Introduction

The Epilobium genus of perennial herbaceous plant which belongs to Onagraceae family consists of about 200 species with worldwide distribution. It has been widely used in traditional medicine and its fresh leaves used in tea and salad (Raven 1976; Vitalone et al. 2001). The extracts of aerial parts of Epilobium taxa have many therapeutic properties, including anti-proliferative, antioxidant, antitumor and also anti-inflammatory activity (Vitalone et al. 2001; Stolarczyk et al. 2013). Today, human societies have shown a high tendency to use herbs and their derivatives, hence increasing their production and yield is very important. The leaves have many different responsibilities in the plant such as photosynthesis, assimilation, and represent the main surface for physiologically active exchange and likewise biologically active components such as, flavonoids (e.g., kaempferol, mirycetin and quercetin) (Hiermann 1983; Averett and Raven 1984), steroids (Hiermann and Mayr 1985) and tannins (Stolarczyk et al. 2013) that in some of the species of Epilobium such as E. hirsutum and E. parviflorum has been found to be concentrated in the leaves. Therefore, leaf traits such as leaf area (LA) can have a significant effect on the estimation and the determination of growth, development and leaf structure. LA is an important characteristic for studying of the parameters such as leaf area ratio and specific leaf area which has been related to crop management (Reich et al. 1992; Borsato et al. 2008; Schmildt et al. 2014). LA is largely evaluated in physiological studies and also has a key role on transpiration, net assimilation rate, plant evapotranspiration (ET), light interception, plant growth, photosynthetic efficiency, plant productivity and survival (Chen et al. 1997; Wright et al. 2005). LA could be evaluated through many destructive (direct methods) and non-destructive (indirect methods) (Kubner and Mosandl 2000). However, most of the direct methods used to estimate LA, require the excision of leaves from the plants and scanning the leaves in the lab, so because of leaf destruction, plant canopy is damaged, which may alter other characters by interfering on physiological and phenological responses due to the reduction in canopy. Furthermore, direct methods are time-consuming and need advanced and expensive equipment, such as portable scanners, area integrators and laser optic apparatuses, (Mousavi Bazaz et al. 2012; de Souza et al. 2015). Whereas, the indirect (non-destructive) methods are based on mathematical equations and linear measurements of plant leaves (including leaf length (L) and leaf width (W)) and also digital images which are relatively more accurate and require less time and can be used without any destruction at different phenological stages of the plant (Cho et al. 2007; Ramesh et al. 2007; Pezzini et al. 2018; Schwab et al. 2014). Several equations have been developed to estimate LA by non-destructive methods. Montgomery (1911) first suggested that LA can be estimated by using linear measurements such as leaf length and width. Non-destructive models have been developed for many plant species such as Bergenia purpurascens (Zhang and Liu 2010), Helianthus (Maldaner et al. 2009), Zizyphus joazeiro (Maracajá et al., 2008), Crotalaria juncea (Cardozo et al. 2011), corylus (Cristofori et al. 2007), castanea (Serdar and Demirsoy 2006), Actinidia deliciosa (Mendoza-de Gyves et al. 2008), and Phaseolus vulgaris (Bhatt and Chanda 2003). Therefore, the objective of this study was to develop and validate the best fitted models to estimate the leaf area based on leaf dimensions (L and W), in some Epilobium species for the first time.

Material and Methods

Plant material

The seeds and the whole plant (Herbarium sample) of five Epilobium species (Onagraceae family) were collected from natural habitats of Iran at the seed full ripening stage in June and July 2014 (Table 1). The identification of plant species was conducted at Iranian Biological Resource Center (IBRC). The species consisted of Epilobium algidum, E. parviflorum, E. sp., E. hirsutum and E. frigidum. The experiment was conducted in the Faculty of Agriculture, Tarbiat Modares University, Tehran, Iran. The seeds were cultured in vitro on MS culture medium (Murashige and Skoog 1962) and incubated at 25 ºC with a 16-h photoperiod under 16/8-h light/dark. After three weeks, plantlets were transferred for acclimatization to pots, containing autoclaved soil within ex vitro condition and kept in a growth chamber. This procedure was described  by  Turker  et  al.   (2008)   with   some

modifications. For leaf area (dependent variable) estimation a total of 250 leaves were randomly collected for each species. The actual leaf area of each leaf was measured with an area meter (Delta-T Ltd., Cambridge, UK) calibrated to 0.01 cm². Then, the largest leaf length (L) and width (W) in cm were measured, using a millimeter ruler that is illustrated in Figure 1, and also the product of length with width was obtained for all leaf samples.

Model development

The dependent variable (leaf area, LA) for each sampled leaf was regressed to build the model with independent variables, including L, W and L×W. The descriptive statistics such as minimum, maximum, mean, standard error, variance (Var.) and Kurtosis of L, W, as well as LA in each species are presented in Table 2. Thereafter, regression models, linear (Y = a + bx), power (Y = ax^b) and quadratic (Y = a + bx + cx²) were examined between the dependent variable (LA) and independent variables, including L, W and L×W. Also, the existence of collinearity between these variables was verified by the variance inflation factor (VIF) (Marquaridt 1970), using SPSS software. If VIF for a variable was >10, the variable should be removed from the model.

For each model, we obtained the coefficient of determination (R²), the root mean square error (RMSE), mean square error (MSE) and Akaike information criteria (AIC) (Table 3). The criteria to select the best fitted model was based on the combination of the highest R² and lowest MSE, RMSE and AIC for each species (Floriano et al., 2006; Souza and Amaral 2015). The formula for AIC is as follows:

AIC = n * Ln (SSE/n) + 2k

n= number of observations

k = number of parameters

Table 1. Geographical information of collected Iranian endemic Epilobium species.

Figure 1. Epilobium leaf indicating the position of leaf length (L) and width (W) linear measurement.

Table 2. Minimum (Min), maximum (Max), mean, standard error (SE), variance (Var.) and kurtosis for leaf length, leaf width, length × width and leaf area of Epilobium species.

Table 2 (continued)

Validation of models

To validate the best-fitted model (with highest R², and lowest MSE, RMSE, and AIC), an experiment was performed in the summer-autumn 2018 on leaf samples of five Epilobium species grown at the same condition (described previously) in the growth chamber. In this regard about 50 leaves from different plants of each species were used to measure independent variables (L and W) and dependent variable (LA), using the same procedures described above to obtain observed LA (OLA). Leaf area (PLA) was predicted for each species using the best fitted model. Then, a PLA and OLA of each Epilobium species were regressed. Regression analyses were conducted using the SigmaPlot 12.5 package and Excel (version. 2016). Scatter plot of OLA against PLA is presented in Figure 2 (Mousavi Bazaz et al. 2012).

Software and tools

Statistical analyses were performed using the Microsoft Office Excel® 2013 and SPSS (Version 22, SPSS Inc, Chicago, IL, USA). Regression equations were fitted using SigmaPlot (ver.12.5, Richmond, California, USA).

Results

This study used a simple non-destructive model to predict leaf area of Epilobium species by measuring of length, width and the number of leaves. All the data for each five species (including L, W, L×W and also the actual leaf area) are documented in Table 2. Leaf length, Leaf width and observed leaf area for all species varied from 1.60 to 7.80 cm, 0.5 to 3.30 cm and 1 to 9 cm², respectively (Table 2). Among five Epilobium species examined in the present study, E. hirsutum and E. sp. had the highest and the lowest LA, respectively, and likewise the species differed in leaf dimensions (Table 2). The VIF varied between 1.25 and 2.78, depending on the species and leaf traits. Because VIF was < 10 in all Epilobium species, collinearity among independent variables (L, W, L × W) can be inconsiderable, hence all variables were included in the model (Gill 1986). The three models (linear, power, quadratic) and their  statistical criteria such

Table 3. Parameter and statistic estimates from regression models to estimate the leaf area (LA) from leaf length (L) and leaf width (W). Statistic estimates are coefficient of determination (R²), root mean square error (RMSE) mean square error (MSE), and Akaike information criteria (AIC).

as MSE, RMSE and AIC, are shown in Table 3. Among the models, we selected the best model based on several selection criteria (higher R² and lower MSE, RMSE, AIC). The coefficient of determination (R²) was more than 0.65 for the power and quadratic models of E. hirsutum and E. sp. In this regard the quadratic models based on the L×W with the highest coefficient of determination (R² ≥ 0.80) and the lowest values of MSE and RMSE compared with other models were selected as the best models for five Epilobium species (Table 3). Thus, both L and W variables were needed to estimate Epilobium LA accurately.

Figure 2. Plot of predicted leaf area (PLA) vs. the observed leaf area (OLA) for Epilobium hirsutum (a), E. algidum (b), Epilobium sp. (c), E. frigidum (d), and E. parviflorum (e) by using the model LA = a + b (L×W).

**Significant at p ≤ 0.01.

The regression between PLA and OLA showed strong relationship (R² ≥ 80) by using a non-destructive model based on L×W for five Epilobium species. According to these results, the quadratic model based on L×W showed higher coefficient of determination (R² ≥ 0.80) and lower MSE as compared to linear and power equations for the five species of Epilobium that are shown as follows:

1. algidum (LA = 0.1264 + 0.6562 (L×W) + 0.0366 (L×W)²), E. parviflorum (LA = – 3.144 + 1.323 (L×W) – 0.030 (L×W)²(, E. sp. (LA = 0.4236 + 0.3033 (L×W) + 0.1368 (L×W)²), E. hirsutum (LA= 2.2417 + 0.2202 (L×W) + 0.0029 (L×W)²), and E. frigidum (LA = 0.2119 + 0.4162 (L×W) + 0.1191 (L×W)²), R² ≥ 0.80.

Discussion

LA is one of the important physiological growth parameters for plants and measuring it accurately without damaging the plant is necessary in some researches. In this regards several studies have been conducted to estimate LA, by using linear dimensions (L, W, L², W², L×W, L²×W²), indirect (non-destructive) methods, and mathematical models of linear, power and quadratic types (Cho et al. 2007; Rouphael et al. 2010; de Carvalho et al. 2017). In the present study, we evaluated the non-destructive estimation of LA in Epilobium species from linear dimensions to select the best model. Result of the current study indicated that area of Epilobium leaves is well related to L×W with high R² values (R² ≥ 0.80), so presenting the best-fitted parameters for the quadratic model. These R² values (Table 3) agree with other previous reports to select the best fitted model for LA estimation in plants, i.e. (durian (Durio zibethinus, LA = 0.888 (LW) – 4.961, R² = 0.91), (cerrado species: Styrax pohlii, LA = 0.582 + 0.683 LW, R² = 0.98; Styrax ferrugineu, LA = – 0.666 + 0.704 LW, R² = 0.97; V. ferruginea; LA = 0.463 + 0.676 LW, R² = 0.96) (Souza and Habermann 2014; Souza and Amaral 2015; Kumar et al. 2017).

To determine the best fitted model, low values of MSE, RMSE, and AIC are also important. Therefore, the models we selected to estimate LA for Epilobium species not only had the highest R² (R² ≥ 0.90) but also had lower value of AIC, MSE, and RMSE than those presented by the other models in our study (Table 3). We found strong relationship between PLA and OLA in Epilobium species based on the product of leaf length and width in the quadratic model (Y = a + b (L×W) + c (L×W)²) with high coefficient of determination R² (R² »0.81-0.92; p < 0.001) (Figure 2). In this regard we propose the best fitted models for Epilobium species as: E. algidum (LA = 0.1264 + 0.6562 (L×W) + 0.0366 (L×W)²), E. parviflorum (LA = –3.144 + 1.323 (L×W) – 0.030 (L×W)²(, E. sp. (LA = 0.4236 + 0.3033 L×W + 0.1368 (L×W)²), E. hirsutum (LA= 2.2417 + 0.2202 (L×W) + 0.0029 (L×W)²), and E. frigidum (LA = 0.2119 + 0.4162 (L×W) + 0.1191 (L×W)²) (Table 3). All the best fitted models for E. parviflorum, E. sp and E. frigidum were derived from the two dimension (LW) regression showed the highest R² value (0.92, 0.84 and 0.81, respectively) while other models based on a single dimension of L or W exhibited the lowest R² (R² »  0.55-0.69 for L, R² » 0.54-0.76 for W)  (Table 3).These results are in agreement with previous reports in which the model for LA estimation was based on the combination of leaf length and width and is derived from the two-dimension regression (L and W), showing high R² values (Cristofori et al. 2007; Karimi et al. 2009; de Souza et al. 2015). Souza and Amaral (2015) in the study on Vernonia ferruginea reported low R² for the models derived from the single dimension regressions [R² »  0.40 (for L) and R² »  0.66 (for W and W²)]. They also indicated high R² for the models derived from the two-dimension regressions [R² » 0.96 (for LW) and 0.95 (for L²W²)]. de Souza et al. (2015) in a study on the multiple Vochysiaceae species, reported the lowest R² (0.79) for the model that derived from a single-dimension regression (L) and the highest R² (0.99) for the models derived from the two-dimension regressions (LW). However, Oliveira et al. (2019) developed a model to estimate LA by using linear measurements (L and W) on Schinus terebinthifolius Raddi and mentioned the best fitted model based on only leaf dimension W (LA = -2.6646 + 2.2124 (W) + 1.3953 (W)²) due to its high precision in the estimation of LA.

In case of E. algidum and E. hirsutum speices, we observed the highest R²  (0.84), respectively for the best fitted model from two-dimension regressions and the model derived from single-dimension (L) also showed high R² (R² »0.81-0.84 and (R² »0.73-0.81 in E. frigium and E. hirsutum speices, respectively, so the R² range observed in E. algidum and E. hirsutum by single (L)- and two-dimension (LW)-derived models was very narrow. Narrow R² range has been observed when developing the best model for estimating LA in vitis (Williams III and Martinson 2003), castanea plants (Serdar and Demirsoy 2006) and Vernonia ferruginea (Souza and Amaral 2015). The reason for observing narrow R² range in the models of E. algidum and E. hirsutum speices might be due to the ratio between L and W, so it can be considered an exception for these species. de Souza et al. (2015) reported that in the cases of narrow R² range in dwas is considered in our study. Moreover, Nakanwagi et al. (2018) reported in Salvia hispanica L. and Solanum aethiopicum that the models with L and combination of both L and W provided high accuracy and good LA estimation, which can be considered in E. algidum and E. hirsutum speices to estimate LA

In overall, we showed that the quadratic model (Y = a + b (L×W) + c (L×W)²) based on the combination of L and W for each five Epilobium species, estimates LA better than the other models. In agreement with our results, Mousavi Bazaz et al. (2012) in their study on two cultivars of Ocimum basilicum (Purple Ruffles, Genovese) to estimate LA by using non-destructive method, established the best fitted model, containing L and W for each cultivar separately (Mousavi Bazaz et al. 2012). Hence, the quadratic model derived from the two dimensions (L and W) that we proposed, could be used to estimate LA of E. algidum, E. parviflorum, E. sp, E. hirsutum and E. frigidum with high accuracy. In the present study, the validation tests also determined the quadratic models with the highest R² (R²≥ 0.90) and the lowest MSE, RMSE, and AIC for each species separately, and these models can be used to estimate LA for these species without any destructive method, just by using a ruler and a calculator.

Conclusions

The acquisition of nondestructive methods to estimate LA accurately as an important growth parameter in plants are useful. In this regard to accurately estimate LA, validation tests are very critical to determine the best fitted model derived from two-dimension regression of leaf length (L) and width (W), with the highest R² and the lowest MSE, RMSE, and AIC. Accordingly, we highlighted in the present study, the quadratic model based on the two-dimension regression (L and W) which is recommended for the leaf area prediction of five Epilobium species with high accuracy and without any destructive effect for the first time.

Acknowledgments

Authors gratefully acknowledge the support provided for this research project by the Tarbiat Modares University and by Iranian Research Organization for Science and Technology.

Conflict of Interest

The authors declare that they have no conflict of interest with any organization concerning the subject of the manuscript.