Optimal plot size estimation in field experiment with purple passion fruit

The species P. edulis Sims f. edulis, native to Brazil, known as purple passion fruit, has purple fruits and lower acidity. With the growing demand for passion fruits, there is greater need for research on their cultivation to reduce production costs and improve fruit quality. The adequate determination of the size and number of plots has been a fundamental limitation in studies with several crops, as it is difficult to obtain constant data on plants per plot in most experiments, making it impossible to use usual methodologies for data analysis. As a result, testing can be performed with less labor and implementation costs, making plot size optimization a step of interest. Thus, this work aims to determine the ideal size of experimental plots with purple passion fruit in the field using three methods. The variables analyzed were fruit length, fruit diameter, peel thickness, juice yield, soluble solids content, citric acid, number of fruits, and average fruit weight. The use of optimal plot size of six basic units for fruit-related variables, five for pulp-related variables, and seven basic units for production variables, is recommended.

Index terms
Passiflora edulis Sims f. edulis; experimental planning; blank test; maximum curvature; quadratic plateau

Authorship

Beatriz Garcia Lopes Beatriz Garcia Lopes E-mail:biagarcialopes@gmail.com

Luiz de Queiroz College of Agriculture, University of São Paulo, Piracicaba, São Paulo, Brazil University of São PauloBrasilPiracicaba, SP, Brasil Luiz de Queiroz College of Agriculture, University of São Paulo, Piracicaba, São Paulo, Brazil

http://orcid.org/0000-0003-2605-6443

Taciana Villela Savian

http://orcid.org/0000-0002-3309-6075

Glaucia Amorim Faria

Paulista State University ‘Júlio de Mesquita Filho’, Ilha Solteira, São Paulo, Brazil. Paulista State University ‘Júlio de Mesquita Filho’BrasilIlha Solteira, São Paulo, Brasil Paulista State University ‘Júlio de Mesquita Filho’, Ilha Solteira, São Paulo, Brazil.

http://orcid.org/0000-0003-2474-4840

Beatriz Garcia Lopes E-mail:biagarcialopes@gmail.com

SCIMAGO INSTITUTIONS RANKINGS

Figures | Tables | Formulas

Figures (3)
Tables (4)
Formulas (5)

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Figure 1
Relationship between coefficient of variation (CV%) and plot size ( ), by the maximum curvature method, in basic units for the variables under study in the uniformity test with purple passion fruit. A) FL: fruit length (mm), FD: fruit diameter (mm), and FW: average fruit weight (g); B) PT: peel thickness (mm), JY: juice yield (mL), Brix: soluble solids content (°Bx), and Acidity: citric acid (%); C) NF: number of fruits (NF). Source: Authors.

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Figure 2
Relationship between the coefficient of variation (CV%) and plot size (Xc), by the modified maximum curvature method, in basic units for the variables under study in the uniformity test with purple passion fruit. A) FL: fruit length (mm), FD: fruit diameter (mm), and FW: average fruit weight (g); B) PT: peel thickness (mm), JY: juice yield (mL), Brix: soluble solids content (°Bx), and Acidity: citric acid (%); C) NF: number of fruits (NF). Source: Authors.

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Figure 3
Relationship between the coefficient of variation (CV%) and plot size (Xc) by the Segmented quadratic model with plateau, in basic units for the variables under study in the uniformity test with purple passion fruit. A) FL: fruit length (mm), FD: fruit diameter (mm), and FW: average fruit weight (g); B) PT: peel thickness (mm), JY: juice yield (mL), Brix: soluble solids content (°Bx) and Acidity: citric acid (%); C) NF: number of fruits (NF). Source: Authors.

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Table 1
Number of simulations (NS), number of plots (NP), plot size (PS) and plot shape (PSH) for the basic units of a field experiment with passion fruit in the field.

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Table 2
Estimates of the parameter of the model, by the modified maximum curvature method, coefficient of variation corresponding to the maximum curvature point (CV%), the value of the abscissa at which the maximum curvature point (X_c ) occurs, coefficient of determination (R² ) for the variables under study in the uniformity test with purple passion fruit.

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Table 3
Estimates of the parameters of the segmented quadratic model method with plateau. coef-ficient of variation corresponding to the point of maximum curvature (P), the value of the abscissa at which the point of maximum curvature (Xc) occurs, coefficient of determination (R²) for the vari¬ables under study in the uniformity test with purple passion fruit.

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Table 4
Range of variation of the coefficient of determination (R²) for the modified maximum cur-vature method (MCM), and segmented quadrat¬ic model with plateau (QMP) method.

Thumbnail

Figure 1 Relationship between coefficient of variation (CV%) and plot size ( ), by the maximum curvature method, in basic units for the variables under study in the uniformity test with purple passion fruit. A) FL: fruit length (mm), FD: fruit diameter (mm), and FW: average fruit weight (g); B) PT: peel thickness (mm), JY: juice yield (mL), Brix: soluble solids content (°Bx), and Acidity: citric acid (%); C) NF: number of fruits (NF). Source: Authors.

Figure 2 Relationship between the coefficient of variation (CV%) and plot size (Xc), by the modified maximum curvature method, in basic units for the variables under study in the uniformity test with purple passion fruit. A) FL: fruit length (mm), FD: fruit diameter (mm), and FW: average fruit weight (g); B) PT: peel thickness (mm), JY: juice yield (mL), Brix: soluble solids content (°Bx), and Acidity: citric acid (%); C) NF: number of fruits (NF). Source: Authors.

Figure 3 Relationship between the coefficient of variation (CV%) and plot size (Xc) by the Segmented quadratic model with plateau, in basic units for the variables under study in the uniformity test with purple passion fruit. A) FL: fruit length (mm), FD: fruit diameter (mm), and FW: average fruit weight (g); B) PT: peel thickness (mm), JY: juice yield (mL), Brix: soluble solids content (°Bx) and Acidity: citric acid (%); C) NF: number of fruits (NF). Source: Authors.

Table 1 Number of simulations (NS), number of plots (NP), plot size (PS) and plot shape (PSH) for the basic units of a field experiment with passion fruit in the field.

NS	NP	PS	PSH	NS	NP	PS	PSH
1	77	1	1x1	15	5	8	4x2
2	30	2	2x1	16	6	10	2x5
3	30	2	1x2	17	5	10	5x2
4	20	3	3x1	18	4	12	3x4
5	21	3	1x3	19	3	12	4x3
6	15	3	2+1	20	4	15	3x5
7	15	3	1+2	21	3	15	5x3
8	15	4	2x2	22	2	16	4x4
9	9	5	2x2+1	23	2	18	3x6
10	9	6	2x3	24	3	18	6x3
11	10	6	3x2	25	2	20	4x5
12	6	7	2x3+1	26	2	20	5x4
13	6	7	3x2+1	27	2	25	5x5
14	6	8	2x4	28	2	30	6x5

^*
1x1, reads: one row value by one column value, 2x1, reads: two row values added in each column; 2+1, reads: add two row values adding one more column value; 2x2+1, reads: sum of two row values, two column values adding one more unit. Source: Authors.

Table 2 Estimates of the parameter of the model, by the modified maximum curvature method, coefficient of variation corresponding to the maximum curvature point (CV%), the value of the abscissa at which the maximum curvature point (X_c ) occurs, coefficient of determination (R² ) for the variables under study in the uniformity test with purple passion fruit.

Variables
FL	7,04	0,63	3,15	2,59	0,98
FD	6,21	0,59	3,95	2,15	0,92
PT	24,79	0,68	8,16	5,17	0,95
JY	20,89	0,58	8,63	4,59	0,85
Brix	15,15	0,49	8,10	3,56	0,90
Acidity	16,31	0,41	9,85	3,47	0,92
NF	36,53	0,61	16,36	6,54	0,93
FW	12,45	0,58	6,22	3,30	0,93

^*
FL: fruit length (mm); FD: fruit diameter (mm); PT: peel thickness (mm); JY: juice yield (mL); NF: number of fruits (NF); FW: average fruit weight (g).Source: Authors.

Table 3 Estimates of the parameters of the segmented quadratic model method with plateau. coef-ficient of variation corresponding to the point of maximum curvature (P), the value of the abscissa at which the point of maximum curvature (Xc) occurs, coefficient of determination (R²) for the vari¬ables under study in the uniformity test with purple passion fruit.

Variables
FL	8,25	-2,02	0,07	0,72	7,43	0,94
FD	7,69	-1,81	0,13	1,46	6,89	0,93
PT	24,78	-3,90	0,17	3,04	11,16	0,93
JY	18,58	-1,94	0,06	2,33	16,77	0,85
Brix	15,33	-2,02	0,09	3,63	11,57	0,88
Acidity	16,08	-1,66	0,06	4,74	13,63	0,89
NF	49,93	-14,28	1,23	8,56	5,79	0,95
FW	10,90	-1,11	0,03	1,42	17,16	0,92

^*
FL: fruit length (mm); FD: fruit diameter (mm); PT: peel thickness (mm); JY: juice yield (mL); NF: number of fruits (NF); FW: average fruit weight (kg).Source: Authors

Table 4 Range of variation of the coefficient of determination (R²) for the modified maximum cur-vature method (MCM), and segmented quadrat¬ic model with plateau (QMP) method.

Methods
MCM	85 a 98%
QMP	85 a 95%

^*
Source:Authors.

1

C V = a X^{- b}

2

X_{C} = {[\frac{a^{2} b^{2} (2 b + 1)}{b + 2}]}^{\frac{1}{2 b + 2}}

3

{C V}_{X} = [\begin{matrix} β_{0} + β_{1} X + β_{2} X^{2} + ε_{i}, s e X \leq X_{C} \\ P + ε_{i}, s e X #62; X_{C} \end{matrix}]

4

X_{C} = - \frac{β_{1}}{2 β_{2}}

5

P = β_{0} - \frac{β_{1}^{2}}{4 β_{2}}

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Optimal plot size estimation in field experiment with purple passion fruit

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[1] Beatriz Garcia Lopes E-mail:biagarcialopes@gmail.com