Dealing with the variability of biofumigation efficiency through epidemiological modelling

(1)

Dealing with the

variability in

biofumigation efficiency

through epidemiological

modelling

Natacha MOTISI

Melen LECLERC

5th In terna ti onal S ympos ium of Biofum ig ati on 9 -12 Sep temb er 2014

(2)

Plan

I. Modes of action of a biofumigant crop

II. Objectives

III. Experiments

IV. Modelling

a. Temporal modelling with a simple mechanistic model b. Spatially explicit model

(3)

Managing soilborne diseases by diversifying

crops in the rotation

March October- November March

Time Inoculum density Sugar beet Host Wheat Non host Sugar beet Host

I

_initial

I

_final 5th In terna ti onal S ympos ium of Biofum ig ati on 9 -12 Sep temb er 2014

(4)

5th In terna ti onal S ympos ium of Biofum ig ati on 9 -12 Sep temb er

2014

The intercrop period : action on soil inoculum

reservoir

March October- November March

Time Inoculum density Sugar beet Host Wheat Non host Sugar beet Host July - August

?

Intercrop period

I

_initial

I

_final

I

_{final 2}

I

_{final 1}

(5)

Managing the intercrop period

March October - November

Sugar beet Wheat Sugar beet

July- August March

White mustard

Allelopathic properties of Brassica intercrops

Intercrop period 5th In terna ti onal S ympos ium of Biofum ig ati on 9 -12 Sep temb er 2014

(6)

Set up of the biofumigation technics

Time August

Cropping

phase

Crushing and incorporating

residues

Sugar beet commercial crop + Irrigation October March 5th In terna ti onal S ympos ium of Biofum ig ati on 9 -12 Sep temb er 2014

(7)

Biofumigation efficiency after incorporation of

Brassica residues

– extract from Motisi et al. (2010)

Gaeumannomyces graminis var. tritici

Rhizoctonia solani Fusarium sp. Verticillium dahliae Davis et al., 1996

₊

Hartz et al., 2005

_-

₀

Kirkegaard et al., 2004

₊

Stephens et al., 1999

₀

Gardner et al., 1998

₊

-

Kirkegaard et al., 2000

₀

van Os et al., 2002

₀

Little et al., 2004

₀

Larkin et al., 2007

₊

0

Njoroge et al., 2008

₀

Snapp et al., 2007

₊

(8)

Plan

I. Modes of action of a biofumigant crop

II. Objectives

III. Experiments

IV. Modelling

(9)

Using an epidemiological framework

To explain the action of biofumigant crops on

soilborne diseases dynamics and

epidemiological mechanisms

To understand how biofumigation affects the

variability of epidemics and, thus, how it impacts

the uncertainty of the spread of disease in field

conditions

5th In terna ti onal S ympos ium of Biofum ig ati on 9 -12 Sep temb er 2014 II. Objectives

(10)

Plan

I. Modes of action of a biofumigant crop

II. Objectives

III. Experiments

IV. Modelling

(11)

How?

Field experiment

By disentangling the mechanisms of biofumigation

By monitoring disease spread over time

Modelling

Temporal mechanistic model Spatio-temporal model

Partial

biofumigation

+

Complete biofumigation

5th In terna ti onal S ympos ium of Biofum ig ati on 9 -12 Sep temb er 2014 III. Experiments

(12)

Partial

biofumigation

Complete

biofumigation

bloc I

bloc IV

bloc III

bloc II

18m 6m

The experiment

Partial

biofumigation Complete biofumigation

+

Motisi et al. (2009)

Control

Without mustard

III. Experiments

(13)

The pathosystem

Hidden epidemic: cryptic infections

Destructive sampling Necrosis

Visible epidemic: wilted plants

Non destructive sampling

Above ground Below ground wilting 5th In terna ti onal S ympos ium of Biofum ig ati on 9 -12 Sep temb er 2014 III. Experiments

(14)

Tracking epidemic progression in the field

5th In terna ti onal S ympos ium of Biofum ig ati on 9 -12 Sep temb er 2014 III. Experiments

(15)

Plan

I. Modes of action of a biofumigant crop

II. Objectives

III. Experiments

IV. Modelling

(16)

Initial inspection

of the disease progress

curves

0 2 4 6 8 10 12 0 500 1000 1500 2000 2500

Time (°C.days)

Wilted

plants

(%)

Control without mustard Partial biofumigation Complete biofumigation Secondary infections Primary infections Primary inoculum Motisi et al. (2013) 5th In terna ti onal S ympos ium of Biofum ig ati on 9 -12 Sep temb er 2014

(17)

Considering the dynamics of the pathogen

to be controlled

Primary inoculum Lesion extension Auto-infections Primary infections Allo-infections Secondary infections

Rhizoctonia solani on sugar beet

(18)

General modelling approach

Temporal dynamics

S

I

R

X

Primary infection rate α Secondary infection rate β Removal rate µ

SIR model

(Susceptible – Infected – Removed)

Kermack & McKendrick (1927) Van der Plank (1963)

(19)

S

I

D

X

Primary infection rate α Secondary infection rate β Detectability rate 𝛾

Adapting the SIR model to our pathosystem

SID model

Susceptible plants 𝑑𝑆 𝑑𝑡 = − 𝛼 𝑡 𝑋 𝑡 + 𝛽 𝑡 𝐼 𝑡 𝑆 𝑡 Infected plants 𝑑𝐼 𝑑𝑡 = 𝛼 𝑡 𝑋 𝑡 + 𝛽 𝑡 𝐼 𝑡 𝑆 𝑡 Detectable wilted plants

𝐷 = 𝛾𝐼 Motisi et al. (2013) 5th In terna ti onal S ympos ium of Biofum ig ati on 9 -12 Sep temb er 2014

(20)

Derivation of the model

0 2 4 6 8 10 12 0 500 1000 1500 2000 2500 Degrés-jours ( C) In c id e n c e « a p p a re n te » ( %) Time (°C.days) For c e of infec ti on Detec tabl e w ilted pl ants (% )

α

β

Primary infection rate

𝛼 𝑡 = 𝛼₁exp⁡(−𝛼₂𝑡) Secondary infection rate _{𝛽 𝑡 = 𝛽}₁_{exp −0.5 log 𝑡 𝛽}₃ _/𝛽₂ 2

Motisi et al. (2013) 5th In terna ti onal S ympos ium of Biofum ig ati on 9 -12 Sep temb er 2014

(21)

Results

Biofumigation

mostly reduces

primary

infections

Biofumigation can

affect secondary

infections with a

variable pattern

Motisi et al. (2013) 5th In terna ti onal S ympos ium of Biofum ig ati on 9 -12 Sep temb er 2014 _Detectable wilted plants Infected plants Primary infection rate Secondary infection rate

IV. a. Temporal modelling

Control without mustard Partial biofumigation Complete biofumigation

(22)

Discussion

Variability in efficiency of biofumigation to

control the rate of transmission of secondary

infection can explain the variability observed

among studies

(23)

Small differences in the initial growth of inoculum

combined to the non linear multiplicative effects

of secondary infections

can lead to great differences in the final size of

disease foci

(Kleczkowski et al., 1996) 5th In terna ti onal S ympos ium of Biofum ig ati on 9 -12 Sep temb er 2014

Discussion

(24)

Possible scenario

0.00E+00 1.00E-05 2.00E-05 3.00E-05 4.00E-05 0 500 1000 1500 2000 2500 T a u x d e tr a n s m is s io n rp 0.00E+00 1.00E-06 2.00E-06 3.00E-06 4.00E-06 0 500 1000 1500 2000 2500 T a u x d e tr a n s m is s io n rs 0 20 40 60 80 100 120 0 500 1000 1500 2000 2500 sol nu

Moutarde "résidus" taux initial x 1

N o m b re d e b e tt e ra v e s fl é tr ie s

Control without mustard

De tec tabl e wil ted pl an ts (% ) Ra te of primar y in fec ti on Ra te of sec onda ry in fec ti on Complete biofumigation Primary infection x1 Motisi et al. (2010) 5th In terna ti onal S ympos ium of Biofum ig ati on 9 -12 Sep temb er 2014

(25)

0.00E+00 1.00E-05 2.00E-05 3.00E-05 4.00E-05 0 500 1000 1500 2000 2500 T a u x d e tr a n s m is s io n rp 0.00E+00 1.00E-06 2.00E-06 3.00E-06 4.00E-06 0 500 1000 1500 2000 2500 T a u x d e tr a n s m is s io n rs 0 20 40 60 80 100 120 0 500 1000 1500 2000 2500 sol nu

Moutarde "résidus" taux initial x 1 Moutarde "résidus" taux initial x 2

N o m b re d e b e tt e ra v e s fl é tr ie s

Possible scenario

De tec tabl e wil ted pl an ts (% ) Ra te of primar y in fec ti on Ra te of sec onda ry in fec ti on Complete biofumigation Primary infection x2

Complete biofumigation Primary infection x1 Motisi et al. (2010) 5th In terna ti onal S ympos ium of Biofum ig ati on 9 -12 Sep temb er 2014

(26)

0.00E+00 1.00E-05 2.00E-05 3.00E-05 4.00E-05 0 500 1000 1500 2000 2500 T a u x d e tr a n s m is s io n rp 0 20 40 60 80 100 120 0 500 1000 1500 2000 2500 sol nu

Moutarde "résidus" taux initial x 1 Moutarde "résidus" taux initial x 2 Moutarde "résidus" taux initial x 3

N o m b re d e b e tt e ra v e s fl é tr ie s 0.00E+00 1.00E-06 2.00E-06 3.00E-06 4.00E-06 0 500 1000 1500 2000 2500 T a u x d e tr a n s m is s io n rs

Possible scenario

De tec tabl e wil ted pl an ts (% ) Ra te of sec onda ry in fec ti on Complete biofumigation Primary infection x2

Complete biofumigation Primary infection x1 Complete biofumigation Primary infection x3 Motisi et al. (2010) 5th In terna ti onal S ympos ium of Biofum ig ati on 9 -12 Sep temb er 2014 Ra te of primar y in fec ti on

(27)

Conclusions on the first model

First simple model

Good insight into epidemiological mechanisms

affected by biofumigation

Not allowed when looking only at the final stage of

disease development (harvest)

Good efficiency of biofumigation depends on first

efficacy on primary infections

Variability in efficiency of biofumigation on

secondary infections can provide variable results at

the field scale

(28)

New avenues

Why using spatially explicit

models for this pathosystem ?

→ predict accurately epidemic

development

Filipe & Gibson (2001)

How biofumigation affects the variability of

R. solani epidemics ?

Design of new modelling framework to predict the

spatio-temporal spread of R. solani

Use of stochastic model to predict the

variability/uncertainty of epidemics

(29)

Plan

I. Modes of action of a biofumigant crop

II. Objectives

III. Experiments

IV. Modelling

(30)

Spatial individual-based model with stochastic spread of the

pathogen

Host plants are at vertices of a regular lattice

SI model with primary and secondary infections

Structure of the stochastic spatially explicit

model for forecasting

(31)

Introduce a more realistic

incubation period (time between

hidden infection and detection of

above-ground symptoms) for

inferring epidemiological parameters

incubation period is

age-dependent

(Leclerc et al. 2014)

Statistical inference of

spatio-temporal parameters can be difficult

and time consuming…

Estimate spatial rates of infection

using a semi-spatial model

(Filipe et

al., 2004)

Estimation of « spatial parameters » from

temporal data

(32)

Model fitting and

estimated rates of

infection

Biofumigation reduced rates of primary and secondary infection in this trial (2007)

Rate of primary infection Rate of secondary infection 5th In terna ti onal S ympos ium of Biofum ig ati on 9 -12 Sep temb er 2014 Detec tabl e w ilted pl ants (% )

IV. b. Spatial modelling

Control without mustard Partial biofumigation

(33)

Spatial model predictions

Biofumigation provides 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 (%)

Partial biofumigation

Complete biofumigation

(34)

Conclusions on the second model

Analyses are consistent with previous results

obtained with the temporal model 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

(35)

Many thanks for your

attention

Bibliography linked to this work

Motisi N, Montfort F, Faloya V, Lucas P, Dore T, 2009. Growing Brassica juncea as a cover crop, then incorporating its residues provide

complementary control of Rhizoctonia root rot of sugar beet. Field Crops Research 113, 238-45.

Motisi N, Dore T, Lucas P, Montfort F, 2010. Dealing with the variability in biofumigation efficacy through an epidemiological framework. Soil Biology & Biochemistry 42, 2044-57.

Motisi N, Poggi S, Filipe JAN, et al., 2013. Epidemiological analysis of the effects of biofumigation for biological control of root rot in sugar beet. Plant Pathology 62, 69-78.

Leclerc M, Dore T, Gilligan CA, Lucas P, Filipe JAN, 2014. Estimating the Delay between Host Infection and Disease (Incubation Period) and Assessing Its Significance to the Epidemiology of Plant Diseases. Plos One 9, 15.