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Ann Bot. 2011 April; 107(5): 865–873.
Published online 2010 October 7. doi:  10.1093/aob/mcq181
PMCID: PMC3077976

A comparative analysis of leaf shape of wheat, barley and maize using an empirical shape model

Abstract

Background and Aims

The phenotypes of grasses show differences depending on growth conditions and ontogenetic stage. Understanding these responses and finding suitable mathematical formalizations are an essential part of the development of plant and crop models. Usually, a marked change in architecture between juvenile and adult plants is observed, where dimension and shape of leaves are likely to change. In this paper, the plasticity of leaf shape is analysed according to growth conditions and ontogeny.

Methods

Leaf shape of Triticum aestivum, Hordeum vulgare and Zea mays cultivars grown under varying conditions was measured using digital image processing. An empirical leaf shape model was fitted to measured shape data of single leaves. Obtained values of model parameters were used to analyse the patterns in leaf shape.

Key Results

The model was able to delineate leaf shape of all studied species. The model error was small. Differences in leaf shape between juvenile and adult leaves in T. aestivum and H. vulgare were observed. Varying growth conditions impacted leaf dimensions but did not impact leaf shape of the respective species.

Conclusions

Leaf shape of the studied T. aestivum and H. vulgare cultivars was remarkably stable for a comparable ontogenetic stage (leaf rank), but differed between stages. Along with other aspects of grass architecture, leaf shape changed during the transition from juvenile to adult growth phase. Model-based analysis of leaf shape is a method to investigate these differences. Presented results can be integrated into architectural models of plant development to delineate leaf shape for different species, cultivars and environmental conditions.

Keywords: Leaf shape, model, model-based analysis, ontogeny, image processing, Triticum aestivum, Hordeum vulgare, Zea mays

INTRODUCTION

Architecture of higher plants changes in response to environmental conditions. These responses are affected by ontogenic contingency (Watson et al., 1995). Architectural plasticity has been discussed widely (Schlichting, 1986; Sultan, 2000; Niklas, 2003; Vandenbussche et al., 2005) and − as formulated by de Kroon et al. (2005) − can be expressed at the level of plant individual sub-units, whole plant reaction being an integrative by-product. Two aspects of phenotypic plasticity are the size and shape of leaves. Here, the term ‘leaf shape’ is used as the pattern resulting from the projection of a leaf surface onto a two-dimensional surface. Heteroblasty of leaves is most obvious and has mainly been studied in dicotyledonous plants (Goebel, 1900; Poethig, 2003). Little is known about differences in the shape of grass leaves and how this trait is affected by environmental factors and the ontogenetic stage of the plant.

The vegetative growth of grasses can be divided into two distinct phases: a juvenile and an adult phase (Sylvester et al., 1990; Kerstetter and Poethig, 1998) with distinct architectural characteristics. During the juvenile phase, grasses mainly produce leaves and axillary tillers. Internodes remain short. In the adult phase, internodes are visibly elongated and the inflorescence develops. In parallel to the transition of the shoot apical meristem, changes in morphological leaf traits have been described for several graminaceous species, e.g. epidermal cell shape or presence or absence of epicuticular waxes (Sylvester et al., 1990, 2001; Evans and Poethig, 1995). Concerning leaf plasticity, most studies have focused on differences in leaf length and width (Kirby and Faris, 1970; Bos and Neuteboom, 1998; Andrieu et al., 2006). Some of these differences are likely caused by ontogeny, as for instance Abbe et al. (1941) associated an increase in maximum leaf width in maize with an increase in apex diameter and leaf primordial size. Moreover, leaf dimensions also depend on resource availability (Schnyder and Nelson, 1987; Kavanova et al., 2008), external cues regulating tissue expansion (Beemster and Masle, 1996; Fiorani et al., 2000) and the length of the whorl they grow in (Wilson and Laidlaw, 1985; Casey et al., 1999; Louarn et al., 2008; Verdenal et al., 2008). However ontogeny, environment, resource availability and whorl size highly influence each other during plant growth. Therefore the impact of each factor on morphological leaf traits is difficult to assess.

The shape of a grass leaf is relatively simple and can be formalized mathematically as a function that describes width (w) − perpendicular to the proximodistal axis − in relation to the distance from the tip (l), called leaf width function w(l) here. Digital image processing facilitates a large-scale quantitative assessment of leaf shape and dimension (Bylesjo et al., 2008; Weight et al., 2008; Dornbusch and Andrieu, 2010).

Montgomery (1911) proposed an approach to compute leaf area = length × width × form factor, where the form factor can be interpreted as a shape characteristic. However, the form factor does not give any information about the spatial distribution of leaf area along the proximodistal leaf axis. Empirical shape models (Bonhomme and Varlet-Grancher, 1978; Prévot et al., 1991; Stewart and Dwyer, 1999; Dornbusch et al., 2007; Evers et al., 2007) have been proposed to compute w(l). However, until now, these models have been evaluated on a dataset representing generally one single cultivar in one environment. Moreover, parameters in these models are difficult to interpret as shape characteristics. Dornbusch et al. (2010) proposed an empirical model that includes two distinct features compared from previous ones: (1) it divides the leaf surface into two segments allowing independent parameterizations of the curvature towards leaf tip and towards leaf base; (2) parameters in the model have a simple interpretation – they represent the form factor and the relative length of each segment.

Beside botanical interests, the need for an appropriate description of leaf shape is required in plant models that explicitly take the three-dimensional (3D) grass architecture into account (Drouet, 2003; Fournier et al., 2003; Dornbusch et al., 2007). These models are an important part of functional structural plant models (FSPMs) that are increasingly used to study plant growth processes (Prusinkiewicz, 1998; Godin and Sinoquet, 2005; Vos et al., 2007) and to describe emission, deposition and transfer of biotic and abiotic entities (e.g. fungal spores, water, light) within plant canopies (Saint-Jean et al., 2004; Chelle, 2005; Robert et al., 2008). Using FSPMs, factors (e.g. temperature, radiation) modulating leaf dimensions and shape can be studied towards an understanding of plastic responses of plants and their consequences for plant-environment interactions.

In this paper, (a) it is demonstrated that leaf shape of a range of grass species grown in varying environments can be sufficiently well described with the empirical shape model proposed by Dornbusch et al. (2010) (summarized below), (b) species-specific differences in leaf shape between juvenile and adult leaves are addressed using estimated parameter values in the shape model, and (c) a database on leaf shape and size of wheat, barley and maize cultivars is made available. Results presented here can be used in crop models and FSPMs, respectively.

MATERIALS AND METHODS

Experimental set-ups

Winter wheat (dataset Wheat I–III; Supplementary Data 6, available online) was cultivated under field conditions at the research unit of INRA at Thiverval-Grignon (48°51′N, 1°57′E) in 2003/4, 2004/5, 2007/8 and 2008/9 using six cultivars and a varied range of sowing dates and plant population densities (only for ‘Soissons’; Table 1). Plots were irrigated and fertilized to sustain good growth conditions. Several plants were tagged with coloured rings to ensure the identification of main stem leaves. Depending on the experiment, at two to eight occasions during crop growth, 15–45 tagged plants were collected.

Table 1.
Main experimental set-ups for the cereal species studied

Spring barley (dataset Barley I–III; Supplementary Data 6) was cultivated, both in a growth cabinet (2004, 2005) and in the field (2005; Table 1). In the growth cabinet, plants were sown equidistantly into pots filled with quartz sand and nutrients. Plants were watered daily to maintain 25 % volumetric water content and sufficient nutrients were provided. The location of pots in the cabinet was changed every 2 d. Average photon flux density was approx. 380 µmol m−2 s−1 and CO2 concentration was maintained around ambient level. Three to six tagged plants were sampled twice per week. The field trial was conducted at Bad Lauchtstaedt (51°24′N, 11°53′E). Management of nutrients and cultivation was performed to sustain a healthy canopy. At each sampling, five to ten previously marked median plants were removed from the plot.

Maize (dataset Maize; Supplementary Data 6) was cultivated under field conditions at the research unit of INRA at Thiverval-Grignon in 2004 (three cultivars; Table 1). Plots were irrigated and fertilized to sustain good growth conditions. Leaves were tagged using coloured spray to identify leaf ranks at sampling. Twenty plants were harvested at the end of June and August, respectively.

Measurement of leaf shape

Grass leaf shape can schematically be approximated by an axial-symmetric convex pentagon, leaf length (lmax) and width (wmax) being the two principal axes (Fig. 1). Leaf width (w) increases starting from the tip (l = 0) until a maximum (wmax) and then decreases towards the ligule (l = lmax). Numerically the leaf width function w(l) is approximated by a 2 × n matrix with discrete values for w and l. To estimate w(l) in the laboratory, leaves from the main stem were placed on transparencies and digitized on a flat-bed scanner (Barley I–III, Epson GT 15000, Seiko Epson Corp., Nagano, Japan; Wheat I–III, Epson Expression 1640XL) using a unicoloured panel to cover them. Leaves of maize were fixed on a unicoloured board and covered with a glass panel. The photo was taken from 2 m distance with a length reference. Images containing a sequence of main stem leaves were subsequently processed. Fully expanded leaves without damage were used to compute w(l). The Matlab program Lamina2Shape (Dornbusch and Andrieu, 2010) was used for the analysis of datasets Wheat I–II and Barley I–III. For the datasets Wheat III and Maize, images were processed using the skeletonization algorithm (Pratt, 1991) and the distance transformation algorithm (Borgefors, 1986) to compute w(l).

Fig. 1.
Leaf silhouette computed with the shape model (Dornbusch et al., 2010) using a given set of parameters: lmax/wmax = 10 and klig = 0·4. Values for the remaining parameters swmax, f1 and f2 are given in the figure. Using swmax, the leaf surface ...

Leaf shape model

Following Montgomery (1911) leaf area can be computed as:

equation image
(1)

where A = leaf area and ft = overall form factor. In a previous paper, a more detailed model to delineate the cereal leaf shape was proposed (Dornbusch et al., 2010). The model contains three dimension parameters: lmax, wmax and klig = width at the leaf base divided by wmax; and three shape parameters. First, swmax is defined as the distance from the tip to the point where wmax is reached divided by lmax. Using swmax, the leaf surface is divided into two segments. Thus swmax gives the relative length of the distal, and 1 – swmax the relative length of the basal segment. The shape of each leaf segment is given by c1 = curvature parameter of the distal segment, and c2 = curvature parameter of the basal segment (see Fig. 1) and computed by two separate functions:

equation image
(2)

equation image
(3)

Analytical functions (eqn 4) and (eqn 5) link the curvature parameters c1 and c2 and the form factors f1 and f2 of each leaf segment:

equation image
(4)

equation image
(5)

These functions are bijective so that f1 and f2 are used as input parameters and inverse functions were tabulated to compute c1 and c2 matching any predefined values of f1 and f2. Matlab source code of the model is provided as m-files (Supplementary Data, available online).

Data processing and curve fitting

For each cultivar and treatment, a median function w(l) of main stem leaves was calculated. To do that, stems with the same number of leaves (Nmax) were grouped. To compute a median w(l) for a given leaf rank, matrices were scaled to the same size by computing 100 values for w and l of each individual leaf using spline interpolation. The estimation of parameters in the shape model was done by fitting it to w(l) of each measured individual leaf using ordinary least squares minimization (Matlab function lsqnonlin). Matlab source code of the fitting procedure is provided as m-files (Supplementary Data). The optimization converged in all cases. Root mean squared error (RMSE) and root mean squared error normalized by wmax (RMSEn) were calculated. Each fit resulted in the estimates of the parameters (swmax, f1, f2, klig) for a considered leaf. Leaf dimensions lmax, wmax, leaf area A and overall form factor ft (eqn 1) were obtained from the corresponding scanned leaf image. Further, mean, median and confidence interval (95 %) of parameter values for fully expanded leaves were calculated for each treatment and leaf rank. The non-parametric Wilcoxon–Mann–Whitney test was applied to test statistical significant differences in estimated parameter values.

RESULTS

Leaf shape showed a species-dependent response to ontogenetic stage

Figure 2 gives an overview of the range of leaf shapes found in the wheat, barley and maize cultivars. Presented shapes represent the median of a given main stem leaf rank (N) scaled to the same length and width. Data on dimensions and estimated parameters for all treatments are given in Supplementary Data 1. Further, detailed plots of median w(l) for all species, cultivars and treatments are presented in Supplementary Data 2–4, and data for w(l) is provided in a csv-file (Supplementary Data 6; also supplied as a .txt file).

Fig. 2.
Silhouettes of main stem median leaves of wheat (A, B), barley (C) and maize (D–F) cultivars (cultivar names given in each subplot); leaf rank (N) is counted acropetally from the first emerged leaf; all leaves where scaled to the same dimension ...

In wheat (dataset Wheat I and II), the emerging first leaf (N = 1) differed from the others having a more convex shape of the distal leaf segment and small reduction in w before the ligule (data in Tables S1–S2 in Supplementary Data 1). The other main stem leaves (2 ≤ NNmax) had similar values of the overall form factor ft (data in Table S1 in Supplementary Data 1). However, plotting ft against N (Fig. 3A) for Wheat I–II data, showed an ontogenetic pattern for ft(N): (a) a decrease in ft(1 ≤ N ≤ 4) by 0·15; (b) an increase in ft(4 ≤ N ≤ 8) by 0·05; (c) no change in ft = 0·8(8 ≤ NNmax – 1); and (d) a decrease in ft for the flag leaf (N = Nmax) by 0·05 (not shown in Fig. 3A). This pattern of ft(N) was highly conserved in the data, independently of the range of population densities and the two experimental years. The impact of sowing date on ft(N) can be attributed to differences in Nmax mainly due to a shorter juvenile period in late sown wheat (Wheat II). After a late sowing (Wheat II), four or five leaves were observed growing in the juvenile phase before visible stem elongation started, whereas after an early sowing (Wheat I) there were eight or nine leaves. In the adult phase, five or six leaves were growing irrespective of sowing date. Leaf shape of the other studied wheat cultivars (dataset Wheat III) was very similar to that of ‘Soissons’ (Fig. 4). There, ft for leaves (Nmax – 4 ≤ NNmax – 1) growing in the adult phase was in the same magnitude (ft = 0·8) for all species (data in Table S3 in Supplementary Data 1). As for ‘Soissons’, ft for the flag leaf (Nmax) was 0·03–0·08 lower compared with ft for the penultimate leaf (N = Nmax – 1) for all cultivars (Fig. 4). The shape of juvenile leaves was not measured for all cultivars and leaf ranks.

Fig. 3.
Mean values for the overall form factor ft versus leaf rank N. (A) Triticum aestivum ‘Soissons’ in which open symbols represent dataset Wheat I (early sowing) and closed symbols Wheat II (late sowing) with three plant population densities ...
Fig. 4.
Silhouettes of median (A) penultimate (N = Nmax –1) and (B) flag leaves (N = Nmax) on the main stem of six wheat cultivars: ‘Soissons’ (So), ‘Caphorn’ (Ca), ‘Apache’ (Ap), ‘Arminda’ ...

In barley (dataset Barley I–III), the first leaf (N = 1) differed in shape from the others as previously described for wheat (data in Tables S4–S6 in Supplementary Data 1). The shape of barley leaves in the juvenile phase (2 ≤ N ≤ 4) was similar to that for the corresponding wheat leaf ranks (Fig. 2) with the same magnitude for ft = 0·77 (Fig. 3). In the adult phase (N ≥ 5), the value of ft decreased almost linearly up to the flag leaf ft(Nmax) = 0·65 (Fig. 3). As discussed in wheat, the ontogenetic pattern of ft(N) of the studied barley cultivar was conserved under varying environmental conditions (field vs. growth cabinet) that resulted in remarkable differences in the magnitude and the pattern leaf length and width as a function of N (Supplementary Data 1).

In maize (dataset Maize), the available data of one experimental year did not show a common trend in ft(N) that may be ascribed to differences in leaf shape between the juvenile and adult phases (data in Table S7 in Supplementary Data 1). The average value ft = 0·74 was similar for the three measured cultivars. Contrary to wheat ft(Nmax) was about 0·02–0·06 bigger than ft(Nmax – 1).

The model delineated leaf shape with high accuracy

The shape model (eqns 25) approximated w(l) of individual barley and wheat leaves with high accuracy (RMSEn < 0·041; Fig. 5) for all treatments and growth conditions (see also Supplementary Data 2–4). Each fit yielded one set of parameters (swmax, f1, f2, klig). For maize, the goodness-of-fit was lower (RMSEn = 0·082), because w(l) was not a smooth curve in a lot of cases, which also introduced more uncertainty in the parameter estimation. In all cases, predicted values for leaf area (Apred) by the shape model were very close to the measured ones (Ameas). However, the deviation of Apred from Ameas increased as Ameas got bigger and Apred tended to be underestimated. That was observed for all species, but was more severe for maize (Fig. 5B).

Fig. 5.
(A) Root mean squared error normalized by wmax (RMSEn) as a measure for the deviation of the model from the measured values of the leaf width function w(l) (main stem) for the datasets considered (cf. Table 1). The number of measured leaves ( ...

Differences in parameter values between leaves growing in juvenile and adult phases

Previously, a different pattern of ft(N) had been indicated for leaves growing in the juvenile and adult phases. A look at the estimated parameter values swmax, f1, f2 and klig as a function of N allows a more detailed look at divergences in shape. As previously discussed for ft, there were no obvious differences in the magnitude of swmax, f1 and f2 for a given N for wheat and barley in response to different growth conditions (Fig. 6). The estimated value of klig largely depended on the way a leaf was cut at the base before measuring. No distinct pattern of klig(N) was found. Mean values for barley were klig = 0·58; and for wheat klig = 0·60, which differed from klig = 0·66 used in a previous paper (Dornbusch et al., 2010). Here, klig had minor impact on the shape of the basal leaf segment.

Fig. 6.
Mean parameter values in the model (swmax, f1, f2) for each leaf rank (N) on the main stem for (A) the dataset Barley I–III, (B) the dataset Wheat I (S1 early sowing, D1–D3 three densities), (C) the dataset Wheat II (S2 late sowing; two ...

For the first leaf (N = 1), values for f1(1) were higher compared with the second leaf [in barley, f1(1) = 0·73 (P < 0·001); in wheat, f1(1) = 0·80 (P < 0·05)]. For the other leaves (N ≥ 2 in barley; N ≥ 3 in wheat) estimated values for f1(N) varied little and were lower for barley (f1 = 0·59) than for wheat (f1 = 0·64). The second leaf (N = 2) in wheat had a value f1(2) = 0·72, which was higher than f1(3) (P < 0·05).

Likewise, there was also little variation in the magnitude of f2(N). No distinct trend of f2(N) could be identified. Mean values for barley were f2 = 0·95; and for wheat, f2 = 0·92.

In contrast, a pattern in the values of swmax(N) could be identified, which was different for the juvenile and adult phase, both in barley and in wheat. For the first leaf, values for swmax(1) = 0·41 were lower compared with the second leaf in barley (P < 0·001), and in wheat swmax(1) = 0·38 (P < 0·05), respectively. In barley, for juvenile leaves (2 ≤ N ≤ 4), swmax was quite constant (swmax = 0·51). At the beginning of the adult phase (N = 5), there was an increase in the value of swmax(5) = 0·68 compared with swmax(4) (P < 0·001). Thereafter, with increasing N, the value of swmax increased up to the flag leaf [swmax(Nmax) = 0·86]. In contrast, a different pattern was observed in wheat. For juvenile wheat leaves (2 ≤ N ≤ 8 in Wheat I; 2 ≤ N ≤ 5 in Wheat II), values for swmax decreased from swmax(2) = 0·62 to swmax(8) = 0·42 (Wheat I) and from swmax(2) = 0·62 to swmax(5) = 0·52 (Wheat II). For N = 9 (Wheat I) and N = 6 (Wheat II), which was considered to be the beginning of the adult phase, an increase in the magnitude of swmax (Wheat I: swmax(9) = 0·48; Wheat II: swmax(6) = 0·55) was also obtained compared with the previous leaf. Differences were significant for some treatments only. In contrast to barley, values for swmax were constant in the adult phase of wheat. For the flag leaf, the value of swmax increased compared with the previous leaf (P < 0·05) in all treatments. The values for the dimension parameters lmax and wmax and the observed patterns as a function of leaf rank are not discussed here (values given in Supplementary Data 1).

Simple relationships describing parameter values as a function of leaf rank yielded a good estimation of leaf shape

To simulate leaf shape in architectural models using eqns (2)–(5), it is functional to use a simple, reduced set of model parameters swmax, f1, f2, klig instead of measuring them for each individual leaf. Therefore, w(l) for each leaf of rank N in the dataset was computed using a simplified description of the parameters as a function of leaf rank N: swmax(N), f1(N), f2(N), klig(N). In the previous section we proposed a pattern of swmax(N), f1(N) − plotted as continuous lines in Fig. 6 − for wheat and barley described by characteristic mean parameter values for specific N. The parameters f2(N) and klig(N) were constantly independent of N and treatment and unique values defined barley and wheat, respectively. The set of parameters is listed in Table 2. Values for swmax(N) and f1(N) not specified in Table 2 were estimated by linear interpolation. Then computed values for swmax(N), f1(N), f2(N) and klig(N), together with measured values for lmax(N) and wmax(N), were used to simulate w(l) for each individual leaf of rank N. This newly computed w(l) was compared with the initially measured values of w(l) for the respective leaf using the RMSEn. Compared with simulating w(l) using fitted parameter values, RMSEn increased, but the value was still relatively low (RMSEn < 0·068).

Table 2.
Set of shape parameter values as a function of leaf rank N (Nmax = rank of flag leaf) swmax(N), f1(N), f2(N), klig(N) to describe the main stem leaf shape in the datasets Barley I–III and Wheat I–II

DISCUSSION

Data on leaf shape of six wheat, one barley and three maize cultivars from different growing conditions and years were analysed. Differences were found in shape and a different pattern of the overall form factor ft for juvenile and adult leaves in the wheat cultivar ‘Soissons’ and the barley cultivar ‘Barke’. In the adult phase of barley, values for the overall form factor ft decreased with increasing leaf rank (Fig. 4), which could mainly be attributed to an increase in the relative length of the distal leaf segment (swmax). This effect was observed as well in the climate chamber with constant temperature and relatively low radiation input as under natural field conditions. In both cases, the shape of leaves of comparable ontogenetic stage was similar. However, only three to four juvenile leaves grew in the experimental set-ups. It would be interesting to compare spring barley with winter barley that has a longer juvenile phase. This would allow assessing the impact of growth condition in winter – notably temperature and photoperiod – on leaf growth and to verify further observed ontogenetic differences in barley leaf shape.

In wheat, ft of juvenile leaves decreased with rank, whereas adult leaves were of similar shape (value of ft = 0·8; Fig. 3). In all cultivars, the flag leaf had a lower value of ft, which can mainly be attributed to a decrease in relative length of the basal leaf segment. There were no clear differences in the shape of adult leaves between the studied cultivars that were grown in the same field experiment. In this experiment (Wheat III) data for juvenile leaves was not available. As discussed for barley, growth conditions did not notably influence leaf shape of a given rank.

Following the present data, ontogenetic stage had more impact on leaf shape than growth conditions or genotypic variation in wheat and barley, but this needs to be validated on a larger range of cultivars. In maize, data were not sufficient (only one experimental year) to derive a clear pattern of model parameter values related to ontogeny, environment or genotype. There were also more difficulties in the acquisition of w(l) from images due to undulations in the leaves of maize.

The presented shape model could be fitted to measured w(l) with a small error. The parameter values in this model − compared with the overall form factor ft − allowed a more precise discussion of the differences in leaf shape. No data were found in literature that previously described differences in shape between juvenile and adult cereal leaves. Here, swmax, − the relative length of the distal leaf segment (see Fig. 1) − was identified as the parameter that mainly changes between juvenile and adult leaves. Interestingly for each species, the values of the form factors f1 and f2 specified for the two leaf segments were relatively similar for all leaf ranks apart from the first leaf. The ontogenetic trend in ft reflects thus mainly the change in the contribution of each leaf segment to the leaf area.

The shape model could be improved to take more shape characteristics of cereal leaves into account. First, an indent in wheat and barley leaves caused by a mechanical compression of leaves by the ligule of the previous leaf was observed (Lock, 2003). This effect becomes more marked in the upper wider leaves. Second, it was found that some leaves had a quasi plateau in width in the basal leaf segment, which was mainly found in barley growing under low light conditions in the growth cabinet (see Fig. S5 in Supplementary Data 3). The value of f2 = 0·95 leads to an almost rectangular shape computed by the model, but it does not fully capture this characteristic. However, adding these two features to the shape model would increase the number of parameters (at least two) and thus increase the degrees of freedom for parameter fitting. The error predicting shape with the present model is already low and the parameters can be well interpreted to detect differences in leaf shape. Therefore we think that adding more complexity to this descriptive model is not useful.

Analysis of leaf shape using the proposed model allowed a more detailed look at differences according to species, ontogeny and environmental conditions, although these differences are relatively small compared with the change in leaf dimensions. An application of the shape model, is the simulation of leaf shape in 3D plant models. The observed ontogenetic pattern of leaf shape for ‘Soissons’ and ‘Barke’ could be sufficiently well described using the proposed set of parameters for swmax, f1, f2 and klig (Table 2). The relative stability of the observed parameter values irrespective of environmental conditions suggest that even for other cultivars of the same species similar responses of shape might be expected.

ACKNOWLEDGEMENTS

We thank the Ministère des Affaires Etrangères (Dossier 2008453) and the German Research Foundation (DFG Do 1408/2-1) for granting the post-doctoral fellowship for T. Dornbusch. Support in our experiments from F. Duhamel, E. Fovart and M. Marques is gratefully acknowledged. We thank two anonymous reviewers for constructive suggestions to improve the manuscript.

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