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					      Use of ecophysiological approaches and
             biophysic plant modelling
  in determination of complex phenotypic traits
         and analysis of interactions GxE




Pr. Jérémie LECOEUR
Professor of Plant Biology
Director of Plant Science Department
Montpellier SupAgro
1. Context
Context : a need to understand the building of the plant phenotype

The plant phenotype is always a complex object resulting from the spatial
and temporal integration of various biological processes  « Integrated
Plant Phenotype »


Integrated plant phenotype: Plant traits resulting of the integration of the
major plant functions in response to environment.

                                                                    Corresponding
An example of an « Integrated Plant Phenotype »:          Picture    Virtual plant

The architecture of the At rosette                  Col


   This integrated phenotype results from:
        • organogenesis
                                                    se
        • morphogenesis
        • carbon metabolism…
   in interaction with the environment
                                                    rot
Context : a need to understand the building of the plant phenotype

The plant phenotype is always a complex object resulting from the spatial
and temporal integration of various biological processes  « Integrated
Plant Phenotype »


Integrated plant phenotype: Plant traits resulting of the integration of the
major plant functions in response to environment.




    Genotype x    Environment   =    Responses                   =   Phenotype
                                    Response         genotype 2
                                               genotype 1
              x                 =                                 =

                                               Environment
Context : a need to understand the building of the plant phenotype


Choice of the plant representation

Process based models (crop models)   Ecophysiological modelling
                                     Organ populations in relation with environment
                  fruits             through correlative relationships




                                                                  Response
                                                                                      géno 2




                                                              
                                                                             géno 1
                 Leaves
                                                          =
                  roots                                                      Environment


Genetic modelling                    « Virtual plants »
Mainly statistical approaches        Set   of    phytomeres     with              topological
                                     connections with matter flows

   phenotype = G + E + GxE + e
 Context : a need to understand the building of the plant phenotype

The plant is a complex system = a large number of sub-units with the
same organisation and topological connection resulting in a network


Purslane plant                               Cell protein tree




                                             (d’après Jeong, 2003)


The same level of complexity could be find at organelle, cell, tissue…
Context : a need to understand the building of the plant phenotype


Theory of the increase in scientific progress through combinatories
of conceptual and technic artefacts (Lebeau, 2005)



 A postulate ?
 «The only way to make significant progress in understanding the
 genotype - environment interaction is to associate several scientific
 disciplines»

 The needed scientific disciplines would be:
        - genetic and genomic,
        - plant biology and plant physiology,
        - ecophysiology and biophysic
        - applied mathematics,
2. Advances in Ecophysiology
Step 0 : Characterization of the physical
      environment at plant boundaries
                                                    Advances in Ecophysiology

The absolute necessary to take into account the physical environment


Systematic characterization of plant microclimate
       In field                  The minimum data set includes
                                 temperature, radiation and atmospheric
                                 humidity, wind speed and rainfall




                                   In growth chamber



To allow the comparison between experiments and the establishment of
trial network typologies or a future use of models
                                                                            Advances in Ecophysiology

To be as close as possible to the microclimate sensed by the plant or
                            by its organs

First use of modelling: to estimate the environmental variables
instead of measuring them.

 To model the energy, radiative and water balances….




     (from Rey, 2003; Lhomme and Guilioni, 2004 and 2006; Chenu et al., 2005 and 2007; Louarn et al., 2007)
                                                                                                                                                                                                Advances in Ecophysiology

To be as close as possible to the microclimate sensed by the plant or
                            by its organs

To identify the environmental variables quantitatively related to
plant development and growth.


           For instance, what is the                                                                            radiative                                                        variable well related              to    the
           organogenesis on At?
                                0.10                                                                 0.10
Vitesse d'initiation (°Cj -1)




                                                                     Vitesse d'initiation (°Cj -1)




                                                    Incident PAR                                                              Light quality                                                    Absorbed
                                                                                                                                              (R/FR - Blue)                                      PAR
                                0.05                                                                 0.05                                     2.5
                                                                                                                 Densité de flux de photons




                                                                                                                                                      10.8 mol m-2 j-1
                                                                                                                                                      5.2 mol m-2 j-1
                                                                                                                    (µmol m s nm )




                                                                                                                                              2.0
                                                                                                                                     -1




                                                                                                                                                      2.5 mol m-2 j-1

                                                                                                                                              1.5
                                                                                                                             -2 -1




                                                                                                                                              1.0

                                                                                                                                              0.5

                                                                                                                                              0.0
                                                                                                                                                    400        600       800     1000

                                                                                                                                                          Longueur d'onde (nm)


                                0.00                                                                 0.00
                                       0   2    4     6   8    10    12                                 0.0 0.2 0.44 0.6 6 0.8 8 1.0 10 12
                                                                                                          0   2                       1.2 1.4                                                  0.01      0.1       1       10
                                           Incident PAR (mol m-2-1d-1)
                                                              -2
                                                                                                               PAR incident (mol plt-1-1)-1
                                                                                                            Absorbed PAR (mmol m-2 -1 d-1)                                                    Absorbed PAR (log ) [échelle
                                                                                                                                                                                        PAR absorbé (mmol plte-1 j-1scale) log]
                                           PAR incident (mol m j )                                           PAR absorbé (mmol plte j )
                                                                                                                                     j

                                                                                                                                                                                                      (from Chenu et al., 2005)
                                                  Advances in Ecophysiology

To be as close as possible to the microclimate sensed by the plant or
                            by its organs

A lot can be done by using standard bioclimatological indicators…



Thermal time,
Cumulative solar radiation,
Photothermal coefficient,
Climatic water balance…
Step 1 : Ecophysiologic diagnosis of the
          phenotypic variability

  To dissect the genotype – environment interaction
                                                        Advances in Ecophysiology

      Second use of modelling: formalization of plant – environment
               interaction to identify unknown phenotypes

  Analysis of a panel of wild types and their mutants in At

    Wild type

                 Col       Ws    Ler   Dij




     mutants     se        3.5   ron



                 rot




(from Chenu et al, 2007)
                                                                                                                      Advances in Ecophysiology

        Second use of modelling: formalization of plant – environment
                 interaction to identify unknown phenotypes
                                                                                                                               All wild type
           0.15                                                                                                        0.15
                  Col                       Ws                        Ler                     Dij
           0.10                                                                                                        0.10

           0.05                                                                                                        0.05

           0.00                                                                                                        0.00
                  se                        3.5                       ron                       0.01   0.1   1   10       0.001 0.01   0.1   1   10
           0.10

           0.05

           0.00
                                              0.01     0.1   1   10     0.01   0.1   1   10
           0.10

           0.05

           0.00
              0.001 0.01   0.1     1   10

                  Comparison wild types vs corresponding mutants                                                              All genotypes
           0.15                                                                                                        0.15
                  Col / se / rot            Ws / 3.5                  Ler / ron                                               Génotypes
           0.10                                                                                                        0.10

           0.05                                                                                                        0.05

           0.00                                                                                                        0.00
              0.001 0.01   0.1     1   10     0.01     0.1   1   10     0.01   0.1   1   10                               0.001 0.01   0.1   1   10

                                                                                     -1 -1
                                                     Absorbed PAR (mmol plte j ) [log scale]

(from Chenu et al, 2007)
                                                                                                                                                                       Déficit hydrique
  Establishment of consistent
                                                                                                                                                                                                                                                                                 Rayonnement
                                                                                      Température
                                                                                                                                                                         édaphique                                                                                                 absorbé


  relatioship betwen plant and




                                                                                                                              Vitesse relative d'expansion
                                           Vitesse relative d'expansion
                                                                          1.0
                                                                                                              a                                                1.0
                                                                          0.8                                                                                  0.8


      environment variables
                                                                          0.6                                                                                  0.6
                                 Pois
                                                                          0.4                                                                                  0.4
                                                                          0.2                                                                                  0.2
                                                                                                                                                                                                   b
                                                                          0.0                                                                                  0.0
                                                                                0        10      20      30         40                                               0.0   0.2   0.4   0.6   0.8       1.0

                                                                                    Température des feuilles (°c)                                                                 FTSW




                                                                                                                                                                                                                                      Vitesse relative d'expansion
                                                                                                                           Vitesse relative d'expansion
Response curve families
                                                                                                                                                               1.0                                                                                                    1.0
                                                                                                                                                               0.8                                                                                                    0.8
                                 Tournesol                                                                                                                     0.6                                                                                                    0.6
                                                                                                                                                               0.4                                                                                                    0.4

                                                                                                                                                                                                   c                                                                  0.2
                                                                                                                                                                                                                                                                                                               d
For instance, leaf expansion…
                                                                                                                                                               0.2
                                                                                                                                                               0.0                                                                                                    0.0
                                                                                                                                                                     0.0   0.2   0.4   0.6   0.8   1.0                                                                       0       10      20         30         40

                                                                                                                                                                                  FTSW                                                                                              PARa (m-2 mol j-1)




                                                                                                                             Vitesse relative d'expansion
                                                                                                                                                               1.0
                                                                                                                                                               0.8
                                                                                                                                                               0.6
                                 Vigne
                                                                                                                                                               0.4
                                                                                                                                                               0.2
                                                                                                                                                                                                   e
                                                                                                                                                               0.0
                                                                                                                                                                     0.0   0.2   0.4   0.6   0.8       1.0

                                                                                                                                                                                  FTSW




                                                                                                                                Vitesse relative d'expansion
                                                                                                                                                               1.4




                                                                                                                                                                                                                     RER (mm2 mm-2 °Cj-1)
                                                                                                                                                               1.2                                                                                                   0.06
                                                                                                                                                               1.0
                                                                                                                                                               0.8                                                                                                   0.04
                                 Laitue                                                                                                                        0.6
                                                                                                                                                               0.4                                                                                                   0.02
                                                                                                                                                               0.2                                 f                                                                                                          g
                                                                                                                                                               0.0                                                                                                   0.00
                                                                                                                                                                     0.0   0.2   0.4   0.6   0.8       1.0                                                                    0.1      0.2        0.3        0.4

                                                                                                                                                                                  FTSW                                                                                               PARa (mol j-1)
                                                                                                                                                                                                                                                              0.050




                                                                                                                                                                                                             RER (mm2 mm-2 °Cj-1)
                                                                                                                                                                                                                                                              0.045
                                 Arabidopsis                                                                                                                                                                                                                  0.040
                                 thaliana
                                                                                                                                                                                                                                                              0.035
                                                                                                                                                                                                                                                                                                              h
                                                                                                                                                                                                                                                              0.030
                                                                                                                                                                                                                                                                                0.001
                                                                                                                                                                                                                                                                            0.000       0.003
                                                                                                                                                                                                                                                                                    0.002       0.005
                                                                                                                                                                                                                                                                                            0.004   0.006

                                                                                                                                                                                                                                                                                     PARa (mol j-1)




                                                                                                                         Vitesse relative d'expansion
                                                                                                                                                               1.0
                                                                                                                                                               0.8

                                 Haricot                                                                                                                       0.6
                                                                                                                                                               0.4
                                                                                                                                                               0.2                                 i
                                                                                                                                                               0.0
                                                                                                                                                                     0.0   0.2   0.4   0.6   0.8   1.0

                                                                                                                                                                                  FTSW
                                                      Advances in Ecophysiology

        Second use of modelling: formalization of plant – environment
                 interaction to identify unknown phenotypes



                    Columbia
                    Serrate




                                            Vini = aini log(PARa) + bini


 This approach allowed to identify a new
 involvement of the Serrate gene in plant         G       GxE            G
 organogenesis.


(from Chenu et al., 2007)
                                                         Advances in Ecophysiology

      Time consuming ecophysiological measurements require
     « industrial phenotyping » or a large field trail network

It will be necessary to increase by 10 to 100 the number of
characterized experimental situations




                                (From Joined Unit LEPSE – INRA / SupAgro, 2006 report)
Step 2 : To quantify the impact of the
    observed phenotypic differences
                                                        Advances in Ecophysiology

 Third use of modelling: to analyse the consequences of multi-trait
            differences on integrated plant phenotypes

The sensitivity analyses allow to rank the traits in term of their
quantitative effects on the integrated phenotype.


 An example: phenotypic variability in light interception in sunflower during
 seed development.

 Among a panel of 20 genotypes, the following phenotypic differences were
 observed:
         - plant leaf area,
         - individual leaf area,
         - leaf number,
         - leaf size distribution along the stem,
         - blade angle,
         - duration of leaf life.
                                                 Advances in Ecophysiology

 Third use of modelling: to analyse the consequences of multi-trait
            differences on integrated plant phenotypes


Virtual sensitivity analysis of                                  Changes in
                                                               position of the
light interception to various                                  largest leaf on
phenotypic traits                                                 the stem




                                                                 Changes in
                                                                 plant leaf
                                                                    area




         Average virtual
             plant                                               Changes in
                                                                leaf number




(from Casadebaig, 2004)
                                            Virtual plot at flowering (6.6 plants m-2
  Estimation of light                       cv Heliasol)
     interception




                                      1.2
                                                                                                    Y = 0.98 X + 0.01
                          Estimated    1                                                               R2 = 0.993


                                      0.8
                                             Fraction of radiation intercepted   1.0

                                      0.6                                        0.8


                                      0.4                                        0.6


                                      0.2                                        0.4                      ei                               Ei




                                                                                 0.2
                                       0
                                            0                                    0.0
                                                                                  0.2   0.4   0.6      0.8      1       1.2
                                                                                                             Days
Sunflower virtual plant                                                                  Measured
cv Heliasol                                                                                                   (from Rey, 2003; Casadebaig, 2004)
                                                                                                                                Advances in Ecophysiology

Third use of modelling: to analyse the consequences of multi-trait
           differences on integrated plant phenotypes
Sensitivity analysis                                                                                                             (from Casadebaig, 2004)


                                                                      Plant leaf area
                                                                      Leaf number
      Changes in light interception



                                                         200

                                                                      Position of the largest leaf on the stem
                                                                      Plant heigth
                               (in % of average plant)




                                                                      Duration of leaf life
                                                                      Blade angle
                                                         150
                                                         100
                                                         50




                                                               -400                     -200                     0       200     400

                                                                         Evaluated ranges of variation in observed traits
                                                                                                  (in % of the average value)

A hidden trait affecting the light interception was identified: the distribution
of leaf sizes along the stem
                                                                                                                                                               Relative leaf irridi
                                                                                                                                                                                                                              Advances in Ecophysiology
                                                                                                                                                                                                        85

                                                                                                            level in At?
                                                                              Emerging properties at plant Exp. 1
                                                                                                                                                                                                              Exp. 2
                                                                                                                                                                                                        80
                                                                                                                                                                                                              Exp. 3


The changes in organogenesis, organ expansion-0.78and r² morphology lead to
                                                  Y=     X + 92; = 0.618


                                            improved in 4response to reductions in
unexpected property: the life irradiance is 75  0   2           6     8  10      12 14 16
incident light                                        Incident PAR (mol m-2 d-1)
                                                                                                                                                                                                        10




                                                                                                                     Effect on light interception efficiency
                                                       95

                                                                                                                                                                                                        8




                                                                                                                                                               (relatively to the standard treatment)
                        Relative leaf irridiance (%)




                                                       90                                                                                                                                               6


                                                                                                                                                                                                        4

                                                       85
                                                                                                                                                                                                        2

                                                                Exp. 1
                                                                Exp. 2                                                                                                                                  0
                                                       80
                                                                Exp. 3
                                                                                                                                                                                                        -2
                                                                Y = -0.78 X + 92; r² = 0.618                                                                                                                 Overall    Petiole    Leaf   Phenology
                                                                                                                                                                                                             effects    length    shape     delay
                                                       75                                                                                                                                               -4
                                                            0     2       4      6       8     10   12   14     16

                                                                      Incident PAR (mol m-2 d-1)                                                                                                                   Nature of effects analyzed
                                                       10
 erception efficiency




                                                                                                          (b)
                                                       8                                                                                                                                                               (adapted from Chenu et al., 2005)
                        standard treatment)




                                                       6


                                                       4
                               Change with time in trophic competition inside the grapevine shoot



                                                                                                                                • 3 phases

                                                         0C                                    6C
                                         A                                     B                                                1- decrease in trophic
                              0.25

                              0.20                                                        F                  V                  competition due to the
                                                                                                                                increase in sources
                              0.15                                                                               'GRENACHE N'
                                             1            2           3a           1            2          3b
Q/D ratio (arbitrary units)




                              0.10
                                                                                                                                2- Increase in trophic
                              0.05
                                                                                                                                competition due to rapid
                              0.00
                                         C                                     D
                                                                                                                                production of new sinks
                              0.25
                                                                                                                                3-(0C)- Decreasein
                              0.20                                                         F                 V
                                                                                                                                trophic competition due
                              0.15                                                                               'SYRAH'        to the end of secondary
                                             1            2            3a          1            2          3b
                              0.10                                                                                              axes development
                              0.05

                              0.00
                                                                                                                                3-(6C)- Increase trophic
                                     0       200   400   600     800 1000 1200
                                                                            0      200   400   600   800 1000 1200              competition due the
                                                               Thermal time from budburst (°Cd)                                 second growth phasis of
                                                                                                                                clusters
                     Relationship between axis development and trophic competition



             Relationship between Q/D values and the probability of end of secondary axes development
  Probability to maintain the




                                          Primary axes                         P0 secondary axes                  P1- P2 secondary axe
                                1.0
        development




                                0.8
                                0.6             Sigmoidial adjustment
                                                Syr 0C
                                0.4             Syr 6C
                                                Gre 0C
                                0.2             Gre 6C

                                0.0
                                      A                                   B                                 C
                                  0.00 0.05 0.10 0.15 0.20 0.25                           0.00 0.05 0.10 0.15 0.20 0.25
                                                              0.00 0.05 0.10 0.15 0.20 0.25
                                                                        Q/D ratio (arbitrary units)


• Primary axes are not affected by the trophic competition
                                                                                                      1.0

                                                                                                      0.8

• Secondary axis are affected by the trophic competition                                              0.6


• A single sigmoidal relationship P=f(Q/D).
                                                                                                      0.4                     Primary axis
                                                                                                                              P0 secondary axis
                                                                                                      0.2
                                                                                                                              P1-P2 secondary axis

• A difference in sensitivity according to the type of axes                                           0.0
                                                                                                        0.00    0.05   0.10     0.15    0.20    0.25
     Relationship between axis development and trophic competition
Relationship between Q/D values and the probability of end of secondary axes
development according to their type and size



       1.0 A
             1-5
       0.8
       0.6                   1-5 leaves
       0.4                    (0.31g)
       0.2
       0.0 B
       1.0
             6-10
       0.8
       0.6                   6-10 leaves
                             (2.87g)
       0.4
       0.2
       0.0 C
       1.0
             11-16
       0.8                   11-16 leaves
       0.6                   (10.21g)
                        P0 secondary axes
       0.4              P1-P2 secondary axes
                        P1-P2 sigmoid adjustment
       0.2              P0 sigmoid adjustment
       0.0
         0.00 0.05 0.10 0.15 0.20 0.25
               Q/D ratio (arbitrary units)
3. The front of « modelling experiences »
  Step 3 : To model the impact of genotypic
   variability on the plant phenotypic plasticity

To associate various kind of models to predict the integrated plant
                              phenotypes
                                                     The front of modelling experiences


                 To evaluate the genotype performances

The biophysical modelling approaches are now enough tried and tested to be
revisited to predict the genotype – environment interaction.


The available modelling approaches (not exhaustive):
        - biophysical balances,
        - crop models,
        - ecophysiological descriptions of regulations and signals in plants,
        - 3D architectural plant and canopy models,
        - mathematical models to estimate parameters in complex systems…
                                                                                                                                      The front of modelling experiences

                               To evaluate the genotype performances

                                          Construction of dedicated models

  Flow chart of potential yield estimation in sunflower
                                                                              Rendement en graines
                                  Fin
                                                                          MSgraine = MScapi x HI_grainegen
     Input data                                                                                                                oui

                                        Temps thermique depuis la levée                                                                             TT>TT_M3gen
                                                                                        Données climatiques
     Phenology                                  t i
                                          TTi (Tmoy Tbase)dt                         Tmoy           Tmin                          non
                                               levée                                    Tmax           PARi
     Architecture (3D)
                                                                                                                                                        Biomasse du capitule
                                           Phénologie
     Light interception (3D)               TT_E1gen           TT_F1gen                                                          TTi<TT_E1        MScapii = 0
                                           TT_M0grn           TT_M3gen
                                                                                                                                                                 0,632
                                                                                                                                                                                 
                                                                                                                                                 MScapi i                         2.83    MSi
                                                                                                                                                          1 TTiTT_E1gen
                                                                                                                                TTi<TT_M3
     Biomass production           Nombre de feuilles à fin expansion                                                                                             774
                                                                                                                                MScapi >= MSi x HI_capigen MScapi = MSi x HI_capigen
     Biomass partitioning         NF<NFfinalgen NF = Phyllochronegen x TTj
                                                NF=NFfinalgen
                                                                                                                                                     Biomasse aérienne totale
                                                                                                                                                        MSi= MSi-1+dMSi
                                                 Rang de la dernière feuille morte
                                                                               TT_M3 genTT i
                                                  NFmorte  NFfinal gen  
                                                                           TT_M3 genTT_M0
                                                                                                          
                                                                                                          
                                TTi>TT_M0gen                                                       gen                                        Production journalière de biomasse
                                                                                                                                                        dMSi = eb x ei x PARi


                                               Surface foliaire de la plante produite                                                                   Efficience biologique
                                                          jNF
                                    SF plante_p roduite               aSF gen               dj                                                           ebi = ebpoti x FTi
                                                                              
                                                                                bSF gen j 
                                                           j0
                                                               1exp(4cSFgen
                                                                               aSF gen 
                                                                                           
                                                                                           )
                                                                                          

                                                                                                                                                         Facteur thermique
                                               Surface foliaire sénescente                                                                 FTi = 1 – 0,0025 (0,25 Tmin + 0,75 Tmax –25)²
                                                        k NFmorte
                                  SFplante_s énescence                    aSF gen             dk
                                                                   1exp(4cSFgen bSF genk )
                                                                                            
                                                            k 0                            
                                                                                            
                                                                                  aSF gen 
                                                                                                                                 Efficience biologique potentielle
                                                                                                                                 TTi<TT_E1gen,     ebpoti = 1 TT_F1 - TTi 
                                                                                                                                                           1                        (e -1)
                                                                                                                                                                            gen

                                                                                                                                                   ebpoti =  TT-F1 -TT_E1   TT TT_ M0
                                                                                                                                                                                        bgen
                                                                                                                                                                      gen         gen
                                            Surface foliaire de la plante                                                        TTi<TT_F1gen,                                                                       
                                                                                                                                                                    0 ,3 8  e x p( 2 ( 1 - 
                                                                                                                                                                                                   i         gen
                                                                                                                                                                                                                     
                                SFplante = SFplante_produite – SFplante_sénescente                                               TTi<TT_M0gen,     ebpoti = ebgen                            TT_ M3 -TT_ M0
                                                                                                                                                                                                       gen           
                                                                                                                                                                                                                   gen




                                                   Indice foliaire                                 Efficience d’interception     TTi<TT_M3gen,     ebpoti = ebgen x
                                               LAI = dens x SFplante                           ei = 1 – exp ( - kgen x LAIi)
(adapted from Lecoeur et al., 2008)
                                                                                                                                      The front of modelling experiences

                               To evaluate the genotype performances

                                          Construction of dedicated models

  Flow chart of potential yield estimation in sunflower
                                                                              Rendement en graines
                                  Fin
                                                                          MSgraine = MScapi x HI_grainegen
     Input data                                                                                                                oui

                                        Temps thermique depuis la levée                                                                             TT>TT_M3gen
                                                                                        Données climatiques
     Phenology                                  t i
                                          TTi (Tmoy Tbase)dt                         Tmoy           Tmin                          non
                                               levée                                    Tmax           PARi
     Architecture (3D)
                                                                                                                                                        Biomasse du capitule
                                           Phénologie
     Light interception (3D)               TT_E1gen           TT_F1gen                                                          TTi<TT_E1        MScapii = 0
                                           TT_M0grn           TT_M3gen
                                                                                                                                                                 0,632
                                                                                                                                                                                 
                                                                                                                                                 MScapi i                         2.83    MSi
                                                                                                                                                          1 TTiTT_E1gen
                                                                                                                                TTi<TT_M3
     Biomass production           Nombre de feuilles à fin expansion                                                                                             774
                                                                                                                                MScapi >= MSi x HI_capigen MScapi = MSi x HI_capigen
     Biomass partitioning         NF<NFfinalgen NF = Phyllochronegen x TTj
                                                NF=NFfinalgen
                                                                                                                                                     Biomasse aérienne totale
                                                                                                                                                        MSi= MSi-1+dMSi
                                                 Rang de la dernière feuille morte
                                                                               TT_M3 genTT i
                                                  NFmorte  NFfinal gen  
                                                                           TT_M3 genTT_M0
                                                                                                          
                                                                                                          
                                TTi>TT_M0gen                                                       gen                                        Production journalière de biomasse
                                                                                                                                                        dMSi = eb x ei x PARi


                                               Surface foliaire de la plante produite                                                                   Efficience biologique
                                                          jNF
                                    SF plante_p roduite               aSF gen               dj                                                           ebi = ebpoti x FTi
                                                                              
                                                                                bSF gen j 
                                                           j0
                                                               1exp(4cSFgen
                                                                               aSF gen 
                                                                                           
                                                                                           )
                                                                                          

                                                                                                                                                         Facteur thermique
                                               Surface foliaire sénescente                                                                 FTi = 1 – 0,0025 (0,25 Tmin + 0,75 Tmax –25)²
                                                        k NFmorte
                                  SFplante_s énescence                    aSF gen             dk
                                                                   1exp(4cSFgen bSF genk )
                                                                                            
                                                            k 0                            
                                                                                            
                                                                                  aSF gen 
                                                                                                                                 Efficience biologique potentielle
                                                                                                                                 TTi<TT_E1gen,     ebpoti = 1 TT_F1 - TTi 
                                                                                                                                                           1                        (e -1)
                                                                                                                                                                            gen

                                                                                                                                                   ebpoti =  TT-F1 -TT_E1   TT TT_ M0
                                                                                                                                                                                        bgen
                                                                                                                                                                      gen         gen
                                            Surface foliaire de la plante                                                        TTi<TT_F1gen,                                                                       
                                                                                                                                                                    0 ,3 8  e x p( 2 ( 1 - 
                                                                                                                                                                                                   i         gen
                                                                                                                                                                                                                     
                                SFplante = SFplante_produite – SFplante_sénescente                                               TTi<TT_M0gen,     ebpoti = ebgen                            TT_ M3 -TT_ M0
                                                                                                                                                                                                       gen           
                                                                                                                                                                                                                   gen




                                                   Indice foliaire                                 Efficience d’interception     TTi<TT_M3gen,     ebpoti = ebgen x
                                               LAI = dens x SFplante                           ei = 1 – exp ( - kgen x LAIi)
(adapted from Lecoeur et al., 2008)
                                                                                                        The front of modelling experiences
                                               To evaluate the genotype performances

           Estimation of a productivity index from the genotypic traits
                                              180

                                                         y = 0,997x
                                                         r² = 0,934
                 Observed productiviy index

                                              160
                                                         RMSE = 16,4%
                                              140


                                              120


                                              100


                                               80


                                               60


                                               40


                                               20
                                                    20     40     60        80     100     120    140      160    180

(from Lecoeur et al., 2008)                                            Estimated productivity index


A simple biophysic model allows to take into account from 80 to 90% of the
observed phenotypic variability in potential yield among a panel of 30 genotypes.
                                                                                                                 The front of modelling experiences
                        To evaluate the genotype performances
A sensitivity analysis allowed to quantify the impact on plant productivity of the
genotypic traits                                                                   C1 C
                                                                                           Total


                                                                          Biomass partitioning
                                                                                Photosynthesis
                                                                                    Architecture



                              Yield coefficient of variation
                                                                                     Phenology


                                                                                  Harvest index
                                                               Biomass allocation to capitulum
                                                                       Radiation use efficiency
                                                                   Light interception coefficient
                                                                        Area of the largest leaf
                                                                     Position of the largest leaf
                                                                                 Plant leaf area
                                                                                   Leaf number
All the major functions                                             Phytomere production rate

contributed       to      the                                                  M3 thermal time

productivity variability.                                                      M0 thermal time
                                                                                F1 thermal time

Classical ANOVA detected                                                    E1 thermal thermal

only the contribution of the                                                                   0.000   0.050    0.100      0.150       0.200    0.250   0.300

harvest index                                                                                                  Genotypic traits or trait sets

(from Lecoeur et al., 2008)
     Reminder : first setting of the biomass partitioning model (Greenlab)
     Objective : to understand the genotype variability of harvest index



  Fitting on experimental data on 4 genotypes



  Leaf             Sink strengths : petiole < leaf < stem < capitulum
  area

                                                                      0,45 < 1,00 < 1,07 < 3000

 Leaf
biomass                                                                                                                 biomass production and partitioning
                                                                                                                               along growth cycles

             petiole we are
        Actually,sink variation combining SunFlo (crop model) with                        biomass production
                                                                                                               20
                                                                                                                                 Biom Tot
                                                                                                                                 internode

         GreenLab (FSPM) in order to analyse the genotypic
                        0.020
                                                                                                               15                blade


                          variability of harvest index
                                                                                                                                 petiol
Leaf sink
           sink value




                                                                                                               10
                        0.015                                                                                                    Flow er

strength
                                                                                                                5
                        0.010
                        0.005                                                                                   0

                        0.000                                                                                       1   7   13   19 25    31 37 43   49 55   61 67 73 79 85   91 97 103 109 115 121 127 133
                                1
                                    9
                                        17
                                             25
                                                  33
                                                       41
                                                            49
                                                                 57
                                                                      65
                                                                           73
                                                                                81
                                                                                     89




                                                                                                                                                     grow th cycles
                                             cycle of expansion

                                                                                                                                                                 (d’après Rey et al., 2006)
                                                  The front of modelling experiences

 First attempt in combining genetics modules and crop model to test the
               potentialities of a virtual breeding on index

Sunflo, a crop model including :
• A description of plant compartiments (vegetative parts, reproductive parts,
roots),
• A description of main processes (organogenesis, morphogenesis,
photosynthesis, biomass partitioning),
• Responses to temperature, solar radiation and water availability.
• Each genotype is described by a set of 15 to 20 traits


Quantitative Genetics Modules :
• Estimation of genetic correlation between phenotypic traits,
• Estimation of heritabilities,
• Choice of selection pressure on the traits according             the    target
environnement,

Applying several selection cycles resulting in population with new phenotypic
characterics. The performance of each new genotype is tested in various
environnement. This leads to estimate the potential genetic progress.
3. Potentialities and present limitations
                                 Conclusions

Potentialities

The past 10-20 years plant modelling could be now an effective tool to analyse
and model the genotype – environment interaction:

    • Estimations of microclimate variables
    • Modelling plant responses to environment
    • Ranking plant traits in term of quantitative impact on phenotypic
    variability
    • Predictions of integrated plant phenotypic

The links between concepts and methologies from various disciplines may
increase the progress in understanding integrated plant phenotypes.
                                  Conclusions

Present limitations

• Low spreading of the biophysical modelling culture.

• Heavy cost of phenotypic information.

• Lack of applied mathematic adapted to complex systems.

				
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