Rosa hybrida “Radrazz” rose bushes were grown in Angers, France, in three experiments. Experiment 1 took place in spring 2007 (2007-Sp), experiment 2 in summer 2007 (2007-Su), and experiment 3 in spring 2010, with a low (2010-LD) or high (2010-HD) plant density. Single-node cuttings bearing a five- or seven-leaflet leaf were harvested from the medial part of mother plant stems and grown for 4–5 weeks in humid conditions until rooting was achieved. Well rooted cuttings were planted in individual pots containing a mixture of neutral peat, coconut fibers and perlite. Plants were transferred to a greenhouse before bud break and grown, with a border row, at a density of 23 plants m⁻² in experiments 1 and 2, and at a density of 21 or 100 plants m⁻² in experiment 3. The bud from the cutting produced the primary axis. After floral bud and last leaf appearance, a variable number of lateral buds burst and developed in secondary shoots. These shoots were let to grow but not measured. Plants were subirrigated, with tensiometer monitoring to ensure an absence of water stress. Mineral nutrition was provided by fertigation (5.0 mM KNO₃, 2.0 mM Ca(NO₃)₂, 2.0 mM NH₄NO₃, 2.0 mM KH₂PO₄, 2.0 mM MgSO₄, 0.25 mM NaOH; trace elements (Kanieltra 6-Fe,0.1 ml.l⁻¹, Hydro Azote, Nanterre, France); pH 5.6; EC 1.77 mS.cm⁻¹). Air temperature was measured above the canopy, in a ventilated shelter, with a platinum sensor. Leaf temperature was measured in experiment 3 on the abaxial surface of leaves, at about the height of the apex, with copper-constantan thermocouples. Photosynthetically active radiation (PAR) was continuously measured above each canopy, with a line quantum sensor (LI-191 LI-COR, Lincoln, Neb. USA). It was also measured with line quantum sensors at both the base and the top of the canopy, at various locations, at solar noon, under a cloudy sky, on three dates during primary shoot expansion in experiment 3, for the calculation of intercepted PAR. The climatic conditions prevailing during the period of primary shoot expansion are presented in Table 1.

The three scenarios were evaluated by the leave-one-out cross-validation method (Linhart and Zucchini, 1986).

For each plant p of the original data set consisting of n plants:

– We removed plant p and estimated the model parameters from the n − 1 remaining plants.

Mean MSEP_{p, k} (i) was then calculated for all plants, both per rounded relative rank and for all phytomer relative ranks pooled together. The square root of MSEP (RMSEP) was then calculated.

Principal component analyses were performed with SPAD software (V7.4, Coheris, Suresnes, France). All other statistical analyses were performed with SAS software (V 9.3, SAS Institute). For the fitting of logistic functions Equation (3) and of piecewise linear functions Equation (2), we used the NLIN procedure. For the establishment of relationships between relative rank i on the one hand and w^m_k (i), t⁰_k (i), or L^m_k (i) on the other, we used non-parametric methods and the LOESS procedure.

High levels of variation were observed in all three crops used for time-course measurements. Primary shoots comprised between 10 and 16 phytomers on the plants used for time-course measurements (Table 2). The rate of leaf appearance was highly variable, with the phyllochron during the phase of slow leaf appearance varying from 20.6 to 53.4°Cd between plants within a crop, resulting in considerable variation of the dates of leaf appearance at equivalent phytomer positions (e.g., at rank 10, leaf appearance on the first plant occurred 172°Cd before that on the last plant within a crop). Final lengths were between 6.5 and 87.5 mm for terminal leaflets and between 1.0 and 63.5 mm for internodes, considering all ranks together. At a given phytomer position, final lengths also varied considerably between plants. For example, at a rounded relative rank of 0.8, the range of final lengths was 58.0–86.0 mm for terminal leaflets and 9.0–49.5 mm for internodes. Differences in mean values between crops, for phytomer numbers, timing of leaf appearance and final lengths, were significant.

Rose leaves have generally odd numbers of leaflets, with between one and nine leaflets per leaf, except at the base of the shoot, where leaves are reduced to scales or stipules. Principal component analysis (PCA) was performed on the lengths, widths and square roots of the areas of all individual leaflets of both growing and mature leaves collected from the 2007-Sp, 2010-LD, and 2010-HD crops. The percentage of the variance explained by the first principal component was 97, 79, 79, and 80% for 1-, 3-, 5-, and 7-leaflet leaves, respectively (no nine-leaflet leaf sampled in these experiments). These very high values for a single component indicate that all the dimensions (lengths, widths and square roots of areas) of all the leaflets were correlated within a given leaf, for both growing and mature leaves. Consequently, we were able to simplify the study of leaf expansion by focusing on a single dimension. We chose to study terminal leaflet length, because all leaves composed of leaflets have a terminal leaflet and this dimension is easily measured earlier in expansion than the other possible dimensions.

Terminal leaflet length (L) can be used to calculate whole leaf area (A) at any growth stage, given the number of leaflets of the leaf (N_L), from the following equation: (9)A=0.287 L2 NL0.746  (n=201, R2=0.93) With a multiplicative model for terminal leaflet length and leaflet number per leaf, the residual distribution did not depend on leaflet number per leaf as with a linear model. The two parameter values (0.287 and 0.746) were adjusted so as to maximize R².

In individual organs, changes in terminal leaflet or internode length as a function of thermal time followed a sigmoidal pattern (Figure 2). This pattern of change was well fitted by a logistic function (Table 3): R² close to 1 and RMSEP around 1 mm. For all phytomers, the period of internode expansion was included within the expansion period of the terminal leaflet of the same phytomer (Figure 2). Terminal leaflets reached 10% of their final size a mean of 31°Cd before the corresponding internodes reached 10% of their final size, and the leaflets reached 90% of their final size a mean of 35°Cd after the internodes.

Figure 5 shows the mid-expansion times for individual leaflets (n = 629) and internodes (n = 584) plotted against time of leaf appearance. These relationships integrate both the rate at which expansion occurs on successive phytomers and the duration of expansion, because the predicted variable is the time at the middle and not at the beginning of expansion. For terminal leaflets, the relationship between time at mid-expansion and time of leaf appearance gradually curves, because expansion duration changes gradually with phytomer relative rank (Figure 4B). We therefore decided to use second-order polynomials to adjust the relationship for terminal leaflets. For the internodes, expansion duration was almost stable for vegetative internodes and much longer for peduncles (Figure 4D). We therefore, used first-order polynomials to adjust the relationship between time at mid-expansion and time of leaf appearance, using different parameters for vegetative internodes and peduncles. Estimates for the parameters of the relationships defined in the Equations (4.1) and (4.2) are given in Table 4.

The intercepts δ_lea,0 and δ_int,0 correspond, for phytomers whose leaf appears at bud break, to the time lag between leaf appearance and organ (leaflet or internode, respectively) maximal expansion rate. The other parameters of Equations (4.1) and (4.2) have no direct biological meaning. The adjusted determination coefficients were R²_adj = 0.97 (n = 627) for terminal leaflets, R²_adj = 0.96 (n = 525) for vegetative internodes and R²_adj = 0.86 (n = 59) for peduncles. These high R² indicate that time of leaf appearance can be used to estimate time at mid-expansion for individual leaflets and internodes, because these relationships capture the variability between crops, between individual plants and between phytomer positions.

From the results presented above, we developed a model reproducing the terminal leaflet and internode expansion of a crop of rose bush primary shoots. The three scenarios of the model, differing in the number of input variables, were evaluated by cross-validation.

In the reference scenario (S₀), input variables accounted for interplant variability in both organ final lengths and time of leaf appearance. The term w^m_k (i) depends only on phytomer position and does not vary between individual plants. This term represents the maximal expansion rate for a normalized expansion curve and is inversely proportional to expansion duration. The parameters of S₀ are given in Table 4 and the values of w^m_k (i) estimated by the LOESS method are given in Table 5. S₀ correctly reproduced the expansion kinetics of the different terminal leaflets and internodes of an individual plant (Figures 6A,C) and of different plants within a given crop (Figures 6B,D). The RMSEP for all ranks together was 4.5 mm for leaflets and 2.5 mm for internodes, corresponding to 7.3 and 10.2%, respectively, of organ final lengths. The accuracy of the model was similar for the different phytomer positions, for both leaflets (Figure 7A) and internodes (Figure 7B).

Scenario 1 was designed to assess model accuracy assuming that the time at which expansion occurred depended only on phytomer position, rather than being estimated, as in S₀, from an input variable. The parameters of S₁ are given in Table 5. In S₁, the RMSEP for all ranks together was 8.6 mm for leaflets and 4.5 mm for internodes (14.2 and 18.2% of final lengths, respectively). The RMSEP calculated for each phytomer position increased from the base to the top of the shoot (Figure 7). This was due to an increase in variability between plants for mid-expansion time, from the base to the top of the shoot (Figure 5). The optimal scenario would thus involve estimating the time at mid-expansion from a value dependent only on relative rank for basal phytomer positions and from measurements of leaf appearance time for more central and apical positions. In practical terms, this would decrease measurement time with respect to S₀, because the leaf-like structures at the base of the shoot are the most difficult to observe.

Scenario 2 simulates the kinetics of expansion of plants differing only in terms of phytomer number. The parameters of S₂ are given in Table 5. For S₂, RMSEP was calculated by plant, so the comparison of the RMSEP values for S₀ and S₂ provides an estimate of the gain in accuracy when a scenario accounting for interplant variability (S₀) is used to simulate the expansion kinetics of a heterogeneous crop over a scenario reproducing n mean plants. In S₂, RMSEP for all ranks together was 10.6 mm (17.4 %) for leaflets and 6.0 mm (24.2%) for internodes, these values being 2.4 times higher than those for S₀. This loss of accuracy for S₂ with respect to S₀ concerned all phytomer positions (Figure 7). It should be borne in mind that the method used to calculate MSEP does not aim to assess the ability of S₂ to simulate a mean plant, because simulated lengths were not compared with mean observed lengths.

We studied expansion in three crops (2007-Su, 2010-LD, and 2010-HD) subjected to different growing conditions, contrasting in terms of incident PAR, humidity and plant density in particular, to ensure that we obtained robust results. Contrasted experimental conditions were used to find regularities in expansion kinetics, but not to establish quantitative relationships between architectural traits and environmental factors, such as density, light intensity or quality. This would require specific experiments. The large differences in PAR interception between densities in 2010 (Table 1) suggest that light quality in the canopies, including the red-far red ratio in particular, differs between plant densities. These differences in growing conditions resulted in significant differences between crops in terms of the mean values of architectural variables. Within each growing condition, the plants also displayed considerable variability. This level of interplant variability is typical of rose bush crops. This variability was observed although we selected cuttings to reduce heterogeneity due to topophysis (Bredmose et al., 2001) and differences in cutting leaf area (Costa and Heuvelink, 2003).

Our results show that it is possible to reconstitute the dimensions of the different leaflets of a rose leaf from a single dimension at any time during leaf expansion, given the number of leaflets per leaf. These results generalize those of Gao et al. (2012), who established that, for fully expanded leaves, total leaf area could be inferred from one leaf dimension and number of leaflets, within a genotype. The allometric relationships using terminal leaflet length as a predictor of either whole leaf area (presented here, section Terminal Leaflet Length can be Used to Simulate the Dimensions of all Leaflets Within a Leaf) or leaflet dimensions (Demotes-Mainard et al., 2009) should probably be established for each genotype. Indeed, only relationships based on the product of length by width have been found to be stable across a range of genotypes, both at the leaflet level (Rouphael et al., 2010) and the leaf level (Gao et al., 2012), because the shape of leaflets and their insertion position along the rachis (loose or close) vary between genotypes.

Differences in organ final size between phytomer positions and between plants at a given position resulted mainly from differences in maximal expansion rate, rather than expansion duration. This is similar to the behavior of other species. For example, whereas final leaf and internode size widely varies between phytomers along the main shoot, organ expansion duration little varies in narrow-leafed lupin (Dracup and Kirby, 1993) and is stable in arabidopsis (Mündermann et al., 2005). At a given phytomer position, expansion duration is stable in thermal time between plants grown in contrasted growing conditions for sunflower leaves (Granier and Tardieu, 1998; Dosio et al., 2003), sorghum leaves (Lafarge and Tardieu, 2002) and internodes (Xue et al., 2012). In tall fescue and wheat, expansion duration is more stable if expressed in phyllochronic time (thermal time divided by the phyllochron) than if expressed in thermal time (Fournier et al., 2005). This stability in phyllochronic time has been interpreted as an emerging property of a self-regulated system, in which the appearance of an organ triggers changes in expansion (Fournier et al., 2005; Verdenal et al., 2008). Under this hypothesis, the link between phyllochron and duration results from a large proportion of expansion occurring when the leaf is still in the whorl generated by previous leaves.

In rose bush, as in many other species (for example lupin, Dracup and Kirby, 1993; wheat, Evers et al., 2005; cucumber, Kahlen, 2006; sorghum, Xue et al., 2012), there was a general gradient of final organ length with phytomer relative rank common to all three crops and plants. This gradient can be used to model a mean plant, as in scenario S₂. However, this gradient varied between individual plants: a plant with a high (or low) leaflet or internode final length at a particular phytomer position did not systematically present a high (or low) length at the next phytomer. This was unexpected, at least for basal phytomer positions. Indeed, during their expansion basal phytomers depend on the cutting, both for nitrogen, which is provided by remobilization (Cabrera, 2003) and for photosynthesis (Costa and Heuvelink, 2003). In addition, on average eight phytomers closest to the base of the plant are preformed in the bud in the variety studied here (Girault et al., 2008), suggesting that they may be influenced similarly by the physiological state of the mother stem. We therefore, assume that the differences in leaflet or internode final size between plants may reflect differences in the phylloclimate perceived by the organs during their expansion. Indeed, final size is dependent, in several species, on phylloclimate (or climate) at the time of organ expansion (Granier and Tardieu, 1999, for sunflower leaves; Gautier et al., 2000, for white clover internodes, petioles and leaves; Andrieu et al., 2004, for maize leaves; Kahlen and Stützel, 2011, for cucumber internodes). Our model could be used to test this hypothesis, by accurately defining the timing of individual organ expansion.

We developed a model reproducing the kinetics of leaflet and internode expansion on rose bush primary shoots, based on non-destructive and easy-to-measure input variables. The comparison of the three scenarios showed that, to reproduce accurately the variability of expansion within a crop, it was necessary to measure the final lengths of terminal leaflets and internodes and to count the number of phytomers per shoot and of leaflets per leaf, all of which can be done after the final primary shoot has ceased to elongate. The timing of leaf appearance must also be established, at least for leaves in the middle and upper part of the shoot, as fixed values of time at mid-expansion can be used for the basal phytomers. These data are easy to acquire, but their acquisition is labor-intensive. The model based on these input variables satisfactorily simulated the diversity of individual plants. For ecophysiological studies, this model will make it possible to relate traits of interest measured on specific plants to features of expansion for the same plants, which is important for experimental crops with high levels of interplant variability.

In order to represent architectural development, our model of organ expansion can be easily integrated in a FSPM of rose bush using L-systems. The addition of a three-dimensional structure to the expansion model implies to model organs' shape and spatial position, as done for FSPMs of other species (e.g., Evers et al., 2005; Mündermann et al., 2005; Kahlen et al., 2008). This 3D model would provide essential information to study the environmental regulation of bud break, which strongly influences plant architecture and still remains a major research area (Domagalska and Leyser, 2011). Indeed, when coupled with a light model, the model will give information about light phylloclimate, which is a key factor controlling bud break through carbohydrate availability (Girault et al., 2010; Henry et al., 2011; Rabot et al., 2012), and light quality (Mor and Halevy, 1984; Girault et al., 2008). In rose bush, there is considerable interplant variability in the number and position of buds breaking along the primary shoot (for instance, in 2007-Su between 2 and 8 buds outgrew on primary shoots with the same number of axillary buds). It may therefore, be particularly relevant to be able to investigate the relationships between light phylloclimate and bud break at the level of individual plants.

The differences in organ expansion kinetics between plants within a relative rank resulted mainly from differences in maximal expansion rate, rather than differences in expansion duration. This had two related implications, which were used in the model. Firstly, variations in organ final size were sufficient to capture interplant variability in size at any time during expansion, within a relative rank, as in scenarios S₀ and S₁. Secondly, in the model, the term w^m_k (i), which is inversely proportional to expansion duration, can be predicted from a single value common to all plants within a relative rank with little loss of accuracy (all scenarios). In the model the term w^m_k (i) depends on relative rank. However, the variations of expansion duration between phytomer positions were moderate for terminal leaflets and for vegetative internodes. In scenario S₀, if w^m_k (i) was replaced by only three values, one common to all terminal leaflets (w^m_lea = 5.96 × 10^−3°Cd), one common to all vegetative internodes (w^m_int = 9.04 × 10^−3°Cd) and one for peduncles (w^m_ped = 5.17 × 10^−3°Cd), the accuracy of the model remained the same (RMSEP = 7.4 and 10.2% of final length, for terminal leaflets and internodes, respectively, data not shown) as with w^m_k (i). Thus, if the model has to be calibrated for a new genotype, this process could be simplified by estimating the model parameters from a limited number of phytomer positions.

The time of leaf appearance has been used in several architectural models for the prediction of ontogenic development (for example in wheat: Fournier et al., 2003; Evers et al., 2005; in cucumber: Kahlen, 2006; in ryegrass: Verdenal et al., 2008). In our model, we used this parameter in the reference scenario S₀ to predict the mid-expansion time for both leaflets and internodes. This coordinates expansion between different phytomer positions for the same kind of organ, and between leaflets and internodes.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.