University of

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Models for plant pathogen invasion in crop and
natural systems Seven posts are available for
initiatives funded by Defra, BBSRC-INRA, USDA,
NSF
University of Cambridge
Post 1) PDRA Modeller/Statistical
Physicist Cambridge (3 years) Post 2) PDRA
Modeller/Theoretical Biologist Rothamsted (3
years) Post 3) PDRA Evolutionary ecologist
Rothamsted (4 years) Post 4) PDRA
Statistician Cambridge (4 years) Post 5)
PDRA Modeller/Epidemiologist Cambridge (2
years) Post 6) Computer Programmer Cambridge (3
years) Post 7) PA/Computing Assistant Cambridg
e (3 years)
Further details of the posts are given
at http//www-epidem.plantsci.cam.ac.uk
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Parameter estimation in botanical epidemics
Christopher Gilligan Epidemiology Modelling
Group cag1_at_cam.ac.uk
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Parameter estimation in botanical epidemics
Botanical epidemics current problems
Epidemiological models Stochastic temporal
models inference Stochastic temporal
models application Temporal and spatial
scales Model discrimination
Messages and challenges
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Current team (05-06)
Dr Jon Ludlam
Based at Rothamsted gt
Dr Frank van den Bosch Rothamsted
Current external collaborators
Dr Mike Asher Brooms Barn
Dr Jane White Bath
Dr Tim Gottwald USDA
Dr Ivana Gudelj Imperial
Dr Ramanan Laxminaryan RFF
Dr Jonathan Swinton
Recent members of team
Dr Richard Hall
Dr Cerian Webb Vet Science
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Disease in a changing landscape
Why is the landscape changing?

• Population growth 30 increase in cereals by
  2020

• EU expansion Changing balance of crops

• Consumer demands Reduced inputs healthier food

• Exhaustion of resources Non-food crops to
  replace oil

• Climate change New pests and disease

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Scales of spread
?
Phase transition Recent spread to S. America
Currently risk of spread to U.S.
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Scales of spread
Phase transition Fungicide (Strobilurin)
resistance in wheat powdery mildew
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Scales of spread
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Scales of spread
Sudden oak death
http//kellylab.berkeley.edu/SODmonitoring/,
http//www.coastalconservancy.ca.gov/coastocean/
winter2002/pages/one.htm, http//www.na.fs.fed.us
/spfo/pubs/pest_al/sodeast/sodeast.htm,
http//www.suddenoakdeath.org/
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Model structures
Capturing the biology
Introducing stochasticity
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Generic model for primary and secondary
infection with vital dynamics
?
Infecteds I
Removals R
Susceptibles S
External Inoculum X
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Generic model for primary and secondary
infection with vital dynamics and quenching
?
Infecteds I
Removals R
Susceptibles S
External Inoculum X
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Pulsed Systems Biocontrol of S. minor Data
Susceptible Sclerotia
Infected Sclerotia
Introduce the host crop pulsed return
of inoculum
seasonal variation changes in epidemic
rates
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Biocontrol of S. minor model fitting and
persistence
Successful fit and prediction pulsed
inputs seasonal variation heterogeneous
mixing
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Model structures
Removed R
Susceptible S
Infected I
Exposed (Latent) E
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Model structures
Kleczkowski, A., Bailey, D. J. Gilligan, C. A.
(1996) Proc. R. Soc. Lond. Ser. B. 263,
777-783. Truscott, J. T. Gilligan, C. A. (2003)
PNAS 100, 9067-9072.
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Model structures spatio-temporal
Percolation
Dybiec, B., Kleczkowski, A. Gilligan, C. A.
(2004) Phys Rev. E. 70, 066145 Bailey, D. J.,
Otten, W. Gilligan, C. A. (2000) New Phytol.
146, 535-544.
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Motivation
Matching scale of epidemics matters Taking
account of stochasticity
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Invasion of Rhizomania

• Will it invade?

• Will a statutory containment policy work?

• What alternative strategy will work?

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Control of Rhizomania
Containment policy Cease growth of sugar beet on
symptomatic fields Field-scale strategy
Stewardship scheme Sell sugar beet quota when
symptoms appear on nth neighbouring
farm Farm-scale strategy
Stacey, A. J., Truscott, J. E., Asher, M. J. C.
Gilligan, C. A. (2004) Phytopathology 94, 209-215.
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Control of an invading disease Rhizomania
Farm scale
Field scale
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Control of an invading disease Rhizomania
Farm scale
Field scale
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Control of an invading disease Rhizomania
Farm scale
Field scale
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Control of an invading disease Rhizomania
Farm scale
Field scale
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Control of an invading disease Rhizomania
Farm scale
Field scale
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Control of an invading disease Rhizomania
Farm scale
Field scale
Matching the scale of the control strategy with
epidemic scale works
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Stochastic realisations Rhizomania
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Stochastic realisations Rhizomania
Risk assessment requires us to look at the entire
probability distribution for disease
Stacey, A. J., Truscott, J. E., Asher, M. J. C.
Gilligan, C. A. (2004) Phytopathology, In press.
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Introducing stochasticity
Can we assess the risk of failure of a new
technology?
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Biological control of Rhizoctonia
solani by Trichoderma viride
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Effect of biocontrol on damping-off
Average disease progress curves hide the
underlying dynamics
-Tv
Tv
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Effect of biocontrol on damping-off
Individual disease curves reveal the underlying
variability
-Tv
Tv
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Demographically generated variability
Small variations in initial conditions or
parameters can account for differences in the
mean and variance of this quenched system
-Tv
Tv
Kleczkowski, A., Bailey, D. J. Gilligan, C. A.
(1996) Proc. R. Soc. Lond. Ser. B. 263, 777-783.
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Identification of epidemiological mechanisms
How does Trichoderma control Rhizoctonia at the
population level?
Does Trichoderma influence - the mean levels of
disease?
- the variance with and between
epidemics?
Is the effect mediated via - primary infection?
- secondary infection?
Trichoderma viride on Rhizoctonia solani
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Demographic stochastic model
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Demographic stochastic model
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Demographic stochastic model
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Profile likelihoods identify critical parameters
Trichoderma affects primary infection ß p
under these conditions
Gibson, G. J., Gilligan, C. A. Kleczkowski, A.
(1999) Proc. R. Soc. Lond. Ser. B. 266,
1743-1753. Gibson, G. J., Kleczkowski, A.
Gilligan, C. A. (2004) PNAS 101, 12120-24
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What happens over a large population of sites?
Natural variability
Example What is the risk of failure for
biological control of damping-off disease?
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Evolution of replicate epidemics /-T.viride
- T. viride
t1
t2
t3
t5
t10
t15
Number of inf. Plants / site (I)
Propn of sites with I inf. plants
T. viride
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Variability and disease management
Suppose we can select isolates of T.v. with
different effects on rp
The model allows us to predict the performance
and risk of failure of biocontrol
e.g. probability of infection-free sites
Gibson, G. J., Gilligan, C. A. Kleczkowski, A.
(1999) Proc. R. Soc. Lond. Ser. B. 266,
1743-1753. Gibson, G. J., Kleczkowski, A.
Gilligan, C. A. 2004 PNAS 101, 12120-24
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Introducing space
Dealing with emerging epidemics
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Data
Dealing with single snap-shots
Find parameters minimise expected rate of change
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Single snap-shots during invasion
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Single snap-shots during invasion
Citrus tristeza virus in orchard kernel unknown
Method suggests power-law kernel captures the
spatial dynamics supported by MCMC estimation
of successive snap-shots
Keeling, M., Brooks, S. P. Gilligan, C. A.
2004. PNAS 101, 9155-9160.
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Analysis of successive snap-shots during invasion

Keeling, M. Brooks, S.P. Gilligan, C. A.
(2004) PNAS 101, 9155-916
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Citrus canker an emerging epidemic
Dr Tim Gottwald USDA
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Citrus canker in Miami backyards an emerging
epidemic
Target Control of disease on urban trees to
prevent spread to commercial plantings
Statistical modelling objectives Identify a
parsimonious model for disease spread Estimate
the parameters as early as possible during
epidemic Use inferences to inform disease control
strategies
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Estimation of the parameters
Dr Lara Jamieson Stats Lab/ Plant Sci/ MRC
Dr Tim Gottwald USDA
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Citrus canker the data multiple snap-shots
Citrus canker in Miami backyards
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Multiple snap-shots MCMC
Inference - likelihood based upon Order of
infections ? ? (Spatial
scale) Order and timing of infections ? ?
(Spatial scale) ? ß (Temporal scale)
Hypothesis ? (Spatial scale) constant over
snap-shots ß (Temporal scale) varies with time
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Citrus canker candidate dispersal models
Priors ?g, ?e log-normal ß, ? gamma
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Model discrimination
Conclude RJMCMC Exponential kernel with
external infection (? gt 0) in 4/5 sites
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Parameter estimation successive snap-shots
How soon? Are estimates consistent over time?
How many sites? Are estimates consistent over
space?
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Broward county (BIA) Posterior densities
trends over time
Posterior densities for ß (Transmission rate)
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Broward county (BIA) Posterior densities
trends over time
Posterior densities for ß (transmission rate)
Conclusion ß varies over time
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Posterior densities trends over locations
Cumulative 3 monthly windows between 0-12 months
Posterior densities for ß (transmission rate)
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Posterior densities trends over locations
Cumulative 3 monthly windows between 0-12 months
Posterior densities for ß (transmission rate)
Conclusion consistency over space
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Citrus canker controlling an emerging epidemic
Options for control Radius of removal Frequency
of revisit
Objectives for control Minimise duration of
epidemic Minimise removals
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Dade county control of disease
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Citrus canker controlling an emerging epidemic
1) Objectives for control Minimise duration of
epidemic Minimise removals
2) Take account of uncertainty Impose control
strategies on ensemble of epidemics Weight
against extreme events
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Citrus canker controlling an emerging epidemic
3) Consider distribution for ensemble of epidemics
Generated according to posterior densities for
epidemic model parameters
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Citrus canker controlling an emerging epidemic
5) Derive and minimise an objective function
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Citrus canker controlling an emerging epidemic
Preliminary result Evidence for minimum Differs
from common practice
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Messages and challenges
Single snap-shot can provide useful
information gt 1 provides a lot more
Primary (external) infection matters Challenges
Strategy for emerging epidemics
Unobserved classes Optimal design for
data Estimation for decision
making
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Current team (05-06)
Dr Jon Ludlam
Based at Rothamsted gt
Dr Frank van den Bosch Rothamsted
Current external collaborators
Dr Mike Asher Brooms Barn
Dr Jane White Bath
Dr Tim Gottwald USDA
Dr Ivana Gudelj Imperial
Dr Ramanan Laxminaryan RFF
Dr Jonathan Swinton
Recent members of team
Dr Richard Hall
Dr Cerian Webb Vet Science
67
Models for plant pathogen invasion in crop and
natural systems Seven posts are available for
initiatives funded by Defra, BBSRC-INRA, USDA,
NSF
University of Cambridge
Post 1) PDRA Modeller/Statistical
Physicist Cambridge (3 years) Post 2) PDRA
Modeller/Theoretical Biologist Rothamsted (3
years) Post 3) PDRA Evolutionary ecologist
Rothamsted (4 years) Post 4) PDRA
Statistician Cambridge (4 years) Post 5)
PDRA Modeller/Epidemiologist Cambridge (2
years) Post 6) Computer Programmer Cambridge (3
years) Post 7) PA/Computing Assistant Cambridg
e (3 years)
Further details of the posts are given
at http//www-epidem.plantsci.cam.ac.uk
68
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Normalising the infection kernel
Beta now equates to per capita transmission rates
Transmission rates from epidemics of different
sizes will be comparable.
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Single snap-shots relative error two primary
infection sites
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Single snap-shots relative error boundary
effects
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Single snap-shots relative error
spatially-heterogeneous transmission rate
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Environmental stochasticity
Demographically generated variability
Switching processes
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Demographically generated variability
Small variations in initial conditions or
parameters can account for differences in the
mean and variance of this quenched system
-Tv
Tv
Kleczkowski, A., Bailey, D. J. Gilligan, C. A.
(1996) Proc. R. Soc. Lond. Ser. B. 263, 777-783.
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Environmental stochasticity switching process
Truscott, J.E. Gilligan, C. A. (2003) PNAS.
100, 1067-1072
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Cryptic infection and disease on networks
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Networks and invasion
Cryptic infection Small world topology
Is there a minimum control neighbourhood?
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Networks and invasion
Cryptic infection local spread gt Minimum
control neighbourhood
Impact (X)
Control neighbourhood z
Dybiec, B., Kleczkowski, A. Gilligan, C. A.
(2004) Phys Rev. E. 70, 066145
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Preventing disease spread by local control
Local spread only
Local control lt local spread z
Local control local spread z
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Preventing disease spread by local control
Local spread Short cuts
Local control gt local spread z Disease constrained
Local control local spread z Disease escapes
via short cuts
Local control lt local spread z