Assessment of Non-Linearity in Functional-Structural Plant Models

International audienceGlobal sensitivity analysis (SA) has known an increasing interest to assess the relative importance of parameters in ecological models [Cariboni et al., 2007] or crop models [Makowski et al., 2006]. Such methods have an important role to play in functional-structural plant growth modeling. The complexity of the underlying biological processes, especially the interaction between functioning and structure [Vos et al., 2009], usually makes parameterization a key step in modeling, and the analysis of model sensitivity to parameters provides useful information in this process. A side result of global SA is that it provides an indicator of the degree of non-linearity of the model by computing the level of interaction between parameters and how this interaction contributes to the variance of the output. Plants are known as complex systems with a strong level of interactions and compensations, and the aim of FSPMs is to describe and understand this complexity. As such, non-linearity is expected to play a key role in the study, since it reveals the interactions between parameters [Cariboni et al., 2007] [Saltelli, 2002]. The knowledge of the intrinsic non-linearity of the model and of its dynamic evolution throughout plant growth is very useful to study model behavior and properties, to underline the occurrence of particular biological phenomena or to improve the statistical analysis when confronting models to experimental data (e.g. statistical properties of estimators or numerical methods to compute the propagation of errors [Julier et al., 2000]). The objective of this paper is thus to explore the level of linearity of 3 FSPMs with different levels of complexity, and infer in each case what information can be drawn from this analysis. We first introduce the basic principles of Standard Regression Coefficients (SRC) method which is used for the analysis and gives a short overview of the different models addressed. We then analyze the results of the linearity study, particularly stressing on the emergence of non-linearity. We end by discussing the interest and potential extensions of this work