Functional–structural plant models (FSPM, Sievänen et al., 2000) or virtual plants (Room et al., 1996) allow us to analyze the consequences of changes in plant architecture for the functioning of individual organs and, conversely, the effects of processes at organ level on development at plant level. Plant architecture comprises the geometrical and topological organization of the component plant parts in three dimensions (Godin, 2000), whereas the adjective ‘functional’ refers to physiological processes, primarily the production and partitioning of carbon in relation to the plant environment, notably radiation.
The current experimental and modelling study focuses on the plastic response of tillering in spring wheat (Triticum aestivum). Bos (1999) hypothesized that the appearance of a tiller particularly depends on the local light regime experienced by the parent leaf during a certain phase of development of the tiller bud. Whether or not a tiller emerges clearly affects the architecture of the plant which, in turn, affects the light environment of many leaves. Here the term architecture is extended to represent the shape and orientation in 3D of all organs of a group of individual plants, i.e. a (micro)canopy. The approach taken in this study includes the following steps: (i) the design and parameterization of an architectural model of (spring) wheat; (ii) coupling of the architectural model to a model that calculates absorption of sunlight for each element of the 3D structure as it develops over time; and (iii) implementation and hypothesis testing of the relationship between local light absorption and growth of tillers. The current paper addresses only the first step, the objectives being (i) to present a general approach to architectural modelling in wheat; (ii) to present the experimental procedures to determine model parameter values specific for spring wheat; and (iii) to discuss the generality of the parameterization, primarily by comparison with parameter values obtained for winter wheat cultivar Soisson (Ljutovac, 2002; Fournier et al., 2003).
General approach to architectural modelling of wheat
The current paper builds on and expands the ADEL-Wheat model, presented earlier (Fournier et al., 2003), which pertained to winter wheat cv. Soisson. A modular approach is taken to model the plant, the phytomer (Fig. 1) being the basic unit. The wheat phytomer consists of an internode with a tiller bud at the bottom, a node above the internode, a sheath which is inserted on the node, and a leaf blade (Briske, 1991; Moore & Moser, 1995; Scanlon & Freeling, 1997); the collar marks the transition between sheath and blade. Phytomers are counted in acropetal direction. The main stem (ms) arises from the embryonal axis and produces first-order tillers from its axillary buds. Primary tillers give rise to second-order tillers, etc. The tillers are denoted according to the phytomer number the tiller emerges from, and after the order of the parent shoot. A tiller and a leaf from the axil of which the tiller has emerged are not considered to be part of the same phytomer (Fig. 1). For example, a tiller that emerges from the axil of main stem leaf 1 is tiller t2, as it is attached to phytomer 2 of the main stem. A tiller that appears from the prophyll of tiller t2 originates on the first phytomer of that tiller, and is therefore denoted as t2.1. The coleoptile tiller is denoted as t1, as it is the first primary tiller. This notation system is adapted from Klepper et al. (1982), the difference being the assignment of successive phytomer numbers to a leaf and the tiller in its axil (n and n + 1, respectively) instead of equal numbers (both n).
Figure 1. Schematic representation of two phytomers (n – 1 and n) of the wheat (Triticum aestivum) plant. Note that tiller n is located in the axil of leaf n – 1, as they belong to different phytomers.
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Architectural modelling of wheat needs to quantify (i) the (relative) timing of developmental events, i.e. rates and duration of initiation, appearance and extension of the components of the phytomers and the relay over time of developmental events; (ii) the (final) dimensions of these components; and (iii) their geometric properties, for example the curvature of leaves in space and azimuth angle between successive leaves, as derived from measurement of the leaf azimuth.
In the current modelling approach the plastochron, the phyllochron and final leaf number are input parameters of the model. Thermal time (°Cd) is used to express time-related events, assuming the base temperature for development to be 0°C. On initiation at the apex, the components of phytomers start to elongate in sequence. The leaf blade elongates first, immediately followed by the sheath. The last four or five internodes elongate, and do so after completion of the sheath. Collar emergence of phytomer n is closely linked to the timing of various phases of phytomer extension in maize and wheat (Fournier & Andrieu, 2000b; Fournier et al., 2004): collar emergence of phytomer n occurs close to the end of sheath extension and the onset of internode elongation of phytomer n, and to the onset of blade elongation of phytomer n + 2. The duration of extension of leaf parts and internodes showed little variation, regardless of phytomer rank or tiller type. The above-mentioned coordination features are incorporated in ADEL-wheat, and allow calculation of the timing of blade, sheath and internode extension on a shoot from the time course of collar appearance. They are supposed to be generic for wheat, and were not specifically investigated in the present experiment.
The time of appearance of the different orders of tillers is linked to the stage of foliar development (e.g. Haun stage: Haun, 1973) of the main stem (Klepper et al., 1982). For instance, Bos & Neuteboom (1998a) proposed to characterize the difference in foliar development between main stem and tillers with the ‘Haun-stage delay’. In the current study these delays were also quantified. The time between the appearances of two successive tillers is defined as the time, expressed in fractional phyllochrons, between the emergence of the first leaf of a tiller or main stem, and the emergence of the first leaf of the next tiller. In the model, two types of this tiller-appearance delay (TAD) are distinguished, which differ in the definition of ‘next tiller’. In TAD1, the next tiller is the tiller that develops on the same shoot as the tiller under consideration, but from one phytomer higher. The delay between appearance of t2 and t3 is an example of TAD1, as these tillers emerge from phytomer ranks 2 and 3 on the main stem, respectively. In TAD2, the next tiller is the first tiller that originates from a phytomer of the tiller in question, with tiller order +1. The delay between appearance of t2 and t2.1 is an example of TAD2.
The inclination of tiller stems is considered to be the same for all tillers; the basal inclination is fixed at 60°, and tillers straighten progressively during development of the first four internodes.
Dimensions of (fully grown) organs and their associations with other plant properties were explored and quantified. In a wheat canopy, probably no two individual leaves are exactly similar. However, when modelling, particularly when dealing with individual phytomers in 3D, it is important to simplify the representation of the system to such a degree that it can be parameterized while still simulating the essential features of the system in the real world. Therefore it is important to recognize similarity rather than differences between properties, and to seek for conservative associations between the properties of successively appearing phytomers. Properties of phytomer components, such as final leaf length, commonly show a characteristic pattern of change with phytomer number (Bos & Neuteboom, 1998a; Fournier & Andrieu, 2000a; Lafarge et al., 2002), i.e. the properties of element n + 1 are conservatively associated with the properties of element n.
L-systems (Lindenmayer, 1968; Prusinkiewicz, 1999) provide a basically modular approach to modelling, enabling plants and canopies to be described as a collection of modules. In a functional–structural approach, l-systems embed physiology, or are combined with physiological or process-based growth models (Hanan & Hearn, 2003), or exchange data with environmental models. In the current work the wheat architecture is programmed in the plant-modelling language CPFG within the l-studio shell (Prusinkiewicz et al., 2000); the original ADEL-wheat was programmed in graphtal (Streit, 1992). Light absorption per individual leaf element of the 3D structure (beyond the subject of this paper) can be achieved by interfacing the l-system with the nested radiosity model (Chelle & Andrieu, 1998).
The current paper presents the concept of modelling the 3D representation of cereal development, which is independent of the programming environment used.