Published on *The James Hutton Institute* (https://www.hutton.ac.uk)

Currently, most plant root architectural models use computer simulations to mimic the developmental processes of root apical meristems and to construct virtual root architectures: single roots are assembled incrementally through the growth of a set of virtual apical meristems whose activity is determined at each time step of the simulation.

However, using such models at larger scales, for example, in population models, remains a great computational challenge. Effective modelling of plant-soil interactions also requires coupling discrete structures, that is, roots, to continuous descriptions of the environments for example, soil mechanics and hydraulics models.

A continuous approach has been developed, based on the continuity equation of meristem quantity. It integrates the elementary developmental processes such as expansion, tropisms and branching rate as independent terms of the equation. A semi-Lagrangian method was developed to solve the equation on discretized domains that were allowed to deform as a result of growth.

These models are still under development. However, preliminary results indicate that more efficient whole plant architectural models could be developed using this principle. Potential applications include individual based population modelling or the design and engineering of more efficient crops.

**Figure 1:** Model of barley root system using deformable domains. top: depletion zone created as a result of uptake by plant roots. bottom: the evolution of root length density (RGB colormap) and root meristem number (yellow colormap).