A Bayesian approach to analyzing ecotoxicological data

Environmental Risk Assessment with Energy Budget Models: A Comparison Between Two Models of Different Complexity

The extrapolation of effects from controlled standard laboratory tests to real environmental conditions is a major challenge facing ecological risk assessment (ERA) of chemicals. Toxicokinetic-toxicodynamic (TKTD) models, such as those based on dynamic energy budget (DEB) theory, can play an important role in filling this gap. Through the years, different practical TKTD models have been derived from DEB theory, ranging from the full "standard" DEB animal model to simplified "DEBtox" models. It is currently unclear what impact a different level of model complexity can have on the regulatory risk assessment. In the present study, we compare the performance of two DEB-TKTD models with different levels of complexity, focusing on model calibration on standard test data and on forward predictions for untested time-variable exposure profiles. The first model is based on the standard DEB model with primary parameters, whereas the second is a reduced version with compound parameters, based on DEBkiss. After harmonization of the modeling choices, we demonstrate that these two models can achieve very similar performances both in the calibration step and in the forward prediction step. With the data presented in the present study, selection of the most suitable TKTD model for ERA therefore cannot be based alone on goodness-of-fit or on the precision of model predictions (within current ERA procedures for pesticides) but would likely be based on the trade-off between ease of use and model flexibility. We also stress the importance of modeling choices, such as how to fill gaps in the information content of experimental toxicity data and how to accommodate differences in growth and reproduction between different data sets for the same chemical-species combination. Environ Toxicol Chem 2024;43:440-449. © 2023 ibacon GmbH. Bayer AG and The Authors. Environmental Toxicology and Chemistry published by Wiley Periodicals LLC on behalf of SETAC.

A Toxicokinetic-Toxicodynamic Modeling Workflow Assessing the Quality of Input Mortality Data

Toxicokinetic-toxicodynamic (TKTD) models simulate organismal uptake and elimination of a substance (TK) and its effects on the organism (TD). The Reduced General Unified Threshold model of Survival (GUTS-RED) is a TKTD modeling framework that is well established for aquatic risk assessment to simulate effects on survival. The TKTD models are applied in three steps: parameterization based on experimental data (calibration), comparing predictions with independent data (validation), and prediction of endpoints under environmental scenarios. Despite a clear understanding of the sensitivity of GUTS-RED predictions to the model parameters, the influence of the input data on the quality of GUTS-RED calibration and validation has not been systematically explored. We analyzed the performance of GUTS-RED calibration and validation based on a unique, comprehensive data set, covering different types of substances, exposure patterns, and aquatic animal species taxa that are regularly used for risk assessment of plant protection products. We developed a software code to automatically calibrate and validate GUTS-RED against survival measurements from 59 toxicity tests and to calculate selected model evaluation metrics. To assess whether specific survival data sets were better suited for calibration or validation, we applied a design in which all possible combinations of studies for the same species-substance combination are used for calibration and validation. We found that uncertainty of calibrated parameters was lower when the full range of effects (i.e., from high survival to high mortality) was covered by input data. Increasing the number of toxicity studies used for calibration further decreased parameter uncertainty. Including data from both acute and chronic studies as well as studies under pulsed and constant exposure in model calibrations improved model predictions on different types of validation data. Using our results, we derived a workflow, including recommendations for the sequence of modeling steps from the selection of input data to a final judgment on the suitability of GUTS-RED for the data set. Environ Toxicol Chem 2024;43:197-210. © 2023 Bayer AG and The Authors. Environmental Toxicology and Chemistry published by Wiley Periodicals LLC on behalf of SETAC.

Sublethal effects of binary mixtures of Cu2+ and Cd2+ on Daphnia magna: Standard Dynamic Energy Budget (DEB) model analysis

Dynamic Energy Budget theory (DEB) describes mass and energy fluxes that occur in living organisms. DEB models were successfully used to assess the influence of stress, including toxic substances, and changes in pH and temperature, on different organisms. In this study, the Standard DEB model was used to evaluate the toxicity of copper and cadmium ions and their binary mixtures on Daphnia magna. Both metal ions have a significant influence on daphnia growth and reproduction. Different physiological modes of action (pMoA) were applied to primary DEB model parameters. Model predictions for chosen modes of interaction of mixture components were evaluated. The goodness of model fit and the model prediction was assessed to indicate the most likely pMoA and interaction mode. Copper and cadmium influence more than one DEB model primary parameter. Different pMoAs can result in similar model fits, and therefore it is difficult to identify pMoA only by evaluation of the goodness of fit of the model to the growth and reproduction data. Some critical discussion and ideas for model development are therefore provided.

Introducing the No-Significant-Effect Concentration

The no-effect concentration (NEC) is the preferred threshold metric for single-species toxicity tests applied to derive safe concentration thresholds for contaminants in the environment for use in species sensitivity distributions. However, the NEC is only suitable when concentration-response (C-R) data exhibit a threshold response. We describe an alternative toxicity estimate, the no-significant-effect concentration (NSEC), which is better suited to C-R data for which the response is a monotonically decreasing function of concentration and no threshold effects are evident. We use a flexible, three-parameter sigmoidal function to describe the C-R relationship and detail both Bayesian and frequentist approaches to estimation and inference for the NSEC. While the NSEC is conceptually linked to the traditional no-observed-effect concentration (NOEC), it is a substantial improvement over the NOEC because it decouples the estimate from being directly dependent on the placement of treatment concentrations as well as admitting statements of precision of the resulting toxicity estimate. Environ Toxicol Chem 2023;42:2019-2028. © 2023 Commonwealth of Australia and The Authors. Environmental Toxicology and Chemistry published by Wiley Periodicals LLC on behalf of SETAC.

hb or not hb - when and why accounting for background mortality in toxicological survival models matters?

Decisions in Environmental Risk Assessment (ERA) about impacts of chemical compounds on different species are based on critical effect indicators such as the 50% lethal concentration (LC₅₀). Regulatory documents recommend concentration-response (or concentration-effect) model fitting on standard toxicity test data to get LC₅₀ values. However, toxicokinetic-toxicodynamic (TKTD) models proved their efficiency to better exploit toxicity test data, at Tier-2 but also at Tier-1, delivering time-independent indicators. In particular, LC₅₀ values can be obtained from the reduced General Unified Threshold model of Survival (GUTS-RED) with both variants, Stochastic Death and Individual Tolerance, that include parameter h_b, the background mortality. Estimating h_b during the fitting process or not depends on studies and fitting habits, while it may strongly influence the other GUTS-RED parameters, and consequently the LC₅₀ estimate. We hypothesized that estimating h_b from all data in all replicates over time should provide more precise LC₅₀ estimates. We then explored how estimating h_b impacted: (i) GUTS-RED model parameters; (ii) goodness-of-fit criteria (fitting plot, posterior predictive check, parameter correlations); (iii) LC₅₀ accuracy and precision. We finally show that estimating h_b does not impact the LC₅₀ precision while providing more accurate and precise GUTS parameter estimates. Hence, estimating h_b would lead to a more protective ERA.

In Silico Methods for Environmental Risk Assessment: Principles, Tiered Approaches, Applications, and Future Perspectives

This chapter aims to introduce the reader to the basic principles of environmental risk assessment of chemicals and highlights the usefulness of tiered approaches within weight of evidence approaches in relation to problem formulation i.e., data availability, time and resource availability. In silico models are then introduced and include quantitative structure-activity relationship (QSAR) models, which support filling data gaps when no chemical property or ecotoxicological data are available. In addition, biologically-based models can be applied in more data rich situations and these include generic or species-specific models such as toxicokinetic-toxicodynamic models, dynamic energy budget models, physiologically based models, and models for ecosystem hazard assessment i.e. species sensitivity distributions and ultimately for landscape assessment i.e. landscape-based modeling approaches. Throughout this chapter, particular attention is given to provide practical examples supporting the application of such in silico models in real-world settings. Future perspectives are discussed to address environmental risk assessment in a more holistic manner particularly for relevant complex questions, such as the risk assessment of multiple stressors and the development of harmonized approaches to ultimately quantify the relative contribution and impact of single chemicals, multiple chemicals and multiple stressors on living organisms.

Measuring mutagenicity in ecotoxicology: A case study of Cd exposure in Chironomus riparius

Existing mutagenicity tests for metazoans lack the direct observation of enhanced germline mutation rates after exposure to anthropogenic substances, therefore being inefficient. Cadmium (Cd) is a metal described as a mutagen in mammalian cells and listed as a group 1 carcinogenic and mutagenic substance. But Cd mutagenesis mechanism is not yet clear. Therefore, in the present study, we propose a method coupling short-term mutation accumulation (MA) lines with subsequent whole genome sequencing (WGS) and a dedicated data analysis pipeline to investigate if chronic Cd exposure on Chironomus riparius can alter the rate at which de novo point mutations appear. Results show that Cd exposure did not affect the basal germline mutation rate nor the mutational spectrum in C. riparius, thereby arguing that exposed organisms might experience a range of other toxic effects before any mutagenic effect may occur. We show that it is possible to establish a practical and easily implemented pipeline to rapidly detect germ cell mutagens in a metazoan test organism. Furthermore, our data implicate that it is questionable to transfer mutagenicity assessments based on in vitro methods to complex metazoans.

Bayesian approach in estimating flood waste generation: A case study in South Korea

Accurate estimations of flood waste generation are a crucial issue in disaster waste management. Multilinear regression of related parameters has been recognized as a promising technique for flood waste estimation. There are two types of flood waste estimation methods: pre-event predictions using factors related to regional properties and rainfall hazards, and post-event predictions using damage variables due to floods, such as the number of damaged buildings. Previous attempts to establish these models used deterministic approaches; however, probabilistic methods have never been applied. Considering the large degrees of uncertainty in waste generation from floods, a probabilistic approach can provide a more accurate model compared to models developed by the conventional deterministic approach. This study applied Bayesian inference to develop a flood waste regression model in South Korea. The aims of the study are as follows: (1) to analyze the characteristics of coefficients estimated by the Bayesian approach; (2) evaluate the performance of the prediction model by Bayesian inference; and (3) assess the effectiveness of Bayesian updating in a flood waste estimation. According to the results, the coefficients obtained via Bayesian inference showed a more significant p-value compared to those developed through the deterministic approach. Bayesian inference with a null prior distribution was effective in error reduction, specifically for post-event prediction. Bayesian updating did not effectively increase the accuracy of the model, while iterative updating required a complex calculation process. These results reveal the potential of the Bayesian approach in flood waste estimations, which can be transferred to other countries.

Consensus versus Individual QSARs in Classification: Comparison on a Large-Scale Case Study

Consensus strategies have been widely applied in many different scientific fields, based on the assumption that the fusion of several sources of information increases the outcome reliability. Despite the widespread application of consensus approaches, their advantages in quantitative structure–activity relationship (QSAR) modeling have not been thoroughly evaluated, mainly due to the lack of appropriate large-scale data sets. In this study, we evaluated the advantages and drawbacks of consensus approaches compared to single classification QSAR models. To this end, we used a data set of three properties (androgen receptor binding, agonism, and antagonism) for approximately 4000 molecules with predictions performed by more than 20 QSAR models, made available in a large-scale collaborative project. The individual QSAR models were compared with two consensus approaches, majority voting and the Bayes consensus with discrete probability distributions, in both protective and nonprotective forms. Consensus strategies proved to be more accurate and to better cover the analyzed chemical space than individual QSARs on average, thus motivating their widespread application for property prediction. Scripts and data to reproduce the results of this study are available for download.

Predicting the toxic effects of Cu and Cd on Chlamydomonas reinhardtii with a DEBtox model

Predicting the sublethal effects of pollutants to aquatic organism is essential in realistic chemical risk assessment. However, only a few dynamics models for sublethal endpoints are available. Here, we investigated the toxic effects of the essential metal Cu and the nonessential metal Cd on Chlamydomonas reinhardtiiunder both single and combined exposure, compared the effectiveness of different effect endpoints as toxic effect factors, and developed a Dynamic Energy Budget toxicology (DEBtox) model to predict the sublethal effects of Cu and Cd on C. reinhardtii. The results showed that the chlorophyll fluorescence parameter is a better toxic effect indicator than others for short-term exposure (<24 h), while algal cell growth is preferred for long-term exposure (2-6 days). The developed DEBtox model could successfully predict single metal toxicity to C. reinhardtii, while the combined metal DEBtox model slightly overestimates the joint toxicity of Cu-Cd due to the antagonistic effect of Cu-Cd on C. reinhardtii. This study is helpful to understanding and better predictions of metal sublethal toxic effects on aquatic organisms.

Integrated QSAR Models to Predict Acute Oral Systemic Toxicity

The ICCVAM Acute Toxicity Workgroup (U.S. Department of Health and Human Services), in collaboration with the U.S. Environmental Protection Agency (U.S. EPA, National Center for Computational Toxicology), coordinated the "Predictive Models for Acute Oral Systemic Toxicity" collaborative project to develop in silico models to predict acute oral systemic toxicity for filling regulatory needs. In this framework, new Quantitative Structure-Activity Relationship (QSAR) models for the prediction of very toxic (LD₅₀ lower than 50 mg/kg) and nontoxic (LD₅₀ greater than or equal to 2,000 mg/kg) endpoints were developed, as described in this study. Models were developed on a large set of chemicals (8992), provided by the project coordinators, considering the five OCED principles for QSAR applicability to regulatory endpoints. A Bayesian consensus approach integrating three different classification QSAR algorithms was applied as modelling method. For both the considered endpoints, the proposed approach demonstrated to be robust and predictive, as determined by a blind validation on a set of external molecules provided in a later stage by the coordinators of the collaborative project. Finally, the integration of predictions obtained for the very toxic and nontoxic endpoints allowed the identification of compounds associated to medium toxicity, as well as the analysis of consistency between the predictions obtained for the two endpoints on the same molecules. Predictions of the proposed consensus approach will be integrated with those originated from models proposed by the participants of the collaborative project to facilitate the regulatory acceptance of in-silico predictions and thus reduce or replace experimental tests for acute toxicity.

Predictive Models in Ecotoxicology: Bridging the Gap Between Scientific Progress and Regulatory Applicability

This special series is the outcome of the session "Predictive models in ecotoxicology: Bridging the gap between scientific progress and regulatory applicability," held at the 27th SETAC Europe annual meeting (Brussels, May 2017). In this foreword the rationale behind the special series, the reasons for proposing it, and its objectives are described briefly. Integr Environ Assess Manag 2018;14:601-603. © 2018 SETAC.

Scientific Opinion on the state of the art of Toxicokinetic/Toxicodynamic (TKTD) effect models for regulatory risk assessment of pesticides for aquatic organisms

Following a request from EFSA, the Panel on Plant Protection Products and their Residues (PPR) developed an opinion on the state of the art of Toxicokinetic/Toxicodynamic (TKTD) models and their use in prospective environmental risk assessment (ERA) for pesticides and aquatic organisms. TKTD models are species‐ and compound‐specific and can be used to predict (sub)lethal effects of pesticides under untested (time‐variable) exposure conditions. Three different types of TKTD models are described, viz., (i) the ‘General Unified Threshold models of Survival’ (GUTS), (ii) those based on the Dynamic Energy Budget theory (DEBtox models), and (iii) models for primary producers. All these TKTD models follow the principle that the processes influencing internal exposure of an organism, (TK), are separated from the processes that lead to damage and effects/mortality (TD). GUTS models can be used to predict survival rate under untested exposure conditions. DEBtox models explore the effects on growth and reproduction of toxicants over time, even over the entire life cycle. TKTD model for primary producers and pesticides have been developed for algae, Lemna and Myriophyllum. For all TKTD model calibration, both toxicity data on standard test species and/or additional species can be used. For validation, substance and species‐specific data sets from independent refined‐exposure experiments are required. Based on the current state of the art (e.g. lack of documented and evaluated examples), the DEBtox modelling approach is currently limited to research applications. However, its great potential for future use in prospective ERA for pesticides is recognised. The GUTS model and the Lemna model are considered ready to be used in risk assessment.

Estimation of population-level effect of the endocrine disruptor pyriproxyfen in Daphnia magna by using changes in sex ratio and reproductive output

Here we developed an analytical means of estimating population-level effects of endocrine disruptors on Daphnia magna. Our approach was based on the fact that the endocrine-disrupting juvenile hormone analogs induce the production of male neonates if they are exposed to the analogs during a particular period in their prenatal development; the method also assumed that the abnormal production of male neonates in the sake of production of female neonates reduces population growth. We constructed a linear toxicodynamics model to elucidate the period in which D. magna neonates are sensitive to exposure to the analog and also the probability of an individual neonate changing sex under specific exposure concentrations. The proposed model was applied to D. magna reproduction test data obtained under time-varying exposure to pyriproxyfen to derive the maximum-likelihood estimates and the posterior distributions of the model parameters. To quantitatively assess the ecological risk at the population level, we conducted a population dynamics simulation under two time-varying exposure scenarios (i.e., constant or pulsed exposure) by using an age-structured population model. When the change in sex ratio was based on the time-weighted average concentration during the period of sensitivity, change in sex ratio caused approximately equivalent population-level effects as did reproductive inhibition (i.e., reduction in the total number of neonates per female parent) regardless of the exposure scenario. In contrast, when change in sex ratio was based on maximum concentration during the sensitive period, change in sex ratio caused only half the population-level effects as did reproductive inhibition under constant exposure, whereas it caused a much larger population-level effect than did reproductive inhibition under pulsed exposure.

Recent Developments and Digital Perspectives in Food Safety and Authenticity

Food safety is of fundamental importance for the food processing industry, food retailers and distributors, and competent authorities because of its potentially direct impact on the health of consumers. Next to the prevention of microbiological, chemical, and physical hazards, increasing efforts are currently made to combat risks associated with food fraud or food authenticity. Food safety management systems nowadays comprise food safety, food defense, and food fraud prevention measures, trying to cope with the increasing complexity and globalization of the food supply chains. Future digital opportunities include the prediction of food safety and food authenticity issues by handling structured and unstructured data retrieved from various sources and origins to ensure the health of consumers and to minimize economical losses.

When significance becomes insignificant: Effect sizes and their uncertainties in Bayesian and frequentist frameworks as an alternative approach when analyzing ecotoxicological data

Bayesian methods and frequentist confidence intervals are proposed as an alternative approach in ecotoxicology, emphasizing effect sizes and associated (un)certainties to judge the biological relevance of effects instead of basing decisions on p values. These approaches show advantages over null hypothesis significance testing. In particular, Bayesian methods revealed more potential than frequentist counterparts, as the posterior distribution and its credible intervals can be directly interpreted as the probability of effect sizes. Environ Toxicol Chem 2018;37:1949-1955. © 2018 SETAC.

Chemical profiling and multivariate data fusion methods for the identification of the botanical origin of honey

The characterization of 72 Italian honey samples from 8 botanical varieties was carried out by a comprehensive approach exploiting data fusion of IR, NIR and Raman spectroscopies, Proton Transfer Reaction - Time of Flight - Mass Spectrometry (PTR-MS) and electronic nose. High-, mid- and low-level data fusion approaches were tested to verify if the combination of several analytical sources can improve the classification ability of honeys from different botanical origins. Classification was performed on the fused data by Partial Least Squares - Discriminant Analysis; a strict validation protocol was used to estimate the predictive performances of the models. The best results were obtained with high-level data fusion combining Raman and NIR spectroscopy and PTR-MS, with classification performances better than those obtained on single analytical sources (accuracy of 99% and 100% on test and training samples respectively). The combination of just three analytical sources assures a limited time of analysis.

New Insights to Compare and Choose TKTD Models for Survival Based on an Interlaboratory Study for Lymnaea stagnalis Exposed to Cd

Toxicokinetic-toxicodynamic (TKTD) models, as the General Unified Threshold model of Survival (GUTS), provide a consistent process-based framework compared to classical dose-response models to analyze both time and concentration-dependent data sets. However, the extent to which GUTS models (Stochastic Death (SD) and Individual Tolerance (IT)) lead to a better fitting than classical dose-response model at a given target time (TT) has poorly been investigated. Our paper highlights that GUTS estimates are generally more conservative and have a reduced uncertainty through smaller credible intervals for the studied data sets than classical TT approaches. Also, GUTS models enable estimating any x% lethal concentration at any time (LC_x,t), and provide biological information on the internal processes occurring during the experiments. While both GUTS-SD and GUTS-IT models outcompete classical TT approaches, choosing one preferentially to the other is still challenging. Indeed, the estimates of survival rate over time and LC_x,t are very close between both models, but our study also points out that the joint posterior distributions of SD model parameters are sometimes bimodal, while two parameters of the IT model seems strongly correlated. Therefore, the selection between these two models has to be supported by the experimental design and the biological objectives, and this paper provides some insights to drive this choice.

Physiological modes of action across species and toxicants: the key to predictive ecotoxicology

As ecotoxicologists we strive for a better understanding of how chemicals affect our environment. Humanity needs tools to identify those combinations of man-made chemicals and organisms most likely to cause problems. In other words: which of the millions of species are at risk from pollution? And which of the tens of thousands of chemicals contribute most to the risk? We identified our poor knowledge on physiological modes of action (how a chemical affects the energy allocation in an organism), and how they vary across species and toxicants, as a major knowledge gap. We also find that the key to predictive ecotoxicology is the systematic, rigorous characterization of physiological modes of action because that will enable more powerful in vitro to in vivo toxicity extrapolation and in silico ecotoxicology. In the near future, we expect a step change in our ability to study physiological modes of action by improved, and partially automated, experimental methods. Once we have populated the matrix of species and toxicants with sufficient physiological mode of action data we can look for patterns, and from those patterns infer general rules, theory and models.

Robust Fit of Toxicokinetic-Toxicodynamic Models Using Prior Knowledge Contained in the Design of Survival Toxicity Tests

Toxicokinetics-toxicodynamic (TKTD) models have emerged as a powerful means to describe survival as a function of time and concentration in ecotoxicology. They are especially powerful to extrapolate survival observed under constant exposure conditions to survival predicted under realistic fluctuating exposure conditions. But despite their obvious benefits, these models have not yet been adopted as a standard to analyze data of survival toxicity tests. Instead simple dose-response models are still often used although they only exploit data observed at the end of the experiment. We believe a reason precluding a wider adoption of TKTD models is that available software still requires strong expertise in model fitting. In this work, we propose a fully automated fitting procedure that extracts prior knowledge on parameters of the model from the design of the toxicity test (tested concentrations and observation times). We evaluated our procedure on three experimental and 300 simulated data sets and showed that it provides robust fits of the model, both in the frequentist and the Bayesian framework, with a better robustness of the Bayesian approach for the sparsest data sets.

A Bayesian network model for predicting aquatic toxicity mode of action using two dimensional theoretical molecular descriptors

The mode of toxic action (MoA) has been recognized as a key determinant of chemical toxicity, but development of predictive MoA classification models in aquatic toxicology has been limited. We developed a Bayesian network model to classify aquatic toxicity MoA using a recently published dataset containing over one thousand chemicals with MoA assignments for aquatic animal toxicity. Two dimensional theoretical chemical descriptors were generated for each chemical using the Toxicity Estimation Software Tool. The model was developed through augmented Markov blanket discovery from the dataset of 1098 chemicals with the MoA broad classifications as a target node. From cross validation, the overall precision for the model was 80.2%. The best precision was for the AChEI MoA (93.5%) where 257 chemicals out of 275 were correctly classified. Model precision was poorest for the reactivity MoA (48.5%) where 48 out of 99 reactive chemicals were correctly classified. Narcosis represented the largest class within the MoA dataset and had a precision and reliability of 80.0%, reflecting the global precision across all of the MoAs. False negatives for narcosis most often fell into electron transport inhibition, neurotoxicity or reactivity MoAs. False negatives for all other MoAs were most often narcosis. A probabilistic sensitivity analysis was undertaken for each MoA to examine the sensitivity to individual and multiple descriptor findings. The results show that the Markov blanket of a structurally complex dataset can simplify analysis and interpretation by identifying a subset of the key chemical descriptors associated with broad aquatic toxicity MoAs, and by providing a computational chemistry-based network classification model with reasonable prediction accuracy.

Energy-based modelling to assess effects of chemicals on Caenorhabditis elegans: a case study on uranium

The ubiquitous free-living nematode Caenorhabditis elegans is a powerful animal model for measuring the evolutionary effects of pollutants which is increasingly used in (eco) toxicological studies. Indeed, toxicity tests with this nematode can provide in a few days data on the whole life cycle. These data can be analysed with mathematical tools such as toxicokinetic-toxicodynamic modelling approaches. In this study, we assessed how a chronic exposure to a radioactive heavy metal (uranium) affects the life-cycle of C. elegans using a mechanistic model. In order to achieve this, we exposed individuals to a range of seven concentrations of uranium. Growth and reproduction were followed daily. These data were analysed with a model for nematodes based on the Dynamic Energy Budget theory, able to handle a wide range of plausible biological parameters values. Parameter estimations were performed using a Bayesian framework. Our results showed that uranium affects the assimilation of energy from food with a no-effect concentration (NEC) of 0.42 mM U which would be the threshold for effects on both growth and reproduction. The sensitivity analysis showed that the main contributors to the model output were parameters linked to the feeding processes and the actual exposure concentration. This confirms that the real exposure concentration should be measured accurately and that the feeding parameters should not be fixed, but need to be reestimated during the parameter estimation process.

Statistical handling of reproduction data for exposure-response modeling

Reproduction data collected through standard bioassays are classically analyzed by regression in order to fit exposure-response curves and estimate ECx values (x% effective concentration). But regression is often misused on such data, ignoring statistical issues related to (i) the special nature of reproduction data (count data), (ii) a potential inter-replicate variability, and (iii) a possible concomitant mortality. This paper offers new insights in dealing with those issues. Concerning mortality, particular attention was paid not to waste any valuable data-by dropping all the replicates with mortality-or to bias ECx values. For that purpose we defined a new covariate summing the observation periods during which each individual contributes to the reproduction process. This covariate was then used to quantify reproduction-for each replicate at each concentration-as a number of offspring per individual-day. We formulated three exposure-response models differing by their stochastic part. Those models were fitted to four data sets and compared using a Bayesian framework. The individual-day unit proved to be a suitable approach to use all the available data and prevent bias in the estimation of ECx values. Furthermore, a nonclassical negative-binomial model was shown to correctly describe the inter-replicate variability observed in the studied data sets.

Consequences of a multi-generation exposure to uranium on Caenorhabditis elegans life parameters and sensitivity

The assessment of toxic effects at biologically and ecologically relevant scales is an important challenge in ecosystem protection. Indeed, stressors may impact populations at much longer term than the usual timescale of toxicity tests. It is therefore important to study the evolutionary response of a population under chronic stress. We performed a 16-generation study to assess the evolution of two populations of the ubiquitous nematode Caenorhabditis elegans in control conditions or exposed to 1.1 mM of uranium. Several generations were selected to assess growth, reproduction, survival, and dose-responses relationships, through exposure to a range of concentrations (from 0 to 1.2 mM U) with all endpoints measured daily. Our experiment showed an adaptation of individuals to experimental conditions (increase of maximal length and decrease of fecundity) for both populations. We also observed an increase of adverse effects (reduction of growth and fertility) as a function of uranium concentration. We pointed out the emergence of population differentiation for reproduction traits. In contrast, no differentiation was observed on growth traits. Our results confirm the importance of assessing environmental risk related to pollutant through multi-generational studies.

All individuals are not created equal; accounting for interindividual variation in fitting life-history responses to toxicants

The individuals of a species are not equal. These differences frustrate experimental biologists and ecotoxicologists who wish to study the response of a species (in general) to a treatment. In the analysis of data, differences between model predictions and observations on individual animals are usually treated as random measurement error around the true response. These deviations, however, are mainly caused by real differences between the individuals (e.g., differences in physiology and in initial conditions). Understanding these intraspecies differences, and accounting for them in the data analysis, will improve our understanding of the response to the treatment we are investigating and allow for a more powerful, less biased, statistical analysis. Here, I explore a basic scheme for statistical inference to estimate parameters governing stress that allows individuals to differ in their basic physiology. This scheme is illustrated using a simple toxicokinetic-toxicodynamic model and a data set for growth of the springtail Folsomia candida exposed to cadmium in food. This article should be seen as proof of concept; a first step in bringing more realism into the statistical inference for process-based models in ecotoxicology.

Quantitative consensus of bioaccumulation models for integrated testing strategies

A quantitative consensus model based on bioconcentration factor (BCF) predictions obtained from five quantitative structure-activity relationship models was developed for bioaccumulation assessment as an integrated testing approach for waiving. Three categories were considered: non-bioaccumulative, bioaccumulative and very bioaccumulative. Five in silico BCF models were selected and included into a quantitative consensus model by means of the continuous formulation of Bayes' theorem. The discrete likelihoods commonly used in the qualitative Bayesian model were substituted by probability density functions to reduce the loss of information that occurred when continuous BCF values were distributed across the three bioaccumulation categories. Results showed that the continuous Bayesian model yielded the best classification predictions compared not only to the discrete Bayesian model, but also to the individual BCF models. The proposed quantitative consensus model proved to be a suitable approach for integrated testing strategies for continuous endpoints of environmental interest.

Individual sensitivity distribution evaluation from survival data using a mechanistic model: implications for ecotoxicological risk assessment

Two main alternatives are typically used to model mechanistically dose-survival relationship in ecotoxicity tests. Effects are related to a concentration of concern, for instance body concentration, and, to account for their differences relative to time-to-death, individuals have either different concentration thresholds for death ("individual tolerance approach"), or equal probability to die, with death occurring randomly ("stochastic death approach"). A general framework to unify both approaches has recently been proposed. We derived a model from this framework to analyse five datasets (daphnids exposed to selenium, guppies exposed to dieldrin and second, third and fourth instars chironomids exposed to copper), by extending the standard stochastic death approach. We showed the possibility to estimate properly the toxicity parameters together with inter-organisms differences of sensitivity for at least one of these parameters (here the threshold for effect). For the daphnids, there was no improvement of using the extended model, which confirms the expected low variability among genetically identical individuals. For all the other datasets, our model outperformed the standard approach without accounting for differences of sensitivity. We estimated coefficients of variations in the distribution of the logarithm of the threshold from 44% to 4% and showed, for chironomids, a decrease of inter-individual differences of sensitivity with the age of the larvae. All standard threshold estimates were close but above the medium value of the distribution in the new approach, which means that a concentration equal to the standard threshold would ultimately result in the death of more than half of the exposed organisms. A more relevant parameter, such as the concentration protecting 95% of the population, would be 2-4 times inferior to the standard threshold.

Survival data analyses in ecotoxicology: critical effect concentrations, methods and models. What should we use?

In ecotoxicology, critical effect concentrations are the most common indicators to quantitatively assess risks for species exposed to contaminants. Three types of critical effect concentrations are classically used: lowest/ no observed effect concentration (LOEC/NOEC), LC( x) (x% lethal concentration) and NEC (no effect concentration). In this article, for each of these three types of critical effect concentration, we compared methods or models used for their estimation and proposed one as the most appropriate. We then compared these critical effect concentrations to each other. For that, we used nine survival data sets corresponding to D. magna exposition to nine different contaminants, for which the time-course of the response was monitored. Our results showed that: (i) LOEC/NOEC values at day 21 were method-dependent, and that the Cochran-Armitage test with a step-down procedure appeared to be the most protective for the environment; (ii) all tested concentration-response models we compared gave close values of LC50 at day 21, nevertheless the Weibull model had the lowest global mean deviance; (iii) a simple threshold NEC-model both concentration and time dependent more completely described whole data (i.e. all timepoints) and enabled a precise estimation of the NEC. We then compared the three critical effect concentrations and argued that the use of the NEC might be a good option for environmental risk assessment.

Time to get off the fence: the need for definitive international guidance on statistical analysis of ecotoxicity data

The use of the no observed effect concentration (NOEC) and lowest observed effect concentration (LOEC) in ecotoxicology has been consistently criticized for over 30 years. A search of the literature from the past 30 years found 22 articles challenging the validity and/or appropriateness of NOEC/LOEC data compared to only one in defense of such data. Notwithstanding this compelling weight of evidence, the NOEC and LOEC remain commonly published measures of toxicity from ecotoxicological studies. In this article we argue that the major reason for the continued generation and publication of NOEC/LOEC data is that key government and intergovernmental organizations have been "sitting on the fence" on the issue for more than a decade. Although most key environmental quality guideline, toxicity testing, and associated guidance documents have now recognized the limitations of NOEC/LOEC data, to date no such document or standard toxicity test method has formally ceased recommending or providing guidance on the generation of such data. This is a problem because it is these very guidance documents and test methods that regulatory agencies demand be used by industry for regulatory activities, and on which commercial testing facilities attain and maintain their testing accreditation. Consequently, there will be little impetus for change to statistical analysis practices unless changes to the key guidance documents and test methods necessitate it. Although some progress on this has been made (e.g., in Canada, Australia and New Zealand), there needs to be stronger and universal action to ensure NOEC/LOEC data are no longer generated.

Population-level modeling to account for multigenerational effects of uranium in Daphnia magna

As part of the ecological risk assessment associated with radionuclides in freshwater ecosystems, toxicity of waterborne uranium was recently investigated in the microcrustacean Daphnia magna over a three-generation exposure (F0, F1, and F2). Toxic effects on daphnid life history and physiology, increasing over generations, were demonstrated at the organism level under controlled laboratory conditions. These effects were modeled using an approach based on the dynamic energy budget (DEB). For each of the three successive generations, DEBtox (dynamic energy budget applied to toxicity data) models were fitted to experimental data. Lethal and sublethal DEBtox outcomes and their uncertainty were projected to the population level using population matrix techniques. To do so, we compared two modeling approaches in which experimental results from F0, F1, and F2 generations were either considered separately (F0-, F1-, and F2-based simulations) or together in the actual succession of F0, F1, and F2 generations (multi-F-based simulation). The first approach showed that considering results from F0 only (equivalent to a standard toxicity test) would lead to a severe underestimation of uranium toxicity at the population level. Results from the second approach showed that combining effects in successive generations cannot generally be simplified to the worst case among F0-, F1-, and F2-based population dynamics.

Comparison of bioassays with different exposure time patterns: the added value of dynamic modelling in predictive ecotoxicology

The purpose of this study was to compare Daphnia magna responses to cadmium between two toxicity experiments performed in static and flow-through conditions. As a consequence of how water was renewed, the two experiments were characterised by two different exposure time patterns for daphnids, time-varying and constant, respectively. Basing on survival, growth and reproduction, we addressed the questions of organism development and sensitivity to cadmium. Classical analysis methods are not designed to deal with the time dimension and therefore not suitable to compare effects of different exposure time patterns. We used instead a dynamic modelling framework taking all timepoints and the time course of exposure into account, making comparable the results obtained from our two experiments. This modelling framework enabled us to detect an improvement of organism development in flow-through conditions compared to static ones and infer similar sensitivity to cadmium for both exposure time patterns.

Modeling the Ecological Footprint of Nations via Evolutionary Computation and Machine Learning Models

The per capita Ecological Footprint (EF) is one of the most-widely recognized measures of environmental sustainability. It seeks to quantify the Earth’s biological capacity required to support human activity. This study uses gene expression programming and Self-organizing Maps (SOM) to predict, classify and cluster the EF of 140 nations. A Bayesian approach was used to formally test the research hypotheses. By formulating the linear regression in a probabilistic framework, a Bayesian linear regression model is derived, and a specific simulation method, i.e., Markov Chain Monte Carlo (MCMC), is utilized to estimate the model parameters. Bayesian MCMC methods allow a richer and more complete representation of complex EF data. It also provides a computationally attractive and straightforward method to develop a full and complete description of the inherent uncertainty in parameters, quantiles and performance metrics.

A new perspective on the Dunnett procedure: filling the gap between NOEC/LOEC and ECx concepts

The no-observed-effect concentration (NOEC) is known to be based on a wrong usage of hypothesis tests, and the use of confidence intervals is preferred. The purpose of the present study is to provide an easy and proper way to interpret ecotoxicological tests based on simultaneous confidence intervals associated with the commonly used Dunnett procedure, and to show how these intervals may allow one to infer ECx values (effective concentrations).

Bayesian modelling of daphnid responses to time-varying cadmium exposure in laboratory aquatic microcosms

Experiments were carried out to test the effects of cadmium on five aquatic species in 2-L indoor freshwater/sediment microcosms. Experimental data were collected over 21 days in static conditions, i.e. the microcosms evolved without water renewal. Because of speciation, the total cadmium concentration in water decreased with time. Here we present a focus on Daphnia magna responses. For the three life history traits we considered (survival, growth and reproduction), mathematical effect models were built based on threshold stress functions involving no effect concentrations (NECs). These models took the time-varying conditions of exposure into account through a time-recurrent formalism. Within a Bayesian framework, four kinds of data were fitted simultaneously (exposure, survival, growth and reproduction), using an appropriate error model for each endpoint. Hence, NECs were determined as well as their associated estimation uncertainty. Through this modelling approach, we demonstrate that thresholds for stress functions can be successfully inferred even in experimental setup more complex than standard bioassays.

Biology-based modeling to analyze uranium toxicity data on Daphnia magna in a multigeneration study

Recent studies have investigated chronic toxicity of waterborne depleted uranium on the life cycle and physiology of Daphnia magna. In particular, a reduction in food assimilation was observed. Our aims here were to examine whether this reduction could fully account for observed effects on both growth and reproduction, for three successive generations, and to investigate through microscope analyses whether this reduction resulted from direct damage to the intestinal epithelium. We analyzed data obtained by exposing Daphnia magna to uranium over three successive generations. We used energy-based models, which are both able to fit simultaneously growth and reproduction and are biologically relevant. Two possible modes of action were compared - decrease in food assimilation rate and increase in maintenance costs. In our models, effects were related either to internal concentration or to exposure concentration. The model that fitted the data best represented a decrease in food assimilation related to exposure concentration. Furthermore, observations of consequent histological damage to the intestinal epithelium, together with uranium precipitates in the epithelial cells, supported the assumption that uranium has direct effects on the digestive tract. We were able to model the data in all generations and showed that sensitivity increased from one generation to the next, in particular through a significant increase of the intensity of effect, once the threshold for appearance of effects was exceeded.

General unified threshold model of survival--a toxicokinetic-toxicodynamic framework for ecotoxicology

Toxicokinetic-toxicodynamic models (TKTD models) simulate the time-course of processes leading to toxic effects on organisms. Even for an apparently simple endpoint as survival, a large number of very different TKTD approaches exist. These differ in their underlying hypotheses and assumptions, although often the assumptions are not explicitly stated. Thus, our first objective was to illuminate the underlying assumptions (individual tolerance or stochastic death, speed of toxicodynamic damage recovery, threshold distribution) of various existing modeling approaches for survival and show how they relate to each other (e.g., critical body residue, critical target occupation, damage assessment, DEBtox survival, threshold damage). Our second objective was to develop a general unified threshold model for survival (GUTS), from which a large range of existing models can be derived as special cases. Specific assumptions to arrive at these special cases are made and explained. Finally, we illustrate how special cases of GUTS can be fitted to survival data. We envision that GUTS will help increase the application of TKTD models in ecotoxicological research as well as environmental risk assessment of chemicals. It unifies a wide range of previously unrelated approaches, clarifies their underlying assumptions, and facilitates further improvement in the modeling of survival under chemical stress.

Bioaccumulation kinetics of organic xenobiotic pollutants in the freshwater invertebrate Gammarus pulex modeled with prediction intervals

Uptake and elimination rate constants, bioaccumulation factors, and elimination times in the freshwater arthropod Gammarus pulex were measured for 14 organic micropollutants covering a wide range of hydrophobicity (imidacloprid, aldicarb, ethylacrylate, 4,6-dinitro-o-cresol, carbofuran, malathion, 4-nitrobenzyl-chloride, 2,4-dichloroaniline, Sea-Nine, 2,4-dichlorophenol, diazinon, 2,4,5-trichlorophenol, 1,2,3-trichlorobenzene, and hexachlorobenzene; all 14C-labeled). The toxicokinetic parameters were determined by least-square fitting of a one-compartment first-order toxicokinetic model, followed by Markov Chain Monte Carlo parameter estimation. The parameter estimation methods used here account for decreasing aqueous concentrations during the exposure phase or increasing aqueous concentrations during the elimination phase of bioaccumulation experiments. It is not necessary to keep exposure concentrations constant or zero during uptake and elimination, respectively. Neither is it required to achieve steady state during the exposure phase; hence, tests can be shorter. Prediction intervals, which take the between-parameter correlation into account, were calculated for bioaccumulation factors and simulations of internal concentrations under variable exposure. The lipid content of Gammarus pulex was 1.3% of wet weight, consisting of 25% phospholipids and 75% triglycerides. Size-dependent bioaccumulation was observed for eight compounds, although the magnitudes of the relationships were too small to be of practical relevance. Elimination times ranged from 0.45 to 20 d, and bioaccumulation factors ranged from 1.7 to 4,449 L/kg. The identified compounds with unexpectedly long elimination times should be given priority in future studies investigating the biotransformation of these compounds.

From individual to population level effects of toxicants in the tubicifid Branchiura sowerbyi using threshold effect models in a Bayesian framework

Effects of zinc were studied in the freshwater worm Branchiura sowerbyi using partial and full life-cycle tests. Only newborn and juveniles were sensitive to zinc, displaying effects on survival, growth, and age at first brood at environmentally relevant concentrations. Threshold effect models were proposed to assess toxic effects on individuals. They were fitted to life-cycle test data using Bayesian inference and adequately described life-history trait data in exposed organisms. The daily asymptotic growth rate of theoretical populations was then simulated with a matrix population model, based upon individual-level outputs. Population-level outputs were in accordance with existing literature for controls. Working in a Bayesian framework allowed incorporating parameter uncertainty in the simulation of the population-level response to zinc exposure, thus increasing the relevance of test results in the context of ecological risk assessment.

A Bayesian approach for determining the no effect concentration and hazardous concentration in ecotoxicology

This paper describes a Bayesian modeling approach to the estimation of the no effect concentration (NEC) and the hazardous concentration (HC(x)) as an alternative to conventional methods based on NOECs - the no observed effect concentration. The advantage of the proposed method is that it combines a plausible model for dose-response data with prior information or belief about the model's parameters to generate posterior distributions for the parameters - one of those being the NEC. The posterior distribution can be used to derive point and interval estimates for the NEC as well as providing uncertainty bounds when used in the development of a species sensitivity distribution (SSD). This latter feature is particularly attractive and overcomes a recognized deficiency of the NOEC-based approach. Examples using previously published data sets are provided which illustrate how the NEC/HC(x) estimation problem is re-cast and solved in this Bayesian framework.

Uncertainty reduction in environmental data with conflicting information

The assessment of ecotoxicological effects of chemicals for regulatory purposes requires large amounts of experimental data which are expensive to obtain and eventually might entail exhaustive animal testing. The required decision-making processes in this regulatory context, must often be carried out with limited or even contradictory sources of information. To benefit from all sources of information without compromising the quality of the decision process, uncertainty management and reduction techniques, such as the Dempster-Shafer theory of evidence, have to be applied. This theory was applied to both experimental and in silico biodegradation data sources to assess chemical persistence. Uncertainties of the initially lass uncertain estimates for biodegradation rates in water were reduced by as much as 20-60%. The analysis showed that conflicting evidence can be detected, quantified, and redistributed proportionally among all the feasible subsets of hypotheses. The advantages of the Dempster-Shafer theory over Bayesian approaches to represent evidence concerning hypotheses by assigning probabilities were also analyzed.