Background Document Biology-Based Methods

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1 1 Background Document Biology-Based Methods Tjalling Jager and Sebastiaan A.L.M. Kooijman Dept. Theoretical Biology, Fac. Earth & Life Sciences Vrije Universiteit, de Boelelaan 1085, NL-1081 HV Amsterdam, The Netherlands url: August 20, 2007 Abstract At this moment, environmental effects assessment relies on simple summary statistics, such as NOEC and EC50, as derived from standardised toxicity tests. However, these statistics have limitations. Most importantly, the value of these statistics changes in time in a manner that depends on the species, toxicant and endpoint, and further, the methods to derive these statistics lack a biological background. If we want to understand the time patterns of toxic effects, and if we ever want to be able to extrapolate from laboratory tests to effects on populations under field conditions, we definitely require models that focus on the underlying biological and toxicological processes. In fact, valuable process information is already being collected when tests are conducted according to the current standard protocols, but descriptive statistical methods cannot unlock this information from the data set. Biology-based models attempt to fill this gap, making assumptions about the underlying processes and explicitly analyse the toxicity data over time. One particular method (the DEBtox method) has been described in recent OECD and ISO guidances on the analysis of toxicity data. However, such models are not currently used in risk assessment. This document describes the philosophy behind biology-based models in general, and the DEBtox method in detail, and discusses the potential usefulness in environmental risk assessment. Contents 1 Introduction 2 2 Limitations of current methods for dose-response analysis Limitations of hypothesis testing Limitations of regression analysis Exposure time affects toxicity Biological and toxicological background Biology-based modelling The DEBtox software Toxicokinetics No-effect concentrations Survival Short introduction to Dynamic Energy Budgets (DEB) Toxic effects on growth and reproduction Algal population growth File-name: background.tex

2 2 4 Technical description of DEBtox Toxicokinetics Survival Growth and reproduction Assimilation and feeding Costs for structure and costs for maturation Costs for somatic and maturity maintenance Hazards to developing egg Costs for reproduction General effect patterns Algal population growth Costs for growth Hazard model Adaptation model General pattern Statistics: fitting the models to the data Derived results: population growth Data requirements for DEBtox Survival Body growth Reproduction Fish life-cycle tests Algal population growth Examples of DEBtox applications Survival data Daphnia reproduction data Daphnia reproduction data, including observations on survival and size Algae population growth Usefulness in regulatory context Using DEBtox to analyse the time-dependence of effects Using DEBtox to analyse multiple endpoints from the same test Using DEBtox to identify problems with the data set Using DEBtox to analyse non-standard data Possibilities for educated extrapolations to field conditions Final remarks 43 1 Introduction Chemical risk assessment aims to ensure that the manufacture and use of chemicals will not endanger human health and the environment. In the European Union, the guidelines for chemical risk assessment are laid down in Technical Guidance Documents (TGD, [19]). For the environment, the risk assessment boils down to a comparison of exposure levels (PECs) to predicted safe concentrations for various populations and ecosystems (PNECs). As long as the PEC does not exceed the PNEC, it is assumed that the risks posed by a chemical are acceptable. The input for this analysis is formed by a dataset delivered by the manufacturer of the chemical. For exposure assessment, the data set contains physico-chemical properties of the chemical in question, such as hydrophobicity, water solubility, and results from (bio-)degradation tests. For effects assessment, the available data in the initial tiers typically include the results from standard toxicity tests, reported as NOECs or ECx 1 (after a specified exposure time). Interestingly, the philosophy behind the methods to derive the PEC and the PNECs from the available data set are markedly different (see Figure 1). In the exposure assessment, process-based fate models are used. In these models, 1 In this document, we will use the term ECx for all endpoints, including survival.

3 3 the available data are used to estimate environmental process parameters such as volatilization rates, degradation rates and partition coefficients. Using these models, it is possible to simulate the chemical s fate and transport in the environment for different release scenarios. Although these models are highly simplified in comparison to the real environment, they include many realistic features, and allow for the simulation of chemical behaviour in different environments (e.g., arctic and tropical regions, and different EU countries). In contrast, the method to derive the PNEC does not use process-based models; the available data are not used to estimate ecotoxicological process parameters. Instead, the approach departs from simple summary statistics, such as NOEC and EC50, and relies on the use of assessment factors (generally multiples of 10, see [10], for historical overview and discussion) to derive a predicted no-effect concentration (PNEC) as a concentration below which an unacceptable effect will most likely not occur [19]. The assessment factors reflect the translation from laboratory tests (short term, high exposure, one species, and controlled environment) to the field (long term, low exposure, multiple species, variable environment). Although ecotoxicological experience and common sense forms the basis of these factors, the scientific rigor of the extrapolation from test result contrasts the process-based models used for the exposure assessment 2. What is the reason for this difference in approach? According to Michael Newman [63]: The ecotoxicological literature is replete with statements that a working knowledge of ecosystems is impossible because of ecosystem complexity, yet such statements are inconsistent with the rapid growth of knowledge in equally complex disciplines.... What then is the reason for our limited knowledge base in ecotoxicology? I believe that a significant impediment to the growth of ecotoxicological knowledge lies in the approach by which such knowledge is sought, not in the complexity of the systems being studied. Figure 1: Illustrating the conceptual difference in the approaches for exposure assessment and effects assessment in the EU-TGD. It is possible that a chemical s fate in the environment is easier to predict than it s effects on all of the species that make up an ecosystem. This is not to say that environmental fate models are perfect representations of reality, but the chemists have two major advantages over the ecotoxicologists: they have a reasonably defined endpoint that can be quantitatively determined (concentrations in the environment), and they have a long tradition of simplifying the real world all the way down to an idealised system with only the most dominant processes. Ecotoxicologists 2 More recently, species-sensitivity distributions (see [72]) are accepted as an alternative extrapolation from single species to ecosystems, when many long-term studies are available (in general, at least 10 NOECs from 8 taxonomic groups). Although this method improves effects assessment in some aspects, it does not include any knowledge regarding biological or toxicological processes. In essence, this is an assessment factor approach, where the factor itself is derived from the available data in a statistical manner.

4 4 have to deal with vaguely defined endpoints such as ecosystem health, ecosystem functioning or resilience, and furthermore, they are not used to simplify their problem like they do in environmental chemistry or physics 3 (see also [85]). Extrapolating laboratory test results to field populations and ecosystems will always be associated with (large) uncertainties, but in our opinion, there is a lot to be gained from a process-based view using a simplified portion of reality. The current methods for analyzing toxicity test results are largely descriptive, and are not developed to extract process information from the toxicity test. However, toxicity tests performed according to the standard test protocols already contain valuable process information, and even more information can be obtained by (simple) changes to the test protocols to accommodate a process-based view. A promising way to unlock this information are so-called biology-based models, which make explicit assumptions regarding the processes behind the toxic effect, and simplify the organism to its most dominant processes. At this moment, such methods are not used within the regulatory context. However, they are described (next to the more classical approaches of hypothesis testing and regression analysis) in recent ISO and OECD guidances on the statistical analysis of ecotoxicity data [68, 34]. In this paper, we will focus on the DEBtox method; an integrated biology-based approach that formed the basis for the biology-based sections in the ISO and OECD guidances. Chapter summary In contrast to environmental exposure assessment, the effects assessment does not make use of process-based models. Instead, the approaches applied are mostly descriptive. Biology-based models form a promising alternative, and one specific method (DEBtox) will be presented and discussed in the rest of this document. 2 Limitations of current methods for dose-response analysis The current approaches for dose-response analysis are well described in guidances (e.g. [68, 34, 21]) and standard textbooks (e.g. [82, 63]). Basically, they can be classified in two categories: hypothesis testing and regression analysis. Before we go into a description of biology-based methods, it needs to be clear what the limitations of these current methods are. 2.1 Limitations of hypothesis testing Hypothesis testing is used to select the highest tested concentration that does not have a significant effect, in comparison to the control. This concentration is generally designated as a NOEC (noobserved effect concentration), although other terms are also used for no-effects (e.g., NOAEL, NOEL) or low-effects (the first dose with a significant effect, e.g., LOEC, LOAEL). Several methods are used to derive the NOEC such as multiple comparisons to the control and trend tests (described in detail in [68, 34]), but the basic idea behind the methods is the same. Although the NOEC and similar statistics are widely used in both scientific and regulatory context, they have received serious critique (e.g. [15, 33, 13, 55, 79]). The main objection raised against the NOEC is that it is not a measure of no-effects; the fact that effects are not significant does not mean that there are no effects. The ability to detect significant effects depends on the experimental design, variation within the treatments, and the power of the statistical test. The level of effect at the NOEC may thus be substantial (even exceed 50% in more extreme cases), and varies between different tests [13]. In general, poorly-conducted tests (few animals, large variations) lead to high (unprotective) NOECs. This is undesirable behaviour for a summary statistic used in risk assessment. For this reason, the OECD [67] concluded that the NOEC is inappropriate as the main summary parameter of aquatic ecotoxicity tests, and should be phased out. It must be stressed that multispecies or (semi-)field NOECs suffer from the exact same problems as the laboratory NOECs do, but to a larger extent. Generally, the variation in the response is large (also in the controls), making it very difficult to identify adverse toxic effects, thus yielding high (unprotective) NOECs. The current methods for extrapolation in effects assessment (SSDs and assessment factors, based on NOECs) are sometimes justified by comparing the resulting 3 For example, in the multi-media fate model of the EU-TGD, the surface water in Western Europe is treated as a single well-mixed homogeneous compartment. This is a clear example of a heroic simplification of reality.

5 5 PNECs to NOECs from multispecies experiments [20, 86]. However, the fact that no significant effects are observed in (semi-)field tests at the PNEC can hardly express confidence in the methods used for effects assessment. 2.2 Limitations of regression analysis The use of ECx values has several advantages over the NOEC. Regression analysis is used to fit a curve (the log-logistic is a popular choice) to all of the data at a single exposure time, and the concentration yielding x% effect is interpolated (x can be any number, but usually 5, 10 or 50% are used). A result of this procedure is that the summary statistic is, compared to the NOEC, less dependent on details of the experimental design and can be estimated with a confidence interval. Poorly conducted testing will not generally affect the value of the ECx, but will result in a wider confidence interval. The main concern raised against the NOEC is thus addressed. However, although perhaps not broadly recognised, limitations remain [44, 39]. In particular, regression analysis fails to address the factor of exposure time and lacks a biological and toxicological background 4. In the following sections, we will elaborate in more detail on these limitations Exposure time affects toxicity Toxicity is a process in time; the observed effects develop over the course of a toxicity test in a manner that is specific to the test organism, the tested chemical, and the observed endpoint. It is probably for this reason that many standard test protocols require that measurements are taken at several points in time. In practice, only the results at the last time point are used, although the earlier measurements contain valuable information. Regression models and hypothesis testing are inefficient in the sense that they cannot make use of these data in an integrated manner (at best only as a covariate in the regression, see e.g., [76]). Furthermore, the value of the resulting summary statistics (e.g., ECx and NOEC) will change with the exposure time. For lethality, it is well known that the EC50 tends to decrease approximately exponentially in time until it reaches a so-called incipient level [78]. This incipient EC50 is a rather good measure of lethal toxicity, but the test duration prescribed by current test protocols may not be sufficient to actually reach this level. The time needed to observe the incipient EC50 will depend on the compound and the species, which makes it impossible to specifiy the best test duration for all situations. For sublethal endpoints, the ECx may show a much less predictable relationship with time. To illustrate this time dependency, Figure 2 shows an example for two chemicals in a nematode species [3]. Clearly, there is no single ECx value that can be said to represent the ECx for a chemical in this species. This example illustrates that the time pattern of the ECx depends on the endpoint selected, the species and the compound tested, which limits the representativeness of this summary statistic. In practice, the time-dependence of the ECx is ignored by fixing the exposure period in standard protocols (e.g. an acute Daphnia test takes 2 days, and a chronic test 21 days; for fish an acute test takes 4 days, and a juvenile growth test 28 days). However, these test durations are the same for all chemicals and selected on the basis of pragmatic arguments (and probably guesswork). Already in 1969, Sprague [78] stated in relation to acute toxicity tests with fish: How long should acute toxicity tests be continued, in view of this information? Apparently no single time can be stated. It would seem prudent to continue tests for 4 days as a rule. Tests could then be stopped if mortality had ceased and the toxicity curve [in time] showed a threshold. If this were not the case, research tests should be continued until the shape of the toxicity curve is clearly established.... If no threshold were apparent, this should be clearly reported since it is of considerable interest. The time dependency of the current test summaries makes it difficult to compare differences in the apparent sensitivities of different species, or differences in the toxicities of different chemicals. Apparent differences in sensitivity or toxicity may simply reflect the (arbitrary) choices in testing protocols regarding the endpoint (e.g., growth in fish and reproduction in Daphnia) and test 4 It should be noted that these concerns also apply to the NOEC.

6 6 Figure 2: Example of the time-dependence of the EC10. This example is for two compounds in the nematode Caenorhabditis elegans, exposed in agar [3]. For pentachlorobenzene, no effects on survival were observed at the tested concentrations. duration (28 days for a fish growth test and 21 days for Daphnia reproduction). The inability to properly compare species using the traditional summary statistics will provide bias in speciessensitivity distributions, where ECx or NOEC values of different species (and often different endpoints) are combined without considering the time-pattern of the effect. The time-dependency of ECx also hampers the comparison of the toxicity between chemicals, as no single ECx value can be said to represent the toxicity. This hampers priority-setting and comparative risk assessment (one of the explicit aims of the new EU chemical policy REACH [12]), and also provides a source of bias in the development of QSARs Biological and toxicological background As clearly stated in the ISO and OECD reports [68, 34]: A statistical regression model itself does not have any biological meaning, and the choice of the model (expression) is to some extent arbitrary. The curve is only used to describe the data and interpolate to an x% effect level. Ecotoxicologists traditionally favour inverse cumulative distribution functions such as the loglogistic, log-normal and Weibull functions 6. These curves often fit well in practice, and it is often claimed that these functions represent the distribution of the sensitivities of the individuals in the test population (see e.g., [24, 65]). This idea can even be used in a process-based manner to include exposure time in the analysis (see e.g., [43, 58]). Nevertheless, there are problems with this interpretation. Firstly, this argument can only be invoked for quantal responses, that is to say, responses of the on/off type such as mortality and immobilization. For quantal responses, the response is the fraction of affected individuals and differences between individuals thus affect the slope of the dose response, but for graded responses such as growth and reproduction, the effect is the averaged response of each animal. Inter-individual variation merely leads to scatter around the curve but will not affect the slope. The slope of the dose-response model for graded responses therefore cannot be interpreted as a measure of the variation in sensitivity between individuals in the test population (although this is often misunderstood, see e.g., [27, 77, 87]). However, even for quantal responses, the interpretation of a sensitivity distribution has several theoretical and practical problems that show that this explanation fails as the (dominant) explanation of the doseresponse curve [44, 5, 65, 88]. Traditional regression models should thus be seen as descriptive statistical models, which do not follow from underlying processes. Although the choice of regression model is indeed rather arbitrary (as long as it fits the data well), this choice will not generally affect the numerical value of the EC50 estimates. However, the 5 We will discuss the topic of QSARs in a separate document, where we will also show how biology-based methods may help to provide more meaningful estimation routines 6 Some of these curves actually have a semi-mechanistic background in a rather different context. The log-logistic model is equivalent to the Hill equation that is used in enzyme kinetics.

7 7 interest of risk assessment is usually in small or no effects. When doses with effects around x% are scarce, the estimation of low effect levels will be quite uncertain and more strongly dependent on the selected regression model. A more important point is that the regression models have no biological or toxicological meaning. It does not really matter what the data represent, as long the model fits the observations (at the end of the test) well. The same, or similar, models are used to describe survival, fish body growth, reproduction for Daphnia, and population development for algae. Using descriptive models, it will never be possible to make educated extrapolations from the effects observed in laboratory tests to impacts populations under field conditions (e.g., acute to chronic, individual to population, constant to time-varying exposure, ad libitum food to limited food). Such extrapolations require models that make assumptions about the biological and toxicological mechanisms underlying the response. Furthermore, this background is critical to use all available data in a consistent manner as regression models cannot deal with toxicity data in time or effects on multiple endpoints from the same organisms, in an integrated manner It should be noted that not only in dose-response analysis, but also in risk assessment, the biological background is detached from the number. All sub-lethal endpoints are treated similarly (although an algal tests has a lower status when it is the only sub-lethal result available [19]). This can be problematic in practice; for some compounds, effects on reproduction and survival (and thus on the population) occur without effects on body size whatsoever [37], and effects on body size may change in time in a very different manner than effects on reproduction ([3], see Figure 2). Clearly, there is no simple relation between the effects on various endpoints, and small (or even no) effects on growth may be accompanied by large effects on reproduction. The focus on a different endpoint for each species may lead to bias in the risk assessment, and hamper the comparison of sensitivities of species. Furthermore, no single endpoint relates to effects at the population level [42, 25], it is only the integrated effect on all endpoints in time that makes ecological sense [23] (which will be discussed in more detail in Section 4.6). Chapter summary The current methods to analyse dose-response data are limited. These methods do not use all of the data from the toxicity test, and produce summary statistics that change with exposure time in a manner that depends on species, toxicant and endpoint. Furthermore, because of their descriptive nature, these methods do not allow for useful extrapolations. 3 Biology-based modelling With biology-based modelling, we attempt to explain the toxic effects as a function of exposure concentration and time, from a set of consistent assumptions about the underlying processes. As illustrated in Figure 3, this requires consideration of toxicokinetics and toxicodynamics 7. This type of approach is well known from human toxicology and pharmacology (see e.g., [6]), but hardly ever consistently applied in ecotoxicology. Toxicokinetics has traditionally received a lot of attention in ecotoxicology, but toxicodynamics has been neglected to a large extent. One of the reasons is that, in many respects, toxicodynamics in ecotoxicology is more complicated than in human toxicology. For humans, the interest is usually in very specific endpoints such as birth weight, tumor induction and growth, liver necrosis, or enzyme induction. In ecotoxicology, the endpoints of interest are much more integrated at overall performance of the individual (total reproductive output, mortality), or the population (population growth or recovery). The reason for this discrepancy is that risk assessment for humans focuses on well-being of the individual, whereas in ecotoxicology the main focus is on persistence of populations and ecosystems. For human toxicology, it may be sufficient to know the maximum level in a certain target organ, or the time-weighted average (area under the curve), to state that there is a potential problem with human health. In ecotoxicology, it will take a more process-based approach to go from the internal concentration to the effects of interest. Biology-based models aim to include as much 7 The distinction between toxicokinetics and toxicodynamics is not always strictly defined or definable. Here we consider for the kinetics phase all models needed to go from external concentrations to their interaction with the target receptor (the site of action); dynamics considers the relationship between target occupation and the pattern of effects on the endpoints in the toxicity test over time.

8 8 of the underlying processes (biological and toxicological) as possible, without becoming overly complicated. One of the most fundamental features of such models is that they explicitly include these processes as a function of time. There are several approaches available that can be called biology-based, but the DEBtox method is currently the only available approach that deals with both lethal and sub-lethal effects, and is able to deal with ecotoxicity data as currently produced using standard OECD test protocols. We therefore limit our description of biology-based models to this method. Figure 3: Schematic representation of biology-based models for toxic effects. In ecotoxicology, there is a long history of developing and testing toxicokinetic models, many of which can be used in a biology-based analysis of toxicity data. The biggest challenge for biology-based models is to develop toxicodynamic models that are simple enough to be useful for general dose-response analysis and risk assessment. Toxicodynamic modelling implies that we have to make explicit assumptions about the relationship between the internal concentration in the organism and the toxic effects. For example, before we can analyse survival data, we have to make assumptions regarding the mechanism of death (why do animals die); before we can understand sub-lethal effects, we have to understand growth and reproduction in the untreated organism. In order to grow and reproduce, an animal needs to feed, and the resources obtaind from food have to be allocated to the various metabolic processes in the organism s body, ensuring closed budgets for mass and energy (energy used to grow cannot be used to reproduce). The theory of Dynamic Energy Budgets (DEB [45, 46, 66], explained in more detail in Section 3.5) serves as a starting point for ecotoxidynamic models. The theory is simple enough to be applied to limited ecotoxicological data, yet powerful enough to capture the life-cycle details of a broad range of organisms from yeast to birds. The DEB approach allows ecotoxicological questions to be rephrased in a more meaningful manner. If a chemical decreases reproduction, the question what is the EC10 for reproduction? is hardly relevant, which is clear from the previous chapter. The question why is reproduction decreasing? is far more interesting. The answer to the why question will help to us to better understand what the toxicant is doing to the organisms and thus helps to predict and prevent unacceptable toxic effects in the environment. An observed decrease in reproduction must have an origin in resource allocation (because energy and mass balances have to be preserved). Offspring are produced from food, so one possibility is that ingestion has declined as a result of toxic stress. Alternatively, feeding may be unaltered, but there may be an additional energy drain for metabolic repair, leaving less energy for the production of eggs. Other hypotheses as to the observed reproductive effects can be put forward, obviously. The DEB theory provides a framework for addressing this question by providing the rules for how individuals acquire and use energy. It is important to note that a DEB model simplifies the metabolic organisation of organisms by focussing on rather large-scale allocation processes. For example, a chemical can be said to affect the maintenance rate of the organism (which has a specific effect on growth and reproduction), but the theory is not involved with the molecular and cellular mechanisms of how the chemical affects maintenance. These mechanisms will be highly species specific anyway, but all living organisms have to devote energy to maintain their integrity. Further, maintenance is a lump sum of a large number of contributing physiological processes. Although it would be very interesting to link molecular mechanisms to these large-scale allocation processes, this is not necessary for most ecotoxicological applications. A DEB model is a simplification of an organism, just like the multimedia fate models are a simplification of the environment. In detail, such simplifications will not be realistic, but as long as they capture the dominant processes, such simplifications can be of great help for risk assessment, for example by simulating different scenarios (e.g., discontinuous releases into the environment, and different environmental temperatures).

9 9 3.1 The DEBtox software The first version of the DEBtox software was developed in 1996, and has been described in a book [47], and a series of papers [9, 48, 49, 51]. A free version of the Windows-based software protocol can be downloaded 8. This software can be used to analyse data from acute survival studies, fish growth, Daphnia reproduction, and algal population growth. The observations (in time) from the experimental test are entered, and the software estimates the parameter values that provide the best fit of the model to the data. One of these parameters is a no-effect concentration: the concentration that produces no effect on an endpoint, even after prolonged exposure. Advantages of the DEBtox software over more traditional dose-response anlysis include: Use of all of the available data in time in a single analysis. This implies that more information is used to fit the model, thus resulting in more precise parameter estimates. On the other hand, more precision means that we can still obtain good results when using less test animals. As such, DEBtox can help to decrease the number of experimental animals used. A time-independent no-effect concentration (NEC) can be derived with a confidence interval. Unlike ECx and NOEC, this NEC does not change in time. The NEC is a parameter in the model, and therefore does not depend on a chosen significance level. DEBtox also allows estimation of ECx for any x at any time point. The resulting parameters have a physiological interpretation. The advantage is that these parameter estimates can than be used to make educated extrapolations, e.g., to time-varying concentrations or to populations under food limitation (e.g., [36]). These extrapolations are not part of the current software. Large flexibility in the data that can be used. For example, DEBtox is able to work with tests using a single exposure concentration (as long as data in time are available), tests without control, or tests with a single animal per dose group (although such set ups are certainly not optimal). There is thus less need to discard existing test data that have not been conducted using standard test protocols. The current version of the software is specifically intended for the analysis of data resulting from standard OECD test protocols. However, the DEBtox method itself has far more possibilities, which have not been included into the current version of the software 9, such as: simultaneous analysis of multiple endpoints [36], dealing with time-varying exposure [69, 70], toxicity of mixtures [7], prediction of population effects [36], food and temperature effects [35] etcetera. However, these extensions are beyond the scope of the current document. 3.2 Toxicokinetics The first assumption in biology-based modelling is that a chemical has to be taken up by an organism before it can exert a toxic effect. This assumption is quite basic to ecotoxicology, and has been realised for quite some time (see e.g., [16]). The role of the internal concentration has led to the popular concept of critical body residues (linking a body concentration to a summary statistic such as the EC50 for lethality, see [59]). The first model in a process-based approach should therefore be a toxicokinetic model to predict the relevant internal concentration over time from the concentration in the exposure medium (in time). We cannot consider toxic effects in time without considering toxicokinetics. The simplest model for toxicokinetics is the one-compartment model with first-order kinetics (Figure 4). Despite its simplicity, it generally offers a good description of the internal concentration for many compounds and many organisms. It is rarely accurate in detail, but frequently captures the main features of toxicokinetics. The uptake flux is proportional to the concentration in the local environment, and the elimination flux is proportional to the concentration inside the organism. This model has two parameters (any two out of the trio elimination rate, uptake rate and bioconcentration factor), but for the purpose of analysing toxicity data, one parameter suffices: the elimination rate (which fully determines the shape of the concentration-time curve, but not its 8 The software for Windows can be downloaded free of charge from 9 The above mentioned website also contains Octave and MatLab scripts to perform such calculations.

10 10 Figure 4: Schematic representation of the one-compartment model. The graph shows a typical time pattern (when growth is neglibible). scale), which is explained in detail in Section 4.1. Interestingly, the simple one-compartment model still seems to perform well to describe toxicity in cases where we know that additional toxicokinetic processes occur (e.g., for organophosphate pesticides interacting with acetylcholinesterase, see [40]). If the receptor binding is still described by a curve with the shape as shown in Figure 4, than a simple one-compartment model can be still be used to analyse the toxicity data. Howver, in those cases, the resulting estimate for the elimination rate will not reflect the total internal concentrations, but the binding kinetics to the specific receptors. If the organism grows during exposure, specific deviations from first-order kinetics can be expected, and taken into account [45]. Using the standard OECD protocols, organisms are not fed in survival experiments, and growth is thus limited. However, effects of growth on the toxicokinetics should always be taken into account in the analysis of data for body growth and reproduction, since such this process can affect the effect-time profiles substantially. Apart from the effects of dilution by growth, growth will also decrease the surface area:volume ratio of the organism, and thereby the toxicokinetics. In the DEBtox software, the effects of growth on kinetics and growth dilution are incorporated for the endpoints growth and reproduction, but not for survival (see Section 4.1). For the basic DEBtox model, we have to be able to work with toxicity data only, in the absence of any information on internal concentrations. Therefore, the only model that can generally be successfully applied to such data is the simple one-compartment model (accounting for growth, if needed). This simple model may of course be replaced by more advanced toxicokinetic models, if there are sound reasons (and data of sufficient strength to test this). Possible extensions are to account for changes in the individual over time (size and lipid content), different forms of kinetics (metabolic transformation, receptor interactions, satiation of uptake or elimination), or additional compartments (gut contents, organs). A thorough discussion of these extensions is beyond the scope of this document, but more information can be obtained from reviews [57, 8] and text books [82, 45, 63]. A toxicokinetic extension that has gained popularity over the last few years is the addition of a state of damage [5, 56] 10. According to this concept, the internal concentration causes a kind of damage that accumulates in the organism, and is also repaired according to a first-order process. The reason for this addition was the same as for the receptor extension of DEBtox [40]; the observation that the kinetics of survival did not always match the kinetics of whole-body residues, thus requiring an additional kinetic stage. As was the case with the receptor model, this extension is not needed as long as the damage accumulation is reasonably well described by a first-order process (which will generally be the case). As with the receptor model, the resulting estimate for the elimination rate will than reflect the damage component, and not the whole-body residues (unless the repair rate is very high, in which case the damage will simply follow the 10 The state of damage can also be considered a toxicodynamic aspect, but we would like to treat them as toxicokinetic due to the conceptual similarity to receptor binding (see [40]).

11 11 uptake kinetics). To summarise, a receptor or damage extension will generally be of little use to analyse toxicity test data, unless detailed information on the kinetics of the internal concentration is available. 3.3 No-effect concentrations DEBtox makes use of the concept of a no-effect concentration (NEC), or a threshold for effects. It is difficult to prove the existence of a threshold directly [75], but there are very good indications of the general validity of the threshold concept [11]. Below a certain level, a component of the environment has no negative effects on the organism. At least implicitly, all methods for the analysis of toxicity data make use of the concept of a no-effect-concentration, because they assume that compounds in the medium, apart from the tested chemical, do not affect the organism s response. The NOEC explicitly assumes a threshold for effects, but fails as a quantifier for that threshold, as large effects generally occur at the NOEC [13]. It should be realised that the objections against the NOEC do not disprove the existence of thresholds or endanger the usefulness of the threshold concept [84]. The methods for the ECx for lethality also assume a threshold for effects (when the curve is interpreted as a distribution of sensitivities), but this is a threshold at the level of the individual (the critical body residue), usually not at the population level. Generally, each chemical can be said to have three domains in concentration, as illustrated in Figure 5: 1. Effects due to shortage. Think, for instance, of elemental copper, which is required in trace amounts for several co-enzymes of most species. 2. No-effect range. The physiological performance of the organism is independent of the concentration, provided that it remains in the no-effect range. Think, for instance, of the concentration of nitrate in phosphate-limited algal populations; Liebig s famous minimum law rests on the no-effect concept. With regard to toxicants, there are numerous mechanisms that help defend the organism against the action of toxicants, thus giving rise to an effects threshold [84, 11]. 3. Toxic effects, which is the concentration range of main interest for ecotoxicology. Think, for instance, of glucose, which is a nutritious substrate for most bacteria in low concentrations, but inhibits growth if the concentration is as high as in jam. Most xenobiotic compounds are not required for the organisms physiology, which means that their range of concentrations that cause effects due to shortage is zero. Some compounds (e.g., genotoxic ones) are likely to have a no-effect range of zero as well. This gives no theoretical problems in biology-based methods, a NEC of zero is just a special case, and a point estimate for this concentration from effect-data should (ideally) not deviate significantly from zero. It is essential to realise that the judgement no-effect is specific for the level of organisation under consideration. At the molecular level, molecules cannot be classified into one type that does not give effects, and another type that gives effects. However, effects at the molecular level do not necessarily lead to a response of the individual as a whole. As an illustration, the concept no-effect-concentration can be used to describe the situation that it is possible to remove a kidney from a human subject (so a clear effect at the sub-organism level), without any obvious adverse effects at the individual s survival or reproduction on the short term. This example, therefore, shows that below the NEC effects can occur at the sub-organismic level (e.g., enzyme induction), as well as on other endpoints that are not included in the analysis (e.g., changes in behaviour in a reproduction test). Furthermore, the NEC may change as a result of other stresses (such as disease or starvation). 3.4 Survival First we have to answer the question why do animals die? The most popular explanation in ecotoxicology proposes that an organism dies instantly as soon as an internal threshold is exceeded. Not all animals die at the same time because the threshold does not have the same value in all individuals. The frequency distribution of the threshold thus determines the shape of the

12 12 Figure 5: Every chemical has three domains of concentration, regarding their effect on an organism s performance (for a specific chemical, any of these ranges may be zero). dose-response curve (together with the toxicokinetics). Even though this theory is immensely popular and quoted in most ecotoxicological textbooks without criticism, it fails as the (dominant) explanation of survival curves. It is more likely that death is actually stochastic at the level of the individual [44, 65, 88]. In other words, the individuals that die were simply the unlucky ones, and not essentially different from the survivors. Of course, there are differences in sensitivity between individuals (especially in field populations), but in standardised laboratory tests with a homogeneous test population, stochasticity is probably the dominant mechanism to explain the observations. The statistical method to deal with stochastic events in time is called hazard modelling or time-to-event modeling. This technique is broadly used in industry and engineering under the term failure-time analysis to describe or predict the failure of a product or structure over its lifetime (e.g., a light bulb). In ecotoxicological applications, the event of interest is obviously death (although immobilisation, or any other quantal property, could also be used as an endpoint). The use of this method in eco(toxico)logy has been propagated by a.o., [62, 64, 9, 63]. The probability for an event to occur in a certain time interval is determined by the hazard rate. The hazard rate has the dimensions of a probability per time. Multiplied by a (short) time interval, the hazard rate gives the probability to die in that interval (given that you are alive at the start of the interval). The hazard rate can change in time; e.g., as an animal ages, or when the internal concentration of a toxicant increases. Similarly, the probability for a light bulb to fail increases with the number of burn hours. The hazard rate as a function of time can be translated into the survival probability over time, using a simple calculation (see Section 4.2). Now the question is how the result of the toxicokinetics model (e.g., the internal concentration) can be linked to the hazard rate. Organisms are able to deal with all kinds of chemicals, so xenobiotic compounds will not necessarily be very different. It is thus likely that small internal concentrations do not have an effect on the animal s survival, and thus on the hazard rate. At higher concentrations, the hazard rate will likely increase with the internal concentration. The basic DEBtox model therefore assumes a simple two-parameter relationship between the internal concentration and the hazard rate. Below a threshold concentration (the no-effect concentration or NEC), there is no effect on survival apart from the background mortality rate. Above this threshold, the hazard rate is assumed to linearly increase with the internal dose (see Figure 6). The biological mechanism of a linear relationship between the parameter value and internal concentration boils down to the independent action at the molecular level. Each molecule that exceeds individual s capacity to suppress effects acts independent of the other molecules. Think of the analogy where photosynthesis of a tree is just proportional to the number of leaves as long as this number is small; as soon as the number grows large, self shading occurs and photosynthesis is likely to be less than predicted. We doubtlessly require non-linear responses for larger effect levels, but then also need to include more types of effects. However, any regular function can be approximated with any degree of accuracy for a limited domain by a polynomial of sufficiently large order (Taylor s theorem). Toxicity data are

13 13 usually quite noisy, and do not provide enough information to estimate anything more than the first term of a Taylor expansion (i.e., a linear relationship). If detailed and precise toxicity data would be available, higher-order terms may be added, if this improves the fit. It should further be noted that the assumption that the target parameter is linear in the internal concentration does not translate into a linear response of the endpoint; it usually translates into sigmoid concentrationendpoint relationships, which are well known from toxicity tests. Figure 6: Relationship between the (scaled) internal concentration and the hazard rate in DEBtox. Organisms may also die for reasons unrelated to the exposure to the test toxicant. This background mortality is included in DEBtox as a constant hazard rate. This is reasonable because the toxicity experiments are mostly short in relation to the organism s lifetime. Deaths in the controls are therefore not related to scenescence but to accidental deaths (e.g., related to handling). It is reasonable to assume that the probability for an accidental death does not change over the course of an experiment. This assumption does not hold for experiments that are long in relation to the lifetime (e.g., life-cycle tests), or where the organisms are dying from starvation. Such situations will reveal a hazard rate that is an accelerating function of time (see e.g., [31, 36]). The DEBtox survival model was first published in 1994 [9]. The detailed model equations are given in Section Short introduction to Dynamic Energy Budgets (DEB) Dealing with sub-lethal effects, it is essential to have a model capable of showing the relations between feeding, maintenance, growth, development and reproduction. For example, reproduction rates depend on growth as body size determines the onset of reproduction as well as the feeding rate (and thereby the resources available for the production of offspring). The theory of dynamic energy budgets (DEB; see [45, 46, 66]) provides one of the most simple and consistent frameworks for addressing these relationships. DEB theory describes how individuals acquire and use energy based on a set of simple rules for metabolic organization. Within this theory, organisms are treated as dynamic systems with explicit mass and energy balances. The basic allocation pathways in DEB are shown in Figure 7, and the basic assumptions are: Structural body mass, reserves, and maturity are the state variables of the individual; the structure and reserves have a constant composition. Food is converted into faeces, and assimilates derived from food are added to reserves. The reserves fuel all other metabolic processes. If the individual propagates via reproduction (rather than via division), it starts in the embryonic stage with a negligibly small structural body mass but a substantial amount of reserves. The reserve density of the hatchling equals that of the mother at egg formation. Foetuses develop in the same way as embryos in eggs, but at a rate that is unrestricted by energy reserves.