Non-destructive estimation of leaf area and leaf weight of Cinchona officinalis L. (Rubiaceae) based on linear models
Descripción general
The results obtained in this research showed that LA and LW of leaves of C. officinalis can be estimated through linear regression based on leaf width. Based on R2, RMSE, AIC and ABL, Model 2 is recommended for estimating both the LA (LA = 11.521(Wi) − 21.422) and LW (LW = 0.2419(Wi) − 0.4936). The use of these models in estimation and their validation was based on a data set obtained for this purpose. The equations were shown to be a simple, accurate, and time-saving tool for evaluating the growth of C. officinalis plants. There are some limitations regarding accuracy; however, the use of a larger amount of data would decrease extent of deviation. In addition, to increase the model accuracy, the incorporation of environmental factors, nursery management practices, and other growth factors is suggested. Finally, future work should test the applicability of the suggested models to other species of the genus Cinchona.
Resumen
Non-destructive methods that accurately estimate leaf area (LA) and leaf weight (LW) aresimple and inexpensive, and represent powerful tools in the development of physiologicaland agronomic research. The objective of this research is to generate mathematical modelsfor estimating theLAandLWofCinchona officinalisleaves. A total of 220 leaves were col-lected fromC. officinalisplants 10months after transplantation. Each leaf was measured forlength, width, weight, and leaf area. Data for 80% of leaves were used to form the trainingset, and data for the remaining 20% were used as the validation set. The training set wasused for model fit and choice, whereas the validation set al.lowed assessment of the of themodel’s predictive ability. TheLAandLWwere modeled using seven linear regression mod-els based on the length (L) and width (Wi) of leaves. In addition, the models were assessedbased on calculation of the following statistics: goodness of fit (R2), root mean squared error(RMSE), Akaike’s information criterion (AIC), and the deviation between the regression line ofthe observed versus expected values and the reference line, determined by the areabetween these lines (ABL). ForLAestimation, the modelLA¼11.521(Wi)21.422 (R2¼0.96,RMSE¼28.16,AIC¼3.48, andABL¼140.34) was chosen, while forLWdetermination,LW¼0.2419(Wi)0.4936 (R2¼0.93,RMSE¼0.56,AIC¼37.36, andABL¼0.03) was selected.Finally, theLAandLWofC. officinaliscould be estimated through linear regression involvingleaf width, proving to be a simple and accurate tool.
Metodologia
Study area Data on the L, Wi and weight of leaves of C. officinalis were collected and processed in June 2022 from the Fernandez Zarate family forest nursery, located in the community La Cascarilla (5°40′21.12″ S and 78°53′55.65″ W) province of Jaen at 1810 m, which is characterized by annual precipitation of 1730 mm, minimum temperature of 13 °C, and maximum temperature of 20.5 °C (Fernandez et al. 2022). Characteristics of the leaves of C. officinalis They are elliptic-ovate, simple, opposite and decussate, with petiole, acute or acuminate apex, with entire margin (Zevallos 1989; Huamán 2020). Data collection Fifty-five C. officinalis plants were randomly selected at nursery level and were 10 months old. Four leaves per plant were extracted (Figure 1), in total 220 leaves were collected without visible damage that could alter their shape (Suárez et al. 2018). The fresh weight of each selected leaf was then determined using a Kmt Style electronic balance (200 ± 0.01 g). In addition, each leaf was photographed according to the methodology described in (Fernandez-Zarate et al. 2022). Leaf length (L) from base to apex and maximum leaf width (Wi) were measured using ImageJ software (Figure 2) (Baker et al. 1996). These measurements were independently performed by three people in order to decrease bias in image processing. Statistical analysis Boxx and whisker plots were used for each morphometric variable evaluated (L, Wi, LA, and LW). In addition, since the data were not normally distributed, pairwise Spearman correlation coefficients were calculated between the sets of independent variables (L, Wi, L2, Wi2, (L + Wi)2, and L × Wi) and dependent variables (LA and LW). Linear regression was performed between the dependent variables (LA) and LW with different independent variables, including L, Wi, L2, Wi2, (L + Wi)2, and the product L × Wi (Keramatlou et al. 2015). Finally, the root mean squared error (RMSE) and Akaike’s information criterion (AIC) were calculated. Model validation Of the 220 leaves sampled, data from 80% of the leaves were randomly selected to form a training set that was used to determine the models, and data of the remaining 20% were used as a validation set to estimate the predictive capacity of the fitted model (Suárez et al. 2022). The mathematical model was chosen taking into account the highest coefficient of determination (R2) and the lowest RMSE and AIC. In addition, in order to analyze trends in the deviation of observed to expected values, scatter plots of observed versus expected values were made, and a reference line and the regression line of the observed versus expected values were superimposed. The deviation between the regression line of the observed versus the expected reference line indicated that there was bias. To determine this bias, the area between these lines (ABL) was calculated; the lower the ABL, the lower the bias, thereby indicating the higher performance of the model in terms of more accurate prediction (Suárez et al. 2018).
Resultados
LA is used to infer plant biomass accumulation (Weraduwage et al. 2015) in addition to estimating leaf growth (Nihayati et al. 2018; Budiarto et al. 2022). The calculation of LA and LW through non-destructive methods has been used in various physiological studies (photosynthetic capacity) and to assess the agronomic behavior of plants (fertilization intensity, water availability) (Lizaso et al. 2003; Swart et al. 2004; Blanco and Folegatti 2005; Rouphael et al. 2007; Suárez et al. 2018). For this reason, the L and Wi of a leaf have been used in regression as predictors of leaf variables that are more complex to measure non-destructively (LA and LW) (Ma et al. 1992; Serdar and Demirsoy 2006; Rouphael et al. 2007; Bakhshandeh et al. 2011; Erdoğan 2012; Pompelli et al. 2012; Fascella et al. 2013; Nehbandani et al. 2013; Keramatlou et al. 2015; Oliveira et al. 2015; Pezzini et al. 2018; Suárez et al. 2018; Wang et al. 2019; Montelatto et al. 2020; Sabouri et al. 2022). The research results showed a high correlation between the independent variables and dependent variables, with Spearman correlation coefficients ranging from 0.98 to 1 for the estimation of LA and from 0.96 to 0.98 for the estimation of LW of C. officinalis. Similarly, Spearman correlation coefficients of 0.93 have been reported between the weight and length of a leaf and of 0.89 between the weight and width (Suárez et al. 2018), whereas Serdar and Demirsoy (2006) determined a high correlation between the width, length, and area of chestnut leaves, with correlation coefficients ranging from 0.95 to 0.98. The highest R2 values (0.998 and 0.966) were obtained for the linear model using the product between leaf length and leaf width (L × Wi) to estimate the LA and LW of C. officinalis, respectively, however, this behavior is different when calculating the RMSE and AIC, this is evidence that the models either underestimate or overestimate the LA or LW of the leaves (Basak et al. 2019; Mela et al. 2022). In this study, in addition to R2 and RMSE, we calculated the AIC and the area between the fitted versus predicted line and the baseline (ABL) as additional criteria for selecting a model, taking into account bias in the same way as reported by (Suárez et al. 2018). Considering models that were superior in more than one statistic, either obtaining a higher R2 or a lower RMSE, AIC, or ABL, we found that the best model to predict LA and LW of C. officinalis leaves is Model 2, which used as the independent variable leaf width, since it had a lower RMSE, AIC, and ABL (for estimating LA) and lower AIC and ABL (for estimating We). Similar results were reported by (Sabouri et al. 2022), who found that models using the L or Wi of the leaves provided more accurate estimates of LA and LW, Cristofori et al. (2007) found R2 values between 0.70 and 0.81 when estimating the LA as a function of the L or Wi of apple leaves, resulting in higher R2 when Wi of leaves was used as independent variable, for the case of rose leaves, Rouphael et al. (2007) showed several models that allowed estimating LA and LW as a function of leaf L and Wi, Rouphael et al. (2007) developed three mathematical models that estimated LA, fresh and dry weight of maize leaves from measurements of leaf L and Wi, resulting in strong relationships between L and Wi with LA and LW (R2 > 0.85).