# WHEAMM: a functional-structural model to study plant growth and interactions with neighbors in wheat variety mixtures

Meije Gawinowski, Jérôme Enjalbert, Paul-Henry P.-H. Cournède, Timothée Flutre

<figure><img src="image_1.png" /></figure>

## ► To cite this version:

Meije Gawinowski, Jérôme Enjalbert, Paul-Henry P.-H. Cournède, Timothée Flutre. WHEAMM: a functional-structural model to study plant growth and interactions with neighbors in wheat variety mixtures. FSPM 2020: 9th International Conference on FUNCTIONAL-STRUCTURAL PLANT MODELS, Oct 2020, Hanovre (Virtual Conference), Germany. hal-02961398

HAL Id: hal-02961398

https://hal.science/hal-02961398

Submitted on 8 Oct 2020

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

<figure><img src="image_2.png" /></figure>

Distributed under a Creative Commons Attribution - ShareAlike 4.0 International License
<figure><img src="image_3.png" /></figure>

# WHEAMM: A FUNCTIONAL-STRUCTURAL MODEL TO STUDY PLANT GROWTH AND INTERACTIONS WITH NEIGHBORS IN WHEAT VARIETY MIXTURES

MEIJE GAWINOWSKI¹,², JÉRÔME ENJALBERT¹, PAUL-HENRY COURNÈDE² & TIMOTHÉE FLUTRE¹

¹Université Paris-Saclay, INRAE, CNRS, AgroParisTech, GQE - Le Moulon, 91190, Gif-sur-Yvette, France
²Université Paris-Saclay, CentraleSupélec, Lab MICS, 91190, Gif-sur-Yvette, France

<figure><img src="image_4.png" /></figure>

## INTRODUCTION

Crop diversification was identified as a key leverage for the **agroecological transition**. In particular, increasing within-field diversity with **variety mixtures** for wheat may allow to stabilize yield and reduce the use of chemical inputs [Borg et al., 2018]. However, this technique is restrained in part because of a lack of practical rules for the assembly of varieties.

In order to study plant growth and interactions in mixtures, we chose an approach combining field experiment and **plant modeling**, with a main focus on **light competition** as plant interaction and **tillering** as a plastic response to this interaction. Even though, many wheat models already exist, none of them include light competition, accurate tillering dynamics and biomass production and allocation at the same time. WHEAMM (Wheat Model for Mixtures) is hence conceived as a combination of different existing models to assess mixture performance in terms of yield.

## WHEAMM MODELING CONCEPT

WHEAMM is an individual-based FSPM. It is a combination of these different modeling methods:

* A **source-sink model** based on Greenlab-wheat for an individual plant [Kang et al., 2008]
  - Three organ types: leaf, stem and ear
  - Phenology, organ initiation, extension and senescence according to a thermal time calendar
  - Plant biomass computed with usual Beer-Lambert law based on light interception, plant leaf surface and radiation use efficiency
  - Biomass allocation between growing organs according to their sink strength

<figure><img src="image_5.png" /><figcaption>**Figure 1:** Simulation of plant biomass as a function of time with WHEAMM for one plant with arbitrary parameters</figcaption></figure>

* More accurate **tillering dynamics** based on Ecomeristem model for regression phase [Larue et al., 2019]: allocation rules prioritizing tillers by age with simultaneous senescence processes

<figure><img src="image_6.png" /><figcaption>**Figure 2:** Simulation of the number of tillers as a function of time with WHEAMM for one plant with arbitrary parameters</figcaption></figure>

### NEXT STEPS:

Computation of **competition for light** in a plant population based on surface partition [Cournède et al., 2008]

* Determination of plant surface of influence $S_p$
* Partition of $S_p$ surface according to neighbouring competitors into subsurfaces
* Computation of probabilities that a plant is covering a subsurface and is above the others
* Computation on actual exposed leaf surface accordingly to these probabilities

## EXPERIMENTS FOR MODEL CALIBRATION

For WHEAMM calibration there is a need for data of individual plants during their growth. A field experiment was hence conducted in the frame of the Perfomix project:

* 2 different balanced mixtures of 4 components of 264 plants, 2 replicates at density 160 and one replicate at density 250 and 8 pure stands for corresponding varieties at density 160
* Sowing on October, 30 2019 and harvest on July, 20 2020 at Le Moulon, Gif-sur-Yvette (France)
* Precision sowing for mixtures according to a determined and randomized spatial layout

Collected data for calibration:

<table><caption>**Table 1:** Table of scorings for the Perfomix 2019-2020 experiment during growth. Leaf number, weight and surface were also recorded for a few plants, and yield components were recorded for all plants in mixtures at harvest</caption><thead><tr><th>Scoring</th><th>Stand</th><th>Number plants per point per stand</th><th>Number of scorings</th></tr></thead><tbody><tr><td rowspan="4">Height, Tillers, Biomass</td><td>Pure</td><td>20-30</td><td>7</td></tr><tr><td rowspan="2">Mixtures 250</td><td>20</td><td>1</td></tr><tr><td>All</td><td>1 (harvest)</td></tr><tr><td rowspan="2">Mixtures 160, rep1</td><td>30</td><td>1</td></tr><tr><td>30</td><td>1 (harvest)</td></tr><tr><td>Tillers</td><td>Mixtures 160</td><td>All</td><td>5</td></tr><tr><td>Height</td><td>Mixtures 160</td><td>All</td><td>7</td></tr><tr><td rowspan="2">Ear biomass</td><td>Pure</td><td>20-30</td><td>3</td></tr><tr><td>Mixtures</td><td>All</td><td>1 (harvest)</td></tr></tbody></table>

<figure><img src="image_7.png" /><figcaption>**Figure 3:** Number of tillers averaged by variety at each observation point in pure stands and in one mixture of the Perfomix experiment 2019-2020</figcaption></figure>

On Figure 3 we can see an important difference in tillering between pure stands of early varieties Accroc and Aubusson, and later varieties Bergamo and Expert. In the mixture of these four varieties, this gap is not as noticeable, as early varieties reach a higher tillering plateau.

### NEXT STEPS:

* Renewal of Perfomix experiment in 2020-2021
* Calibration in the Bayesian paradigm using a hybrid Metropolis-Hastings-Gibbs algorithm [Viaud, 2018].

## REFERENCES

[Borg et al., 2018] Borg, J., Kiær, L., Lecarpentier, C., Goldringer, I., Gauffreteau, A., Saint-Jean, S., Barot, S., and Enjalbert, J. (2018). Unfolding the potential of wheat cultivar mixtures: A meta-analysis perspective and identification of knowledge gaps. *Field Crops Research*, 221:298-313.

[Cournède et al., 2008] Cournède, P.-H., Mathieu, A., Houllier, F., Barthélémy, D., and de Reffye, P. (2008). Computing Competition for Light in the GREENLAB Model of Plant Growth: A Contribution to the Study of the Effects of Density on Resource Acquisition and Architectural Development. *Annals of Botany*, (101):1207-1219.

[Kang et al., 2008] Kang, M. Z., Evers, J. B., Vos, J., and De Reffye, P. (2008). The derivation of sink functions of wheat organs using the GREENLAB Model. *Annals of Botany*, (101):1099-1108.

[Larue et al., 2019] Larue, F., Fumey, D., Rouan, L., Soulié, J.-C., Roques, S., Beurier, G., and Luquet, D. (2019). Modelling tiller growth and mortality as a sink-driven process using Ecomeristem: implications for biomass sorghum ideotyping. *Annals of Botany*, 124(4):675-690.

[Viaud, 2018] Viaud, G. (2018). *Méthodes statistiques pour la différenciation génotypique des plantes à l'aide des modèles de croissance*. PhD thesis, Paris-Saclay, Gif-sur-Yvette.

This work is supported by the FIRE PhD program with the support of Fondation Bettencourt Schueller, the Perfomix project and the INRAE BAP department for Perfomix funding and M. Gawinowski PhD funding.