ABMs in Ecology
Richard Sibly
University 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.
Classical models of population dynamics
• Population dynamics is the study changes in population
numbers over time
• Why do numbers change?
Classical models of population dynamics
birth
rate
death
rate
population density
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
birth
rate
death
rate
population density
population density
population growth rate
= birth rate – death rate
population density
population
growth
rate
population density
Number of Paramecium/mL
Logistic population growth
1,000
800
600
400
200
0
0
5
10
15
Time (days)
A Paramecium population in the lab
Both density and chemicals affect pgr
population
growth
rate
population
growth
rate
population density
dose of chemical
Both density and chemicals affect pgr
population density
birth rate
population growth rate
dose of chemical
death rate
Population Size (N)
How stress affects population growth
Baseline
A
AR
ARx2
10000
7500
5000
2500
0
0
50
100
Simulation Year
150
200
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
With Insecticide
Time
Skylark abundance
g)
No Insecticide
Skylark abundance
f)
Time
Broad Habitats
Time
Time
Broad Habitats
h)
With Insecticide
Skylark abundance
Time
Winter Wheat
Skylark abundance
No Insecticide
Skylark abundance
e)
Skylark abundance
Skylark abundance
Skylark abundance
Time
Winter Wheat
Time
Time
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
Legend
Main road
Roadside verge
Permanent grass
Unmanaged grassland
Rotational field (same colours for all crops)
Coniferous forest
Deciduous forest
c) BEHAVIORAL STATE
FM = FINDING MATE
F
M
Agent specification
D
Y
Is it past
breeding
date
(June
19th)?
YES
Is it past
covey
hopping
time
(June
1st)?
NO
YES
NO
Are
coveys
within
500m of
you?
NO
Are you
visiting
some
other
covey?
NO
Are
you in
a new
covey
now?
YES
Jump to a
new covey
FL
NO
YES
Leave the
covey
Fly to a new
area
YES
Revoke
visitors pass
NO
Join this
covey
YES
Find Mate in area
(500 m2)
Make your
covey
FM
G
M
Did you
find
mate in
new
covey?
YES
Does
your
mate
have a
territory?
YES
NO
FO
M
Did you
find mate
in your
search
area?
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
Time
Skylark
Time
Skylark abundance
d)
Time
Time
h)
Skylark abundance
Time
With Insecticide
Broad Habitats
With Insecticide
Time
g)
Skylark abundance
Time
c)
Time
f)
Skylark abundance
e)
Broad Habitats
No Insecticide
h)
Skylark abundance
Time
No Insecticide
Skylark abundance
Winter Wheat
With Insecticide
g)
Time
Broad Habitats
Skylark abundance
b)
With Insecticide
Time
Broad Habitats
Skylark abundance
Time
f)
Skylark abundance
Winter Wheat
No Insecticide
Skylark abundance
a)
No Insecticide
Time
Winter Wheat
Skylark abundance
Skylark abundance
e)
Skylark
Skylark
Skylark
Time
Winter Wheat
Time
Time
ABM vs. Classical methods
•
ABM can be parameterised
•
Classical models cannot be parameterised
•
ABM is complex
•
Classical models are very simple
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
CREAM questions
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 methods
• 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.
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
of model parameters
Other causes parameter
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 data
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?
eggs predated per year
egg deaths other causes
nestlings predated per year
nestling deaths other causes
Prior distributions
Predation parameter
of model parameters
Other causes parameter
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 computation with complex agent-based models for cancer research. In: Saporta, G.,
and Y. Lechevallie, editors, COMPSTAT 2010: Proceedings in Computational
Statistics. 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