Towards quantitative root hydraulic phenotyping: novel mathematical functions to calculate plant-scale hydraulic parameters from root system functional and structural traits.

Predicting root water uptake and plant transpiration is crucial for managing plant irrigation and developing drought-tolerant root system ideotypes (i.e. ideal root systems). Today, three-dimensional structural functional models exist, which allows solving the water flow equation in the soil and in the root systems under transient conditions and in heterogeneous soils. Yet, these models rely on the full representation of the three-dimensional distribution of the root hydraulic properties, which is not always easy to access. Recently, new models able to represent this complex system without the full knowledge of the plant 3D hydraulic architecture and with a limited number of parameters have been developed. However, the estimation of the macroscopic parameters a priori still requires a numerical model and the knowledge of the full three-dimensional hydraulic architecture. The objective of this study is to provide analytical mathematical models to estimate the values of these parameters as a function of local plant general features, like the distance between laterals, the number of primaries or the ratio of radial to axial root conductances. Such functions would allow one to characterize the behaviour of a root system (as characterized by its macroscopic parameters) directly from averaged plant root traits, thereby opening new possibilities for developing quantitative ideotypes, by linking plant scale parameters to mean functional or structural properties. With its simple form, the proposed model offers the chance to perform sensitivity and optimization analyses as presented in this study.