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E-books / Support: Marine Ecotox

Supporting information of the modelling chapter


This web page supports the chapter on modelling (Ch. 3) in the book "Marine Ecotoxicology". It contains links to further information, relevant books and papers, and links to useful software. This is a 'living' web page, so things will added as something relevant pops up. If you have an Elsevier subscription, you might have access to the PDF version of the book through ScienceDirect.

Below, information is provided for each section in the chapter, but there are also some general links, which I want to give first. More information on toxicokinetics and toxicodynamic modelling in an energy-budget framework can be found in my e-books “Making sense of chemical stress” and "DEBkiss". They can be downloaded from Leanpub, and you set the price (you can also opt to download them for free).
https://leanpub.com/debtox_book
https://leanpub.com/debkiss_book

The refresher that I wrote for the TKTD summer course explains ODE’s, and how to work with them, in more detail than in the book chapter. Furthermore, it explains the likelihood concept as relevant for fitting models. The course would be a good way forward, if you want to learn more about TKTD modelling with energy budgets.
http://www.debtox.info/downloads/coursemat/refresher.pdf

All case studies have been performed with the BYOM platform in Matlab. The implementations for the case studies can be downloaded as a package, but make sure to start by downloading and installing the BYOM platform (which is required to run the case-study files). The case-study package can be downloaded from:
http://www.debtox.info/downloads/byom/support_marecotox.zip 









 

3.2 General modelling principles

A general book on modelling that I liked at the time is the book “Mathematical modelling in the life sciences” by Doucet and Sloep (ISBN 0-13-562018-X). It is a bit dated (1992/1992) but still worthwhile reading (and readable with limited background in mathematics).
http://www.amazon.com/Mathematical-Modeling-Sciences-Mathematics-Applications/dp/013562018X

The freely-downloadable PDF "Basic methods in theoretical biology" of Bas Kooijman contains much more information about modelling approaches and methods (and goes deeper into the math, much deeper than needed for most model applications).
http://www.bio.vu.nl/thb/course/tb/tb.pdf

3.2.1 Systems and states

Wikipedia is a good place to read more general information about systems and state variables:
https://en.wikipedia.org/wiki/System
https://en.wikipedia.org/wiki/State_variable

The refresher (see top of page) has an extended (gentle) introduction into modelling basics and associated statistics.

3.2.7 Confronting models with data

With regards to model evaluation and validation, a good paper to consult is the following:
  • Augusiak J, Van den Brink PJ and Grimm V (2014). Merging validation and evaluation of ecological models to ‘evaludation’:
    a review of terminology and a practical approach. Ecol Mod 280:117-128. http://dx.doi.org/10.1016/j.ecolmodel.2013.11.009  

3.3 Toxicokinetics

A detailed introduction in the theory behind toxicokinetic models can be found in my PhD thesis (Chapter 2). It contains worked-out examples for simple more-compartment models (e.g., including the test container as a dynamic compartment in the TK model) and dealing with bioavailability issues.
https://leanpub.com/jager_phd_thesis

My e-book "Making sense ..." (see top of page) contains a section on toxicokinetics (Chapter 3) that deals with the basics of TK topic in more conceptual detail. The associated technical document contains the dirty math.

3.3.1 The one compartment model with first-order kinetics

More on the distinction between steady state and equilibrium (that is not made in mathematics).
https://en.wikipedia.org/wiki/Steady_state_%28chemistry%29

On solving ODEs, see refresher (see top of page), Section 1.3.

3.3.2 Beyond the simple one-compartment model

Paper on the comparison of one-compartment model to a PBPK model.
  • Stadnicka J, Schirmer K and Ashauer R (2012). Predicting concentrations of organic chemicals in fish by using toxicokinetic models. Environ Sci Technol 46:3273-3280 http://dx.doi.org/10.1021/es2043728 
Spawning as elimination route.
  • McManus GB, Wyman KD, Peterson WT and Wurster CF (1983). Factors affecting the elimination of PCBs in the marine copepod Acartia tonsa. Estuarine Coastal and Shelf Science 17:421-430 http://dx.doi.org/10.1016/0272-7714(83)90127-0 
  • Vodicnik MJ and Peterson RE (1985). The enhancing effect of spawning on elimination of a persistent polychlorinated biphenyl from female yellow perch. Fundamental and Applied Toxicology 5:770-776 http://dx.doi.org/10.1016/0272-0590(85)90201-5 
Examples of Michaelis-Menten in TK (and also using a two-compartment model).
  • Steen Redeker E, Blust R. 2004. Accumulation and toxicity of cadmium in the aquatic oligochaete Tubifex tubifex: a kinetic modeling approach. Environ Sci Technol 38:537-543 http://dx.doi.org/10.1021/es0343858 
Moving from one to two compartment is described in detail in the refresher (see top of page), Section 2.1-2.2. The extension for growth dilution is derived in the refresher, Section 2.5.

3.4 General introduction on toxicodynamics

General papers on TKTD modelling.
  • Ashauer R and Escher BI (2010). Advantages of toxicokinetic and toxicodynamic modelling in aquatic ecotoxicology and risk assessment. J Environ Monit 12:2056-2061 http://dx.doi.org/10.1039/c0em00234h 
  • Jager T, Heugens EHW and Kooijman SALM (2006). Making sense of ecotoxicological test results: towards application of process-based models. Ecotoxicology 15:305-314 http://dx.doi.org/10.1007/s10646-006-0060-x 
  • Ashauer R, Agatz A, Albert C, Ducrot V, Galic N, Hendriks J, Jager T, Kretschmann A, O'Connor I, Rubach MN, Nyman AM, Schmitt W, Stadnicka J, Van den Brink PJ and Preuss TG (2011). Toxicokinetic-toxicodynamic modeling of quantal and graded sublethal endpoints: a brief discussion of concepts. Environ Toxicol Chem 30:2519-2524 http://dx.doi.org/10.1002/etc.639   
3.4.2 Using TK models in the absence of body-residue data

More detailed explanation of the scaled TK model can be found in the "Making sense ..." e-book, Section 3.1.

3.5 Effects on survival

To get a better understanding about likelihood functions in general and the multinomial likelihood in particular, I suggest starting with Chapter 3 from the refresher document (see top of page).

More details on the GUTS framework for survival modelling can be obtained from the publication.
  • Jager T, Albert C, Preuss TG, Ashauer R (2011). General Unified Threshold model of Survival - a toxicokinetic-toxicodynamic framework for ecotoxicology. Environ Sci Technol 45:2529-2540 http://dx.doi.org/10.1021/es103092a
A full (I hope) list of publications (with links to the DOI) applying dynamic hazard models for survival can be found here.
http://www.debtox.info/papers_survival.html

We are preparing an e-book specifically on GUTS and how to use it. We expect to publish it by the end of 2017. More information.

3.5.1 Why do animals die?

On stochastic death versus individual tolerance.
3.5.2 The stochastic death model

Wikipedia on survival analysis in various fields
https://en.wikipedia.org/wiki/Survival_analysis

On application of survival analysis in ecology.

3.6 Effects on sub-lethal endpoints

More information on toxicodynamic modelling using energy-budget models can be found in my e-book “Making sense of chemical stress.” This book deals with the concepts; the associated technical document contains the technical details. However, for a more smooth transition from concepts to math, I recommend following up with the second free e-book “DEBkiss. A simple framework for animal energy budgets.” (see top of page).

3.6.4 Fitting energy-budget models to data

More information on fitting TKTD models to data is provided in the “Making sense of chemical stress” book (see top of this page), and its associated technical document. In more condensed form, this topic is treated in the following paper and its supporting information:
A paper discussing the complexities and possibilities for including inter-individual differences in model fitting:
  • Jager T (2013). All individuals are not created equal; accounting for inter-individual variation in fitting life-history responses to toxicants. Environ Sci Technol 47:1664-1669 http://dx.doi.org/10.1021/es303870g

3.6.5 Case study

Underlying papers for the case study
More information on hormesis in an energy-budget context
The case study is worked out in greater detail in the "Making sense ..." e-book, Section 6.2 (see top of page).

3.7 Population level and higher

General papers on populations models and energy budgets:

A long list of textbooks on population modelling is maintained here: http://homepage.ruhr-uni-bochum.de/Michael.Knorrenschild/embooks.html

3.7.1 Individual-based models

A general book on individual based modelling is that of Grimm and Railsback, entitled "Individual-based Modeling and Ecology" (ISBN 9780691096667).
http://press.princeton.edu/titles/8108.html

Several papers on coupling IBMs and energy budgets:
  • Martin B, Zimmer EI, Grimm V and Jager T (2012). Dynamic Energy Budget theory meets individual-based modelling: a generic and accessible implementation. Methods Ecol Evol 3:445-449 http://dx.doi.org/10.1111/j.2041-210X.2011.00168.x
  • Martin B, Jager T, Nisbet RM, Preuss TG and Grimm V (2013). Predicting population dynamics from the properties of individuals: a cross-level test of Dynamic Energy Budget theory. American Naturalist 181(4):506-519 http://dx.doi.org/10.1086/669904
  • Martin BT, Jager T, Nisbet RM, Preuss TG, Hammers-Wirtz M and Grimm V (2013). Extrapolating ecotoxicological effects from individuals to populations: a generic approach based on Dynamic Energy Budget theory and individual-based modeling. Ecotoxicology 22:574-583 http://dx.doi.org/10.1007/s10646-013-1049-x  
  • Martin B, Jager T, Nisbet RM, Preuss TG and Grimm V (2014). Limitations of extrapolating toxic effects on reproduction to the population level. Ecol Appl 24(8):1972-1983 http://dx.doi.org/10.1890/14-0656.1   

3.7.2 Matrix models

A general book on matrix modelling is that of Caswell, entitled: "Matrix population models: construction, analysis, and interpretation" (ISBN 978-0-87893-121-7)
http://www.sinauer.com/matrix-population-models-construction-analysis-and-interpretation.html

Wikipedia on matrix modelling.
https://en.wikipedia.org/wiki/Leslie_matrix

Several papers on the coupling between matrix models and energy budgets:

  • Klok C and De Roos AM (1996). Population level consequences of toxicological influences on individual growth and reproduction in Lumbricus rubellus. Ecotox Environ Saf 33:118–127 http://dx.doi.org/10.1006/eesa.1996.0015
  • Lopes C, Péry ARR, Chaumot A and Charles S (2005). Ecotoxicology and population dynamics: using DEBtox models in a Leslie modeling approach. Ecol Mod 188(1):30-40 http://dx.doi.org/10.1016/j.ecolmodel.2005.05.004 
  • Klanjscek T, Caswell, H, Neubert G and Nisbet RM (2006). Integrating dynamic energy budgets into matrix population models. Ecol Mod 196:407-420 http://dx.doi.org/10.1016/j.ecolmodel.2006.02.023 
  • Billoir E, Péry ARR and Charles S (2007). Integrating the lethal and sublethal effects of toxic compounds into the population dynamics of Daphnia magna: a combination of the DEBtox and matrix population models. Ecol Mod 203(3-4):204-214 http://dx.doi.org/10.1016/j.ecolmodel.2006.11.021 
  • Billoir E, Ferrao AD, Delignette-Muller ML and Charles S (2009). DEBtox theory and matrix population models as helpful tools in understanding the interaction between toxic cyanobacteria and zooplankton. J Theor Biol 258(3):380-388 http://dx.doi.org/10.1016/j.jtbi.2008.07.029 
  • Biron PA, Massarin S, Alonzo F, Garcia-Sanchez L, Charles S and Billoir E (2012). Population-level modeling to account for multigenerational effects of uranium in Daphnia magna. Environ Sci Technol 46:1136−1143 http://dx.doi.org/10.1021/es202658b

3.7.3 Intrinsic rate of increase

Wikipedia on the Euler-Lotka equation to calculate the intrinsic rate of increase.
https://en.wikipedia.org/wiki/Euler%E2%80%93Lotka_equation

Several papers on coupling the Euler-Lotka equation and energy budgets:

  • Jager T, Crommentuijn T, Van Gestel CAM and Kooijman SALM (2004). Simultaneous modeling of multiple endpoints in life-cycle toxicity tests. Environ Sci Technol 38:2894-2900 http://dx.doi.org/10.1021/es0352348
  • Alda Álvarez O, Jager T, Kooijman SALM and Kammenga JE (2005). Responses to stress of Caenorhabditis elegans populations with different reproductive strategies. Funct Ecol 19:656-664 http://dx.doi.org/10.1111/j.1365-2435.2005.01012.x 
  • Alda Álvarez O, Jager T, Marco Redondo E and Kammenga JE (2006). Physiological modes of action of toxic chemicals in the nematode Acrobeloides nanus. Environ Toxicol Chem 25:3230-3237 http://dx.doi.org/10.1897/06-097R.1 
  • Jager T, Heugens EHW and Kooijman SALM (2006). Making sense of ecotoxicological test results: towards application of process-based models. Ecotoxicology 15:305-314 http://dx.doi.org/10.1007/s10646-006-0060-x  

3.8 Future

3.8.1 Closer collaboration between disciplines

Consequences of TKTD modelling for test design.
  • Albert C, Ashauer R, Künsch HR and Reichert P (2012). Bayesian experimental design for a toxicokinetic-toxicodynamic model. J Stat Plan Infer 142:263-275 http://dx.doi.org/10.1016/j.jspi.2011.07.014 
  • Barsi A, Jager T, Collinet M, Lagadic L and Ducrot V (2014). Considerations for test design to accommodate energy-budget models in ecotoxicology: a case study for acetone in the pond snail Lymnaea stagnalis. Environ Toxicol Chem 33(7):1466-1475 http://dx.doi.org/10.1002/etc.2399   
  • Jager T (2014). Reconsidering sufficient and optimal test design in acute toxicity testing. Ecotoxicology 23(1):38-44 http://dx.doi.org/10.1007/s10646-013-1149-7  
Statistics: inter-individual differences.
  • Ashauer R (2010). Toxicokinetic-toxicodynamic modelling in an individual based context-consequences of parameter variability. Ecol Modell 221:1325-1328 http://dx.doi.org/10.1016/j.ecolmodel.2010.01.015 
  • Jager T (2013). All individuals are not created equal; accounting for inter-individual variation in fitting life-history responses to toxicants. Environ Sci Technol 47:1664-1669 http://dx.doi.org/10.1021/es303870g  
The need to link biomarkers/AOPs to TKTD models/energy budgets, and some attempts in that direction.
  • Swain S, Wren J, Stürzenbaum SR, Kille P, Morgan AJ, Jager T, Jonker MJ, Hankard PK, Svendsen C, Chaseley J, Hedley BA, Blaxter M and Spurgeon D (2010). Linking toxicant physiological mode of action in with induced gene expression changes Caenorhabditis elegans. BMC Systems Biology 4:32 http://dx.doi.org/10.1186/1752-0509-4-32
  • Kramer VJ, Etterson MA, Hecker M, Murphy CA, Roesijadi G, Spade DJ, Spromberg JA, Wang M and Ankley GT (2011). Adverse outcome pathways and ecological risk assessment bridging to population-level effects. Environ. Toxicol. Chem. 30 (1):64-76 http://dx.doi.org/10.1002/etc.375  
  • Wren, JF, Kille P, Spurgeon DJ, Swain S, Sturzenbaum SR, and Jager T (2011). Application of physiologically based modelling and transcriptomics to probe the systems toxicology of aldicarb for Caenorhabditis elegans (Maupas 1900). Ecotoxicology 20:397-408 http://dx.doi.org/10.1007/s10646-010-0591-z
  • Jager T and Hansen BH (2013). Linking survival and biomarker responses over time. Environ Toxicol Chem 32(8):1842-1845 http://dx.doi.org/10.1002/etc.2258
  • Groh KJ, Carvalho RN, Chipman JK, Denslow ND, Halder M, Murphy CA, Roelofs D, Rolaki A, Schirmer K and Watanabe KH (2015). Development and application of the adverse outcome pathway framework for understanding and predicting chronic toxicity: I. Challenges and research needs in ecotoxicology. Chemosphere 120:764-777 http://dx.doi.org/10.1016/j.chemosphere.2014.09.068  
  • Jager T (2016). Predicting environmental risk: a road map for the future. J. Toxicol. Environ. Health. 79(13-15):572-584. http://dx.doi.org/10.1080/15287394.2016.1171986  
3.8.2 Topics for future research

Mechanism-based relationships between parameters of TKTD and DEB models:
  • Jager T and Kooijman SALM (2009). A biology-based approach for quantitative structure-activity relationships (QSARs) in ecotoxicity. Ecotoxicology 18:187-196 http://dx.doi.org/10.1007/s10646-008-0271-4 
  • Lika K, Kearney MR, Freitas V, Van der Veer HW, Van der Meer J, Wijsman JWM, Pecquerie L and Kooijman SALM. 2011. The "covariation method" for estimating the parameters of the standard Dynamic Energy Budget model I: Philosophy and approach. J Sea Res 66:270-277 http://dx.doi.org/10.1016/j.seares.2011.07.010 
  • Lika K, Kearney MR and Kooijman SALM. 2011. The "covariation method" for estimating the parameters of the standard Dynamic Energy Budget model II: Properties and preliminary patterns. J Sea Res 66:278-28 http://dx.doi.org/10.1016/j.seares.2011.09.004
  • Lika K, Augustine S, Pecquerie L and Kooijman SALM. 2014. The bijection from data to parameter space with the standard DEB model quantifies the supply-demand spectrum. J Theor Biol 354:35-47 http://dx.doi.org/10.1016/j.jtbi.2014.03.025
  • Baas J and Kooijman SALM. 2015. Sensitivity of animals to chemical compounds links to metabolic rate. Ecotoxicology 24:657-663 http://dx.doi.org/10.1007/s10646-014-1413-5 
  • Ashauer R, O’Connor I, Hintermeister A and Escher BI (2015), Death dilemma and organism recovery in ecotoxicology. Environ Sci Technol 49(16):10136–10146 http://dx.doi.org/10.1021/acs.est.5b03079
TKTD with measured body residues.
  • Heugens EHW, Jager T, Creyghton R, Kraak MHS, Hendriks AJ, Van Straalen NM and Admiraal W (2003). Temperature-dependent effects of cadmium on Daphnia magna: accumulation versus sensitivity. Environ Sci Technol 37:2145-2151 http://dx.doi.org/10.1021/es0264347
  • Ashauer R, Boxall ABA and Brown CD (2007). Simulating toxicity of carbaryl to Gammarus pulex after sequential pulsed exposure. Environ Sci Technol 41:5528-5534 http://dx.doi.org/10.1021/es062977v
  • Ashauer R, Boxall ABA and Brown CD (2007). Modeling combined effects of pulsed exposure to carbaryl and chlorpyrifos on Gammarus pulex. Environ Sci Technol 41:5535-5541 http://dx.doi.org/10.1021/es070283w
  • Ashauer R, Hintermeister A, Caravatti I, Kretschmann A and Escher BI (2010). Toxicokinetic and toxicodynamic modeling explains carry-over toxicity from exposure to diazinon by slow organism recovery. Environ Sci Technol 44:3963-3971 http://dx.doi.org/10.1021/es903478b 
  • Ashauer R, O’Connor I, Hintermeister A and Escher BI (2015), Death dilemma and organism recovery in ecotoxicology. Environ Sci Technol 49(16):10136–10146 http://dx.doi.org/10.1021/acs.est.5b03079 
  • Jager T, Øverjordet IB, Nepstad R and Hansen BH (acc.). Dynamic links between lipid storage, toxicokinetics and mortality in a marine copepod exposed to dimethylnaphthalene. Accepted for publication in Environ Sci Technol. http://dx.doi.org/10.1021/acs.est.7b02212
TK models that include storage
  • Van Haren RJF, Schepers HE and Kooijman SALM (1994). Dynamic Energy Budgets affect kinetics of xenobiotics in the marine mussel Mytilus edulis. Chemosphere 29:163-189 http://dx.doi.org/10.1016/0045-6535(94)90099-x 
  • Hansen BH, Jager T, Altin D, Øverjordet IB, Olsen AJ, Salaberria I and Nordtug T (2016). Acute toxicity of dispersed crude oil on the cold-water copepod Calanus finmarchicus: elusive implications of lipid content. J. Toxicol. Environ. Health. 79(13-15):549-557 http://dx.doi.org/10.1080/15287394.2016.1171981 
  • Jager T, Øverjordet IB, Nepstad R and Hansen BH (acc.). Dynamic links between lipid storage, toxicokinetics and mortality in a marine copepod exposed to dimethylnaphthalene. Accepted for publication in Environ Sci Technol. http://dx.doi.org/10.1021/acs.est.7b02212
TK and/or TD in eggs
  • Daley JM, Leadley TA and Drouillard KG (2009). Evidence for bioamplification of nine polychlorinated biphenyl (PCB) congeners in yellow perch (Perca flavascens) eggs during incubation. Chemosphere 75:1500-1505 http://dx.doi.org/10.1016/j.chemosphere.2009.02.013  
  • Barsi A, Jager T, Collinet M, Lagadic L and Ducrot V (2014). Considerations for test design to accommodate energy-budget models in ecotoxicology: a case study for acetone in the pond snail Lymnaea stagnalis. Environ Toxicol Chem 33:1466-1475 http://dx.doi.org/10.1002/etc.2399
Mixture toxicity and multiple stress.
  • Lee JH and Landrum PF (2006). Development of a multi-component damage assessment model (MDAM) for time-dependent mixture toxicity with toxicokinetic interactions. Environ Sci Technol 40:1341-1349 http://dx.doi.org/10.1021/es051120f
  • Pieters BJ, Jager T, Kraak MHS and Admiraal W (2006). Modeling responses of Daphnia magna to pesticide pulse exposure under varying food conditions: intrinsic versus apparent sensitivity. Ecotoxicology 15:601-608 http://dx.doi.org/10.1007/s10646-006-0100-6
  • Ashauer R, Boxall ABA and Brown CD (2007). Modeling combined effects of pulsed exposure to carbaryl and chlorpyrifos on Gammarus pulex. Environ Sci Technol 41:5535-5541 http://dx.doi.org/10.1021/es070283w
  • Baas J, Van Houte BPP, Van Gestel CAM and Kooijman SALM (2007). Modelling the effects of binary mixtures on survival in time. Environ Toxicol Chem 26:1320-1327 http://dx.doi.org/10.1897/06-437R.1
  • Baas J, Jager T and Kooijman SALM (2009). A model to analyze effects of complex mixtures on survival. Ecotox Environ Saf 72:669-676 http://dx.doi.org/10.1016/j.ecoenv.2008.09.003 
  • Jager T, Vandenbrouck T, Baas J, De Coen WM and Kooijman SALM (2010). A biology-based approach for mixture toxicity of multiple endpoints over the life cycle. Ecotoxicology 19:351-361 http://dx.doi.org/10.1007/s10646-009-0417-z
  • Jager T, Gudmundsdóttir EM and Cedergreen N (2014). Dynamic modeling of sub-lethal mixture toxicity in the nematode Caenorhabditis elegans. Environ Sci Technol 48:7026-7033 http://dx.doi.org/10.1021/es501306t
  • Jager T, Ravagnan E and Dupont S (2016). Near-future ocean acidification impacts maintenance costs in sea-urchin larvae: identification of stress factors and tipping points using a DEB modelling approach. J Exp Mar Biol Ecol 474:11-17 http://dx.doi.org/10.1016/j.jembe.2015.09.016 (shows how DEB can deal with OA, but does not include chemical stress)
  • Ashauer A, O'Connor I, and Escher BI (2017). Toxic mixtures in time – the sequence makes the poison. Environ Sci Technol 51:3084-3092 http://dx.doi.org/10.1021/acs.est.6b06163
Constant to time-varying and vice versa.
  • Nyman AM, Schirmer K and Ashauer R (2012). Toxicokinetic-toxicodynamic modelling of survival of Gammarus pulex in multiple pulse exposures to propiconazole: model assumptions, calibration data requirements and predictive power. Ecotoxicology 21:1828-1840 http://dx.doi.org/10.1007/s10646-012-0917-0
  • Ashauer R, Albert C, Augustine C, Cedergreen N, Charles S, Ducrot V, Focks A, Gabsi F, Gergs A, Goussen B, Jager T, Kramer NI, Nyman AM, Poulsen V, Reichenberger S, Schäfer RB, Van den Brink PJ, Veltman K, Vogel S, Zimmer EI and Preuss TG (2016). Modelling survival: exposure pattern, species sensitivity and uncertainty. Sci Rep 6:29178 http://dx.doi.org/10.1038/srep29178 

Link to risk assessment

  • Jager T, Heugens EHW and Kooijman SALM (2006). Making sense of ecotoxicological test results: towards application of process-based models. Ecotoxicology 15:305-314 http://dx.doi.org/10.1007/s10646-006-0060-x  
  • Ashauer R and Escher BI (2010). Advantages of toxicokinetic and toxicodynamic modelling in aquatic ecotoxicology and risk assessment. J Environ Monit 12:2056-2061 http://dx.doi.org/10.1039/c0em00234h 
  • Ashauer R, Wittmer I, Stamm C and Escher BI (2011). Environmental risk assessment of fluctuating diazinon concentrations in an urban and agricultural catchment using toxicokinetic-toxicodynamic modeling. Environ Sci Technol 45:9783-9792 http://dx.doi.org/10.1021/es202413a 
  • Ducrot V, Ashauer R, Bednarska AJ, Hinarejos S, Thorbek P and Weyman G (2016). Using toxicokinetic-toxicodynamic modeling as an acute risk assessment refinement approach in vertebrate ecological risk assessment. IEAM 12(1):32-45 http://dx.doi.org/10.1002/ieam.1641
  • Jager T (2016). Predicting environmental risk: a road map for the future. J. Toxicol. Environ. Health. 79(13-15):572-584. http://dx.doi.org/10.1080/15287394.2016.1171986  


The DEBtox information site, www.debtox.info, since July 2011