Projet de cooperation CiradAmis et Universite Chinoise dAgriculture

1
AMAP
The World ofVirtual Plants Modelling

• Philippe de Reffye Inria-Cirad

2
The goal of AMAP research unit

• Modeling plant architecture development
• morphogenesis plant topological structure
• ecophysiology plant size geometrical structure
• Simulating the 3D growth process
• Simulating plantenvironment interactions
• Applications in agriculture, forestry and
  environment

3
The need for virtual plants

• Virtual plants can help
• in developing and integrative approach of plant
  growth, including genetic and environment factors
• in assessing the environmental and technological
  quality of harvests and products
• in saving surface and time of field experiments
  and trials
• in designing efficient optimization strategies,
  in terms of cost, product quality, environmental
  consequences

4
Obtaining a virtual plant
By digitalization Coffea arabica
By simulation Coffea robusta
5
Growth of the Coffee tree
6
Modelling Transpiration

• Computing the transpiration of a virtual Plant

7
Virtual plantation concept

• Calibration on real experiment
• Functioning of virtual plantation
• Density optimisation

8
Computing light interceptionin a virtual
plantation
9
A Flight in a Palm tree plantation
10
Roots simulation of Palm tree
1 month 2 months
10 months
11
Virtual plants radar remote sensingModel
coupling
Thierry Castel
12
Simulation of competition for space in a spruce
grove
Spruce grove Top view from aboveBottom side
view Trees 1 and 3 are on the edge of the
stand, and undergo self-pruning on the
inside. Tree 2 is in the center and suffers
competition on all sides. Tree 4 is open grown.
13
Simulation of competition for space in a spruce
grove
14
Simulation of crownstem interactions
Tree 2
Tree 4
Radial growth at a point along the stem depends
on the amount of foliage situated above that point
15
Sawing simulation in a virtual stem
16
Building a virtual table
17
Modelling and simulation of growth stand
Tree in its forest environment AMAPpara
18
Modelling and simulation of growth stand
Tree in its forest environment AMAPpara
19
Treebiomechanicsgrowth model
20
Illumination of a scene using radiosity
Green-Bright software
21
Plant distortion local light effect
22
Virtual Landscapes
23
AMAP a 400 hundred plantData base for computer
graphicsand land scaping
24
AMAP Flowers
Iris Lis
orchidee
tulipe joncquille
25
AMAPbushes
Forsythia
cognassier
rosier
26
AMAPshrubs
Prunier
Albizia
Cypres
27
AMAPTrees
28
AMAPTrees
29
AMAPHorse Chestnut
30
AMAPPruning Horse Chestnut tree
31
Projet daménagement hotelier en Afrique
32
Imago metropolis synthetic land scape from G.I.S.
33
Shangai GVA
34
Lost lanscape (250 millions of years
35
Relevant qualitative and quantitative choices for
building an efficient Dynamic Plant Growth Model
GreenLab Case

• Philippe de Reffye1 and Bao.-Gang. Hu2
• 1CIRAD, INRIA, France
• 2Institute of Automation, Chinese Academy of
  Sciences, Beijing, 100080 China

36
Presentation

• Introduction
• Some considerations about plant architecture and
  plant functioning
• Relevant assumptions to build a efficient
  dynamical Model for Plants Growth and Plants
  Architecture
• A General Mathematical Formalism for Growth at
  the scale of plant Architecture
• The particular case of GreenLab model a
  dynamical formalism
• Applications of substructures algorithms in
  GreenLab
• GreenLab Model Behaviour
• Calibration of the model
• Optimisation and Control
• Plant Development Control

37
Qualitative and quantitative components of Yield

• Quantitative components
• - Number of organs -gt (architectural
  models)
• - Weight of organs -gt (Crop)
• Qualitative components
• - Size of organs density, allometry?
  Plasticity
• - Dry matter ratio in the organ biomass

38
Introduction to Plant Growth and Plant
Architecture modelling

• The Process Based Models for Agronomical issues
  (P.B.M) (computing Yield)
• The Geometric models for Computer Graphics issues
  G.M ( drawing 3D Plants)
• The Structural Functional Models S.F.M
  (combination of PBMGM)

39
Process Based Model

• The Plant is divided in Compartments (leaves,
  wood, roots) that are sources and sinks..
• Photosynthesis is computed according to
  environmental factors (Light, CO2,Temp) and leaf
  area index (LAI)
• The time period of observation is short (hour)

40
Properties of PBM

• Advantages Simple plant description with global
  parameters as LAI, plant height,are used, Simple
  laws for plant functioning. ( Beer Law of light
  interception, W.U.E. for transpiration
• Drawbacks The yield quality ( organ size) is not
  insured, nor plant phenology. Models are forced
  with no feed-back. For long period the computing
  time can be long thanks the short time unit.

41
Geometric Models

• The complet plant Organogenesis is carried out in
  detail (leaves, internodes,fruits, roots)
• Organogenesis is monitored according to a genetic
  program simulated with grammars or automaton
• The time unit for computing is linked to the
  growth cycle whose duration is at least several
  days
• The organs geometry comes from a prefabricated
  library

42
Properties of GM

• Advantages beautiful plant shapes can be
  obtained. 3D realistic architectures can be used
  in computer-graphics applications. The organ
  production can be assessed and the phenology
  monitored upon the rules of the automaton. The
  plant is sensitive to the 3D space (obstacles)
• Drawbacks the organs do not play any functional
  roles, and the plant is not sensitive to the
  environmental factors (Light). The 3D geometry
  can be heavy to compute and to display/ The model
  is forced without interactions.

43
Structural Functional Models

• Organogenesis and photosynthesis are carried out
  simutaneously.
• Biomass acquisition and partitioning are insured
  inside the plant structure where the organs play
  their roles as sources and sinks.
• The plant is sensitive to the environment
  (obstacles, Light)
• The functioning step is short ( as PBM)

44
Properties of a SFM

• Advantages theoreticaly speaking SFM is the
  ultimate goal of plant growth modelling. The true
  living growth process is carried out
• Comments For now SFM are at the beginning. They
  add the drawbacks of both PBM GM. Cumbersom
  files and long time computation. More over they
  are still forced model and are not yet dynamical.
  The complexity of the simulation process makes
  the reliability of the results difficult to
  assess.

45
Some considerations about plant architecture and
plant functioning

• Organs are made of fresh Biomass (20 DM) even
  some organs have lt 5 DM 95 H20.
• The level of observation determines the type of
  measurements.At the level of Architecture the
  plant functioning must be modelised at the same
  scale.
• Tree architecture gives birth to numerous organs.
  Some instantiation up to Botanical knowledge must
  be done to speed up the data processing.

46
Relevant assumptions for Plants Growth and Plants
Architecture modelling

• The scale of observation must be macroscopic (
  Organs sizes and not cells ( stomata))
• The Plant organization must follow the Botany
  (metamer, growth unit, axis, branches)
• The step of computing time must be fitted to the
  duration need for organ creation that is the
  Growth Cycle
• Organs creation, biomass acquisition and
  partitioning must be processed during the same
  Growth Cycle to insure feed back between
  organogenesis and photosynthesis

47
Formalism of a dynamical system

• Recurrence equation between states variables
  during the steps of Growth.

They are the input variables X of the model
associated with hidden parameters U to assess.

• Observed Variables

They are the data that can be directly measured
on the Plant Architecture

• Cost Function

Control of the External parameters E that monitor
the Growth to optimise a criterium.
48
Degrees of complexity of the dynamical model for
Plant Morphogenesis
Pure Organogenesis (GM)
Pure Photosynthesis (PBM)
Organogenesis Photosynthesis without
retroaction (FSM-)
Organogenesis Photosynthesis with retroaction
(FSM)
Un et Vn parameters of the system and of the
environment
49
GreenLab model

• Qualitative assumptions
• Quantitatives assumtions

50
Physiological Age and morphological gradients in
PlantArchitecture Youth Aging
Reiteration Acrotony(D. Barthelemy)
51
Ecophysiological knowledge available on
cultivated Plants

• Law of sum of temperature
• Law of water use efficiency

52
Organo Genesis and Temperature
Effect of thermal time on The stabilization of
organogenesis
Calendar Time
Thermal Time
Leaves number
Leaves number
Number of cycles
Number of days
(Turc et Lecoeur, 1997)
LEPSE
53
Organ Expansion and Temperature
Effect of thermal time on The stabilization of
organ expansion
Number of days
Number of cycles
Temps après initiation (j)
Temps thermique après initiation (Cj)
Sunflower leaf expansion
(Granier et Tardieu, 1998)
LEPSE
54
Experiments on Thermal timein CAU with
cultivated plants
Guo Yan
55
Maize Link Température-CycleFor Organ creation
and expansion
At beginning the Cycle is link to organ
production and expansion. After production stops
we keep the same function for expansion.
56
Experiments on water transpirationin CAU with
cultivated plants
Guo Yan
57
Link transpiration-production robust and rather
independant from Hydric stress
Data Howell et Musick USDA 85
58
Modelling the Growth Cycle (1) Automaton
Physiological age
                                         
GreenLab dual-scale automaton for Organogenesis.
Xing.Zh
59
Modelling the Growth Cycle (2)Matter production
partitioning
Based on thermal time, the same period is used
both for organ creation and matter production
partitioning
60
Non Linear Biomass Production model of Leaves
Equation of Production


Q (n) production de biomasse au cycle n K
W.U.E. , ETP(n)

?tn cycle duration
R(n) plant
resistance
Tf number of leaves at cycle Si
Blade Surface of leaf i
Plant Conductance
Leaf resistance as an non linear empirical
function to assess
61
Biomass Partitioning to Organs(Sinks). Case of
immediate expansion
Model
New Organs in competittion for Biomass Na nb
of leaves Pa sink of one leaf Ne nb
of.internodes Pe sink of internode Nc nb of
layers Pc sink of one layer Nf nb of
fruits Pf sink of one fruit Ps1, Ps2 sinks of
shoots and roots
Biomass reserve Q
Ps1
Ps2
shoots
Biomass going to one leaf
62
Biomass Partitioning to Organs (Sinks). Case of
expansion on several cycles
Leaf sink variation
Biomass Supply at each cycle
PrimaryGrowth
Organ expansion
Biomass going into the first leaf
Q(0)
SecondaryGrowth
63
Expansion effect on organs
P (Organ sink) ? (sink
variation) Q/D (supply/demand) q(n-i1,n
) organ volume
Same volume of organ can be obtained by a lot of
different combinations
Expansion Law B.N. (-2,p)
64
The Global Partitioning Model
Model
Organ increment
Organ biomass
65
Relevant qualitative and quantitative choices for
building an efficient Dynamic Plant Growth Model
GreenLab Case

• Philippe de Reffye1 and Bao.-Gang. Hu2
• 1CIRAD, INRIA, France
• 2Institute of Automation, Chinese Academy of
  Sciences, Beijing, 100080 China

66
Presentation

• Introduction
• Some considerations about plant architecture and
  plant functioning
• Relevant assumptions to build a efficient
  dynamical Model for Plants Growth and Plants
  Architecture
• A General Mathematical Formalism for Growth at
  the scale of plant Architecture
• The particular case of GreenLab model a
  dynamical formalism
• Applications of substructures algorithms in
  GreenLab
• GreenLab Model Behaviour
• Calibration of the model
• Optimisation and Control
• Plant Development Control

67
Qualitative and quantitative components of Yield

• Quantitative components
• - Number of organs -gt (architectural
  models)
• - Weight of organs -gt (Crop)
• Qualitative components
• - Size of organs density, allometry?
  Plasticity
• - Dry matter ratio in the organ biomass

68
Introduction to Plant Growth and Plant
Architecture modelling

• The Process Based Models for Agronomical issues
  (P.B.M) (computing Yield)
• The Geometric models for Computer Graphics issues
  G.M ( drawing 3D Plants)
• The Structural Functional Models S.F.M
  (combination of PBMGM)

69
Process Based Model

• The Plant is divided in Compartments (leaves,
  wood, roots) that are sources and sinks..
• Photosynthesis is computed according to
  environmental factors (Light, CO2,Temp) and leaf
  area index (LAI)
• The time period of observation is short (hour)

70
Properties of PBM

• Advantages Simple plant description with global
  parameters as LAI, plant height,are used, Simple
  laws for plant functioning. ( Beer Law of light
  interception, W.U.E. for transpiration
• Drawbacks The yield quality ( organ size) is not
  insured, nor plant phenology. Models are forced
  with no feed-back. For long period the computing
  time can be long thanks the short time unit.

71
Geometric Models

• The complet plant Organogenesis is carried out in
  detail (leaves, internodes,fruits, roots)
• Organogenesis is monitored according to a genetic
  program simulated with grammars or automaton
• The time unit for computing is linked to the
  growth cycle whose duration is at least several
  days
• The organs geometry comes from a prefabricated
  library

72
Properties of GM

• Advantages beautiful plant shapes can be
  obtained. 3D realistic architectures can be used
  in computer-graphics applications. The organ
  production can be assessed and the phenology
  monitored upon the rules of the automaton. The
  plant is sensitive to the 3D space (obstacles)
• Drawbacks the organs do not play any functional
  roles, and the plant is not sensitive to the
  environmental factors (Light). The 3D geometry
  can be heavy to compute and to display/ The model
  is forced without interactions.

73
Structural Functional Models

• Organogenesis and photosynthesis are carried out
  simutaneously.
• Biomass acquisition and partitioning are insured
  inside the plant structure where the organs play
  their roles as sources and sinks.
• The plant is sensitive to the environment
  (obstacles, Light)
• The functioning step is short ( as PBM)

74
Properties of a SFM

• Advantages theoreticaly speaking SFM is the
  ultimate goal of plant growth modelling. The true
  living growth process is carried out
• Comments For now SFM are at the beginning. They
  add the drawbacks of both PBM GM. Cumbersom
  files and long time computation. More over they
  are still forced model and are not yet dynamical.
  The complexity of the simulation process makes
  the reliability of the results difficult to
  assess.

75
Some considerations about plant architecture and
plant functioning

• Organs are made of fresh Biomass (20 DM) even
  some organs have lt 5 DM 95 H20.
• The level of observation determines the type of
  measurements.At the level of Architecture the
  plant functioning must be modelised at the same
  scale.
• Tree architecture gives birth to numerous organs.
  Some instantiation up to Botanical knowledge must
  be done to speed up the data processing.

76
Relevant assumptions for Plants Growth and Plants
Architecture modelling

• The scale of observation must be macroscopic (
  Organs sizes and not cells ( stomata))
• The Plant organization must follow the Botany
  (metamer, growth unit, axis, branches)
• The step of computing time must be fitted to the
  duration need for organ creation that is the
  Growth Cycle
• Organs creation, biomass acquisition and
  partitioning must be processed during the same
  Growth Cycle to insure feed back between
  organogenesis and photosynthesis

77
Formalism of a dynamical system

• Recurrence equation between states variables
  during the steps of Growth.

They are the input variables X of the model
associated with hidden parameters U to assess.

• Observed Variables

They are the data that can be directly measured
on the Plant Architecture

• Cost Function

Control of the External parameters E that monitor
the Growth to optimise a criterium.
78
Degrees of complexity of the dynamical model for
Plant Morphogenesis
Pure Organogenesis (GM)
Pure Photosynthesis (PBM)
Organogenesis Photosynthesis without
retroaction (FSM-)
Organogenesis Photosynthesis with retroaction
(FSM)
Un et Vn parameters of the system and of the
environment
79
GreenLab model

• Qualitative assumptions
• Quantitatives assumtions

80
Physiological Age and morphological gradients in
PlantArchitecture Youth Aging
Reiteration Acrotony(D. Barthelemy)
81
Ecophysiological knowledge available on
cultivated Plants

• Law of sum of temperature
• Law of water use efficiency

82
Organo Genesis and Temperature
Effect of thermal time on The stabilization of
organogenesis
Calendar Time
Thermal Time
Leaves number
Leaves number
Number of cycles
Number of days
(Turc et Lecoeur, 1997)
LEPSE
83
Organ Expansion and Temperature
Effect of thermal time on The stabilization of
organ expansion
Number of days
Number of cycles
Temps après initiation (j)
Temps thermique après initiation (Cj)
Sunflower leaf expansion
(Granier et Tardieu, 1998)
LEPSE
84
Experiments on Thermal timein CAU with
cultivated plants
Guo Yan
85
Biomass Partitioning to Organs(Sinks). Case of
immediate expansion
Model
New Organs in competittion for Biomass Na nb
of leaves Pa sink of one leaf Ne nb
of.internodes Pe sink of internode Nc nb of
layers Pc sink of one layer Nf nb of
fruits Pf sink of one fruit Ps1, Ps2 sinks of
shoots ans roots
Biomass reserve Q
Ps1
Ps2
shoots
Biomass going to one leaf
86
The Global Partitioning Model
Model
Organ increment
Organ biomass
87
How to write the general equations ofthe Biomass
acquisition
Production Demand
Leaf volume
Leaf surface Leaf production
Plant prod.
88
Flowchart of model simulation
N age of plant. Q0 biomass of seed
89
GreenLab Flowchart
Numbers and volumes of Organs
Compute photosynthesis
Draw 3D Architecture
90
The Substructure method

• Useful (but necessary) tool to speed up the
  computational time of the tree growth and the
  tree architecture
• Substructures are branches instantiations thank
  to the physiological age notion
• Applications are to compute fastly organogenesis,
  organs demand, plant geometry, and stochastic
  behaviour

91
Substructures method to speed upthe computation
of Organogenesis
Phd Yan Hongping
S4
S1
S3
S124 90 440 1428 3918
S224 0 40 108
298 S324 0 0 12 26 S424 0
0 0 2
S2
This Algorithm is very convenient for complex
tree architecture , it speed up Growth
dramatically ( gt 1OOO times for trees )
92
Complex Tree Organogenesis Simulation by GreenLab
Growth units with Acrotony and metamorphosis are
generated
Plant topology
Plant morphology
(Kang MengZhen)
93
Efficiency of Substructures Showned in AMAPsim
(Barczi)
Classical buds parallel Growth The span of
simulation is proportional to the number of
organs to create
Substructure The span of simulation is
proportional to chronological age physiological
age
94
Computing the number of items of a tree using
substructures
Counting items in ultimate structure m
before bud mutation
after bud mutation
completed structure
Counting items in structure k
95
Equations of the Dynamical model leaf
functioning time ta 2 expansion duration
txp 2
Production Model
Supply
Plant Demand
Conductance
Organ Volume
96
The Stochastic case
97
Stochastic growth of plantseffect of
probabilities

• Physiological age 1 2 3 4
• pc 0.99 0.95 0.93
  0.90
• pb 0.95 0.8 0.7 0.6
• pu 0.9 0.85 0.7
  0.65
• pa 0.95 0.85 0.7
  0.6

(Kang MengZhen)
98
Calculation of mean and varianceof microstates
bud production into the tree structure using
stochastic substructures
99
Results-topology
Probability tree
(Kang MengZhen)
100
The Use of Substructures in the stochastic case
to build trees
For each chronological age and physiological age
a set of a given number of substructures is
created belonging to the same distribution
Examples of sets of substructures
(Kang MengZhen)
101
Substructures algorithm flowchart
102
Geometry results 3 random simulations of the
same stochastic Automaton
(Kang MengZhen)
103
Performance-comparison with bud-by-bud simulation

• Compared to bud-by-bud simulation, this algorithm
  can have much gain.

104
Stochastic Biomass ProductionUse of differential
statistics
The stochastic leaves distribution generate a
stochastic biomass distribution. If the
recurrence between Q(n) Q(n-1) according to the
number of leaves X(n) is known we can write
This gives the biomass distribution according to
the leaves distribution and the functional
parameters ( resistances , sinks)
leaves Mth 59.6 Msim 60.6 leaves
Vth 168.8 Vsim 188.6 Biomass Mth
104.2 Msim 105.1 Biomass Vth 360.4
Vsim 351.0
Leaf production Biomass production
105
Use of substructures for computing geometry
One repetition Four repetitions
Each substructure can bend according to its
orientation. We can choose a limited number oàf
repetitions to speed up the plant geometry
106
Use of substructures to compute secondary growth
Thank to substructure method we can know the
number of living leaves seen by each internode.
The ring thickness is then proportional to this
number ( Shinozaki pipe model theory)
107
Computing the secondary growthin a tree
architecture
108
A complex tree architecture with GreenLab
Tree top
Branche (str2)
Tree profile
(Kang MengZhen)
109
GreenLab model Applications

• Mathematical model behaviour
• Sinks optimization
• Optimal control

110
Corner model behavior

• Growth of Corner model for r1 r2 gt0 , ta 1
• Goal to show that the biomass production
  reaches a limit.

Demand
Limit of Biomass production
Biomass production
(a)r225,Ql10 (b)r275,Ql3.3 (c)r2250Ql1,
(d) r2 750 ,Ql0.33
111
Behaviour of Attims Model (Halle)
Demand Equation
Supply Equation
Limit Production Ql of the model
Depends of model parameters values
112
Behaviour of Leeuwenberg model
Condition for a limit size for organs given by
equation
taleaf span Mnb buds/internode Ar1e/pa
Br2 ql metamer size
The behaviour of the model depends of the
parameters values. In these exemples the metamers
can reaches various limit size
a cte biomass prod/cycle size org ? 0 b
biomass prod/cycle size org ? 0 c biomass
prod/cycle size org ? cte
a b c
113
Feed back between Growth and Architecture in
GreenLab
Pruning Effect
Fruiting Effect
fruit sinks 0 1 2 4 8
114
Calibration of GreenLab on MaizeCau-Liama
cornerfit Zhang Zhi Gang
115
Environmental effect on plant morphology
simulated with GreenLab
Water stress simulated in different phases of
development
stress
stress
stress
Constant optimal environment
Stress conditions until 15 cycles
Optimal conditions until 15 cycles
Stress conditions between cycle 10 and 20
116
GreenLab optimal control for irrigationon
Sunflower
For (a), sunflower height is 105.9, fruit weight
is 623.41, total weight is 1586.72 For (b),
sunflower height is 98.3, fruit weight is 656.11,
total weight is 1509.78. For (c), sunflower
height is 112.1, fruit weight is 881.52, total
weight is 1998.97
Lin Phd
117
Toward Feedback between organogenesis
photosynthesis
4.Demand Dorg Biomass Partitioning in New organs
1.Bud Demand Db

• 3.Creation of
• Bud Topology

bud
leaf
2.Photosynthesis Biomass Q
N-1 Cycle N
N1
118
First step in the full feed-back between
Organogenesis and Photosynthesis
Metamers production/GU
4 met/GU
Biomass production/cycle
3 met/GU
2 met/GU
119
Conclusion

• Based on botanical and biology laws,the
  structure-function model GreenLab for plant
  growth was presented. The ecophyioloical process
  and plant structure were combined.

• The nonlinear least squares method was used to
  estimate hidden parameters

• Good calibrations were obtained on single stemmed
  plant wheat, cotton, maize, sunflower, tomato.

• One can expected that Optimization and Control
  will give good result on fields experiments

120
Thank You !