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Modelling and experimentation of the spatio-temporal spread of soilborne pathogens: Rhizoctonia solani on sugar beet as an example pathosystem. Leclerc Melen. PhD defence 1 st February 2013 – Agrocampus Ouest UMR – IGEPP Cifre I.T.B. Reporters: Joël Chadoeuf, Christian Lannou - PowerPoint PPT Presentation
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Modelling and experimentation of the spatio-temporal spread of soilborne pathogens: Rhizoctonia solani on sugar beet as an
example pathosystem
Leclerc Melen
PhD defence
1st February 2013 – Agrocampus Ouest
UMR – IGEPP
Cifre I.T.B
Reporters: Joël Chadoeuf, Christian Lannou
Examiners: Yannick Outreman, Marc Richard-Molard
Supervisors: Philippe Lucas, Thierry Doré, João Filipe
2
General context – current problemsIntroduction
• 50% reduction in pesticide use (Grenelle de l’environnement Ecophyto)
• Find alternatives to pesticide use
• Keep crop production levels and growers’ incomes
3
Proposed approachesIntroduction
• Necessity of considering the complexity of agro-ecosystems (e.g. using system approaches)
• Understand ecological and epidemiological processes involved in the dynamics of pathogens
• Use ecological and epidemiological knowledge to improve pest management and design efficient crop protection strategies
• Combine several controls with partial effects (there is no ‘one fits all’ solution)
• SysPID Casdar Project: Reduce the impact of soilborne diseases in crop systems towards an integrated and sustainable pest management
• Action n°2: Epidemiological processes in field crop systems
4
Soilborne disease epidemicsIntroduction
Soilborne diseases
• Wide range of pathogenic organisms (fungi, bacteria, viruses, nematodes, protozoa)
• Cause substantial damage to crops worldwide (up to 50 % of crop loss in the US (Lewis & Papaizas, 1991) )
• Pathogens often survive for many years in soils (5-7 years for Pythium)
• Difficult to detect, predict and control
Epidemiology
• External source of inoculum X(t) : dynamic pathogen population
• Primary infections : external inoculum epidemic initiation
• Secondary infections : spread of the pathogen within the crop/population
S
X
ISusceptible
hostsInfected/Infectious
hosts
5The host The pathogen
Rhizoctonia solani on sugar beet as an example pathosystemIntroduction
6
The host : sugar beetIntroduction
The plant
• Cultivated Beta vulgaris
• High production of sucrose
The crop
• Grown for sugar production
• France is one of the largest producer (33 Mt in 2009)
7
The pathogen : Rhizoctonia solaniIntroduction
R. solani fungi
• Basidiomycetes
• Polyphagous saprotrophic fungi
• Anastomisis Groups (AG)
R. solani AG2-2 IIIB
• Parasites maize, rice, sugar beet, ginger …
• Important optimal temperature range for growth
• Develops late in the growing season
• Infects mostly mature plants
Aoyagi et al., 1998
8
The disease : the brown root rot disease of sugar beetIntroduction
9
Rhizoctonia root rot disease control Introduction
Current management strategies
• Think crop rotations (host & non-host crops)
• Resistant varieties
• Biological controls ?
Antagonists (e.g. Trichoderma fungi)
Biofumigation
10
Our systemIntroduction
Hidden epidemic:
Cryptic infections
Source of inoculum :
R. solani
Temporal scale : growing season of sugar beet
Spatial scale : field
Visible epidemic:
symptomatic plants
Belowground
Above-ground
11
Research questions and structure of the presentationIntroduction
1. How does R. solani spread in field conditions ? (Understand epidemiology of R. solani in field conditions)
2. How to infer hidden infections from observations of the disease ?
3. How does biofumigation affect epidemic development ?
Study 3 : Effects of biofumigation
2007 data (Motisi, 2009)Modelling
Study 2 : Incubation period
Experimentation Modelling
Study 1 : R. solani spread
Experimentation Modelling
12
Part 1
How does R. solani spread in field conditions ?
13
Pathozone concept and spread of soilborne pathogensPart 1
• Difficult to asses R. solani growth in soils use of pathozone concept
• “Pathozone means the region of soil surrounding a host unit within which the centre of a propagule must lie for infection of the host unit to be possible” (Gilligan, 1985)
Contact distance Tim
e ex
pose
d
to in
ocul
um
Probability of infection
Placement experiment
Inoculum(donor)-host(recipient)
n replicates at distance x
ni number of infected recipients at time t
P(x,t) = ni / n
14
Results of the experiments (Pathozone profiles)Part 1
• Field experiments in 2011 (Le Rheu)
Secondary inoculum
(an infected plant)
• Localised spread (nearest neigbour plants) (Filipe et al., 2004, Gibson et al.,2006)
• Infections occurs further with secondary inoculum ( Kleczkowski et al.,1997)
The fungus translocates nutrients from the parasited host to other parts of the mycelium
Primary inoculum
(5 infested barley seeds)
15
Host growth may increase pathogen transmission at individual levelPart 1
Host-plant growth decreases the contact distance between neighbouring plants
Host growth may increase pathogen transmission at individual level
16
Host growth can trigger the development of epidemicsPart 1
xcc= 11 cm
xcc= 14 cm
xcc= 17 cm
Static contact distance Dynamic contact distance
Host growth can cause a switch from non-invasive to invasive behaviourNon-invasive behaviour (linear trend)
Invasive behaviour (non-linear trend)
17
Conclusion (Part 1)Part 1
• First Pathozone profiles measured in a real soil
• Locality of pathogen spread in field conditions
Importance of considering space : mean-field approximation/homogeneous mixing assumption may fail when predicting the spread of soilborne pathogens (Dieckmann et al., 2000 ; Filipe & Gibson, 2001)
• Host growth can trigger the development of epidemics by decreasing contact distances
Need to take into account host growth for epidemic thresholds – conditions for invasive spread of plant population by pathogens (Grassberger, 1983 ; Brown & Bolker, 2004)
18
Part 2
How to infer hidden infections from observations ?
19
ProblemPart 2
20
A problem of incubation period Part 2
• Time between hidden infection and appearance of detectable symptoms of pathology
Incubation period (Kern, 1956 ; Keeling & Rohani, 2008)
• Incubation period distributions are often described by non-negative probability distributions with a pronounced mode (Keeling & Rohani, 2008 ; Chan & Johansson, 2012)
• Incubation period data are rare …
21
Compartmental models an incubation period distributionsPart 2
• How to describe cryptic infections with compartmental models ?
• Compartmental Markovian models
The time spent in each state is exponentially distributed
In a simple SID model the incubation period is exponentially distributed
• How to introduce realistic distributions in classical compartmental models ?
A tractable way: by subdividing compartments (i.e. introducing transient states)
Sum of exponentialy distributed random variables =
Erlang (or Gamma) distributed random variable
Susceptible hosts Infected/infectious hosts Detectable/symptomatic hosts
Realistic distribution
Distribution in classical Markovian
models
22
Working hypothesis and methodology Part 2
• Hypothesis: the distribution (e.g. mean and range) of the incubation period is age-dependent
• Methodology:
Experimental measures for various ages of infection
Statistical analysis (is Gamma distribution robust enough ?)
Build a model for age-varying distribution of the incubation period
Incorporate it into an SID compartmental model
23
Experimental measures of the incubation periodPart 2
Experiments
• Plant inoculated with 3 infested barley seeds (inoculum)
• 9 ages of plants (14, 32, 46, 60, 74, 88, 102, 116, 130 days)
• For each individual the time of first above-ground symptom was recorded
• At least 45 individual observations for each age distributions of the incubation period
24
Raw data (results of the experiments)Part 2
Inub
atio
n pe
riod
calc
ulat
ed in
deg
ree-
day
s
25
Age-varying model of the incubation period distributionPart 2
• Age by age distribution analysis Gamma distribution (general case of Erlang) can reasonably describe incubation period distributions
• Age-varying model of the incubation period T(t)
( ) ~ [ , ( )] with an integer and ( ) btT t Erlang k t k t ae c
• Compartmental model with realistic incubation distribution (19 transient non-symptomatic states)
k : shape parameter =
number of transient states (=19)
λ: time dependent rate parameter
26
Hidden infections and observationsPart 2
• Simulations of cryptic epidemics (individual-based spatial model with stochastic continuous time)
Infected and detectable/symptomatic individuals have different dynamics
27
Conclusion (Part 2)Part 2
• One of the first epidemiological model for soilborne disease with data-supported incubation period
• Link hidden processes and observations of disease
Estimate rates of infections and cryptic infections from observations
Test management strategies based on the detection of symptomatic individuals
• This end of the incubation period corresponds to a visual detectability
May change with other detection/survey methods, e.g. molecular techniques, remote sensing
• Variability ? (soils, human error, strains, environmental conditions …)
28
Part 3
How does biofumigation affect epidemic development?
29
Background Part 3
Previous work
• The effect of biofumigation on the root rot disease has been analysed using a simple epidemiological model (Motisi, 2009 ; Motisi et al., 2012)
• Observations of symptomatic plants for 3 treatments :
1) without control, 2) with complete biofumigation, 3) with partial biofumigation
Biofumigation affects mostly primary infections
Biofumigation can affect secondary infections with a variable pattern
( ) ( ) ( ) ( )
Susceptible
dSt X t I t S t
dt
Cryptic infections
( ) ( ) ( ) ( )dI
t X t I t S tdt
Detectable plants
D I
1 2
21 3 2
Rates of infection
( ) exp( )
( ) exp( 0.5[log( / ) / ] )
t t
t t
For
ce o
f inf
ectio
n
30
Aim of the current studyPart 3
1. Integrate new epidemiological knowledge and data
2. Improve existing epidemiological models
3. Re-analyse the effects of biofumigation
4. Investigate the variability of epidemics to estimate uncertainty in the outcome of treatments
31
Improved epidemiological model : epidemic predictionsPart 3
• Spatial individual-based model with stochastic spread of the pathogen
Spatial component : better description of epidemics
Stochastic model : introduce variability in outcomes predictions of uncertainty
1 2 0 0
0
( ) exp( ( )) if
( ) 0 if
t t t t t
t t t
1 3 2exp( 0.5[log( / ) / ]²)t
( ) [ ( ) ( ) ].t t dt IP S I t t n dt
Stochastic infections
Rate of primary infection
Rate of secondary infection
32
Estimate parameter for each treatment from observations of diseasePart 3
• Introduce a more realistic incubation period for inferring epidemiological parameters
• Statistical inferrence of spatio-temporal can be difficult and time consuming…
Estimate spatial rates of infection using a semi-spatial model (Filipe et al., 2004)
• Localized spread of infections (see Part 1)
Pair approximation (Matsuda et al., 1992 ; Filipe & Gibson, 1998 ; van Baalen, 2000)
• Need to describe the dynamics of all pairs of the system (i.e. SS, SI II for an SI model)
Tractability : necessity to simplify the incubation period…
33
Model fitting and estimated rates of infectionPart 3
Biofumigation reduced rates of primary and secondary infection in this trial (2007)
1 2 0 0
0
( ) exp( ( )) if
( ) 0 if
t t t t t
t t t
1 3 2exp( 0.5[log( / ) / ]²)t
Rate of primary infection
Rate of secondary infection
Symptomatic plants (2007 data)
34
Spatial model predictionsPart 3
• Biofumigation allows a partial control of epidemics
• Biofumigation seems to reduce the uncertainty in epidemic outcome
• Marginal differences between partial and complete biofumigation in 2007
Distributions of infected plants at harvest (%)
35
Conclusion (Part 3)Part 3
• Analyses are consistent with previous results on the effect of biofumigation on the spread of R. solani, but
• We predict less primary infections and more secondary infections than in the previous study
New vision of epidemic : different disease progress curves
• Biofumigation seems to reduce the uncertainty in epidemic outcome
• Take these results with care
More statistical analyses are required to assess model fitting and conclude on the effects of treatments on epidemic development
Assess the effects of incubation period simplification – Pairwise vs temporal model …
Isotropic space (may overestimate epidemics ?)
• Re-analyse 2008 data
36
General conclusion
1
1 1 1
2
1 2 2 2
2
1 1
1 1 1
1
1 2
2
1
1( 1)[ ]
2
( ) ( 1)[ ]
( ) ( 1)[ ]
( ) ( 1)[ ]
1( ) (
2
SSSS SS SSS
SISS SI SI SSI SS SSS
SISI SI SI SSI
SDSI SD SD SSD
I ISI I I
dPP z P P
dtdP
P P z P P P PdtdP
P P z P PdtdP
P P z P PdtdP
P Pdt
1 1
1 2
2 1 1 1 2 2 2
1
1 2 1
2 2
1 2 2 2
2
2 2 1 2
2
1 1 2
2 1
1 2
2 1 2
2
1)[ ]
( ) ( ) ( 1)[ ]
( ) ( 1)[ ]
1
2
SI SSI
I ISI I I I I SI SSI
I DSD I I I D SD SSD
I II I I I
I DI I I D I D
DDI D
z P P
dPP P P z P P
dtdP
P P P z P PdtdP
P Pdt
dPP P P
dtdP
Pdt
4
t t+dt s,k inf,k 1
Prob( ) ( , ) kS I t t x dt
37
Soilborne disease epidemicsGeneral conclusion
• This work provide insights into root rot disease epidemics
spread of R. solani
incubation period
• Data-supported studies – field experiments
• We still need to improve knowledge on the epidemiology of this disease
• May apply to others pathosystems : perennial and non-perennial plants
38
Control of soilborne disease epidemicsGeneral conclusion
• Biofumigation
partial control of the root rot disease (Motisi et al., 2009 , 2010, 2012)
can reduce the uncertainty in epidemic outcome
• This work points out important epidemiological parameters for disease management
Design and test new strategies
Plant growth use crop mixing, precise key phenological stages to select for resistances
Incubation period improve disease survey
Locality of pathogen spread optimize the effects of treatments, use local treatments ?
• Combine partial controls (new and conventional) improve the control of epidemics
• Models may help to test disease management strategies
39
PerspectivesGeneral conclusion
• Mutltiple perspectives (theoretical, applied, epidemiological, ecological…)
• Consider main environmental parameters (temperature, moisture)
• Investigate pathogen dynamic at the crop rotation scale
• Understand ecological functionning of soils (pathogenic and non pathogenic communities)
Merci…• Doug Bailey
• Philipe Lucas – Thierry Doré – João Filipe
• Françoise Montfort
• Les anciens membres de l’équipe EPSOS
• UMR IGEPP
• Les Unités Expérimentales de Dijon et de Le Rheu
• L’Institut Technique de la Betterave
• Christian Lannou – Joël Chadoeuf – Marc Richard Molard – Yannick Outreman (jury)
• Pauline Ezanno – Marie Gosme – Christian Steinberg – Agnès Champeil – Étienne Rivot (comité de thèse)
• Chris Gilligan et l’Epidemiology and Modelling Group
• Les membres du projet Casdar SysPID
• Le portakabin (qui a eu chaud…)
• Et tous ceux qui m’ont supporté…
Mon bureau…avant-hier
41
Evolution of symptomsIntroduction
42
The pathogen: R. solaniIntroduction
p
p p
Spatial decline due to Time decline due to Delay inMaximum rate
location of inoculum away source of nutrients onset ofof infection ( )
from host ( ) decline ( ) infection
pa
( )
pp p
ss s
( , )( , )[1 ( , )]
( , )( , )[1 ( , )]
dP x tx t P x t
dtdP x t
x t P x tdt
inf ( , ) ~ ( , ( , ))totn x t Binomial n P x t
s
Spatial decline due to Delay inMaximum rate
location of inoculum away onset ofof infection ( )
from host ( ) infection ( )
s
s
a
Rate of primary infection
Rate of secondary infection
Rates of infection and pathozones
Infer parameters from pair experiment data
Pathozones P(x,t)
x: contact distance
t: time of exposure
ninf: number of infected recipients
ntot: number of replicates (25)
43
Incubation period ?Part 2
• Incubation period:
"time required for multiplication of a parasitic organism within a host organism up to the threshold point at which the parasite population is large enough to produce detectable symptoms of pathology“ (Kern, 1956)
Susceptible Latent/Exposed Infectious Recovered
Incubation Disease
Incubation
Incubation
Disease
Disease
Infectiousstatus
Pathologicalstatus
time of infection time sinceinfection
Susceptible Latent/Exposed Infectious Recovered
Incubation Disease
Incubation
Incubation
Disease
Disease
Infectiousstatus
Pathologicalstatus
time of infection time sinceinfection
• Periods in Natural history of disease in a host – these are incorporated as compartments in epidemiological models
44
Host growth and dynamic contact distancesIntroduction
0.4( ) 5 / [1 1000exp( 1.18* )]h t t
• Increase in the radius h(t)
• Radial growth measured with Pepista tools (ITB)
• Simple empirical model
• Dynamic of the contact distance between nearest neighbours xee(t)
• Static centre-centre distance xcc
• Spatial population model
• 30*30 square lattice
• t0= 30 days
• 5% infected
ee cc inf
ee cc inf
ee cc inf
if 30 < < 70
, if 70 < 90
if 90
( ) ( ) ,
( ) 1.5 ( )
( ) 2 ( ) ,
t
t
t
x t x h t
x t x h t
x t x h t
4
t t+dt s,k inf,k 1
Prob( ) ( , ) ( ) ( )
cck k
ee
x xS I t t x t dt
x x t
45
First results Part 3
Previous epidemiological model
Detectable/
symptomatic
Infected
Rate of primary infection
1 2
21 3 2
( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
( ) exp( )
( ) exp( 0.5[log( / ) / ] )
dSt X t I t S t
dtdI
t X t I t S tdt
D I
t t
t t
Assumptions
• Mean field mass action/homogeneous mixing assumption
• Epidemics initiated too soon
• Pre-emergence damping off
• Unrealistic incubation periodMotisi et al., 2012
For
ce o
f inf
ectio
n
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