Leaf area estimation of Congea tomentosa using a non-destructive method ¹

Estimativa de área foliar de Congea tomentosa através de método não destrutivo

ABSTRACT

Congea tomentosa is a climbing plant suitable for covering arbors, railings, and fences. Leaf area determination is useful in understanding the plant-environment relationship and facilitating agronomic studies on transpiration, water requirement, light interception, and photosynthetic activity. The objective of this study was to obtain an allometric equation to estimate the leaf area of C. tomentosa by measuring the leaf dimensions. Analyses were performed on 200 leaves of different shapes and sizes from 10 randomly chosen adult plants grown under field conditions. The leaf length, leaf width, product length and width, and leaf area were determined. Linear, linear without intercept, quadratic, cubic, power, and exponential regression models were used to estimate the leaf area. The coefficient of determination, Willmott’s concordance index, Akaike information criterion, root mean square error and BIAS index were used to determine the best model. The leaf area of C. tomentosa can be satisfactorily estimated using a non-destructive method that uses measurements of leaf dimensions. The equation ŷ = 0.63 × LW (Leaf: L = length, W = width) estimates the leaf area of C. tomentosa in a practical and fast way, with 99.15% of precision. Estimation of the leaf area of C. tomentosa using statistical models is less expensive and easily accessible to researchers and producers of this plant.

Key words:
leaf dimensions; vine; statistical models; modeling

RESUMO

Congea tomentosa é uma trepadeira indicada para cobertura de mandris, grades e cercas. A determinação da área foliar é útil para entender a relação planta-ambiente e facilitar estudos agronômicos sobre transpiração, necessidade de água, interceptação de luz e atividade fotossintética. O objetivo deste estudo foi obter uma equação alométrica para estimar a área foliar de C. tomentosa através da medição das dimensões foliares. As análises foram realizadas em 200 folhas de diferentes formas e tamanhos de 10 plantas adultas escolhidas aleatoriamente cultivadas em condições de campo. O comprimento da folha, a largura da folha, o produto do comprimento pela largura e a área foliar foram determinados. Modelos de regressão linear, linear sem intercepto, quadrático, cúbico, potência e exponencial foram utilizados para estimar a área foliar. O coeficiente de determinação, índice de concordância de Willmott, critério de informação de Akaike, raiz do quadrado médio do erro e índice BIAS foram usados ​​para determinar o melhor modelo. A área foliar de C. tomentosa pode ser satisfatoriamente estimada por meio de um método não destrutivo que utiliza medidas de dimensões foliares. A equação ŷ = 0,63 × LW (Folha: L = comprimento, W = largura) estima a área foliar de C. tomentosa de forma prática e rápida, com 99,15% de precisão. A estimativa da área foliar de C. tomentosa utilizando modelos estatísticos é menos dispendiosa e de fácil acesso aos pesquisadores e produtores desta planta.

Palavras-chave:
dimensões de folhas; planta trepadeira; modelos estatísticos; modelagem

HIGHLIGHTS:

Estimates of leaf area of Congea tomentosa based on measurements of leaf dimensions are a useful non-destructive method.

Estimates of the leaf area of C. tomentosa by statistical models are a non-expensive tool easily accessible to producers.

The equation ŷ = 0.63 × LW (Leaf: L = length, W = width) can be used to estimate the leaf area of C. tomentosa.

Introduction

Congea tomentosa (Verbenaceae) is a woody species and a perennial vine native to India and Malaysia. The leaves are 10 to 16 cm in length and arranged oppositely, with elliptical oval, tomentose, and cartaceous type characteristics, marked by veins on the adaxial surface (Silva et al., 2017). This plant is used in ornamental gardens, including arbors, railings, and fences, in full sun (Sartin et al., 2014) and is used for medicinal purposes by indigenous people (Faruque et al., 2019). Therefore, evaluating its growth, development, and reproduction is relevant, considering the scarcity of information about this plant and its importance in gardening.

Leaves are important for controlling photosynthesis, respiration, transpiration, and other physiological attributes related to different ecosystem processes (Wales et al., 2020). Leaf area directly influences the use of natural resources, such as water, nutrients, and light. Estimation of the leaf area of C. tomentosa is of great importance because the plant is cultivated mainly for its leaves. Leaf area can be measured using direct or indirect and destructive or non-destructive methods (Keramatlou et al., 2015). Successive evaluations of the same plant can be performed quickly and accurately using indirect and non-destructive methods with allometric equations based on the length and width of the leaf (Ribeiro et al., 2020; Silva et al., 2020). Knowledge of the leaf area of ornamental plants is necessary for planning the plant’s acclimatization conditions because of its landscape uses (Toscano et al., 2019) and, at physiological levels, knowing the plant’s growth potential. The objective of this study was to obtain an allometric equation to estimate the leaf area of C. tomentosa by measuring the leaf dimensions.

Material and Methods

The research was performed at the Teaching, Research, and Extension Unit (UEPE), Floricultura-Belvedere, Universidade Federal de Viçosa, Viçosa, Minas Gerais State, Brazil (20º 45’ S, 42° 52’, and altitude of 690 m). Congea tomentosa seedlings were produced in 10 L pots filled with soil and manure (2:1, v:v). The seedlings were transplanted to the soil and placed in a panel (1 × 2.4 m) after the formation of roots and leaves. The plants were grown for 12 months before leaf collection. Two hundred leaves of different shapes and sizes (with greater data variability) were randomly collected from 10 adult plants grown under field conditions in March 2021. Healthy leaves without symptoms of attack by pests, diseases, or the influence of abiotic factors were selected (Figure 1).

Figure 1
Maximum length (L) and width (W) of leaf of Congea tomentosa used to estimate leaf area

The maximum length (L) and maximum width (W) was measured from digitized images using a digital flatbed scanner (Epson Scan I365) with a known scale. The leaf area was measured with ImageJ® software (LA) (Ribeiro et al., 2018). In ImageJ, the images of the leaves were contrasted to facilitate the determination of the leaf area. Descriptive analysis was used to obtain the maximum and minimum values, mean, median, total amplitude, variance, standard deviation, standard error, and coefficient of variation from the length (L), width (W), product (LW), and digital leaf area (LA).

Regression analysis was used to obtain equations for calculating the leaf area of C. tomentosa. The following statistical equations were used for the analysis: linear, linear without intercept (0.0), quadratic, cubic, power, and exponential (Table 1).

Table 1
Statistical models used to estimate the leaf area of Congea tomentosa

Model	Model description
Linear	$\hat{y}={\beta }_0+{\beta }_1*x+e_i$
Linear (0.0)	$\hat{y}={\beta }_1*x+e_i$
Quadratic	$\hat{y}={\beta }_0+{\beta }_1*x+{\beta }_2*x^2+e_i$
Cubic	$\hat{y}={\beta }_0+{\beta }_1*x+{\beta }_2*x^2+{\beta }_3*x^3+e_i$
Power	$\hat{y}={\beta }_0*x^{{\beta }_1}+e_i$
Exponential	$\hat{y}={\beta }_0*{\beta }_1^x+e_i$

• * - Significant at p ≤ 0.05 by F test
• ŷ - Leaf area; x - Leaf dimensios; β₀, β₁, β₂, β₃ - Model coefficients; e_i - Random error

The criteria of the highest coefficient of determination (R²), Pearson’s correlation coefficient (r), Willmott’s agreement index (d) (Willmott,1981), lower Akaike information criterion (AIC) (Akaike, 1974), mean absolute error (MAE), root mean square error (RMSE) (Janssen & Heuberger, 1995), and BIAS index closest to zero (Leite & Andrade, 2002) were used to select the best equations. The statistical program R (R Core Team, 2021) was used to perform all analyses.

Results and Discussion

The descriptive analysis of the data obtained from C. tomentosa, including the minimum, maximum, mean, median, variance, total amplitude, standard deviation, standard error, and coefficient of variation, is presented in Table 2.

Table 2
Minimum, maximum, mean, total amplitude, median, variance, standard deviation, standard error, and coefficient of variation (CV) for length (L), width (W), length by width (L.W) and digital leaf area (LA) of Congea tomentosa leaves

Descriptive statistic	L	W	LW	LA
	(cm)		(cm2)
Minimum	6.56	2.28	14.94	9.79
Maximum	17.77	8.38	143.09	93.91
Mean	12.28	5.48	69.80	43.97
Total amplitude	11.20	6.11	128.15	84.13
Median	12.16	5.39	65.93	41.55
Variance	5.49	1.40	721.56	275.80
Standard deviation	2.34	1.18	26.86	16.61
Standard error	0.17	0.08	1.90	1.17
CV (%)	19.08	21.61	38.48	37.77

Leaf length (L) varied from 6.56 to 17.77 cm, with an average of 12.28-11.20 cm in amplitude. The average leaf width was 5.48 cm, with values ranging from 2.28 to 8.38 cm and 6.11 cm in amplitude. The length and width (LW) product ranged from 14.94 to 143.09 cm², with an average of 69.80 cm² and 128.15 cm in amplitude. The digital leaf area (LA) had an average of 43.97 cm², with a variation from 9.79 to 93.91 cm² and 84.13 in amplitude. Variation among the leaf dimensions is common in plants, especially those with a climbing habit. Climbing plants can adapt to diverse habitats (Fiorello et al., 2020). The statistical models used in this study have several advantages over destructive leaf area methods, as they are simple to use in field conditions and do not require plant destruction (Leite et al., 2019). The scatter plots between the pairs of variables L, W, and LA showed different relationships suggesting adjustments to linear and non-linear models (Figure 2).

Figure 2
Histograms and model adjustments between leaf length (L), leaf width (W), product of length and width (LW) and digital leaf area (LA) of Congea tomentosa leaves

The percentage distribution of the 200 leaves of C. tomentosa concerning size range was determined (Figure 3). The leaf area of more than 20% of the leaves varied between 36.51 to 45.50 cm². This factor is positive for this study because it has different leaf sizes, and the analyses have satisfactory accuracy and good data distribution (Shi et al., 2019).

Figure 3
Percentage distribution of actual leaf area (LA) size classes of 200 leaves of Congea tomentosa

Using simple linear measures to predict the leaf area of horticultural plants eliminates the need for expensive leaf area measurements (Hernández-Fernandéz et al., 2021). Small-scale farmers and researchers with limited financial resources could use this method. Regression models relating length (L), width (W), and their product (LW) to leaf area (LA) were evaluated (Table 3). The coefficient of determination for the linear models ranged from 0.8991 to 0.9978; quadratic models from 0.9115 to 0.9830; cubic models from 0.9130 to 0.9830, and power models from 0.9124 to 0.9832. The exponentials with smaller R² ranged from 0.8991 to 0.9348. Therefore, all the models estimated the leaf area of C. tomentosa with coefficients of determination (R²) of 0.8991-0.9978. Such variations were reported for Triticum aestivum (Apolo-Apolo et al., 2020) and Vitis vinifera (Teobaldelli et al., 2020). The decision on which model to use depends mainly on the study’s objective and the desired accuracy of the estimates (Teobaldelli et al., 2019).

Table 3
Equations, Pearson’s correlation coefficient (r), coefficient of determination (R²), Akaike information (AIC), root mean square error (RMSE), mean absolute error (MAE), and Willmott’ agreement index (d), obtained as a function of measurements of dimensions of Congea tomentosa leaves

Model	x	r	R²	AIC	RMSE	MAE	d	Equation	CV (%)
Linear	L	0.9485	0.8991	1236.86	5.2500	3.9781	0.9729	$\hat{y}=-38.59+6.72**\times L$	36.76
Linear	W	0.9733	0.9471	1107.62	3.8004	2.8562	0.9863	$\hat{y}=-30.84+13.65**\times W$	37.22
Linear	LW	0.9917	0.9832	880.02	2.1300	1.6525	0.9958	$\hat{y}=1.18+0.61**\times LW$	37.56
Linear (0.0)	LW	0.9915	0.9978	885.59	2.1925	1.7095	0.9957	$\hat{y}=0.63**\times LW$	37.25
Quadratic	L	0.9552	0.9115	1211.49	4.9027	3.6013	0.9766	$\hat{y}=-1.78+0.{43}^{ns}\times L+0.26**\times L^2$	36.88
Quadratic	W	0.9765	0.9530	1084.91	3.5728	2.6538	0.9880	$\hat{y}=-9.93+5.75**\times W+0.71**\times W^2$	37.28
Quadratic	LW	0.9915	0.9830	881.91	2.1508	1.6754	0.9957	$\hat{y}=0.89+0.62**\times LW-0.{00005}^{ns}\times L{W}^2$	37.56
Cubic	L	0.9562	0.9130	1209.07	4.8488	3.5910	0.9771	$\hat{y}=48.44-13.06*\times L+1.42*\times L^2-0.03*\times L^3$	36.90
Cubic	W	0.9767	0.9532	1085.09	3.5565	2.6443	0.9881	$\hat{y}=5.60-3.{61}^{ns}\times W+2.51*\times W^2-0.{11}^{ns}\times W^3$	37.28
Cubic	LW	0.9915	0.9830	880.01	2.1514	1.6815	0.9957	$\hat{y}=-2.3+0.78**\times LW-0.002*\times L{W}^2+0.{00001}^{ns}\times L{W}^3$	37.56
Power	L	0.9552	0.9124	1209.43	4.9020	3.6008	0.9766	$\hat{y}=0.31**\times L^{1.96**}$	36.85
Power	W	0.9763	0.9531	1084.58	3.5877	2.6734	0.9878	$\hat{y}=2.26**\times W^{1.73**}$	37.16
Power	LW	0.9915	0.9832	879.64	2.1494	1.6662	0.9957	$\hat{y}=0.71**\times L{W}^{0.97**}$	37.56
Exponential	L	0.9482	0.8991	1239.13	5.2798	3.8593	0.9719	$\hat{y}=6.74**\times 1.{16}^{**L}$	36.25
Exponential	W	0.9668	0.9348	1153.10	4.2581	3.2546	0.9822	$\hat{y}=8.59**\times 1.{33}^{**W}$	36.53
Exponential	LW	0.9668	0.9348	1116.72	4.2581	3.2546	0.9822	$\hat{y}=17.89**\times 1.{01}^{**LW}$	36.56

• x - Measurements of leaf dimensions; ŷ - Estimated leaf area (LA). ^**, ^*, ^ns - Significant at p ≤ 0.01, 0.05 and not significant, respectively, by F test; CV - Coefficient of variation

The equation that satisfactorily estimated the leaf area of C. tomentosa as a function of leaf measurements was the linear model without the intercept using the product of length and width (LW), which had the highest R² value (0.9978) and d (0.9957), with low RMSE (2.1925) and AIC values (885.59) (Table 3). The equation ŷ = 0.63 × LW constructed from this model is the most suitable to estimate the leaf area of C. tomentosa. Similar results were obtained in studies on Tectona grandis(Silva et al., 2020), Theobroma cacao (Schmildt et al., 2017), Manihot sp. (Leite et al., 2021), Erythrina velutina (Ribeiro et al., 2022), Juglans regia (Keramatlou et al., 2015), Talinum triangulare, Talinum paniculatum (Oliveira et al., 2019) and Eustoma grandiflorum (Dias et al., 2022). By estimating the leaf area using non-destructive models, it is possible to explain plants’ agronomic and physiological behavior concerning the availability of radiation and water (Salazar et al., 2018).

The relationship between the digital leaf area and length × width (Figure 4A) and the estimated and observed digital leaf area (Figure 4B) was evaluated. The coefficient of determination (R²) is almost similar (0.9832 and 0.9831), suggesting that the data dispersions were minimal with the objective line, indicating that the linear model with the intercept satisfactorily describes the leaf area (Oliveira et al., 2019).

Figure 4
Relationship between digital leaf area (LA) and length × width (LW) (A) and relationship between estimated digital leaf area and observed digital leaf area (B)

Leaf area estimation by non-destructive methods is used widely in studies of photosynthetic capacity, fertilization levels, and water availability, among others (Suárez et al., 2022), and is an excellent low-cost tool for use in field crops.

Conclusions

1. The leaf area of C. tomentosa can be estimated reasonably with a non-destructive method, which uses measurements of leaf dimensions.

2. The equation ŷ = 0.63 × LW (where L and W are, respectively, the length and width of the leaf) estimates the leaf area of C. tomentosa in a practical and fast way, with a correlation coefficient of 0.9915.

3. The estimation of the leaf area of C. tomentosa by statistical models is less expensive and easily accessible to researchers and producers of this plant.

Acknowledgments

The authors thanks to the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), to the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) (financial code 001) and to the Fundação de Amparo à Pesquisa do Estado de Minas Gerais (FAPEMIG) for the scholarships awarded to authors.

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• ¹ Research developed at Universidade Federal de Viçosa, Viçosa, MG, Brazil

Edited by

Editors: Lauriane Almeida dos Anjos Soares & Carlos Alberto Vieira de Azevedo

Publication Dates

• Publication in this collection
  01 Aug 2022
• Date of issue
  Oct 2022

History

• Received
  18 Feb 2022
• Accepted
  03 June 2022
• Published
  13 June 2022