Leaf area estimation for Psychotria carthagenensis and Psychotria hoffmannseggiana as a function of linear leaf dimensions

Determining leaf area is important for studies involving plant growth and development. The aim of the present study was to obtain models for estimating leaf area of Psychotria carthagenensis and Psychotria hoffmannseggiana using linear measurements of leaf blades (length and width). Two hundred leaf blades of each species were collected in Parque Estadual Mata do Pau-Ferro in the municipality of Areia, Paraíba, Northeast Brazil. The equations evaluated for producing potential models included the following: linear, quadratic, potential and exponential. The criteria used to determine the best model(s) were as follows: high coefficient of determination (R2), low root-mean-square error (RMSE), low Akaike information criterion (AIC), high Willmott concordance index (d) and a BIAS ratio close to zero. All evaluated models satisfactorily estimated leaf area for the two species, but the equation ŷ = 0.6373 * LW0.9804 was the most appropriate for P. carthagenensis, while ŷ = 0.6235 * LW0.9712 was the most appropriate for P. hoffmannseggiana.


Introduction
Psychotria carthagenensis Jacq. is a shrub measuring 2-3 m in height. It is widely distributed in the Neotropical Region, occurring from Costa Rica to Argentina. In Brazil the species occurs from the state of Pará in the north to the state of Rio Grande do Sul in the south, and is found in a variety of habitats at elevations ranging from sea level to 600 m (Vitarelli & Santos, 2009;Taylor & Zappi, 2015). The species is highly significant for the conservation of available ecological resources because it serves as a source of food for fauna throughout the year, which disperse seeds (Blendinger et al., 2015).
Psychotria hoffmannseggiana [(Willd. ex Schult.) Müll.Arg.] is a subshrub measuring 30-60 cm in height. It is distributed throughout Central America and from Cuba to Paraguay (Delprete, 2010); it occurs in all regions of Brazil (Taylor & Zappi, 2015). The species is found in the Amazon, Cerrado, and Atlantic Forest biomes in habitats at elevations from 100 to 1500 m (Margalho, Rocha, & Secco, 2009). In the Northeast Region of the country it occurs in Atlantic Forest physiognomies including moist forests and restingas. The species has great importance in the region as a food source for fauna, mainly birds, which disperse seeds, and for the conservation and management of disturbed sites, such as moist forests (Schupp, 1993).
Due to the importance of these species, ecophysiological studies related to growth, development, reproduction, and propagation are needed. Leaf area is the most important parameter for determining plant growth (Benincasa, 1988), since leaves perform several functions for plants, including the interception and absorption of light for photosynthesis, and gas exchange and transpiration (Taiz, Zeiger, Møller, & Murphy, 2017). Taiz et al. (2017) described leaf area as one of the most difficult parameters to measure because it requires expensive equipment and/or destructive techniques.
Several methods exist for measuring leaf area, including those that are destructive, non-destructive, direct, or indirect (Marshall, 1968). Direct methods may or may not be destructive, while all indirect methods are non-destructive. Destructive methods are generally considered simple and accurate, but by their nature they destroy leaves in the process and require more time and labor (Schmildt, Hueso, & Cuevas, 2014).
The use of non-destructive methods has been gaining importance for studies of plant populations because they allow quick and accurate successive leaf area measurements of the same individual (Bosco, Bergamaschi, Cardoso, Paula, & Casamali, 2012). The development of regression models allows leaf area to be estimated from linear dimensions of the foliar limb (length and width), and thus represents a simple nondestructive method for obtaining this parameter in the most diverse field conditions (Pompelli et al., 2012). In this context, regression models (non-destructive method) used to estimate leaf area are developed based on direct measurements of true leaf area using digitalized images of the collected leaves (destructive method). Several researchers have used such models to estimate leaf area for forest species [Merremia aegyptia (L.) Urb. (Assis, Linhares, Souza, Pereira, & Almeida, 2015) and Juglans regia L. (Keramatlou, Sharifani, Sabouri, Alizadeh, & Kamkar, 2015)] and agricultural species [Litchi chinensis Sonn. (Oliveira, Silva, Costa, Schmildt, & Vitória, 2017) and Annona cherimola Miller (Schmildt, Hueso, Pinillos, Stellfeldt, & Cuevas, 2017)].
The aim of the present study was to obtain models that satisfactorily estimate leaf area of Psychotria carthagenensis and Psychotria hoffmannseggiana using linear dimensions of the foliar limb.

Material and methods
The study was conducted in Parque Estadual Mata do Pau-Ferro (6°58'12" S and 35°42'15" W) located in the municipality of Areia, in the microregion of Brejo Paraibano and mesoregion of Agreste Paraibano (Paraíba, Brazil) ( Figure 1). The climate of the area is classified as Aw according to Peel, Finlayson, and McMahon (2007), which is tropical wet and dry with autumn-winter rains, and an average annual temperature of 22°C (Ribeiro, Barbosa, Lopes, Pereira, & Albuquerque, 2018a). Elevations of the area range between 400 and 600 m. Health, USA) with increased contrast to better delimit the area to be measured (Ribeiro, Barbosa, & Albuquerque, 2018b). The following equations were evaluated for as models for estimating leaf area as a function of the linear dimensions (length and width) of a leaf: linear (ŷ = a + bx), quadratic (ŷ = a + bx + cx²), potential (ŷ = ax b ), and exponential (ŷ = ab x ). The dependent variable (ŷ) estimates leaf area as a function of the independent variable(s) (x), which were length (L), width (W), and/or their product (length x width).
The criteria used to determine the model(s) that best estimates leaf area of P. carthagenensis and P. hoffmannseggiana as a function of the linear dimensions of the leaf limb (L, W and / or L x W) were: coefficient of determination (R 2 ), root-mean-square error (RMSE), Akaike information criterion (AIC), Willmott concordance index (d) and the BIAS ratio. The best models were considered those with highest R² and d, lower values of RMSE and AIC, and a BIAS ratio close to zero. All statistical analyses were performed using R ® v.3.4.3 (R Core Team, 2017).
Extensive variation in the dimensions of the leaf blades of P. carthagenensis and P. hoffmannseggiana, resulted in lower values for the coefficient of variation for length and width, and greater variability in their product (LxW) and leaf area (Table 1). This abundant variability of the data is of fundamental importance for the construction of statistical models that estimate leaf area because it will favor models that can be used for small, medium, and large leaves (Cargnelutti Filho, Toebe, Burin, Fick, & Casarotto, 2012).
The data revealed little dispersion in relation to the adjustment curve, indicating that the models mentioned above satisfactorily estimate the true leaf area of P. carthagenensis and P. hoffmannseggiana ( Figure 4A and B). The models for estimating the leaf area of P. carthagenensis (ŷ = 0.6373 * LW 0.9804 ) and P. hoffmannseggiana (ŷ = 0.6235 * LW 0.9712 ) were satisfactory close at estimating true leaf area, with coefficients of determination of 0.9950 and 0.9925 ( Figure 5A and B). The models identified by the present study may contribute to ecological studies that involve the growth, development, and propagation of these two species, since leaf area is fundamental parameter for research in these areas.

Conclusion
Leaf area of P. carthagenensis and P. hoffmannseggiana can be satisfactory estimated by a non-destructive method that uses linear measurements of leaf blades.
The models found, which incorporate the product of length and width (LxW) sufficiently estimated leaf area for P. carthagenensis and P. hoffmannseggiana. The most suitable model for estimating leaf area of P. carthagenensis was ŷ = 0.6373 * LW 0.9804 , while that for P. hoffmannseggiana was ŷ = 0.6235 * LW 0.9712 .