The present work was aimed to obtain a model for the determination of the leaf area in function of the length and width of the leaves in pepper ( Capsicum annuum L.) hybrid Salvador. The research was carried out in nursery conditions at the Experimental Campus La Teodomira, located in the parish of Lodana, Santa Ana, province of Manabí, Ecuador, in 2016, in the stages of initiation of flowering and flowering-fructification. In each phase 100 physiologically mature leaves of different sizes were collected. Leaves were digitalized in a rectangle with known dimensions, which allowed the area to be calculated through the percentage of pixels of different colors. From the determination of the length and maximum width of each leaf and the estimated area through the digitization process, the regression models were obtained, selecting the better fit generated between the leaf area and the product of the length by the maximum width of the leaf (). In the initiation of flowering stage the quadratic model generated the best coefficient of determination (R2 = 0.958), whereas in the flowering-fructification stage the best coefficient of determination was achieved by the cubic model (R2 = 0.955). The practical applicability of other simpler models among the tested ones, which show a high accuracy and sacrifice a low percentage of error, is discussed.
The determination of the foliar area is an important indicator for physiological, ecophysiological and agricultural investigations in the diversity of species of cultivated plants, given that growth, biomass synthesis by photosynthesis (absorption of CO2 and light), transpiration, consumption of water, mineral nutrition, respiration, production and quality of yield are directly related to the leaf area [
Non-destructive methods for the estimation of leaf area, although dating from the last century, are still valid today, which has been demonstrated in Prunus persica L. Batsch and Prunus salicina Lindl. [
The main advantages of the use of allometric models for the estimation of the foliar area [
・ These non-destructive models allow the measurement in vivo of plant leaves, being able to follow their evolution in the same leaf, which diminishes the variation substantially.
・ The cost associated to equipment and human resources for measuring the leaf area is substantially reduced.
・ If a reliable equation is selected, calculations can be made quickly and with great precision.
・ They are easy, simple, accurate, low-cost useful tools for physiological studies related to the growth and development of plants.
As a main disadvantage [
Several researchers have used regression techniques for the estimation of leaf area as non-destructive methods in diverse crops such as peach, plum, coffee, potato and others [
For the estimation of foliar area of vine Cabernet Sauvignon in three stages of development and subjected to different irrigation schemes, several models were assayed [
Leaf area in jojoba seedlings (Simmondsia chinensis (Link.) CE Schneider) was estimated from linear regression equations which related the product of the length by the width of the leaf, comparing the proportion of leaves with acute and obtuse apex [
The evaluation of allometric models for the estimation of the foliar area in vines (Vitis vinifera L. genotypes), looking for simpler models showed that simple regression models based on the length of the leaf achieve good results but sacrifice accuracy; thus, the estimation of the area depending on the product of the length by the width of the leaf is suggested [
Digital image processing and regression adjustment have been used for constructing models to determine the foliar area of the Persian walnut (Juglans regia L.), also recommending the use of linear models that relate the leaf area with the product of the length by the width of the leaf [
Similar results were obtained in plants of Vernonia ferruginea [
More recent works [
In pepper (Capsicum annuum L.), the estimation of the leaf area by mathematical methods has been reported by several authors, and has been recently reviewed [
The evaluations were carried out on plants of pepper (Capsicum annuum L. hybrid Salvador), growing in a nursery at the Experimental Campus La Teodomira, located in the parish of Lodana, Santa Ana, province of Manabí, Ecuador, in 2016. The process of estimating the leaf area was divided into three steps: the first was sampling, which was executed in two stages of development of the pepper plants (initiation of flowering and flowering-fructification); 100 physiologically mature leaves (two leaves/plant) were randomly selected in each of the stages of development, in 50 plants chosen by the zigzag sampling technique.
In the second step, for each sampled leaf the length and maximum width (in centimeters) were determined with a millimeter ruler.
The third step was to develop a procedure for the calculation of the foliar area in the collected leaves, which was based on a digitalization of the image of each leaf within a figure of easy calculation of the area (rectangle) as represented in
The area of the rectangle (Rectangle Area = a * b) was related to the leaf area, based on the difference of pixels of different colors and the percentage they represent within the area of the rectangle (Foliar Area = % Black pixels * Rectangle Area).
For the calculation, a software was developed to carry on the binarization process of the image, which consists of analyzing each pixel and defining it in two colors, white or black. We used the Java programming language that is part of a large set of free tools [
A code was used, with libraries that allow the handling of images, improving and adapting them to the needs. The system establishes which pixel has a value of 255, determining it with a white color and which pixel has a value of zero, determining it with a black color. For the case of images having different colors, a threshold value (200) was used, which was compared with an average obtained from the value of the pixel of each of the three basic colors (RGB). If this value was lower than the threshold value, it was assumed that the color is black,
otherwise it was set as white (it should be noted that each pixel contains a variation of 256 colors). Another aspect considered was the size of the image in pixels, multiplying the width by the length and obtaining the total number of pixels (area of the rectangle).
The total number of white pixels was counted and divided for the total of pixels to obtain the percentage of free area. The total number of black pixels was divided for the total of pixels, obtaining the percentage of the area of each leaf.
In this example (
b l a c k p i x e l s t o t a l p i x e l s * 100 * ( r e c t a n g l e a r e a ) = ( 24 64 ) * 100 * ( a * b ) = 37.5 % * ( a * b )
To facilitate the use of the application, a graphical interface was developed (
is calculated by multiplying the percentage by 450 cm2 (area of the rectangle pre-established in the digitization process). In addition, the directories of the non-binarized and binarized images are also accesible.
where:
#n: Number of images to be binarized
Img: Number of binarized images
Play: Start of the digitalization
CSV: Generates a standard sheet of comma-delimited format, which can be opened from an Excel spreadsheet and includes all the sorted names of the leaves with their respective area (
Once the areas of leaves were calculated, a descriptive analysis of the variables studied was carried out (length, maximum width and leaf area). Later, a comparison between the mean values in the two sampling stages was conducted, in order to detect possible homogeneity between both moments. For this analysis t-tests were made for comparison of means, as well as box and whisker graphics.
Then, several regression models were tested for the estimation of the leaf area according to the explanatory variables in each of the sampling stages. The models (linear, inverse, quadratic, cubic, power and exponential) were tested for each of these variables (length and maximum width of the leaf) as well as for the product of the length by the maximum width (length * width).
The selection of the best model for each stage was based on the slope significance tests (F Test) and the best determination coefficient (R2) as it has been recommended [
In
The use of six models (linear, inverse, quadratic, cubic, power and exponential) for the independent variables length of the leaf (L), maximum width of leaf (W) and product of the length by the width (L * W) and as dependent variable the leaf area (LA) in the two stages of sampling (initiation of flowering and flowering-fruiting) led to the test of 36 models, 18 for each stage. Results are shown in
Using the criterion of the highest R2 in addition to the analysis of the residues (
Stage | Parameter | Min | Max | Mean | SE | CV |
---|---|---|---|---|---|---|
Initiation of flowering | LA | 72.91 cm2 | 200.66 cm2 | 129.46 cm2 | 2.826 cm2 | 21.83% |
L | 15.70 cm | 25.50 cm | 20.83 cm | 0.232 cm | 11.16% | |
W | 6.60 cm | 12.00 cm | 9.67 cm | 0.117 cm | 12.10% | |
Flowering- fructification | LA | 68.15 cm2 | 190.47 cm2 | 117.91 cm2 | 2.256 cm2 | 19.13% |
L | 14.80 cm | 25.30 cm | 19.59 cm | 0.224 cm | 11.45% | |
W | 7.30 cm | 12.20 cm | 9.20 cm | 0.103 cm | 11.19% |
LA: Leaf area; L: Length; W: Maximum width; N = 100.
Parameter | Stage | Statistic of Levene | T test | |||||
---|---|---|---|---|---|---|---|---|
Initiation of flowering | Flowering-fructification | |||||||
Mean | SE | Mean | SE | F | Sig | t | Sig | |
LA | 129.46 cm2 | 2.826 cm2 | 117.91 cm2 | 2.256 cm2 | 4.602 | 0.033 (*) | 3.194 | 0.002** |
L | 20.83 cm | 0.232 cm | 19.59 cm | 0.224 cm | 0.091 | 0.760 (ns) | 3.81 | 0.000*** |
W | 9.67 cm | 0.117 cm | 9.20 cm | 0.103 cm | 1.020 | 0.310 (ns) | 3.00 | 0.003** |
LA: Leaf area; L: Length; W: Maximum width; (*) p < 0.05; (**) p < 0.01; (***) p < 0.001; (ns) Non-significant; N = 100.
Model | Stages | ||||||||
---|---|---|---|---|---|---|---|---|---|
Initiation of flowering | |||||||||
Assayed model | α | β | δ | ω | R2 | F | Sig | SLA | |
1 | LA = α + β * (L) | −98.506 | 10.946 | - | - | 0.811 | 419.75 | *** | 12.358 |
2 | LA = α +β * (W) | −62.822 | 9.223 | - | - | 0.842 | 520.672 | *** | 9.024 |
3 | LA = α + β * (L * W) | 0.361 | 0.634 | - | - | 0.953 | 1981.67 | *** | 6.166 |
4 | LA = α + β * (L) + δ * (L)2 | −8.797 | 2.111 | 0.215 | - | 0.813 | 210.505 | *** | 12.354 |
5 | LA = α + β * (W) + δ * (W)2 | 134.323 | −10.939 | 0.509 | - | 0.858 | 291.993 | *** | 8.601 |
6 | LA = α + β * (L * W) + δ * (L * W)2 | 37.943 | 0.244 | 0.001 | - | 0.958 | 1095.73 | *** | 5.878 |
7 | LA = α + β * (L) + δ * (L)2 + ω * (L)3 | Non Significant (Multicolinearity in the model terms) | |||||||
8 | LA = α + β * (W) + δ * (W)2 + ω * (W)3 | Non Significant (Multicolinearity in the model terms) | |||||||
9 | LA = α + β * (L * W) + δ * (L * W)2 + ω * (L * W)3 | Non Significant (Multicolinearity in the model terms) | |||||||
10 | LA = α + β/(L) | 343.649 | −4403.45 | - | - | 0.788 | 364.537 | *** | 13.074 |
11 | LA = α + β/(W) | 293.803 | −3402.19 | - | - | 0.801 | 393.761 | *** | 10.122 |
12 | LA = α + β/(L*W) | 241.632 | −21714.45 | - | 0.88 | 718.503 | *** | 9.840 | |
13 | LA = α * L ^ β | 0.547 | 1.796 | - | - | 0.824 | 460.246 | *** | 0.095 |
14 | LA = α * W ^ β | 1.340 | 1.502 | - | - | 0.835 | 497.648 | *** | 0.077 |
15 | LA = α * (W * L) ^ β | 0.698 | 0.982 | - | 0.953 | 1978.392 | *** | 0.049 | |
16 | LA = α * β ^ L | 20.142 | 0.088 | - | - | 0.821 | 450.973 | *** | 0.096 |
17 | LA = α * β ^ W | 25.629 | 0.077 | - | - | 0.841 | 519.726 | *** | 0.075 |
18 | LA = α * β ^ (W * L) | 45.092 | 0.005 | - | 0.948 | 1776.135 | *** | 0.052 | |
Model | Flowering-Fructification | ||||||||
Assayed model | α | β | δ | ω | R2 | F | Sig | SLA | |
19 | LA = α + β * (L) | −62.822 | 9.223 | - | - | 0.842 | 520.672 | *** | 9.024 |
20 | LA = α + β * (W) | −68.178 | 20.218 | - | - | 0.853 | 567.215 | *** | 8.703 |
21 | LA = α + β * (L * W) | 16.973 | 0.554 | - | - | 0.926 | 1719.216 | *** | 5.265 |
22 | LA = α + β * (L) + δ * (L)2 | 134.323 | −10.939 | 0.509 | - | 0.858 | 291.993 | *** | 8.601 |
23 | LA = α + β * (W) + δ * (W)2 | 74.250 | −10.398 | 1.625 | - | 0.861 | 300.442 | *** | 8.497 |
24 | LA = α + β * (L * W) + δ * (L * W)2 | 41.614 | 0.287 | 0.001 | 0.949 | 901.919 | *** | 5.148 | |
25 | LA = α + β * (L) + δ * (L)2 + ω * (L)3 | Non Significant (Multicolinearity in the model terms) | |||||||
26 | LA = α + β * (W) + δ * (W)2 + ω * (W)3 | Non Significant (Multicolinearity in the model terms) | |||||||
27 | LA = α + β * (L * W) + δ * (L * W)2 + ω * (L * W)3 | −101.11 | 2.564 | −0.01 | 1.95 * 10−5 | 0.955 | 685.99 | *** | 4.836 |
28 | LA = α + β/(L) | 293.803 | −3402.195 | - | - | 0.801 | 393.761 | *** | 10.122 |
29 | LA = α + β/(W) | 304.4 | −1695.803 | - | - | 0.820 | 446.167 | *** | 9.622 |
30 | LA = α + β/(L * W) | 219.541 | −17703.3 | - | - | 0.889 | 788.774 | *** | 7.538 |
31 | LA = α * L ^ β | 1.340 | 1.502 | - | - | 0.835 | 497.648 | *** | 0.077 |
32 | LA = α * W ^ β | 3.689 | 1.557 | - | - | 0.837 | 503.641 | *** | 0.076 |
33 | LA = α * (W * L) ^ β | 1.402 | 0.852 | - | - | 0.931 | 1338.087 | *** | 0.049 |
34 | LA = α* β ^ L | 25.629 | 0.077 | - | - | 0.841 | 519.726 | *** | 0.075 |
35 | LA = α* β ^ W | 24.838 | 0.167 | - | - | 0.836 | 506.371 | *** | 0.076 |
36 | LA = α * β ^ (W * L) | 50.371 | 0.005 | - | - | 0.924 | 1196.285 | *** | 0.052 |
depending on the product of the length by the width of the leaf) was selected for the initiation of flowering, and No. 27 (cubic model of the foliar area depending on the product of the length by the width of the leaf) for flowering-fructification, where:
Initiation of flowering: LA = 0.244 * (L * W) + 0.001 * (L * W)2 + 37.9943
R2 = 0.958 SLA = .878
Flowering-fructification: LA = 2.564 * (L * W) − 0.01 * (L * W)2 + 1.95 * 10(−5) * (L * W)3 − 101.11
R2 = 0.955 SLA = 4.836
Under nursery conditions for Capsicum annum L. hybrid Salvador, the variables length and maximum width of leaf guarantee high precision in the estimation of the foliar area, based on models showing coefficients of determination (R2) greater than 0.9 and achieving the best results when the product (length * width) is used as an explanatory variable.
In both stages of growth and development (initiation of flowering and flowering-fructification) 30 of the 35 equations showed high values in the coefficients of determination (amplitude of variation of R2 between 0.877 and 0.93 with p < 0.0001). This result shows that for Capsicum annuum L. is also valid that models using the measures of length, maximum width of the leaves and product of the multiplication of the two foliar attributes can provide high precision estimates for the fast, accurate and economic determination of the foliar area in physiological, biological, environmental and agronomic investigations.
It is worth analyzing the implication of the use of more practical models and the sacrifice that this entails in their accuracy, which highlights the possible use of model 3 in the initiation of flowering stage: LA = 0.634 * (L * W) + 0.361 (R2 = 0.953, SLA = 6.166). This model gains in practicality because it is a simple linear model and only sacrifices 0.5% in the percentage of errors explained with the regression.
Also, in the flowering-fructification stage the model 24 (polynomial grade 2) would be useful: LA = 0.287 * (L * W) + 0.001 * (L * W)2 + 41.614 (R2 = 0.949; SLA = 5.148). In this model 0.6% is sacrificed in the percentage of errors explained with the regression with respect to the best fit model.
In both cases, the sacrifice is not highly significant, so the inclusion of both models in the estimation process can be assessed in order to gain practicality in its application.
The main advantage of the proposed method is that the measurements of the variables can be done in vivo, with a simple instrument (millimeter rule) and without the need of destructive sampling, which has been useful for other species. Besides, costs are reduced and the possibility of studying the evolution of the parameters is clearly available [
Téllez, O.F., Muñoz, E.M., García, A.T., García, J.L.C., Ardisana, E.F.H., Aguilar, R.L. and Obregón, E.F. (2018) Estimation of the Foliar Area by Non-Destructive Methods in Two Stages of Growth of Pepper Plants (Capsicum annuum L.) Hybrid Salvador. American Journal of Plant Sciences, 9, 325-338. https://doi.org/10.4236/ajps.2018.93026