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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
Introduction
General context – current problems
• 50% reduction in pesticide use (Grenelle de l’environnement  Ecophyto)
• Find alternatives to pesticide use
• Keep crop production levels and growers’ incomes
2
Introduction
Proposed approaches
• 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
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Introduction
Soilborne disease epidemics
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
Susceptible
hosts
S
X
I
Infected/Infectious
hosts
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Rhizoctonia solani on sugar beet as an example pathosystem
Introduction
The host
The pathogen
5
Introduction
The host : sugar beet
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)
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Introduction
The pathogen : Rhizoctonia solani
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
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Aoyagi et al., 1998
Introduction
The disease : the brown root rot disease of sugar beet
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Introduction
Rhizoctonia root rot disease control
Current management strategies
• Think crop rotations (host & non-host crops)
• Resistant varieties
• Biological controls ?
Antagonists (e.g. Trichoderma fungi)
Biofumigation
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Introduction
Our system
Visible epidemic:
symptomatic plants
Above-ground
Hidden epidemic:
Cryptic infections
Source of inoculum :
R. solani
Temporal scale : growing season of sugar beet
Belowground
 Spatial scale : field
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Introduction
Research questions and structure of the presentation
1. How does R. solani spread in field conditions ?
(Understand epidemiology of R. solani in field conditions)
Study 1 : R. solani spread
Experimentation
Modelling
2. How to infer hidden infections from observations of the disease ?
Study 2 : Incubation period
Experimentation
Modelling
3. How does biofumigation affect epidemic development ?
Study 3 : Effects of biofumigation
2007 data (Motisi, 2009)
Modelling
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Part 1
How does R. solani spread in field conditions ?
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Part 1
Pathozone concept and spread of soilborne pathogens
• 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)
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
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Part 1
Results of the experiments (Pathozone profiles)
• Field experiments in 2011 (Le Rheu)
Primary inoculum
Secondary inoculum
(5 infested barley seeds)
(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
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Part 1
Host growth may increase pathogen transmission at individual level
 Host-plant growth decreases the contact distance between neighbouring plants
 Host growth may increase pathogen
transmission at individual level
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Part 1
Host growth can trigger the development of epidemics
Static contact distance
Dynamic contact distance
xcc= 11 cm
Non-invasive behaviour (linear trend)
xHost
can cause a switch from non-invasive to invasive behaviour
= 14 growth
cm
cc
xcc= 17 cm
Invasive behaviour (non-linear trend)
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Part 1
Conclusion (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)
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Part 2
How to infer hidden infections from observations ?
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Part 2
Problem
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Part 2
A problem of incubation period
• 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 …
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Part 2
Compartmental models an incubation period distributions
• How to describe cryptic infections with compartmental models ?
Susceptible hosts
Infected/infectious hosts
Detectable/symptomatic hosts
• 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 ?Realistic distribution
A tractable way: by subdividing compartments (i.e. introducing transient states)
Distribution in
classical Markovian
Sum of exponentialy distributed random variables
models
=
Erlang (or Gamma) distributed random variable
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Part 2
Working hypothesis and methodology
• 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
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Part 2
Experimental measures of the incubation period
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
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Part 2
Inubation period calculated in degree- days
Raw data (results of the experiments)
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Part 2
Age-varying model of the incubation period distribution
• 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)
T (t ) ~ Erlang[k ,  (t )] with k an integer and  (t )  aebt  c
k : shape parameter =
λ: time dependent rate parameter
number of transient states (=19)
• Compartmental model with realistic incubation distribution (19 transient non-symptomatic states)
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Part 2
Hidden infections and observations
• Simulations of cryptic epidemics (individual-based spatial model with stochastic continuous time)
 Infected and detectable/symptomatic individuals have different dynamics
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Part 2
Conclusion (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 …)
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Part 3
How does biofumigation affect epidemic development?
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Part 3
Background
Previous work
Susceptible
dS
   (t ) X   (t ) I (t )  S (t )
dt
Cryptic infections
dI
  (t ) X   (t ) I (t ) S (t )
dt
Detectable plants
D I
Rates of infection
 (t )  1 exp( 2t )
Force of infection
• The effect of biofumigation on the root rot disease has been analysed using a simple
epidemiological model (Motisi, 2009 ; Motisi et al., 2012)
 (t )  1 exp(0.5[log(t / 3 ) /  2 ]2 )
• 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
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Part 3
Aim of the current study
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
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Part 3
•
Improved epidemiological model : epidemic predictions
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
Stochastic infections
P( St  I t dt )  [ (t )   (t )nI ].dt
Rate of primary infection
 (t )  1 exp( 2 (t  t0 )) if t0  t

if t0  t
 (t )  0
Rate of secondary infection
  1 exp(0.5[log(t / 3 ) /  2 ]²)
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Part 3
Estimate parameter for each treatment from observations of disease
•
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…
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Part 3
Model fitting and estimated rates of infection
Rate of primary infection
 (t )  1 exp( 2 (t  t0 )) if t0  t

if t0  t
 (t )  0
Symptomatic plants (2007 data)
Rate of secondary infection
  1 exp(0.5[log(t / 3 ) /  2 ]²)
 Biofumigation reduced rates of primary and secondary
infection in this trial (2007)
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Part 3
Spatial model predictions
Distributions of infected plants at
harvest (%)
• 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
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Part 3
Conclusion (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
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General conclusion
1 dPSS
  PSS   ( z  1)[ PSS  PSSS ]
2 dt
dPSI1
  PSS  (    1 ) PSI1   ( z  1)[ PSI1  PSSI1  PSS  PSSS ]
dt
dPSI 2
 1 PSI1  (    2 ) PSI2   ( z  1)[ PSI 2  PSSI 2 ]
dt
dPSD
 2 PSI2  (   ) PSD   ( z  1)[ PSD  PSSD ]
dt
1 dPI1I1
 (   ) PSI1  1 PI1I1   ( z  1)[ PSI1  PSSI1 ]
2 dt
dPI1I 2
 (   ) PSI2  1 PI1I1  (1  2 ) PI1I 2   ( z  1)[ PSI 2  PSSI 2 ]
dt
dPI1D
 (   ) PSD  2 PI1I 2  1 PI1D   ( z  1)[ PSD  PSSD ]
dt
1 dPI 2 I2
 1 PI1I 2  2 PI 2 I 2
2 dt
dPI 2 D
 2 PI 2 I 2  1 PI1D  2 PI 2 D
dt
dPDD
 2 PI 2 D
dt
4
Prob( S t  I t+dt )   s,k (t  tinf, k , x) dt
k 1
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General conclusion
Soilborne disease epidemics
• 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
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General conclusion
Control of soilborne disease epidemics
• 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
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General conclusion
Perspectives
• 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)
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• Doug Bailey
• Philipe Lucas – Thierry Doré – João Filipe
Merci…
• 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)
Mon bureau…avant-hier
• 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…
Introduction
Evolution of symptoms
41
Introduction
The pathogen: R. solani
Rate of primary infection
 Maximum rate 
p  

 of infection (a p ) 
 Spatial decline due to

 location of inoculum away

from host ( p )






 Time decline due to 


 source of nutrients 
 decline ( ) 
p


 Delay in 
 onset of 


 infection ( ) 


Rate of secondary infection



(as ) 
Maximum rate
s  
of infection

 Spatial decline due to
 location of inoculum away


from host ( s )

  Delay in 
  onset of 


  infection ( ) 


Rates of infection and pathozones
dPp ( x, t )
  p ( x, t )[1  Pp ( x, t )]
dt
dPs ( x, t )
 s ( x, t )[1  Ps ( x, t )]
dt
Pathozones P(x,t)
x: contact distance
t: time of exposure
Infer parameters from pair experiment data
ninf: number of infected recipients
ninf ( x, t ) ~ Binomial (ntot , P( x, t ))
ntot: number of replicates (25) 42
Part 2
Incubation period ?
• Periods in Natural history of disease in a host – these are incorporated as compartments in
epidemiological models
Latent/Exposed
Incubation
Infectious
Recovered
Disease
Disease
Incubation
Disease
Pathological status
Incubation
time of infection
Infectious status
Susceptible
time since
infection
• 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)
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Introduction
Host growth and dynamic contact distances
• Increase in the radius h(t)
• Radial growth measured with Pepista tools (ITB)
• Simple empirical model
h(t )  5 / [1  1000exp(1.18* t 0.4 )]
• Dynamic of the contact distance between
nearest neighbours xee(t)
xee (t )  xcc  h(t )
• Static centre-centre distance xcc
xee (t )  xcc  1.5 h(t ) , if 70  tinf < 90
, if 30 < tinf < 70
xee (t )  xcc  2 h(t ) , if 90  tinf
• Spatial population model
• 30*30 square lattice
• t0= 30 days
• 5% infected
4
Prob( S t  I t+dt )   s,k (t  tinf, k , x) k (t ) dt
k 1
 x  xcc

xee (t )
 x  44
Part 3
First results
Previous epidemiological
model
Detectable/
symptomatic
Force of infection
 dS
 dt    (t ) X   (t ) I (t ) S (t )

 dI   (t ) X   (t ) I (t ) S (t )
 dt


D   I
 (t )   exp( t )
1
2

  (t )  1 exp(0.5[log(t / 3 ) /  2 ]2 )
Infected
Assumptions
• Mean field mass action/homogeneous
mixing assumption
• Epidemics initiated too soon
Rate of primary
infection
• Pre-emergence damping off
• Unrealistic incubation period
Motisi et al., 2012
45