Andrieu, B.

Chelle, M.

Evers, J.B.

Fournier, C.

Struik, P.C.

Vos, J.

Wageningen Yield 

FSPM04  ORAL PRESENTATIONS - SESSION 5 
 
4th International Workshop on Functional-Structural Plant Models, 7-11 june 2004 –Montpellier, France 
Edited by C. Godin et al., pp. 210-215 
A 3D approach for modelling tillering in wheat (Triticum aestivum L.) 
J.B. Evers1, J. Vos1, C. Fournier2, B. Andrieu2, M. Chelle2, P.C. Struik1 
1 Group Crop and Weed Ecology, Department of Plant Sciences, Wageningen University, Haarweg 333, 6709 
RZ Wageningen, the Netherlands) 
2 UMR Environnement et Grandes Cultures, Institut National de la Recherche Agronomique, 78850 Thiverval-
Grignon, France) 
 
Introduction 
In crop science and related disciplines, crop development and growth have been analysed in 
models that basically describe development in relation to temperature (and in some cases: 
photoperiod) and in terms of increment of dry matter from light interception. The distribution of dry 
matter over components (e.g. stems, leaves, roots) and the associated increase in leaf area index are 
usually functions of development. Such models have been instrumental to provide references for 
potential crop production in given climates have increased the quantitative insight in crop production 
and have influenced the agenda of experimental research (van Ittersum et al., 2003). 
For wheat (Triticum aestivum L.), various advanced crop growth models have been developed (e.g. 
Jamieson et al., 1998; Ewert et al., 2002). Most of these models do not describe the dynamics of leaf 
and tiller numbers. Therefore, these models are not particularly suited to analyse and design ideotypes 
and to explain interactions between canopy architecture and crop performance. To study the dynamics 
of numbers of organs, their determinants and the consequences of specific physiological responses, 
models are needed that are capable of describing the morphogenesis and ontogeny of plants in more 
detail than is done in current crop growth models. 
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 are combined with environmental models. The virtue is that each next 
step in the development of the 3D structure can be made dependent of external driving forces, acting 
on the structure as a whole, but also (and more interestingly) on each individual module. Such an 
approach is particularly suited for modelling tillering in wheat as influenced by light conditions at the 
level of the individual organs. For this to be correctly simulated, it is necessary to establish accurate 
values for the developmental kinetics and geometry of the cultivar of interest.  
The current work is based on an L-system of winter wheat developed at INRA Grignon (Fournier 
et al., 2003). The objective of the study is to explain the appearance of a tiller, or conversely: the 
suppression of tiller growth, from the light regime experienced by the parent leaf in spring wheat. 
This paper presents the general approach and addresses the parameterisation of the L-system for 
spring wheat 
 
Developmental pattern of the wheat plant and determinants of tillering 
The morphological development of wheat is a highly co-ordinated process. Studies such as those 
by Kirby (1990) and Bos and Neuteboom (1998b) emphasise that the timing of phenological events 
(initiation and appearance of organs) conform to a fairly fixed pattern. For example, the time of the 
possible appearance of a specific tiller can be predicted from the stage of development of the main 
stem or another type of parent tiller.  
Tillering is one of the adaptive mechanisms of the wheat plant to keep sources and sinks in 
balance. The configuration of tillers on a plant (total number and their order, e.g. primary tillers, 
secondary tillers) reflects the outcome of an adaptive process. Whether particular tillers do appear or 
not depends on conditions during a window of opportunity for the axillary bud involved. This window 
is specific in terms of timing and duration. Internal and external conditions that favour growth per 
plant appear to enhance the number of tillers and the order of tillering that is attained ultimately. 
These conditions include moderate temperature, high level of incident radiation, high plant nitrogen 
concentration and low plant density. Unfavourable conditions for growth, e.g. low light level, 
especially per unit thermal time, and high plant density appear to result in reduced tillering.  
Two-way interactions between process-based tree growth models and 3D structural-functional models 
ORAL PRESENTATIONS - SESSION 5 
211
Analysis of effects of plant density and radiation (Bos, 1999) led to the hypothesis that the light 
quantity (Photosynthetically Active Radiation, PAR) received by a parent leaf is decisive for the 
outgrowth of its bud into a tiller. In this view outgrowth of a tiller is prevented if carbon resources are 
insufficient to sustain unrestricted growth and functioning of parent plant organs. Furthermore, 
tillering in wheat appears to be sensitive to changes in light quality, particularly in red/far-red ratio 
(R:FR) (Casal, 1988; Kasperbauer and Karlen, 1986). These changes in R:FR are the result of 
selective reflection of light by leaves in the canopy (Holmes and Smith, 1975), and appear to be an 
environmental cue for impending competition (Ballaré et al., 1987). 
 
The model assembly 
To adequately simulate light interception in a wheat canopy and for the calculation of light 
conditions at the level of the organ (see also Gautier et al., 2000), an L-system of wheat is used in 
combination with a light interception model. The latter is called the “nested radiosity” model, and is 
capable of calculating light conditions anywhere in a virtual canopy, taking into account multiple 
scattering of radiation and changes in its spectral composition (Chelle and Andrieu, 1999). 
The wheat L-system is adapted from the ADEL-wheat model (Fournier et al., 2003), using L-
Studio (Prusinkiewicz, 2000). It simulates the 3D development of winter wheat plant as a function of 
thermal time. The simulation of the dynamics of plant architecture requires calculating (1) geometric 
features such as leaf orientation and midrib curvature, (2) the 2D shape of the leaves, and (3) the 
kinetics of extension growth of individual organs (blades, sheaths and internodes). An example of a 
simulated plot is shown in Figure 1. Basically, the architectural wheat model captures the essential 
features of the temporal and spatial patterns in the formation of plant architecture, which allows 
simulation of the development of the plant using a limited number of parameters. These parameters 
are obtained from geometrical measurements characterising the architecture of the mature plant, and 
the kinetics of collar emergence of successive leaves. 
Modelling of organ extension requires simulation of extension of both main stem and tillers, using 
rules with a restricted number of parameters. These rules were extracted from several detailed 
experiments on winter wheat. Quantification of the coordination of successive events is an important 
issue. The start of leaf and internode extension is described in rules assuming co-ordination between 
phytomers: e.g., the emergence of the collar on phytomer n is considered to be a signal that stops the 
extension of sheath n, and triggers linear extension of internodes n and of blade n+2. Another 
important feature is that the duration of extension of leaves and internodes was found not to vary 
between phytomers, the rate of extension being proportional to the final length in winter wheat. 
Finally, the function of blade length vs. phytomer number showed a “developmental shift”, in which 
all axes are identical except for a parameter describing the developmental state when the bud was 
initiated; see Figure 2 for an example. Similarity was found for the 2D leaf shape variables as well, 
and the midrib curvature parameters were found very similar among leaves on the main stem and the 
tillers. 
In the current work the wheat L-system is extended with rules which process the light information 
provided by nested radiosity, and make tillering dependent on the intercepted radiation. The first 
objective is the calculation of the cumulative amount of absorbed energy of each parent leaf (that can 
potentially produce a tiller from its axil) over time. “Over time” has to be defined more closely as 
being the “window of opportunity” that is decisive for the outgrowth of the tiller bud. It is 
hypothesised that the cumulative amount of energy absorbed during the window of opportunity has to 
exceed a minimum value for the growth of a tiller. Once such a model is calibrated it needs to be 
tested for a range of conditions (plant densities, light regimes, perhaps experimental manipulations of 
parent leaves). When the model proves capable of predicting tillering consistently, the conclusion can 
be drawn that the model essentially reflects the behaviour of the real system. Likewise, hypotheses 
can be tested on effects of light quality on tillering. It can be calculated when the R:FR ratio of light 
falling on particular organs drops below threshold values, and such information can be confronted 
with observed tillering patterns. 
 
Parameterisation  
The parameterisation of the original winter wheat model required data collection and analysis to 
extract robust rules that describe co-ordination of successive events and revealed similarities in 
J.B. Evers et al. 
SESSION 5– ORAL PRESENTATIONS 
212 
properties among phytomers. At present, similar data are collected and processed for spring wheat. It 
is embedded in the concept of the current L-system that the description of thermal time course of 3D 
plant architecture can be simulated based on the knowledge of (1) the final size and geometric 
parameters for successive organs along the main stem, (2) the timing of collar emergence of leaves on 
the main stem, and (3) the (estimated) developmental delay between a tiller and the main stem. 
Geometric parameters are derived from 3D scan data (see Figure 3 for an example of a digitised wheat 
plant). These parameters include leaf orientation (azimuth) and midrib curvature (Fournier et al., 
2003). 
In wheat, published data suggest that the morphology of tillers resembles that of the main stems in 
all cultivars. Similarly, the fact that timing of development of successive phytomers along the main 
stem is highly co-ordinated appears to be a general observation (Kirby, 1990; Bos and Neuteboom, 
1998b), both for spring and winter wheat cultivars. The rules incorporated in the architectural wheat 
model are an economic way of formalizing these patterns, and hopefully will be valid independently 
of the cultivar. Hence, it is probably true that parameter values determined for one cultivar can be 
used to simulate the course of development of other cultivars. This is important, because functional-
architectural modelling is not helpful as a tool to analyse problems if first substantial time has to be 
devoted to model parameterisation. In other words, it is essential in architectural modelling to 
simplify the concept of the system to the largest acceptable degree. In this context it is more important 
to stress similarities in parameter values across different types of leaves and tillers than to stress what 
is different. 
On the other hand, genetic and environmental variation affects the final size and geometric 
parameters of organs along the main stem, as well as the rate of collar emergence. Midrib curvature 
and leaf width are described in the architectural model by purely empirical rules, thus the value of 
parameters will change according to genotype-environment interactions. The range of variation is 
difficult to predict a priori and parameters should be estimated from measurements in any given 
experiment, especially regarding spring and winter wheat. For example, Figure 2 shows the final 
length of spring wheat blades for the main stem and primary tillers. It appears that the length of the 
blades on phytomer 1 vary among stems, whereas for winter wheat these values are more or less 
similar among stems. Therefore, in the architectural wheat model, the blade length function is 
different for spring wheat compared to winter wheat. 
As was mentioned in section 3, the parameterisation of the length of successive organs along the 
main stem is based on the idea of a developmental shift. This may be general for winter wheat, as our 
measurements compare well with published data (e.g. Gallagher et al., 1979). Clearly however, the 
variability is much higher in spring wheat, probably due to conditions of temperature during the 
vegetative period, and possibly interactions with photoperiod (Pinthus and Meiri, 1979). Whereas the 
effect of temperature on leaf length has been demonstrated in numerous studies (Friend and Pomeroy, 
1968; Dale, 1982), no quantitative model yet exists, thus organ length along the main stem and its 
determinants should be investigated for spring wheat. 
 
Concluding remarks 
Morphological modelling involves many parameters, of which values need to be specified. 
Because of the complexity of the various processes and their interactions, creating a complete 
simulation of a crop (i.e. a complete virtual plant) is a very ambitious and time-consuming task. Yet, 
investigating particular well-defined problems using the advantages a 3D approach appears the most 
promising way to go. Using an approach to model tillering behaviour in plants as affected by the light 
environment seems to be very promising, as light interception at the organ level can clearly benefit 
from an approach that considers the 3D aspects of organs, their relation to other parts of the crop and 
to the light microclimate. 
 
Acknowledgements 
The authors would like to thank A. Fortineau for his contribution to the 3D measurements. We gratefully 
acknowledge financial support of the Netherlands Organisation for Scientific Research and of the C.T. de Wit 
Graduate School for Production Ecology and Resource Conservation. 
Two-way interactions between process-based tree growth models and 3D structural-functional models 
ORAL PRESENTATIONS - SESSION 5 
213
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SESSION 5– ORAL PRESENTATIONS 
214 
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Figure 1: Example of a simulated 
winter wheat plot. 
 
 
  
 
 
 
 
Figure 2: Blade length for main stem 
and primary tillers of spring wheat. 
Stem 1 is main stem, stems 1.1 to 1.4 
are primary tillers 1 to 4 (of which 
1.1 is the coleoptile tiller). The arrow 
indicates the “developmental shift” 
of successive tillers. 
 
Two-way interactions between process-based tree growth models and 3D structural-functional models 
ORAL PRESENTATIONS - SESSION 5 
215
 
 
Figure 3: Visualised 3D scanning data (X, Y and Z co-ordinates expressed in distance (cm) to the 
scanning reference point) for the leaves of one spring wheat plant in booting stage.  
 


A 3D approach for modelling tillering in wheat (Triticum aestivum L.)

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A 3D approach for modelling tillering in wheat (Triticum aestivum L.)

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