Hierarchical modelling of species sensitivity distribution: Development and application to the case of diatoms exposed to several herbicides

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Highlights

  • A hierarchical SSD approach to properly include the uncertainty on the ECx.

  • An SSD based on the full response to herbicide exposure not only on a summary (ECx).

  • A new risk indicator based on the global response of the community.

  • Preserving the global response differs from protecting a percentage of the species.

  • Fitting an SSD on EC10 seems unreasonable: it leads to a large uncertainty on the HC5.

Abstract

The species sensitivity distribution (SSD) is a key tool to assess the ecotoxicological threat of contaminants to biodiversity. For a contaminant, it predicts which concentration is safe for a community of species. 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 estimated sensitivities 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. To remedy these drawbacks, we built a global hierarchical model including the concentration–effect model together with the distribution law of the SSD. We revisited the current SSD approach to account for more sources of variability and uncertainty into the prediction than the traditional analysis and to assess a global response for the community. Working within a Bayesian framework, we were able to compute an SSD taking into account the uncertainty from the original raw data. We also developed a quantitative indicator of a global response of the community to the contaminant. We applied this methodology to study the toxicity and the risk of six herbicides to benthic diatoms from Lake Geneva, based on the biomass endpoint. Our approach highlighted a wide variability within the set of diatom species for all the parameters of the concentration–effect model and a potential correlation between them. Remarkably, variability of the shape parameter of the model and correlation had not been considered before. Comparison between the SSD and the global response of the community revealed that protecting 95% of the species might preserve only 80–86% of the global response. Finally, propagating the uncertainty on the estimated sensitivity showed that building an SSD on a low level of effect, such as EC10, might be unreasonable as it induces a large uncertainty on the result.

Introduction

The species sensitivity distribution (SSD) is a cornerstone of ecological risk assessment. Among other uses, it serves to predict concentrations in contaminant which are safe for a community. SSD is essentially an extrapolation of the sensitivity of a community of species from monospecific laboratory tests. The most standard approach (Aldenberg and Slob, 1993, Aldenberg and Jaworska, 2000, Posthuma et al., 2001) models the interspecific sensitivity variability in an assemblage of tested species in three steps. In the first step, the sensitivity of each species is summarized by a single critical effect concentration (CEC). This CEC can be a no observed effect concentration (NOEC) or a lowest observed effect concentration (LOEC). It can also be a no effect concentration (NEC) or an effective concentration at x% (ECx), which are obtained by fitting a model to the concentration–effect curve. In the second step, the CECs in the community are assumed to follow a distribution law. Common choices for the distribution law include log-normal, log-logistic, and BurrIII. The chosen distribution is then fitted to the CECs of the sample of tested species. In the third step, the hazardous concentration to p% of the community (HCp) is computed as a percentile of the previous fitted distribution.

The HCp represents the concentration which affects p% of the community. The term “affect” is directly linked to the type of CEC in terms of level of effect (for example the x of the ECx) and of biological effect (lethal, non-lethal, acute, and chronic). If NOEC or NEC were true no effect concentrations, one would expect the HCp to leave (100p)% of the community species completely unharmed. Using EC50 however, which is a level of effect commonly selected, one expects (100p)% of the community to remain unaffected, which means that they suffer a reduction of less than 50% to their measured endpoint. But it is not possible to determine the reduction suffered by the unaffected species, which could lie anywhere between 0% and 50%.

SSD essentially carries information about the structural response of a community to a contaminant, i.e. the fraction of species affected at a certain level. The HCp for small p, such as the HC5, is ultimately used as a risk indicator. It is compared to the actual concentration of contaminant in an environmental setting to determine if the community living there is at risk, or to define an acceptably safe concentration for that community.

Several sources of uncertainty enter at the various steps of the SSD approach and have an influence on the predicted HCp value. First, there is an uncertainty on the estimate of the CEC from the experimental data: when the CEC is estimated from a concentration–effect curve or more generally from any model, it comes with a confidence interval. Second, uncertainty arises from the fitting of a distribution to the CECs: parameters of the distribution also have their own confidence intervals. This adds to the total uncertainty on the HC5. The uncertainty of this second step has already been studied and methods have been found for specific distribution laws (Aldenberg and Slob, 1993, Aldenberg and Jaworska, 2000, Wagner and Lokke, 1991). For other types of distributions, it is possible to use bootstrap (Efron and Tibshirani, 1994) to obtain confidence intervals, as described by Shao (2000) for the BurrIII distribution or in previous work by Kon Kam King et al. (2014). This uncertainty was also investigated with non-parametric approaches in the estimation of the SSD (Jagoe and Newman, 1997, Verdonck et al., 2001, van der Hoeven, 2001, Grist and Leung, 2009). However, there are currently very few attempts to include together all the sources of uncertainty into the final prediction of the SSD (Aldenberg and Rorije, 2013).

The classical SSD approach described in the previous section and its many variants present a number of flaws (Forbes and Calow, 2002, Power and McCarty, 1997) ranging from ecotoxicological concerns (use of laboratory data to predict field effects, inferring community sensitivity from monospecific sensitivities and chronic vs. acute effects) to statistical issues (fitting a distribution on a small dataset, distributional assumptions and treatment of the uncertainty). This paper focuses on several of these: first, the classical SSD approach does not propagate the uncertainty on the CEC to the prediction. This is a source of concern, because following this approach, the uncertainty on the HCp depends on the number of species, but not on the quality of the data used. Second, the CEC retains only a fraction of the information originally present in the data. Since the aim of SSD is to model the variability in sensitivity in the community, it is important to consider all the information available in the data to obtain the best estimation of that variability. Indeed, there is relevant biological information in all the parameters of the concentration–effect curve and their potential correlations. Third, providing an HCp, the classical SSD approach outputs information about a structural response of the community only. It essentially yields the proportion of affected species for a given concentration in contaminant. It does not give information about the global response of the community (Forbes and Calow, 2002, Kefford et al., 2012, De Laender et al., 2008), i.e. a response of the same nature as the measured endpoint. For instance, when using EC50 for biomass reduction as input, the SSD does not say anything about the change in the biomass of the community. In other words, the SSD aims to protect the structure of the community, but does not consider the effect on the community endpoint linked to the tested species which could be growth, reproduction, biomass, respiration, photosynthesis or any ecosystem process.

To address such issues, we revisited the current SSD approach to account for more sources of variability and uncertainty into the prediction than the traditional analysis and to assess the risk for the community from a global point of view. For this purpose, we built a hierarchical model inspired by Moore et al. (2010) including the concentration–effect model together with the distribution law of the SSD. From this hierarchical model, we were able to develop: (1) an indicator for the global response of the community, which we compared to the structural response predicted by the classical SSD; and (2) an SSD calculated on any level of effect (x of the ECx) including correlation among the parameters of the concentration–effect model and the uncertainty from the original data.

Section snippets

Diatoms sensitivity dataset

Our work was developed on a previously published dataset (Larras et al., 2012) containing 11 diatom species exposed to six herbicides: atrazine, terbutryn, diuron, isoproturon, metolachlor and dimethachlor. Between five and ten species were tested per herbicide. Benthic diatoms are unicellular microalgae which form a group of high diversity and which are often used to monitor water quality. They are well known to evolve in the biofilm matrix, at the interface of water column and substrata. The

Classical SSD

The EC10 and the EC50 of each species were computed for each contaminant. Results for two contaminants, atrazine and diuron, are displayed in Fig. SI B.1. For both herbicides, the confidence intervals appeared to be much larger on the EC10 than on the EC50. Similar results were observed for the four other herbicides.

Convergence of the MCMC algorithm

The MCMC chains converged for all contaminants, according to the Gelman–Rubin statistics (Brooks and Gelman, 1998). Fig. 2 shows for diuron that except for parameter ρ, the vague

Discussion

Classical SSDs are widely used to assess risk of chemicals for natural communities, but they present certain limitations (Forbes and Calow, 2002, Power and McCarty, 1997). In this study, we presented a hierarchical approach to SSD, which includes all the information present in the raw bioassay data to overcome some of these limitations. This hierarchical SSD differs from classical SSD in that the whole concentration–effect curve is used to build the SSD instead of a single CEC per species. This

Acknowledgements

We thank an anonymous reviewer for his careful reading and for suggesting well-thought improvements to the paper. Funding for this project was provided by a Grant from la Région Rhône-Alpes.

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