Risk assessment of chemicals
Ecological risk assessment in the EU aims to protect populations rather than individuals*
*European Commission, 2000. Guidance Document on Terrestrial Ecotoxicology: Directorate General for Agriculture.
• Population dynamics is the study changes in population numbers over time
• Why do numbers change?
Classical models of population dynamics
Classical models of population dynamics
birthrate
population density
deathrate
population density
population growth rate = birth rate – death rate
How to measure population growth rate
population growth rate = birth rate – death rate
= r
Euler-Lotka equation
Classical models of population dynamics
birthrate
population density
deathrate
population density
population growth rate= birth rate – death rate
population density
Logistic population growth
population growth rate
population densityTime (days)
Nu
mb
er
of Paramecium
/mL
1,000
0
400
5
200
100
15
800
600
A Paramecium population in the lab
Both density and chemicals affect pgr
population growth rate
population density
population growth rate
dose of chemical
Both density and chemicals affect pgr
population growth rate
population density
dose of chemical
birth rate
death rate
The York approach: five steps to population risk assessment
• toxicity endpoints in the lab
• extrapolate between species
• assess exposure in the field
• extrapolate from lab to field
• evaluate effects on populations of skylarks and woodmice
Winter Wheat Winter Wheat Broad Habitats Broad Habitats No Insecticide With Insecticide No Insecticide With Insecticide a) b) c) d)
e) f) g) h)
Time
Sky
lark
abu
ndan
ce
Sky
lark
abu
ndan
ce
Sky
lark
abu
ndan
ce
Sky
lark
abu
ndan
ce
Sky
lark
abu
ndan
ce
Sky
lark
abu
ndan
ce
Sky
lark
abu
ndan
ce
Sky
lark
abu
ndan
ce
Time
Time Time Time
Time Time Time
Winter Wheat Winter Wheat Broad Habitats Broad Habitats
No Insecticide With Insecticide No Insecticide With Insecticide
The study landscape
Real 10x10 km Danish landscape by Bjerringbro, 1-m resolution
LegendMain roadRoadside vergePermanent grassUnmanaged grasslandRotational field (same colours for all crops)Coniferous forestDeciduous forest
Agent specification
c) BEHAVIORAL STATEFM = FINDING MATE
FM
Is it past covey
hopping time
(June 1st)?
Is it past breeding
date (June 19th)?
Are you in a new
covey now?Are
coveys within
500m of you?
Are you visiting some other
covey?
Did you find
mate in new
covey?
Did you find mate
in your search area?
Jump to a new covey
Does your mate
have a territory?
Leave the covey
Fly to a new area
Find Mate in area (500 m2)
Join this covey Make your
covey
Revoke visitors pass
DY
FL
FM
GM FO
M
YES
YES
YES
YES
YES
YES
YES
YESNO
NO
NO
NO
NO
NO
NO
NO
Agent-based model (ABM)
Spatially explicit model of animal behaviour of the vole
Population dynamics emerge as result of local interactions
Dynamic landscape with crop rotation and weather-dependent plant growth
Winter Wheat Winter Wheat Broad Habitats Broad Habitats No Insecticide With Insecticide No Insecticide With Insecticide a) b) c) d)
e) f) g) h)
Time
Sky
lark
abu
ndan
ce
Sky
lark
abu
ndan
ce
Sky
lark
abu
ndan
ce
Sky
lark
abu
ndan
ce
Sky
lark
abu
ndan
ce
Sky
lark
abu
ndan
ce
Sky
lark
abu
ndan
ce
Sky
lark
abu
ndan
ce
Time
Time Time Time
Time Time Time
Winter Wheat Winter Wheat Broad Habitats Broad Habitats No Insecticide With Insecticide No Insecticide With Insecticide a) b) c) d)
e) f) g) h)
Time
Sky
lark
abu
ndan
ce
Sky
lark
abu
ndan
ce
Sky
lark
abu
ndan
ce
Sky
lark
abu
ndan
ce
Sky
lark
abu
ndan
ce
Sky
lark
abu
ndan
ce
Sky
lark
abu
ndan
ce
Sky
lark
abu
ndan
ce
Time
Time Time Time
Time Time Time
Winter Wheat Winter Wheat Broad Habitats Broad Habitats
No Insecticide With Insecticide No Insecticide With Insecticide
• ABM can be parameterised
• Classical models cannot be parameterised
• ABM is complex
• Classical models are very simple
ABM vs. Classical methods
Sibly, R.M., Akçakaya, H.R., Topping, C.J., O'Connor, R.J. (2005) Population-level assessment of risks of pesticides to birds and mammals in the UK. Ecotoxicology, 14, 863-876. Topping C.J., Sibly R.M., Akçakaya H.R., Smith G.C., Crocker, D.R. (2005) Comparison of a life-history model and an individual-based landscape model of skylark populations affected by a pesticide. Ecotoxicology, 14, 925-936.
Volker Grimm
Helmholtz Center for Environmental Research, Leipzig
• Grimm, V., and Railsback, S.F., 2005. Individual-Based Modeling and Ecology. Princeton University Press
• Grimm, V. et al. 2005. Pattern-oriented modeling of agent-based complex systems. Science 310, 987-991.
CREAM
20 PhD (three years) and 3 postdoc (two years) projects developing ecological models for the risk assessment of chemicals
http://cream-itn.eu/
started 2010 funded by EC
1) Can we make credible ABMs that will be accepted by
Risk Managers Risk Assessors Scientists
2) How do we
Verify Validate
these models?
CREAM questions
• Chemical – fictitious pesticide
• ABMs using Netlogo to model application of chemical, exposure of individuals and effects on individuals
• Validation: data sets exist for Danish landscapes in northern Jutland for skylark and vole. For woodpigeon, data sets from ITE Monks Wood.
CREAM methods
Classical evaluation of models
• Model: y = a + b1x1 + b2x2 + b3x3 + … + ε
• Some information is known – some values of y, x1, x2, x3. The values of b1, b2, b3 are estimated from the data.
• Evaluation is by calculating R2, the % variance in the y
values that is accounted for by the model.
Bayesian evaluation of models
• Model: ABM predicting population numbers over years
• Some information is known but some parameter values are estimated from the data.
• Evaluation is by calculating the likelihood of the model
given the data.
Bayesian vs classical
• When both methods can be applied they give the same results.
• Bayesian can handle ABMs but classical cannot.
• Classical methods are faster and well established so easier.
Short history of Bayesian methods
• MCMC widely used since computers got faster c.1990.
• MCMC requires likelihood function. But, we cannot derive likelihood function for ABMs.
• Since 2002 Approximate Bayesian Computation (ABC) avoids need to derive likelihood. Also, can use parallel computation and far fewer runs than MCMC. So ABC makes ABM evaluation feasible.
Evaluation of models using ABC
• ABC calculates posterior probability of each model given the data.
• The model with the higher probability is better.
• The ratio of probabilities is called the Bayes factor.
• Bayes factor = 10 means one is 10 times more likely than the other.
Example of ABC
• Tomasz Kułakowski produced a skylark ABM in Netlogo starting February 2010
• 900 lines of code
• ABC on 24 parallel processors, 1 h per run, 1000 runs takes 2 days
Data for skylarks in study area
• 20% eggs predated per year• 10% eggs die other causes• 8% nestlings predated per year• 10% nestlings die other causes
How does ABC do that?
• Runs model 1000 times with parameters chosen from priors
• Retains 10% giving closest match to data20% eggs predated per year10% eggs die other causes8% nestlings predated per year10% nestlings die other causes
How does ABC do that?
eggs predated per year nestlings predated per year
egg deaths other causes nestling deaths other causes
Bayesian evaluation of models
• Model: ABM predicting population numbers over years
• Some information is known but some parameter values are estimated from the data.
• Evaluation is by calculating the likelihood of the model
given the data.
Summary
• ABMs promise realistic models of animal populations in real landscapes.
• Major issue is validation
• ABC offers method of validation
Sottoriva, A., and S. Tavare. 2010. Integrating approximate Bayesian computa-tion with complex agent-based models for cancer research. In: Saporta, G.,and Y. Lechevallie, editors, COMPSTAT 2010: Proceedings in ComputationalStatistics. Springer, Physica Verlag. In Press.
Beaumont, M. 2010. Approximate Bayesian Computation in Evolution and Ecology. Ann. Rev. Ecol. Evol. & Syst. In Press.
Acknowledgements
• Chris Topping, University of Aarhus• Mark Beaumont, University of Bristol• Chris Greenough, Rutherford Appleton Laboratory• Jacob Nabe-Nielsen, University of Aarhus
• Tomasz Kułakowski • Katarzyna Matuszewska • Trine Dalqvist • Chun Liu
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