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 e-book "Mechanistic modelling essentials" (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, good
papers to consult are 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
- Jager T and Ashauer R (2018). How to evaluate the
quality of toxicokinetic-toxicodynamic models in the
context of environmental risk assessment. IEAM
14(5):604-614. https://doi.org/10.1002/ieam.2026
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 (in the context
of TKTD modelling). The e-book "Mechanistic modelling
essentials" contains a more general introduction.
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
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 "essentials" e-book (see top of page), as well as the
derivation for the extension of growth dilution.
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,
consult the "essentials" e-book.
More details on the GUTS framework for survival modelling
can be obtained from the publication or (even better) the
free e-book (see top of the page).
- 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
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
- Vlaeminck K, KPJ Viaene, P Van Sprang, S Baken and KAC
De Schamphelaere (2019). The use of mechanistic
population models in metal risk assessment: combined
effects of copper and food source on Lymnaea
stagnalis populations. Environ Tox Chem
38(5):1104-1119. https://dx.doi.org/10.1002/etc.4391
- Vlaeminck K, KPJ Viaene, P Van Sprang and KAC De
Schamphelaere (2021). Development and validation of a
mixture toxicity implementation in the dynamic energy
budget–individual‐based model: effects of copper and
zinc on Daphnia magna populations. Environ
Toxicol Chem 40(2):513-527. https://doi.org/10.1002/etc.4946
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.
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
- Ashauer R and Jager T (2018). Physiological modes of
action across species and toxicants: The key to
predictive ecotoxicology. Environ. Sci.: Processes
Impacts. http://dx.doi.org/10.1039/C7EM00328E
- Murphy CA, Nisbet RM, Antczak P, Garcia-Reyero N,
Gergs A, Lika K, Mathews T, Muller EB, Nacci D, Peace A,
Remien CH, Schultz IR, Stevenson LM and Watanabe KH
(2018). Incorporating suborganismal processes into
Dynamic Energy Budget models for ecological risk
assessment. IEAM 14(5):615-624 https://doi.org/10.1002/ieam.4063
k
- Muller EB, K Lika, RM Nisbet, IR Schultz, J Casas, A
Gergs, CA Murphy, D Nacci and KH Watanabe (2019).
Regulation of reproductive processes with Dynamic Energy
Budgets. Functional Ecology 33(5):819-832. https://dx.doi.org/10.1111/1365-2435.13298
- ...
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
- Ashauer R and Jager T (2018). Physiological modes of
action across species and toxicants: The key to
predictive ecotoxicology. Environ. Sci.: Processes
Impacts. http://dx.doi.org/10.1039/C7EM00328E
- Singer A, D Nickisch and A Gergs (2023). Joint
survival modelling for multiple species exposed to
toxicants. Sci Total Environ 857(2):159266. https://doi.org/10.1016/j.scitotenv.2022.159266
- ...
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
(2017). Dynamic links between lipid storage,
toxicokinetics and mortality in a marine copepod exposed
to dimethylnaphthalene. Environ Sci Technol
51(13):7707-7713. http://dx.doi.org/10.1021/acs.est.7b02212
- Mangold-Döring A, A Huang, EH van Nes, A Focks and PJ
van den Brink (2022). Explicit consideration of
temperature improves predictions of
toxicokinetic–toxicodynamic models for flupyradifurone
and imidacloprid in Gammarus pulex. Environ Sci
Technol 56:15920-15929. http://dx.doi.org/10.1021/acs.est.2c04085
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
(2017). Dynamic links between lipid storage,
toxicokinetics and mortality in a marine copepod exposed
to dimethylnaphthalene. Environ Sci Technol
51(13):7707-7713. 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
- Zimmer EI, TG Preuss, S Norman, B Minten and V Ducrot
(2018). Modelling effects of time-variable exposure to
the pyrethroid beta-cyfluthrin on rainbow trout early
life stages. Environ Sci Europe 30:36. https://doi.org/10.1186/s12302-018-0162-0
- Jager T, R Nepstad, BH Hansen and J Farkas (2018).
Simple energy-budget model for yolk-feeding stages of
Atlantic cod (Gadus morhua). Ecological Modelling
385:213–219. DOI 10.1016/j.ecolmodel.2018.08.003
(no toxicants, but a simple base model for
embryos/larvae)
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)
- Cedergreen N, Nørhave NJ, Svendsen C and Spurgeon DJ
(2016). Variable temperature stress in the nematode Caenorhabditis
elegans (Maupas) and its implications for
sensitivity to an additional chemical stressor. PLoS ONE
11(1):e0140277. http://dx.doi.org/10.1371/journal.pone.0140277
- 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
- Focks A, Belgers D, Boerwinkel MC, Buijse L, Roessink
I and Van den Brink PJ (2018). Calibration and
validation of toxicokinetic-toxicodynamic models for
three neonicotinoids and some aquatic
macroinvertebrates. Ecotoxicology 27(7):992-1007. https://doi.org/10.1007/s10646-018-1940-6
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
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