Paul-Henry Cournède

Structural Factorization of Plants to Compute Their Functional and Architectural Growth

Numerical simulation of plant growth has been facing a bottleneck due to the cumbersome computation implied by the complex plant topological structure. In this article, the authors present a new mathematical model for plant growth, GreenLab, overcoming these difficulties. GreenLab is based on a powerful factorization of the plant structure. Fast simulation algorithms are derived for deterministic and stochastic trees. The computation time no longer depends on the number of organs and grows at most quadratically with the age of the plant. This factorization finds applications to build trees very efficiently, in the context of geometric models, and to compute biomass production and distribution, in the context of functional structural models.

Quantitative Genetics and Functional-Structural Plant Growth Models: Simulation of Quantitative Trait Loci Detection for Model Parameters and Application to Potential Yield Optimization

BACKGROUND AND AIMS Prediction of phenotypic traits from new genotypes under untested environmental conditions is crucial to build simulations of breeding strategies to improve target traits. Although the plant response to environmental stresses is characterized by both architectural and functional plasticity, recent attempts to integrate biological knowledge into genetics models have mainly concerned specific physiological processes or crop models without architecture, and thus may prove limited when studying genotype x environment interactions. Consequently, this paper presents a simulation study introducing genetics into a functional-structural growth model, which gives access to more fundamental traits for quantitative trait loci (QTL) detection and thus to promising tools for yield optimization. METHODS The GREENLAB model was selected as a reasonable choice to link growth model parameters to QTL. Virtual genes and virtual chromosomes were defined to build a simple genetic model that drove the settings of the species-specific parameters of the model. The QTL Cartographer software was used to study QTL detection of simulated plant traits. A genetic algorithm was implemented to define the ideotype for yield maximization based on the model parameters and the associated allelic combination. KEY RESULTS AND CONCLUSIONS By keeping the environmental factors constant and using a virtual population with a large number of individuals generated by a Mendelian genetic model, results for an ideal case could be simulated. Virtual QTL detection was compared in the case of phenotypic traits--such as cob weight--and when traits were model parameters, and was found to be more accurate in the latter case. The practical interest of this approach is illustrated by calculating the parameters (and the corresponding genotype) associated with yield optimization of a GREENLAB maize model. The paper discusses the potentials of GREENLAB to represent environment x genotype interactions, in particular through its main state variable, the ratio of biomass supply over demand.

Analytical study of a stochastic plant growth model: Application to the GreenLab model

A stochastic functional-structural model simulating plant development and growth is presented. The number of organs (internodes, leaves and fruits) produced by the model is not only a key intermediate variable for biomass production computation, but also an indicator of model complexity. To obtain their mean and variance through simulation is time-consuming and the results are approximate. In this paper, based on the idea of substructure decomposition, the theoretical mean and variance of the number of organs in a plant structure from the model are computed recurrently by applying a compound law of generating functions. This analytical method provides fast and precise results, which facilitates model analysis as well as model calibration and validation with real plants. Furthermore, the mean and variance of the biomass production from the stochastic plant model are of special interest linked to the prediction of yield. In this paper, through differential statistics, their approximate results are computed in an analytical way for any plant age. A case study on sample trees from this functional-structural model shows the theoretical moments of the number of organs and the biomass production, as well as the computation efficiency of the analytical method compared to a Monte-Carlo simulation method. The advantages and the drawbacks of this stochastic model for agricultural applications are discussed.

Characterization of the interactions between architecture and source–sink relationships in winter oilseed rape (Brassica napus) using the GreenLab model

BACKGROUND AND AIMS This study aimed to characterize the interaction between architecture and source-sink relationships in winter oilseed rape (WOSR): do the costs of ramification compromise the source-sink ratio during seed filling? The GreenLab model is a good candidate to address this question because it has been already used to describe interactions between source-sink relationships and architecture for other species. However, its adaptation to WOSR is a challenge because of the complexity of its developmental scheme, especially during the reproductive phase. METHODS Equations were added in GreenLab to compute expansion delays for ramification, flowering of each axis and photosynthesis of pods including the energetic cost of oil synthesis. Experimental field data were used to estimate morphological parameters while source-sink parameters of the model were estimated by adjustment of model outputs to the data. Ecophysiological outputs were used to assess the sources/sink relationships during the whole growth cycle. KEY RESULTS First results indicated that, at the plant scale, the model correctly simulates the dynamics of organ growth. However, at the organ scale, errors were observed that could be explained either by secondary growth that was not incorporated or by uncertainties in morphological parameters (durations of expansion and life). Ecophysiological outputs highlighted the dramatic negative impact of ramification on the source-sink ratio, as well as the decrease in this ratio during seed filling despite pod envelope photosynthesis that allowed significant biomass production to be maintained. CONCLUSIONS This work is a promising first step in the construction of a structure-function model for a plant as complex as WOSR. Once tested for other environments and/or genotypes, the model can be used for studies on WOSR architectural plasticity.

A model-based analysis of the dynamics of carbon balance at the whole-plant level in Arabidopsis thaliana

Arabidopsis thaliana (L.) Heynh. is used as a model plant in many research projects. However, few models simulate its growth at the whole-plant scale. The present study describes the first model of Arabidopsis growth integrating organogenesis, morphogenesis and carbon-partitioning processes for aerial and subterranean parts of the plant throughout its development. The objective was to analyse competition among sinks as they emerge from patterns of plant structural development. The model was adapted from the GreenLab model and was used to estimate organ sink strengths by optimisation against biomass measurements. Dry biomass production was calculated by a radiation use efficiency-based approach. Organogenesis processes were parameterised based on experimental data. The potential of this model for growth analysis was assessed using the Columbia ecotype, which was grown in standard environmental conditions. Three phases were observed in the overall time course of trophic competition within the plant. In the vegetative phase, no competition was observed. In the reproductive phase, competition increased with a strong increase when lateral inflorescences developed. Roots and internodes and structures bearing siliques were strong sinks and had a similar impact on competition. The application of the GreenLab model to the growth analysis of A. thaliana provides new insights into source-sink relationships as functions of phenology and morphogenesis.

An efficient computational method for global sensitivity analysis and its application to tree growth modelling

Global sensitivity analysis has a key role to play in the design and parameterization of functional-structural plant growth models which combine the description of plant structural development(organogenesis and geometry) and functional growth(biomass accumulation and allocation). We are particularly interested in this study in Sobols method which decomposes the variance of the output of interest into terms due to individual parameters but also to interactions between parameters. Such information is crucial for systems with potentially high levels of non-linearity and interactions between processes, like plant growth. However, the computation of Sobols indices relies on Monte Carlo sampling and re-sampling, whose costs can be very high, especially when model evaluation is also expensive, as for tree models. In this paper, we thus propose a new method to compute Sobols indices inspired by Homma-Saltelli, which improves slightly their use of model evaluations, and then derive for this generic type of computational methods an estimator of the error estimation of sensitivity indices with respect to the sampling size. It allows the detailed control of the balance between accuracy and computing time. Numerical tests on a simple non-linear model are convincing and the method is finally applied to a functional-structural model of tree growth, GreenLab, whose particularity is the strong level of interaction between plant functioning and organogenesis.

Positivity statements for a Mixed-Element-Volume scheme on fixed and moving grids

This paper considers a class of second-order accurate vertex centered mixed finite element finite-volume MUSCL schemes. These schemes apply to unstructured triangulations and tetrahedrizations and fluxes are computed on an edge basis. We define conditions under which these schemes satisfy a density-positivity statement for Euler flows, a maximum principle for a scalar conservation law and a multicomponent flow. This extends to an Arbitrary- Lagrangian-Eulerian formulation. Steady and unsteady flow simulations illustrate the accuracy and the robustness of these schemes.

Comparison of three approaches to model grapevine organogenesis in conditions of fluctuating temperature, solar radiation and soil water content.

BACKGROUND AND AIMS There is increasing interest in the development of plant growth models representing the complex system of interactions between the different determinants of plant development. These approaches are particularly relevant for grapevine organogenesis, which is a highly plastic process dependent on temperature, solar radiation, soil water deficit and trophic competition. METHODS The extent to which three plant growth models were able to deal with the observed plasticity of axis organogenesis was assessed. In the first model, axis organogenesis was dependent solely on temperature, through thermal time. In the second model, axis organogenesis was modelled through functional relationships linking meristem activity and trophic competition. In the last model, the rate of phytomer appearence on each axis was modelled as a function of both the trophic status of the plant and the direct effect of soil water content on potential meristem activity. KEY RESULTS The model including relationships between trophic competition and meristem behaviour involved a decrease in the root mean squared error (RMSE) for the simulations of organogenesis by a factor nine compared with the thermal time-based model. Compared with the model in which axis organogenesis was driven only by trophic competition, the implementation of relationships between water deficit and meristem behaviour improved organogenesis simulation results, resulting in a three times divided RMSE. The resulting model can be seen as a first attempt to build a comprehensive complete plant growth model simulating the development of the whole plant in fluctuating conditions of temperature, solar radiation and soil water content. CONCLUSIONS We propose a new hypothesis concerning the effects of the different determinants of axis organogenesis. The rate of phytomer appearance according to thermal time was strongly affected by the plant trophic status and soil water deficit. Furthermore, the decrease in meristem activity when soil water is depleted does not result from source/sink imbalances.

NEMA, a functional-structural model of nitrogen economy within wheat culms after flowering. I. Model description.

BACKGROUND AND AIMS Models simulating nitrogen use by plants are potentially efficient tools to optimize the use of fertilizers in agriculture. Most crop models assume that a target nitrogen concentration can be defined for plant tissues and formalize a demand for nitrogen, depending on the difference between the target and actual nitrogen concentrations. However, the teleonomic nature of the approach has been criticized. This paper proposes a mechanistic model of nitrogen economy, NEMA (Nitrogen Economy Model within plant Architecture), which links nitrogen fluxes to nitrogen concentration and physiological processes. METHODS A functional-structural approach is used: plant aerial parts are described in a botanically realistic way and physiological processes are expressed at the scale of each aerial organ or root compartment as a function of local conditions (light and resources). KEY RESULTS NEMA was developed for winter wheat (Triticum aestivum) after flowering. The model simulates the nitrogen (N) content of each photosynthetic organ as regulated by Rubisco turnover, which depends on intercepted light and a mobile N pool shared by all organs. This pool is enriched by N acquisition from the soil and N release from vegetative organs, and is depleted by grain uptake and protein synthesis in vegetative organs; NEMA accounts for the negative feedback from circulating N on N acquisition from the soil, which is supposed to follow the activities of nitrate transport systems. Organ N content and intercepted light determine dry matter production via photosynthesis, which is distributed between organs according to a demand-driven approach. CONCLUSIONS NEMA integrates the main feedbacks known to regulate plant N economy. Other novel features are the simulation of N for all photosynthetic tissues and the use of an explicit description of the plant that allows how the local environment of tissues regulates their N content to be taken into account. We believe this represents an appropriate frame for modelling nitrogen in functional-structural plant models. A companion paper will present model evaluation and analysis.

Data assimilation to reduce uncertainty of crop model prediction with Convolution Particle Filtering

A reliable and accurate forecasting method for crop yields is very important for the farmer, the economy of a country, and the agricultural stakeholders. However, due to weather extremes and uncertainties as a result of increasing climate change, most crop yield forecasting models are not reliable and accurate. In this paper, a hybrid crop yield probability density forecasting method via quantile regression forest and Epanechnikov kernel function (QRF-SJ) is proposed to capture the uncertainties and extremes of weather in crop yield forecasting. By assigning probability to possible crop yield values, probability density forecast gives a complete description of the yield of crops. A case study using the annual crop yield of groundnut and millet in Ghana is presented to illustrate the efficiency and robustness of the proposed technique. The proposed model is able to capture the nonlinearity between crop yield and the weather variables via random forest. The values of prediction interval coverage probability and prediction interval normalized average width for the two crops show that the constructed prediction intervals cover the target values with perfect probability. The probability density curves show that QRF-SJ method has a very high ability to forecast quality prediction intervals with a higher coverage probability. The feature importance gave a score of the importance of each weather variable in building the quantile regression forest model. The farmer and other stakeholders are able to realize the specific weather variable that affect the yield of a selected crop through feature importance. The proposed method and its application on crop yield dataset is the first of its kind in literature.