However, these commercial instruments are expensive, not readily accessible at all research locations, and require a skilled operator. Consequently, there is an urgent need for an accurate, cheap, and non-destructive method to estimate LAs in agronomic and physiological experiments (Fallovo et al., 2008).

A common approach for the non-destructive estimation of LAs is to develop ratios and regression estimators that involve simple linear measurements such as leaf length (L) and width (W), or some combination of these variables, which often have a high degree of accuracy (Rouphael et al., 2006). Various models have been developed for leaves of fruit trees and nuts (Demirsoy et al., 2004; Cristofori et al., 2007; Mendoza et al., 2007; Mazzini et al., 2010; Kishore et al., 2012), and vegetables (De Swart et al., 2004; Rivera et al., 2007; Rouphael et al., 2010b; Misle et al., 2013), whereas little information exists on the estimation of LAs in ornamental species (Fascella et al., 2009; Rouphael et al., 2010a). In most such studies, the accuracy of these models was not rigorously tested since these models were selected only on the basis of their coefficient of determination (R2) values, whereas the detection of deficiencies in a model requires examination of the residuals (Bland and Altman, 1986).

Based on the above considerations, the aims of the current study were: (i) to develop a simple and accurate model for estimations of LA based on linear measurements that fitted the effects of leaf shape (i.e., the L:W ratio) in several genotypes of P. rubra; and (ii) to validate the accuracy of the selected model on an independent dataset from another experiment. The proposed model could play an important role in plant breeding and physiology experiments in which destructive LA measurements are not possible; for example, in the case of rare plants or genetically segregating populations (De Swart et al., 2004; Misle et al., 2013)

#### MATERIALS AND METHODS

Plant material and growth conditions. Two experiments were conducted, one in 2012 (the calibration experiment) and one in 2013 (the validation experiment) under greenhouse conditions at the Research Unit for Mediterranean Flower Species, Palermo, Italy (38º 5′ N; 13º 30′ E; 23 m asl). In both experiments,30 plants of each of eight genotypes P. rubra

(‘California Sunset’, ‘Christina’, ‘Divine’, ‘Elsie’, ‘Gina’, ‘J.J. Mini White’, ‘Panittas Red’ and ‘Pixie Dust’) were grown in 7 l plastic pots (one plant per pot) containing a 1:1:1 (v/v/v) mix of Mediterranean red soil, black peat, and perlite. A randomised complete-block design with three replicates (ten plants per experimental unit) was adopted.

The pots were placed on aluminium benches at a planting density of 6.4 plants m–2. In both experiments, all P. rubra plants received a nutrient solution containing: 180 mg l–1 N-NO3, 50mg l –1 P, 200 mg l–1 K, 120 mg l–1 Ca, 30 mg l–1, Mg, 1.2 mg l–1 Fe, 0.2 mg l–1 Cu, 0.2 mg l–1 Zn, 0.3 mg l–1 Mn, 0.2 mg l–1 B, and 0.03 mg l–1 Mo. The electrical

conductivity and pH of the nutrient solution were 2.0 dS m–1 and 6.0, respectively. The nutrient solution was pumped from tanks through a drip-irrigation system with one emitter per plant, set at a flow rate of 2 l h–1. Irrigation scheduling was controlled using electronic low-tension tensiometers that controlled irrigation based on the matric potential of the substrate (Norrie et al., 1994). The tensiometers were placed at the midpoint of the pots to provide a representative reading of the substrate moisture level (Rouphael et al., 2008). The tensiometers were connected to an electronic programmer that controlled the start and the end points of each irrigation, pre-set at values of –15.0 kPa and –1.0 kPa substrate matric potential, respectively.

Data collection A wide variety of different-sized, fully-expanded leaves were sampled at random from different levels in the canopy during the various phenological stages, in order to achieve wide morphological variation in sampling in both experiments. A total of 700 leaves (100 leaves per genotype) had their LAs, leaf Ls, and leaf Ws measured in the model-building experiment (Experiment 1; 2012), using the seven genotypes: ‘California Sunset’, ‘Christina’, ‘Elsie’, ‘Gina’, ‘J.J. Mini White’, ‘Panittas Red’ and ‘Pixie Dust’.

For the model validation experiment (Experiment 2; 2013), 100 leaves of ‘Divine’ were used to measure LAs, leaf Ls, and leaf Ws. ‘Divine’ was selected for the 2013 validation experiment as it was considered to be the most representative genotype of

P. rubra in Italy and in several other European countries (Criley, 2009). Harvested leaves were transferred immediately to the laboratory, where maximum leaf L and W values were measured using a ruler, and the area of each leaf (LA) was measured using a LI-3100 area meter (LICOR, Lincoln, NE, USA –

Petioleapp for leaf area measurement using a smartphone camera

is here) area meter calibrated to 0.01 cm

2
#### Model construction

A model to estimate LAs was obtained by linear regression analysis, considering the observed LA as the dependent variable and L, W, L2, W2, or L x W as independent variables. Relationships were evaluated by fitting regression models using the linear regression procedure in the SPSS 10 software package for Windows 2001 (www.ibm.com/software/analytics/spss) and applying the stepwise elimination option (Miranda and Royo, 2003a).

The internal validity of each model was tested based on the following parameters: coefficient of determination (R2), mean square error (MSE), sum of squares for error (SSE), and the predicted residual error in the sum of squares (PRESS). Residual plots were used to evaluate whether the data points in the residual plot were scattered within a horizontal band of constant width around zero for an adequate regression model (Weisberg, 1985). The best model was selected based on a combination of the highest R2, the lowest MSE, and the

lowest PRESS values, and when the PRESS values was close to the SSE.These criteria allowed us to evaluate the occurrence of bias, as well as the precision and accuracy of each model (Walther and Moore, 2005). Moreover, the results of the Wilkes-Shapiro W statistical test revealed that the pooled data from all seven genotypes showed a normal distribution. For this reason, data were pooled and a single relationship was calculated to develop a prediction model for LA in P. rubra.

Taking into account the potential problems of co- linearity caused by the use of two dimensional variables (L and W),the variance inflation factor (VIF = 1/(1R2); Marquardt, 1970), and the tolerance factor (T = 1/VIF; Gill, 1986) were also calculated

#### Model validation

To validate the selected model, and to assess its robustness, 100 leaves of P. rubra ‘Divine’ were used in 2013 to measure LA, leaf L, and leaf W, by previously described procedures. The two techniques reported by Miranda and Royo (2003a, b) were used to validate the models: (i) the validation dataset was used to produce a validation model by estimating the model parameters using the Stepwise Regression Option approach to develop an estimation model and the models were compared for consistency; and (ii) regression parameter

estimates from the estimation models were used to predict the outcomes for observations in the validation dataset and the mean-squared prediction error (MSPR) was then calculated and compared with the MSE of the regression fit to the model-building dataset (Neter et al., 1996).

Graphical procedures (Bland and Altman, 1986) were used to compare the predicted LAs (PLA) and the observed LAs (OLA) for ‘Divine’. Plots of PLA vs. OLA values are presented in Figure 1. The General Linear Model (GLM) procedure in SPSS was used to evaluate the linear relationship between OLA and PLA. In addition, PLA values were subtracted from OLA values for ‘Divine’ and the differences were plotted against the OLA. Lack of agreement was evaluated by calculating the relative bias, estimated by the mean of the difference (d) and the standard deviation (SD) of the differences (Figure 1). A normality (Gaussian distribution) test was carried out to obtain a Wilkes-Shapiro W statistic using the testing procedure in SPSS (Marini, 2001).

#### RESULTS AND DISCUSSION

The individual areas of P. rubra leaves ranged from 34 – 325 cm2, leaf Ls from 10.5 – 38.3 cm, and leaf Ws from 3.5 – 12.6 cm (data not shown). Among all eight genotypes, ‘Panittas Red’ had the highest average LA (200 cm2), whereas ‘J.J. Mini White’ had the lowest average LA (103 cm2). Leaf shape (the L:W ratio) of the eight Plumeria genotypes ranged between 2.1 – 3.1 (Table I), with ‘Elsie’ and ‘Panittas Red’ having the widest and the narrowest leaves, respectively (Table I).

In our experiments, the VIF ranged from 2.1 – 3.8, and T values ranged from 0.26 – 0.48 (Table I), demonstrating that co-linearity between the two leaf measurements (L and W) could be considered negligible (Gill, 1986), since VIF was lower than 10 and T was higher than 0.10 in all genotypes.Consequently, both leaf L and leaf W could be included in model-building. Our results are consistent with those reported by Cristofori et al. (2007), Fallovo et al. (2008), and Giuffrida et al. (2011) on hazelnut, small fruits, and bedding plants, respectively.

Regression analysis demonstrated a significant relationship between the independent variable (LA) and the five dependent variables tested (L, W, L2, W2, L x W), since the coefficient of determination (R2) was always higher than 0.80 (Table II). The five models developed during the calibration experiment were compared based on the selection criteria reported in the methods section (i.e., higher R2, lower MSE, lower PRESS, and when the PRESS value was close to the SSE value).

In some vegetable crops, only one linear measurement (L or W) was required to predict LA accurately for different genotypes of eggplant (Rivera et al., 2007; L) or red cabbage (Olfati et al., 2010;W). This was not the case in our study. Models 2 and 5, with a single measurement of W or W2, were less acceptable for estimating individual LAs in P. rubra due to their lower R2, higher MSE, and higher PRESS values. Models 1 and 4 performed better when L or L2were used as independent variables (Table II), indicating that when accuracy was not important, measuring leaf L gave more precise results than measuring leaf W. Moreover, the L-based models may be useful for LA estimation, since they require only one measurement.

Model selection required a balance between the predictive qualities of the model and the economy of including the least number of variables necessary to predict LA (Robbins and Pharr, 1987). To find a model independent of genotype to estimate LA accurately in P. rubra, measurements of both L and W should be involved. We preferred the linear model [LA = 4.15 x 0.66 (L x W)] for its accuracy. This model had the highest R2(> 0.97), smallest MSE, and smallest PRESS values (Table II). In addition, the PRESS value of P. rubra recorded in the calibration experiment was close to the SSE for the L x W allometric model (Table II), which supports the validity of the fitted regression model and of MSEs as an indication of the predictive capability of this model (Neter et al., 1996).

LA estimations for many potted ornamental plants including Euphorbia xlomi Thai hybrids (Fascella et al., 2009), rose (Rouphael et al., 2010a; Gao et al., 2012), marigold, dahlia, sweet William, geranium, and petunia (Giuffrida et al., 2011) have included both leaf L and W.

These studies concluded that L x W models gave a better prediction of LA than models based on either leaf L or leaf W alone. This was consistent with our findings, since involving both dimensions (L and W) was necessary to estimate LA accurately in P. rubra.

The shape coefficient (i.e.,the regression coefficient of Model 3) can be described by a shape between a triangle (0.50) and an ellipse (0.78) of the same length and maximum width. The shape coefficient of P. rubra recorded in this experiment (0.66; Table II) was within the range calculated for other ornamental plants. Values of 0.70 have been reported for Euphorbia xlomi Thai hybrids (Fascella et al., 2009), 0.72 for rose (Rouphael et al., 2010a), 0.56 for pot marigold, 0.58 for dahlia, 0.69 for sweet William, 0.68 for geranium, 0.64 for petunia, and 0.71 for pansy (Giuffrida et al., 2011).

In 2013, we validated the robustness of the L x W model on an independent dataset from another genotype (‘Divine’). The regression coefficients for L x W in the estimation and validation models were not significantly (P= 0.53) different, and the R2values were similar (0.97 and 0.98; Table III), indicating the applicability of the proposed L x W model to data beyond those on which the model was based (Neter et al., 1996). Moreover, a means to measure the actual predictive capability of the models was to use them to forecast each case in the validation dataset and to calculate the MSPR (Rouphael et al., 2010a). If the MSPR was close to the MSE value, based on the regression fit to the estimation dataset, then the MSE for the selected regression model was not seriously biased and gave a correct indication of the predictive ability of the model. In this study, the MSPR from the validation dataset on P. rubra LA did not differ greatly from the MSE of the estimation dataset (Table III). This implies that the MSE, based on the estimation dataset,was a valid indicator of the predictive ability of the estimation regression model (Neter et al., 1996).

The PLA and OLA values were highly correlated, given the over-estimation of 4.0% in the prediction (Figure 1). However, correlation analysis alone was not sufficient to explain the relationship between PLA and OLA, and plotting the residuals against OLA may be more informative (Bland and Altman, 1986; Marini, 2001). Plotting differences against OLA values also allowed investigation of possible relationships between measurement errors and the true values (Bland and Altman, 1986). Lack of agreement between PLA and OLA values can be evaluated by calculating the relative bias,estimated by the mean of the differences (d) and the SD of the differences. In Figure 1, a solid line represents the mean of the differences (d). If the differences were normally distributed, 97% of the differences should lie between d ± 3 SD. In this study, only a few points lay outside the lines representing d ± 3 SD, but the majority of points were within the lines.

In conclusion, a simple and unbiased model [LA = 4.15 x 0.66 (L x W)] was developed in order to predict LAs in P. rubra, irrespective of genotype. Our results, also showed that neither leaf L nor leaf W could be ignored when estimating LA. The proposed model could be adopted for physiological experiments in which destructive leaf sampling is not possible (e.g., with rare plants or in genetically segregating populations) without the use of expensive instruments.