DigR: a generic model and its open source simulation software to mimic three-dimensional root-system architecture diversity

Abstract

Background and aims: Many studies exist in the literature dealing with mathematical representations of root systems, categorized, for example, as pure structure description, partial derivative equations or functional-structural plant models. However, in these studies, root architecture modelling has seldom been carried out at the organ level with the inclusion of environmental influences that can be integrated into a whole plant characterization.

Methods: We have conducted a multidisciplinary study on root systems including field observations, architectural analysis, and formal and mathematical modelling. This integrative and coherent approach leads to a generic model (DigR) and its software simulator. Architecture analysis applied to root systems helps at root type classification and architectural unit design for each species. Roots belonging to a particular type share dynamic and morphological characteristics which consist of topological and geometric features. The DigR simulator is integrated into the Xplo environment, with a user interface to input parameter values and make output ready for dynamic 3-D visualization, statistical analysis and saving to standard formats. DigR is simulated in a quasi-parallel computing algorithm and may be used either as a standalone tool or integrated into other simulation platforms. The software is open-source and free to download at http://amapstudio.cirad.fr/soft/xplo/download.

Key results: DigR is based on three key points: (1) a root-system architectural analysis, (2) root type classification and modelling and (3) a restricted set of 23 root type parameters with flexible values indexed in terms of root position. Genericity and botanical accuracy of the model is demonstrated for growth, branching, mortality and reiteration processes, and for different root architectures. Plugin examples demonstrate the model's versatility at simulating plastic responses to environmental constraints. Outputs of the model include diverse root system structures such as tap-root, fasciculate, tuberous, nodulated and clustered root systems.

Conclusions: DigR is based on plant architecture analysis which leads to specific root type classification and organization that are directly linked to field measurements. The open source simulator of the model has been included within a friendly user environment. DigR accuracy and versatility are demonstrated for growth simulations of complex root systems for both annual and perennial plants.

Fig. 1.

Cutting eucalypt (Eucalyptus urophylla × grandis) architectural units. (A) Diagram of the root types and their topological links. (B) Picture of a part of a 4-year-old eucalypt root system in Congo Benin showing the main root types coming from architectural analysis. Eucalypt root typology is composed of coarse roots such as plagiotropic delayed roots (PL-ST); proximal (Pi-P) and distal delayed sinker roots (Pi-D); cable-like delayed roots (T); and fine roots such as long (>10 cm, FL) and short roots (<10 cm, FC). The root tip zone of each root, comprising very thin, short-lived and small (<3 cm long) roots which make up the absorbing system, is not taken into account. The index on R (R1, R2 to R5) accounts for branching order for observation convenience. Note that the same root type may appear at different branching orders, for instance the root system may contain R2-FL, R3-FL and R4-FL that share the same properties.

Fig. 2.

Root system simulation showing geometrical features to control root shape in terms of rhizotaxy angle (helicoid angle between two successive lateral roots) and insertion angle (angle between bearing root and laterals), root deformations (local deviation and tortuosity) and root direction within global constraint cones.

Fig. 3.

Simulations of fasciculate oil-palm root systems that show different root types at three different ages. (A) Side view of 1-year-old oil-palm root system (bottom right) and detail of two primary order roots (black rectangle) with colour related to root architectural unit (main). (B) Side view of a global oil-palm root system at 3 years old (main) and top view of a detail (black rectangle) of a horizontal primary root and its laterals (bottom right). (C) Side (main) and top view (bottom right) of an oil-palm root system at 10 years old. The complete root system is made up of eight root types: primary vertical roots (grey in A and B); horizontal primary roots (light blue); vertical secondary roots growing downward (pink); vertical secondary roots growing upward (dark blue); horizontal secondary roots (light green); tertiary surface roots (yellow); tertiary deep roots (blue) and quaternary roots (light red). DigR logo represents 2 × 2 cm scale for (A), 50 × 50 cm for (B) and 1 × 1 m for (C) main windows.

Fig. 4.

Simulations of eucalypt taproot systems depending on their primary (seedling) or secondary origin (cutting). (A) Side view of a 5-year-old seedling (main) and detail (black rectangle) of plagiotropic secondary roots (yellow) and their laterals (bottom right). (B) Side (main) and top views (bottom right) of a eucalypt cutting at the same age. (C) Perspective view of intra-specific variability with six individuals at same age (2 years old). Different root types are shown: taproot (red); distal secondary taproot (light blue); proximal secondary taproot (pink); plagiotropic secondary root (blue); cable-like root (yellow); long fine root (blue); medium fine root (purple); short fine root (red). DigR logo represents 2 × 2 m scale for (A) and (B), and 1 × 1m for (C) main windows.

Fig. 5.

Simulation examples of particular root systems with (A) sugar beet (Beta vulgaris) illustrating tuber roots, (B) chick pea (Cicer arietinum) illustrating nodule roots and (C) lupin (Lupinus sp.) illustrating cluster roots. These root systems are simulated at 50 d (A) and 60 d (B, C) old respectively and grew in homogeneous edaphic environment. DigR logo represents 5 × 5 cm scale for (A), 3 × 3 cm for (B) and 2 × 2 cm for (C).

Fig. 6.

Snapshot of Xplo software running DigR model with a 1-year-old oil-palm simulation. The lower left window (topological view) exhibits the structure of the root system through a graph representation, which details topological relationships between root segments of different root types (left column) and the associated root parameter values (other columns). The lower right window shows the 3-D mock-up display (geometrical view) which highlights the selected root segment (red square) of R3 type whose characteristics are selected (in blue) within the topological view. In the upper left window, all roots belonging to the same R3 root type are extracted (extraction view, left column) and root traits are computed (other columns). The upper right window (plot view) displays, here as an example, the root length distribution of the R3 root type previously extracted.

Fig. 7.

Simulation of a theoretical perennial plant tap-root system without edaphic constraint (right) and with a virtual strong soil compaction located at 50 cm depth (left). Root growth speed and unbranched apical zone are strongly reduced while branching density, root diameter and tortuosity angles are increased. DigR logo represents 40 × 40 cm.

Fig. 8.

Simulation of a 3-year-old oil-palm root system exhibiting uptake zones located behind each root tip. Global view (main window), top view (bottom right) and detail view (bottom left). DigR logo represents 1 × 1 m scale (main window), 2 × 2 m (bottom right) and 50 × 50 cm (left).