ABMs in Ecology

Richard SiblyUniversity of Reading, UK

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

How stress affects population growth

York workshop 2004

Population risk assessment of birds and mammals in the UK

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

Agent-based model (ABM) of Chris Topping

Spatially explicit model of animal behaviour of the vole

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

Validation

Grant applied for by Mark Beaumont: “Bayesian Inference in Agent-Based Modelling”

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

Model parameters

• Predation parameter• Deaths other causes parameter

Prior distributions

Predation parameter Other causes parameter

of model parameters

Posterior distributions of model parameters

Predation parameter Other causes parameter

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

Prior distributions

Predation parameter Other causes parameter

of model parameters

Posterior distributions of model parameters

Predation parameter Other causes parameter

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