How to include organ interactions in models of the root system architecture? The concept ofendogenous environment

A first generation of models describing the development of the root system architecture did not include explicitly the allocation of resources. These models aimed to mimic the morphogenetic programme, by translating the developmental events into a set of formal production rules. The major strength of these models was their ability to simulate simply the relevant topological characteristics of the root systems. However, the root system development is known to be highly sensitive to carbon limitations. These effects appear first at the root system level, whose global size can be greatly affected by the amount of carbohydrates which are available for the root system development (depending on the carbon budget within the whole plant). Moreover, competition for carbohydrates within the root system accounts for multiple architectural variations which appear in the heterogeneous soil environment. For example, compensatory growth is a common behaviour within root systems. These phenomena can be described by merging "source-sink models" to "morphogenetic rule models". The morphogenetic rule model simulates the topology of the system (between root connections), whereas the source-sink model simulates the size (growth rate) of the different organs, and allows the definition of an endogenous environment. But in these source -sink models, the definition of the sink strength is a crucial point, which has received only very little attention for the roots. As an alternative to pre-defined potential growth functions, we suggest to use an instantaneous sink strength of each meristem, related to its size. After having justified this approach by experimental data, we show how this sink strength indicator can vary along time, according to the time-dependent availability of carbohydrates. Thus, the sink strength of each axis can be quantified independently, according to its temporal and spatial position within the whole architecture. Although more buffered than the growth rate of the axis, its sink strength can vary during its development course. This very simple model allows the simulation of various growth patterns. It gives an interesting plasticity to the simulated root systems.