivity levels leading to the following risk probabilities: 0.5% for mean flows and 6.4% for low flow water levels. As shown in Figure 4, the latter value reflects the risk for low flows formed by the product of the probability of PECs being higher than the smallest species sensitivity concentrations and the probability of PSSD values (fraction of organisms) being smaller than the highest PEC. Approximately 0.28 (Figure 4, denoted by *) is the fraction of critical PSSDs and 0.23 (Figure 4, denoted by **) (equivalent to 1–0.77) the one of critical PECs (Figure 4).

Figure 4.

Distributions of predicted environmental concentrations (PEC) and species sensitivity (probabilistic species sensitivity distributions [PSSD]) used in cumulative form to illustrate risk (here 6.4) defined as the product of the fraction of critical PSSD values (0.28*) and the fraction of critical PECs (0.23** [equivalent to 1–0.77]).

This latter case was evaluated in more detail by modeling a risk profile that evaluated risk at concentrations that might be achieved in river water and that at the same time have been seen to affect negatively exposed organisms (Figure 5). The highest risk for the low water conditions was seen at approximately 1 µg/L. Critical concentrations ranged from 0.2 to 8 µg/L; above and below this interval no risk was calculated. The equivalent output for the mean water levels was 0.3 µg/L (0.2 to 2.5 µg/L). The comparison of the risk profiles produced and the aforementioned generic risk probabilities for these 2 PEC scenarios showed that the risk for low water conditions was approximately 20 times higher than the one for mean water flows.

Figure 5.

Probability density functions representing risk profiles for triclosan in surface water covering different environmental concentrations. Risk is produced by multiplying relative frequencies for predicted environmental concentrations (PEC) by corresponding density values (at the same concentrations) of probabilistic species sensitivity distributions (PSSD).


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.


We are very grateful to Paul D Anderson, Vincent J D'Aco and colleagues for providing raw data on environmental concentrations for triclosan. We thank Katja Knauer and Martin Scheringer for their useful comments and suggestions on an earlier draft of this manuscript.