From individual plant to crop level

FSPM approaches show heavy reliance production computation, since they use the plant structure as a biomass storing and transportation pathway.
The main specificity of the GreenLab models lies in the fact that structure is only used as an organ compartment classifier, and not as a transportation network.

Indeed, an interesting way of overcoming this difficulty is to use the crop production model approach, defined at m² level to estimate the photosynthesis.
The structural approach precisely defines organ compartments sharing the same fate, making biomass allocation easier, but does not require exhaustive definition, be it topological (graph), or geometrical.

This positioning, between individual plant and crop models is specific to the GreenLab model.
Taking into account the simplifications established by agronomists from experimental studies, i.e. the common biomass pool, the use of net photosynthesis and, biomass computation from Beer's Law, this approach does away with use of the topological structure in production computation.
The classic crop model equation (Eq. 1) is adapted to the plant scale as follows:

Q = LUE . PAR . Sp . (1 - e ^{- k Sf/Sp}) (Eq. 2)

   where

Q is the increase in biomass of the plant cycle
Sf is the leaf area of the plant
Sp is a parameter which has the dimension of a surface
Sp allows equation (2) to operate even when the canopy is not very dens.
In an high density d stand, the canopy is uniform and Sp verifies:

    Sp = 1 / d (Eq. 3)

This relation has been verified experimentally on crops (see below).

Equations (Eq. 1) and (Eq. 2) are thus equivalent, but the formula (Eq. 2) allows a switch from the individual plant to the plant stand.

Organogenesis

In the GreenLab model, organogenesis is modelled by meristem production equations, according to their physiological age, and deduced from observations.
Growth, mortality and, branching are described by probability laws.

For each cycle of growth, new organ population (cohors) occurrences are simulated.

Each organ takes up biomass from the common biomass pool according to the srentgh of its sink function; (this function varies during organ maturation).
Since all organs of the same cohort and of the same type are in the same state, efficient factorization can be applied. For instance, plant demand D is simply the sum of the demand of all the cohorts.

The biomass increment Δ q of a given organ depends on its sink φ, the available biomass in the common pool Q calculated by equation (Eq. 2) and plant demand D according to the formula:

Δ q = φ . Q / D     (Eq. 4)

Organ weight is then simply defined by summing up the biomass increments (Eq. 4).
Its dimensions (length, diameter, area) are assessed by applying geometric (allometric) rules.
The weight of the organ compartments is obtained by summing up all cohorts of the same organ.
In particular, the total functioning leaf area of the plant Sf is deduced, using the equation (Eq. 2).


Simulation of plant growth and plasticity with the GreenLab model (© Digiplante and LIAMA).

These virtual plants are obtained from field data thanks to the software that takes particular account of how organs (leaves, roots, fruits, etc.) change, which can be very different depending on environmental conditions.
(a) simulating morphological gradients.
The base effect due to low biomass availability at early stages is shown on the right. The left-hand tree is only a structural simulation
(b) structural plasticity simulation on the beech tree.
Left and Right are respectively simulated with the same parameter, except for the Sp (Eq. 2) area value (shown as a grey disk) standing for reversed density.
Other calibrated simulations are for: (c) arabsisdosis, (d) beetroot, (e) sunflower,
(f) maize, (g) cotton, (h) rice, (i) tomato,
(j) chrysanthenum, (k) sweet pepper, (l) Mongolian pine

The GreenLab model is therefore a dynamic model of plant growth which operates by feedback between growth and development.
The calculation of plant production does not need to rely on the details of the architecture, but only on the equations of production and source-sink relations.
Such a model offers efficient computing costs and enables model calibration, optimisation and control methods to be implemented.