Towards a generic architectural model of tillering in Gramineae, as exemplified by spring wheat (Triticum aestivum)


  • Jochem B. Evers,

    Corresponding author
    1. Crop and Weed Ecology, Plant Sciences Group, Wageningen University, Haarweg 333, 6709 RZ Wageningen, the Netherlands;
      Author for correspondence: Jochem B. Evers Tel: +31 317 483251 Fax: +31 317 485572 Email:
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  • Jan Vos,

    1. Crop and Weed Ecology, Plant Sciences Group, Wageningen University, Haarweg 333, 6709 RZ Wageningen, the Netherlands;
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  • Christian Fournier,

    1. UMR Environnement et Grandes Cultures, Institut National de la Recherche Agronomique, 78850 Thiverval-Grignon, France
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  • Bruno Andrieu,

    1. UMR Environnement et Grandes Cultures, Institut National de la Recherche Agronomique, 78850 Thiverval-Grignon, France
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  • Michael Chelle,

    1. UMR Environnement et Grandes Cultures, Institut National de la Recherche Agronomique, 78850 Thiverval-Grignon, France
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  • Paul C. Struik

    1. Crop and Weed Ecology, Plant Sciences Group, Wageningen University, Haarweg 333, 6709 RZ Wageningen, the Netherlands;
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Author for correspondence: Jochem B. Evers Tel: +31 317 483251 Fax: +31 317 485572 Email:


  • This paper presents an architectural model of wheat (Triticum aestivum), designed to explain effects of light conditions at the individual leaf level on tillering kinetics. Various model variables, including blade length and curvature, were parameterized for spring wheat, and compared with winter wheat and other Gramineae species.
  • The architectural model enables simulation of plant properties at the level of individual organs. Parameterization was based on data derived from an outdoor experiment with spring wheat cv. Minaret.
  • Final organ dimensions of tillers could be modelled using the concept of relative phytomer numbers. Various variables in spring wheat showed marked similarities to winter wheat and other species, suggesting possibilities for a general Gramineae architectural model.
  • Our descriptive model is suitable for our objective: investigating light effects on tiller behaviour. However, we plan to replace the descriptive modelling solutions by physiological, mechanistic solutions, starting with the localized production and partitioning of assimilates as affected by abiotic growth factors.


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.

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.

Materials and Methods

Experimental setup

To parameterize the model, an experiment was conducted in natural climatic conditions in Wageningen, the Netherlands (51°58′ N), in the period April to June 2003. Spring wheat plants (Triticum aestivum L., cv. Minaret) were grown in 70 × 90 cm containers. These contained a soil layer of ≈35 cm and a 3 cm layer of coarse gravel on the bottom for drainage purposes. The soil was enriched with fertilizer resulting in a nitrogen content of 15 g m−2, which causes no limitation for vegetative development. The seeds were sown at a density of 100 m−2, in a regular grid of 10 × 10 cm. Sowing depth was ≈5 cm. Weeds, aphids and mildew were controlled by spraying appropriate biocides. The containers were arranged closely together to ensure canopy homogeneity. Part of the plants was used for nondestructive measurements, part for destructive measurements (harvests).


Temperature was recorded with shielded thermocouples (type T, TempControl Industrial Electronic Products, Voorburg, the Netherlands) every hour (Datataker DT600, Datataker Data Loggers, Cambridgeshire, UK). The thermocouples were placed 6 cm deep in the soil, and within the canopy at 20 cm above the soil surface; air temperature was measured at 1.5 m above soil surface.

Leaf and tiller appearance and length of the appearing part of each leaf of 14 individual plants were monitored every 3 or 4 d. These measurements were done on main stems and all primary and higher-order tillers. The dimensions of all fully grown organs (blades, sheaths and internodes) were measured destructively on two sampling occasions using separate batches of plants. The first occasion was at maturity of the fifth main stem leaf (n = 12); the second sampling occasion was at maturity of the flag leaves of all shoots (n = 10). Note that leaves were regarded as fully grown when the ligule had appeared.

Individual plants were digitized using a Polhemus Fastrak magnetic digitizer (Polhemus, Colchester, VT, USA). This device records X, Y and Z coordinates of objects relative to a reference point. Using this method, information on midrib curvature and azimuth of leaf blades was gathered (Fig. 2), digitizing five to 20 points along the midrib depending on the amount of curvature. Digitization of plants was done on three occasions, as it is not possible to digitize all fully grown leaves at once because of leaf senescence. On the first occasion, 30 plants were digitized when the third main stem leaf was fully grown. On the second occasion, 10 plants were digitized when the eighth main stem leaf was fully grown. At that time the plants had grown at least five shoots, all of which were digitized. Finally, on the third occasion, fully grown flag leaves of all shoots of six plants were digitized. Plants digitized at the second and third occasions were also among the plants digitized earlier. It was assumed that shape and inclination of leaves did not change after ligulation. The digitization database ultimately consisted of geometrical data on 435 fully grown leaves, composed of nearly 10 000 digitized points in total.

Figure 2.

Visualized 3D scanning data [X, Y and Z coordinates expressed in distance (cm) to the scanning reference point] for the leaves of one spring wheat (Triticum aestivum) plant at booting stage.

Data analysis

Temperature data were converted into thermal time with a resolution of 1 h. For the first 3 wk after sowing, temperature data from the soil were used, as the apex was still under the soil surface; thereafter thermal time data were calculated from the canopy temperature. Digitization data were analysed using R ver. 1.8.1 (R Development Core Team, 2003). All other data were analysed using Microsoft excel 2002 and SPSS ver. 11.0 (2001). Goodness of fit for the parameterization functions was analysed by calculating the root mean square error (RMSE), which is defined as:

image(Eqn 1 )

with i = sample number, N = total number of measurements, Xsim,i = simulated value, and Xobs,i = observed value.

Results and Discussion

Leaf and tiller appearance

The phyllochron, measured in degree days (°Cd), that is the thermal time between the appearance of two consecutive leaves on the same shoot, showed some variation among the various shoots (Fig. 3). Phyllochron for main stem leaves was 76.2°Cd (SE 3.71). Tiller phyllochron ranged from ≈85–100°Cd, when one disregards tillers that appeared very late in the development of the plant (t5, t2.2, t3.1). One mean value for tiller phyllochron was calculated: 88.0°Cd (SE 1.95). The two values for main stem and tiller leaves were used in the architectural model. The current ≈15% difference in phyllochron between main stem and tillers of spring wheat corroborates observations by Bos & Neuteboom (1998b) on this spring wheat cultivar. As found more often (Bos & Neuteboom, 1998b; Hay, 1999), the observed phyllochron of spring wheat is slightly lower than that found for winter wheat cv. Soisson.

Figure 3.

Average phyllochron (in degree days) for the main stem (ms), primary tillers t1–t5, and secondary tillers t1.1, t1.2, t2.1, t2.2 and t3.1 of spring wheat (Triticum aestivum) plants. Error bars, 2 SE.

Effects of photoperiod on phyllochron differ between wheat cultivars (Cao & Moss, 1989; Pararajasingham & Hunt, 1995; Hay, 1999). Therefore it is clear that phyllochron is a parameter that cannot be regarded as generic, i.e. it will have to be reparameterized experimentally for cultivar and sowing time. Volk & Bugbee (1991) suggest that the phyllochron can be calculated from daily photosynthetic photon flux density (PPFD, µmol m−2 d−1), irrespective of cultivar and sowing time. However, this approach needs to be tested first before implementation in the current architectural model is warranted.

TAD1 was calculated using data from t2, t3 and t4, as other tillers appeared more erratically, rendering an analysis less meaningful. TAD1 between t2 and t3 was 0.99 (SE 0.001) phyllochrons; between t3 and t4, TAD1 was 0.70 (SE 0.13) phyllochrons. For use in the model, one mean value for TAD1 was calculated: 0.84 (SE 0.07) phyllochrons. For parameterization of TAD2 data from ms, t1, t2 and t3 were used yielding 1.60 (SE 0.04) phyllochrons. Note that for calculation of TAD values the actual phyllochron of the shoot in question is used, not the average phyllochron across tiller types as calculated in the previous section.

Relative phytomer number

Properties of the components of phytomers show a gradient with phytomer ranks. Gradients of final blade, sheath and internode dimensions along any tiller of cv. Soisson could be regarded as being similar to gradients along the main stem after applying a certain phytomer shift (Fournier et al., 2003). A phytomer shift is basically a certain decimal number of phytomers, characteristic for each tiller, which is added to the actual phytomer rank, obtaining the relative phytomer number (RPN). That concept appeared to apply to spring wheat as well. The phytomer shift was calculated for primary tillers 1–4 based on the internode length data (Fig. 4) in a two-step fitting process: first, the data points for all tillers were superposed on the main stem data points, which was done by shifting the points to the right (indicated by the arrow in Fig. 4a); this was done several times to obtain the best linear fit. The result of the phytomer shift is shown in Fig. 4b. Next, phytomer shift values for each individual tiller type were calculated precisely by minimizing RMSE between the internode length data and the obtained linear model. The resulting shift values are listed in Table 1. The shifts appeared to vary linearly with tiller number (y = ax + b, with y being phytomer shift, a the slope, x tiller number, and b the intercept [R2 = 0.95 for a = 0.703 (SE = 0.12) and b = 1.19 (SE = 0.32), RMSE = 0.18]. In the rare case of the presence of t5 or t6, the relation for t1 to t4 is extrapolated to calculate the phytomer shift values. The phytomer shifts were applied to derive single associations between RPN and final blade length and width, sheath length, and also internode length. The same method as described here for primary tillers was used to determine phytomer shifts of secondary tillers (Table 1).

Figure 4.

Final internode length vs phytomer number for the main stem (ms) and primary tillers t1–t4 of spring wheat (Triticum aestivum) plants. The arrow in (a) indicates the direction of phytomer shift; (b) shows the same data after the shifts have been applied (relative phytomer number).

Table 1.  Phytomer shifts for primary and secondary tillers of spring wheat (Triticum aestivum)
ShootPhytomer shift
  1. A phytomer shift indicates the amount of fractional phytomer that has to be added to the number of the phytomer in question to make it resemble the main stem in terms of final organ dimensions.


The virtue of a tiller-specific phytomer shift, outlined above, is that properties of phytomers of the next order of tillers can be derived from the parent shoot. In this way, modelling the properties of each tiller independently is avoided. There is another method to reach the same goal, namely the concept of ‘summed phytomer number’ or ‘summed leaf position’ (Bos & Neuteboom, 1998a; Tivet et al., 2001; Buck-Sorlin, 2002), in which phytomer ranks on tillers are calculated as the sum of phytomer numbers from the base of the plant to the phytomer in question. For example, in this view phytomer 3 on tiller t2 would be summed as phytomer number 5 (two phytomers on the main stem plus three phytomers on the primary tiller). It appeared that this concept reflects the similarities between organ dimensions of different tillers well for spring wheat, also. However, phytomer shifts are expressed as fractions, and are therefore more precise than the integers of summed phytomer numbers, and for this reason we have chosen to use the former approach in the model.

The current values for phytomer shifts are comparable with those found for Soisson winter wheat grown at two plant densities. Nevertheless, we suggest calculating the values for each cultivar and density if the purpose of modelling requires an accurate mimicking of the changes in 3D structure over time. The summed phytomer number concept, however, can serve as an acceptable and elegant simplification to relate properties of phytomers of order n + 1 to those of order n, when detailed measurements are not available.

Final leaf number

The final number of leaves produced on the main stem did not vary much among plants: in 86% of cases the final leaf number was nine. Final leaf number in wheat depends on genotype, vernalization, daylength, temperature and nitrogen supply (Rawson & Zajac, 1993; Longnecker & Robson, 1994; Hay, 1999; Brooking & Jamieson, 2002). In the current model, the parameter for final main stem leaf number is set to nine. Subsequently, the final leaf number for tillers is calculated by subtracting the phytomer shift for that specific tiller from the main stem final leaf number, and rounding this value to the nearest integer. This parameterization appears to hold well for all tillers (RMSE = 0.38). A module has been developed (Jamieson et al., 1998) to calculate final leaf number in relation to temperature and photoperiod. That module can be incorporated in the current architectural model, avoiding final leaf number being specified as an input parameter.

Leaf dimensions

Length of the blade of fully grown leaves of all shoots showed a distinct curve when plotted against RPN (Fig. 5). Comparable curves have been found earlier for several spring and winter wheat cultivars (Pararajasingham & Hunt, 1995; Hotsonyame & Hunt, 1997). A nonlinear regression based on the Lorentz peak distribution function was applied to the data (Buck-Sorlin, 2002):

Figure 5.

Final blade length vs relative phytomer number of the main stem (ms) and primary tillers t1–t4 of spring wheat (Triticum aestivum) plants. The curve indicates Lorentz peak distribution function fit (LPD).

image(Eqn 2 )

This function has three parameters: ym, maximum final blade length; b, slope coefficient; and x0, RPN at ym. This function appeared to fit well [R2 = 0.89 for parameter values ym = 31.3 cm (SE = 0.71 cm); b = 3.79 (SE = 0.26); x0 = 7.49 (SE = 0.13)] to the final blade length data (n = 33); see also Fig. 5. The function appears particularly suitable for RPN values of 4 and higher; blade length of phytomers 2–5 of the main stem is underestimated. An alternative approach using a bilinear function, which is used in the winter wheat parameterization, was also explored. However, besides the slightly higher RMSE compared with the Lorentz peak distribution function (2.48 vs 2.30), this method requires five instead of three parameters and was therefore not used in the spring wheat model.

Spring wheat cv. Minaret and winter wheat cv. Soisson differ distinctly in variability in the length of the first fully grown leaf of all shoots. In spring wheat this length varied among shoot types from ≈8–18 cm, whereas in winter wheat it was nearly constant at ≈9 cm (note that in spring wheat this variation in first leaf length is eliminated when phytomer shifts are applied). Apart from this difference, the general shape of the final blade length vs phytomer rank curves is similar across various gramineous species, e.g. maize (Fournier & Andrieu, 1998); sorghum (Kaitaniemi et al., 1999; Lafarge et al., 2002); barley (Buck-Sorlin, 2002); rice (Tivet et al., 2001); and annual bluegrass (Cattani et al., 2002), although in wheat the peak of the curve is commonly situated at the penultimate leaf whereas in the other species the decline in final leaf length starts at lower phytomers. Nevertheless, results on wheat final blade length reported by Pararajasingham & Hunt (1995); Hotsonyame & Hunt (1997); Bos (1999) show a decline in final blade length starting at the top three to four leaves, indicating an effect of photoperiod, nitrogen supply and plant density on the shape of the curve. Therefore the Lorentz peak distribution can be regarded as an appropriate function to describe final leaf-length distribution along a stem in Gramineae; the precise shape is determined by conditions during development of the plant.

Sheath length of fully grown leaves was parameterized in a way similar to blade length. After applying phytomer shifts, several functions that would probably fit the final sheath length data well were tested: linear, exponential, expo-linear and logistic. The best approximation (R2 = 0.95, n = 33) was made by fitting the logistic function:

image(Eqn 3 )

This distribution function (Fig. 6) showed the lowest RMSE (1.20), and contains only three parameters: ym, asymptote for final sheath length; a, lag coefficient; and k, slope coefficient. The parameter values after fitting were ym = 21.5 cm (SE = 1.52); a = 2.83 (SE = 0.25); and k = 0.533 (SE = 0.07).

Figure 6.

Final sheath length vs relative phytomer number of the main stem (ms) and primary tillers t1–t4 of spring wheat (Triticum aestivum) plants. The curve indicates the logistic function fit (log).

This parameterization of sheath length does not suggest an underlying mechanism. It has been chosen for its good description of sheath length distribution along the shoot, as there appears to be some variability in the shapes of the curves in various Gramineae. Sheaths on the main stem had a constant length for the first four to five phytomers in the winter cultivar, consistent with earlier observations (Gallagher, 1979), whereas in spring wheat the length initially increased monotonously with phytomer rank. In spring wheat, sheath length started to level off from RPN values of 7 and higher, instead of showing continued linear increase with phytomer number as in winter wheat; in maize, sheath length was even observed to decrease from phytomer number 7 onwards (Fournier & Andrieu, 1998, 2000a). As a consequence of this variability across species and cultivars, final sheath length vs RPN probably needs reparameterization for every new species, cultivar and sowing time.

Maximum blade width of fully grown leaves did not yield a single association with RPN, either in spring wheat or in winter wheat. However, in spring wheat maximum blade width appeared to correlate well to final sheath length using the linear function y = ax + b, with slope a = 7.8 × 10−2 cm cm−1 (SE = 0.5 × 10−2) and intercept b = 0.21 cm (SE = 0.06) (R2 = 0.90; n = 33; Fig. 7). This relation is used to model final maximum blade width (RMSE = 0.13), and results in a sigmoid curve that describes maximum blade width vs RPN because sheath length was modelled as a logistic function of RPN. A sigmoid shape has also been shown by Bos & Neuteboom (1998a), who fitted a similar sigmoid function to model maximum blade width vs summed phytomer number directly. Additionally, Pararajasingham & Hunt (1995) observed a similar pattern for main stems of several spring and winter wheat cultivars grown at different photoperiods. However, some of the cultivar × photoperiod combinations showed a decrease in maximum blade width at the top three to four phytomers instead of a plateau, whereas other cases could be described using a simple linear function. Similar variability in the blade width of main stem leaves has been observed by Hotsonyame & Hunt (1997). This reinforces the view that maximum blade width of Gramineae cannot be modelled solely as a robust function of RPN; more variables need to be taken into account, such as photoperiod or light intensity (Bos et al., 2000), plant density and nitrogen level. A study on density effects on leaf area growth in spring wheat (Bos, 1999) showed that increasing plant density results in a decrease in maximum blade width for the top four main stem leaves; such a relation can be investigated and incorporated into the model. In the current model, maximum blade width is an input parameter is a second-order polynomial equation (Prévot et al., 1991), yielding the change in leaf width as a function of the distance to the blade base.

Figure 7.

Final maximum blade width vs final sheath length of the main stem (ms) and primary tillers t1–t4 of spring wheat (Triticum aestivum) plants. The line indicates the linear fit (lin).

Leaf geometry

Curvature of the blade midrib was modelled using the method proposed for maize (Prévot et al., 1991), and applied to maize (Fournier & Andrieu, 1998) and winter wheat cv. Soisson. The model describes the wheat blade as a combination of an ascending parabolic part and a descending elliptic part. No twisting of the blade is taken into account; the blade is supposed to be in a plane, bent in the third dimension. A schematic representation of a modelled leaf blade is shown in Fig. 8. Parameters Φ0 and dΦn are angles that define the parabolic part of the curve; Φi and Ψe define the elliptic part. In addition, a further parameter ɛ is used to define eccentricity of the elliptic part, based on the length of the horizontal and vertical axes d and e, respectively; the absolute value of ɛ is the eccentricity, and its sign is the direction of the ellipse main axis. Furthermore, a parameter Pcass was used to define the ratio between length of the parabolic part and length of the blade, to model the transition between parabola and ellipse. Two digitized and modelled spring wheat leaf blades are shown in Fig. 9a,b. The first example (Fig. 9a) was modelled using only the parabolic part; the second example (Fig. 9b) shows both a parabolic and an elliptic part. Over 94% of the digitized fully grown leaves could be fitted using either only the parabolic function or both the parabolic and elliptic functions; the remaining 6% could not be fitted and were therefore unsuitable for parameter derivation. As a clear distinction could be made between leaves situated near the bottom of the plant and the higher leaves, these two groups were parameterized separately. The separation was based on two categories of Pcass as, for most of the lower leaves (phytomer numbers 6 and higher when counting, only for this purpose, from the top downwards), Pcass appeared to be close to 1, meaning the blade does not have a descending part (Fig. 9a). The parameter values for leaf curvature were entered in a database and their distributions calculated. In the architectural model, parameter values for leaf curvature are drawn from these distributions. This stochasticity is implemented to reflect the variation in blade curvature found in the field.

Figure 8.

Model of leaf blade curvature as proposed by Prévot et al. (1991) for maize. Φ0 and dΦn define angles of the parabola (ascending part); Φi and Ψe define angles of the ellipse (descending part); d and e are lengths of the horizontal and vertical ellipse axes, respectively.

Figure 9.

(a,b) Two examples of spring wheat (Triticum aestivum) leaf blades; dots represent digitized points, lines represent the modelled blade curvature. x- and y-axes represent distance to the blade ‘insertion point’– the point at which the blade is touching the stem. The vertical dashed line indicates the transition between parabola and ellipse, Pcass, which is defined as the ratio between length of the ascending part of the blade and length of the entire blade.

Analogous to midrib curvature, parameterization of leaf blade azimuth was done using a purely statistical approach based on the digitization data set. This was done by analysing the angles between consecutive leaves. Phytomer shifts were applied to the tillers to compare fully grown leaves of comparable RPN. A distinction can be made between angles at RPN = 3 (Fig. 10a) and higher ranks (Fig. 10b). For an RPN value of 2, the majority of the angles was near +180° and −180°, indicating the tendency towards opposite azimuth. For an RPN value of 3, the angles were more dispersed, with few points only between −120° and +60°. For RPN values ≥5, a less regular orientation was observed with a slight preference for lower angles. Therefore, in the model two sets of phytomer ranks were distinguished (RPN 1–3, and all higher RPN values; note that in the range of RPN values between 3.5 and 5.5 a limited amount of data were available, therefore it is not precisely known at which RPN the limit is located). For both sets the distribution of observed orientation was calculated, and in the model values were drawn from these distributions.

Figure 10.

Circular histograms showing the distribution of azimuth angle between consecutive leaves, for RPN values 1–3 (a) and >3 (b). Data from all shoots are shown (n = 281).

The observations that blade azimuth was mainly opposite for the lower phytomers, and more towards a spiral configuration in higher phytomers, agree with observations in winter wheat cv. Soisson and in maize (Fournier & Andrieu, 1998; Maddonni et al., 2002). In maize, blade azimuth can be altered during development of the plant, as a result of light signalling caused by scattering by neighbouring plants (Maddonni et al., 2002). It was shown that the leaves adopted azimuth angles perpendicular to the row structure. If any such response would potentially be present in spring wheat, it would not be manifest in the current experiment as the wheat plants were sown in a regular grid without any row structure. Any light signalling would then come from all directions, and would be neutralized as a consequence. Because of this unaffected development of blade orientation, the obtained parameterization defined here for spring wheat can be regarded as being general, although the distributions might differ somewhat among cultivars, depending on final leaf number.

Internode length

When not elongated, internodes were assigned length 0. Length of elongated fully grown internodes showed a very close relationship with RPN and was approximated by a linear function of the form y = ax + b, with slope a = 3.80 cm (SE = 0.23) and intercept b = −17.5 cm (SE = 1.71) (R2 = 0.94, RMSE = 0.95, n = 33). The RPN of the first elongated internode is defined as f = 1 − b/a. This is 1 plus the x-intercept of the linear model (–b/a), as the x-intercept represents the RPN of the last nonelongated internode.

The current value for a is close to the value observed in Soisson, namely 3.42 and 3.58 for 250 and 70 plants m−2, respectively. For new applications of the model, final internode length needs recalibration, including the RPN of the first elongated internode (f). In spring wheat cv. Minaret f was 5.59, but higher values were found in winter wheat cv. Soisson, namely 6.19 and 7.37 for 250 and 70 plants m−2, respectively. As the total number of internodes in wheat that elongate is usually four or five, this parameter is likely to depend on the total number of vegetative phytomers initiated, which is usually much higher in winter wheat than in spring wheat cultivars. In contrast to wheat, maize shows a distinct decline in internode length with increasing phytomer number from phytomer 9 or 10 onwards (Birch et al., 2002; Fournier & Andrieu, 2000b). Therefore, parameterizing this variable for other Gramineae probably requires the function that describes internode length along the stem to be redefined.


This paper describes our efforts to parameterize a 3D architectural model of spring wheat which will be applied to explain the tillering pattern, as influenced by light conditions at the leaf from the axil of which the tiller may or may not emerge. Two aspects of light will be examined, namely the amount of photosynthetically active radiation received per leaf, and the red/far-red ratio of the light received. Such an application requires a detailed 3D description of a wheat canopy in order to simulate light interception and scattering accurately (see Fig. 11 for example of a small simulated wheat plot). The model presented here is highly descriptive, in the sense that properties of organs are predetermined, with the exception of two stochastic elements. However, this does not invalidate the model as a tool to test local effects of light on tillering. The application of the model is straightforward as long as experiments to derive model parameters (reported here) and experiments to test model results (to be reported later) are conducted under comparable conditions. In the current experiments we aimed at potential growth conditions (van Ittersum et al., 2003), i.e. plants grown with ample availability of nutrients and water and in the absence of impact of pests, diseases and weeds. In this context the results of Bos's (1999) sensitivity analysis are relevant: leaf area growth per unit soil surface appeared most sensitive to the number of tillers appearing, and less so to leaf length and leaf width. So our modelling study focuses on the most influential component of leaf area growth.

Figure 11.

Example of a small simulated wheat (Triticum aestivum) plot.

In the long term it is our intention to develop an architectural model for wheat that can serve as a basis to represent cultivars other than Minaret. In order to reduce the amount of time and effort needed to parameterize the model correctly, it may be necessary and possible to introduce simplifications. The incorporation of a more general tiller-simulation routine, based on the concept of summed phytomer numbers (Bos & Neuteboom, 1998a), is an example of such a simplifying concept. Future sensitivity analysis will provide insight into the parameters that critically determine the modelling results. This could lead to fixation of parameter values of which the influence is small, and that could therefore be regarded as being general for wheat.

The differences in final organ dimensions between the spring and winter wheat cultivars used in this study reflect the differences between spring and winter wheat in general. As winter wheat main stems produce more phytomers than those of spring wheat, various parameters and functions are inevitably different. Good examples of this are the difference in sheath length for the first four to five phytomers, and the value of the parameter that determines the RPN of the first elongated internode. The relative ease with which the original winter wheat model could be adapted and parameterized for spring wheat suggests that the approach provides a template for 3D modelling of Gramineae in general. The approach can be extended to account for effects of environmental factors such as water and nutrients, and interplant competition. Such extension needs to be based on incorporating sink–source relations in the model. Steps in that direction have been taken by Allen et al. (2004), and such efforts are on our research agenda.

The present model was implemented using the framework of ADEL-Wheat (Fournier et al., 2003). A description of the computational procedures and the associated source code are available from C. Fournier (


The authors would like to thank Unifarm, Peter van der Putten, Alain Fortineau, Ans Hofman and Henriette Drenth for valuable help and contributions to the experiment. The financial support of the Netherlands Organisation for Scientific Research, the ‘Stichting Fonds Landbouw Export-Bureau’, and the C.T. de Wit Graduate School for Production Ecology and Resource Conservation is gratefully acknowledged.