Amélie Mathieu

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.

Modelling of Branch and Flower Expansion in GreenLab Model to Account for the Whole Crop Cycle of Winter Oilseed Rape (Brassica napus L.)

Functional-structural Plant Models are interesting tools to study interactions between architecture and environmental conditions. In the case of Winter Oilseed Rape (WOSR), we need a plant model that accounts for the role of source:sink relationships in the architectural development. GreenLab model is a good candidate because it was already used to evidence 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 reproductive phase. Indeed, we need to take into account the different timings of branch expansion and pod setting. Therefore two equations were added in GreenLab model to compute expansion delays for respectively branching and flowering of each axis.Experimental field data were used to estimate morphological parameters such as phyllochron, podochron,(equivalent to phyllochron but for pods), leaf expansion duration, and leaf life span. These data were also used to calibrate the source:sink module of the model. First results indicated that the model simulates properly the dynamics of plant growth and development during both vegetative and reproductive phases.

Stochastic Models in Floral Biology and its Application to the Study of Oilseed Rape (Brassica napus L.) Fertility

The number of seeds per pod is an important determinant of yield. New clues of yield and seed quality improvement can be provided by studying the relation between the developmental patterns of floral organs and seed production. In this article, a probabilistic model of plant inflorescence fertility is presented. From a biological point of view, seed development can be viewed as the combination of several physiological processes that can be modeled with stochastic laws. Experiments were made on oilseed rape in Grignon (France) in 2008 to calibrate the model. A Generalized Least Square method was implemented to estimate the model parameters. The variations of parameters were analyzed according to the position of flowers. Furthermore, we discussed the causes that lead to the variation of seed production within the inflorescence and related them to our model. The model reproduces well the distribution of the number of ovules per flower as well as the number of final seeds per pod. We deduced a law to describe the distribution of pollen grains on the stigma that is quite difficult to be observed experimentally. This model is the first step towards a dynamic model taking into account the complexity of the oilseed rape architecture, which is aimed to quantify the influence of pollination or trophic competition on seed production.

Are Yield and Biomass Distribution Affected by Sink Organ Clipping During Reproductive Phase of Winter Oilseed Rape (Brassica napus L.)

As many crops, Winter Oilseed Rape plants are sensitive to biotic or abiotic stresses, but, due to its plasticity reproductive organ losses can be compensated. In this case, biomass is allocated to remaining organs changing yield distribution within the plant. However, compensation remains variable and causes of this variability are still not completely understood. Due to sequential development, pod yield is distributed among axes unevenly. Indeed biomass of axis and biomass allocation to pods varies according to axis position. We suppose that efficiency of compensation at plant scale would depend on the position of axis implied. In the following study axes were clipped. Yield and biomass distribution within plant as well as efficiency of biomass allocation to reproductive organs were characterized. Our data assume that basal axes were mainly involved in compensation and that increase in pod yield on these axes was related to increase in dry mass with no modification of the efficiency allocation of biomass.

Use of a structure-function plant model to assess the morphogenetic plasticity. How does variation in phyllochron modify plant growth and development of Brassica napus in the GreenLab model?

A functional-structural model of winter oilseed rape (WOSR) has been developed to study plant morphogenetic plasticity, i.e. how processes of morphogenesis are adapted in response to environmental constraints. The phyllochron (time between emergence of two successive leaves) is one of the variables sensitive to environment. The aim of this article is to use model sensitivity analysis to quantify the impact of an increase or a reduction in phyllochron on plant growth and source/sink functioning.

Assessment of the Role of initial conditions in the setting of heterogeneity of functional Traits in a population of oilseed rape plants

Individual plant models have been developed in recent years to satisfy different objectives. However most of them focus on average plant and do not integrate the variability observed in cultivated fields. Population scale models are often based on very simplified representation of the plant, and most of them remain theoretical. The objective of this work is to use an experimental design to select the main variables driving plant growth in order to use them as key factors in a plant population scale model. Destructive and non-destructive measurements were carried out from February to June. Measured variables are commonly used in such models. In our experimental conditions, local density has little impact on model outputs. On the contrary, the plant initial size is highly correlated to final height, dry mass and number of ramifications. This result confirms that variability within the field is very dependent on plant development at the first stages.

Sensitivity to Temperature of Epidemiological Processes at Leaf Scale, a Preliminary Step Towards FSPMs of Sick Wheat

Function-Structure Plant models (FSPM) seem attractive to better understand the complex interactions between plant growth, canopy morphogenesis, and epidemics. Epidemics are driven by climate factors and among them, temperature is known to play a major role. Thus, weather station measurement is commonly used to drive epidemics models. However, the relationship between climate and within-canopy microclimate is mainly affected by the canopy architecture. Thus, the general question addressed in this study is: where air temperature should be measured as input of FSPM for sick plants?