Leaf area estimation of squash ‘Brasileirinha’ by leaf dimensions

Toebe, Marcos; Souza, Rafael Rodrigues de; Mello, Anderson Chuquel; Melo, Patrícia Jesus de; Segatto, Alexandre; Castanha, Ana Carla

doi:10.1590/0103-8478cr20180932

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CROP PRODUCTION • Cienc. Rural 49 (4) • 2019 • https://doi.org/10.1590/0103-8478cr20180932 copy

Leaf area estimation of squash ‘Brasileirinha’ by leaf dimensions

Estimação da área foliar de abobrinha ‘Brasileirinha’ por dimensões foliares

Authorship SCIMAGO INSTITUTIONS RANKINGS

ABSTRACT:

The objectives of this work were estimate the leaf area of squash ‘Brasileirinha’ by linear dimensions of the leaves and check models available in the literature. An experiment was conducted in the 2015/16 sowing season. Were collected 500 leaves and in each one, were measured the length (L), width (W) and length×width product (LW) and determined the real leaf area (LA). Then, 400 leaves were separated to generate models of the leaf area (LA) as a function of linear dimension (L, W or LW) of squash. The remaining 100 leaves were used for the validation of models. A second experiment was conducted in the 2016/17 sowing season. Were collected 250 leaves, used only for the validation of the models of the first experiment. There is collinearity between L and W and, therefore, models using the LW product are not recommended. The model LA=0.5482W² + 0.0680W (R²=0.9867) is adequate for leaf area estimation of squash ‘Brasileirinha’.

Key words:
Cucurbita moschata; image processing; non-destructive method; mathematical models

Authorship

Marcos Toebe ^*E-mail: m.toebe@gmail.com. *Corresponding author.

Departamento de Ciências Agronômicas e Ambientais, Universidade Federal de Santa Maria (UFSM), Campus Frederico Westphalen, 98400-000, Frederico Westphalen, RS, Brasil. Universidade Federal de Santa Maria (UFSM)BrazilFrederico Westphalen, RS, BrazilDepartamento de Ciências Agronômicas e Ambientais, Universidade Federal de Santa Maria (UFSM), Campus Frederico Westphalen, 98400-000, Frederico Westphalen, RS, Brasil.

https://orcid.org/0000-0003-2033-1467

Rafael Rodrigues de Souza

Programa de Pós-graduação em Agronomia - Agricultura e Ambiente, Universidade Federal de Santa Maria (UFSM), Campus Frederico Westphalen, Frederico Westphalen, RS, Brasil.Universidade Federal de Santa Maria (UFSM)BrazilFrederico Westphalen, RS, BrazilPrograma de Pós-graduação em Agronomia - Agricultura e Ambiente, Universidade Federal de Santa Maria (UFSM), Campus Frederico Westphalen, Frederico Westphalen, RS, Brasil.

https://orcid.org/0000-0002-7068-4079

Anderson Chuquel Mello

Curso de Agronomia, Universidade Federal do Pampa (Unipampa), Itaqui, RS, Brasil. Universidade Federal do Pampa (Unipampa),BrazilItaqui, RS, BrazilCurso de Agronomia, Universidade Federal do Pampa (Unipampa), Itaqui, RS, Brasil.

https://orcid.org/0000-0003-4509-957X

Patrícia Jesus de Melo

Programa de Pós-graduação em Agronomia, Universidade Federal de Santa Maria (UFSM), Santa Maria, RS, Brasil.Universidade Federal de Santa Maria (UFSM)BrazilSanta Maria, RS, BrazilPrograma de Pós-graduação em Agronomia, Universidade Federal de Santa Maria (UFSM), Santa Maria, RS, Brasil.

https://orcid.org/0000-0001-6080-4930

Alexandre Segatto

https://orcid.org/0000-0003-3586-0409

Ana Carla Castanha

UPL do Brasil, Tangará da Serra, MT, Brasil.UPL do BrasilBrasilTangará da Serra, MT, BrasilUPL do Brasil, Tangará da Serra, MT, Brasil.

https://orcid.org/0000-0001-7889-7274

E-mail: m.toebe@gmail.com. ^*Corresponding author.

DECLARATION OF CONFLICT OF INTEREST

The authors declare no conflict of interest. The founding sponsors had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, and in the decision to publish the results

AUTHORS’ CONTRIBUTIONS

All authors conceived and designed experiments. RRS, ACM, PJM, AS and ACC performed the experiments and data collection. MT supervised and coordinated the experiments, performed the image processing, statistical analyses and prepared the draft of the manuscript. All authors critically revised the manuscript and approved of the final version.

SCIMAGO INSTITUTIONS RANKINGS

UPL do Brasil, Tangará da Serra, MT, Brasil.UPL do BrasilBrasilTangará da Serra, MT, BrasilUPL do Brasil, Tangará da Serra, MT, Brasil.

Figures | Tables

Figures (4)
Tables (2)

Thumbnail

Figure 1
Linear measurements (length and width) of a squash ‘Brasileirinha’ leaf.

Thumbnail

Figure 2
Frequency histogram (diagonally) and scatter plots of length, width, length × width and real leaf area of: a) 400 leaves used for generation; b) 100, and; c) 250 leaves used for validation of the models for leaf area estimation of squash ‘Brasileirinha’.

Thumbnail

Figure 3
Models - linear, quadratic and power - of the real leaf area (LA) estimation of squash ‘Brasileirinha’ as a function of linear dimension: a) Length, in cm; b) Width, in cm; c) Length × Width product, in cm², generated based on n=400 leaves, and respective coefficient of determination (R²) for each model.

Thumbnail

Figure 4
Relationship of real leaf area (LA) and the leaf area estimated (LAE) by the model LA=0.5482W²+0.0680W (R²=0.9867) and the residue for each leaf area (LA_i- LAE_i) in: a) 100 leaves (2015/2016 growing season), and; b) 250 leaves (2016/2017 growing season) of squash ‘Brasileirinha’.

Thumbnail

Table 1
Statistics for the variables: length, width, length×width product and real leaf area of leaves used for generation and for validation of the estimation models for leaf area estimation of squash ‘Brasileirinha’.

Thumbnail

Table 2
Validation of models based on indicators: linear coefficient (a), slope coefficient (b), Pearson correlation coefficient (r) and determination coefficient (R²), mean absolute error (MAE), root mean square error (RMSE) and d Willmott index (d), calculated based on observed leaf area and estimated leaf area of leaves from squash ‘Brasileirinha’.

Figure 1 Linear measurements (length and width) of a squash ‘Brasileirinha’ leaf.

Figure 2 Frequency histogram (diagonally) and scatter plots of length, width, length × width and real leaf area of: a) 400 leaves used for generation; b) 100, and; c) 250 leaves used for validation of the models for leaf area estimation of squash ‘Brasileirinha’.

Figure 3 Models - linear, quadratic and power - of the real leaf area (LA) estimation of squash ‘Brasileirinha’ as a function of linear dimension: a) Length, in cm; b) Width, in cm; c) Length × Width product, in cm², generated based on n=400 leaves, and respective coefficient of determination (R²) for each model.

Figure 4 Relationship of real leaf area (LA) and the leaf area estimated (LAE) by the model LA=0.5482W²+0.0680W (R²=0.9867) and the residue for each leaf area (LA_i- LAE_i) in: a) 100 leaves (2015/2016 growing season), and; b) 250 leaves (2016/2017 growing season) of squash ‘Brasileirinha’.

Table 1 Statistics for the variables: length, width, length×width product and real leaf area of leaves used for generation and for validation of the estimation models for leaf area estimation of squash ‘Brasileirinha’.

Statistics	Length (L, cm)	Width (W, cm)	Length×Width (LW, cm²)	Real Leaf Area (LA, cm²)
--------------------------------Data used in the generation of models (n=400 leaves) - 2015/2016 growing season----------------------------------
Minimum	2.80	3.40	9.52	7.57
Maximum	16.90	22.80	385.32	296.60
Mean	9.05	12.90	125.05	98.97
Median	9.20	13.30	122.76	96.79
Variance	5.87	12.55	3767.01	2402.75
Standard Deviation	2.42	3.54	61.38	49.02
Coefficient of variation	26.79	27.47	49.08	49.53
Standard Error	0.12	0.18	3.07	2.45
Asymmetry⁽¹⁾	-0.23^ns	-0.35*	0.41*	0.36*
Kurtosis⁽²⁾	-0.20^ns	-0.31^ns	0.28^ns	0.11^ns
P-value of K-S⁽³⁾	>0.20	>0.10	>0.20	>0.20
---------------------------------Data used in the validation of models (n=100 leaves)- 2015/2016 growing season----------------------------------
Minimum	2.40	2.70	6.48	5.79
Maximum	14.80	21.00	310.80	240.99
Mean	9.66	13.78	141.64	111.95
Median	10.05	14.50	144.63	114.05
Variance	6.22	12.52	3950.14	2528.38
Standard Deviation	2.49	3.54	62.85	50.28
Coefficient of variation	25.82	25.68	44.37	44.92
Standard Error	0.25	0.35	6.29	5.03
Asymmetry⁽¹⁾	-0.70^*	-0.78^*	0.07^ns	0.02^ns
Kurtosis⁽²⁾	0.54^ns	0.73^ns	0.03^ns	-0.19^ns
P-value of K-S⁽³⁾	>0.10	>0.15	>0.20	>0.20
--------------------------------Data used in the validation of models (n=250 leaves) - 2016/2017 growing season-----------------------------------
Minimum	6.20	8.20	50.84	38.97
Maximum	14.10	20.10	283.41	226.76
Mean	10.30	14.49	152.98	120.95
Median	10.45	14.70	152.95	121.46
Variance	2.73	5.55	2169.91	1438.59
Standard Deviation	1.65	2.36	46.58	37.93
Coefficient of variation	15.82	16.02	30.46	31.23
Standard Error	0.10	0.15	2.95	2.40
Asymmetry⁽¹⁾	-0.34^*	-0.34^*	-0.08^ns	-0.05^ns
Kurtosis⁽²⁾	-0.71^*	-0.74^*	-0.83^*	-0.88^*
P-value of K-S⁽³⁾	>0.15	>0.05	>0.20	>0.15

^(1)*Asymmetry differs from zero by the t-test at 5% probability level. ^nsnon-significant. ^(2)*Kurtosis differs from zero by t-test at 5% probability level. ^nsnon-significant. ⁽³⁾P-value of the normality test of Kolmogorov-Smirnov.

Table 2 Validation of models based on indicators: linear coefficient (a), slope coefficient (b), Pearson correlation coefficient (r) and determination coefficient (R²), mean absolute error (MAE), root mean square error (RMSE) and d Willmott index (d), calculated based on observed leaf area and estimated leaf area of leaves from squash ‘Brasileirinha’.

Model Type	Independent variable	a⁽¹⁾	b⁽²⁾	r⁽³⁾	R²	MAE	RMSE	d
--------------------------------------------Validation of models (n = 100 leaves) - 2015/2016 growing season-----------------------------------------
1) Linear	Length	49.850^*	0.549^*	0.960^*	0.922	19.367	24.059	0.906
2) Quadratic	Length	5.029^ns	0.956^ns	0.972^*	0.946	9.431	11.694	0.986
3) Power	Length	0.995^ns	0.994^ns	0.972^*	0.945	9.737	12.049	0.986
4) Linear	Width	49.545^*	0.552^*	0.970^*	0.943	18.744	23.544	0.910
5) Quadratic	Width	2.958^ns	0.972^ns	0.989^*	0.978	5.303	7.425	0.994
6) Power	Width	3.806^*	0.961^*	0.989^*	0.978	5.274	7.475	0.994
7) Linear	Length×Width	2.593^ns	0.978^ns	0.988^*	0.978	5.721	7.504	0.994
8) Quadratic	Length×Width	3.358^ns	0.972^ns	0.988^*	0.978	5.715	7.482	0.994
9) Power	Length×Width	1.439^ns	0.988^ns	0.988^*	0.978	5.709	7.550	0.994
LA = 6.7940 + 0.8259LW (Grecco et al. 2011GRECCO, E.D. et al. Estimation of leaf area index and determination of light extinction coefficient of pumpkin Cucurbita moschata var. japanese. Idesia, v.29, p.37-41, 2011. Available from: <Available from: http://dx.doi.org/10.4067/S0718-34292011000100006 >. Accessed: Nov. 12, 2018. doi: 10.4067/S0718-34292011000100006. http://dx.doi.org/10.4067/S0718-34292011... )	Length×Width	9.499^*	1.020^ns	0.988^*	0.978	12.187	14.222	0.981
LA = 4.77 + 0.61W² (Rouphael et al. 2006ROUPHAEL, Y. et al. Leaf area estimation from linear measurements in zucchini plants of different ages. Journal of Horticultural Science & Biotechnology, v.81, p.238-241, 2006. Available from: <Available from: http://dx.doi.org/10.1080/14620316.2006.11512056 >. Accessed: Nov. 12, 2018. doi: 10.1080/14620316.2006.11512056. http://dx.doi.org/10.1080/14620316.2006.... )	Width	7.598^*	1.077^*	0.989^*	0.978	16.521	18.600	0.969
-------------------------------------------Validation of models (n = 250 leaves) - 2016/2017 growing season------------------------------------------
1) Linear	Length	59.963^*	0.485^*	0.966^*	0.935	17.091	20.232	0.872
2) Quadratic	Length	9.264^*	0.936^*	0.969^*	0.939	7.470	9.498	0.984
3) Power	Length	4.531^*	0.978^ns	0.968^*	0.939	7.474	9.709	0.984
4) Linear	Width	57.289^*	0.494^*	0.984^*	0.970	16.706	19.848	0.878
5) Quadratic	Width	3.452^*	0.955^*	0.988^*	0.977	4.704	6.092	0.993
6) Power	Width	4.523^*	0.943^*	0.988^*	0.977	4.868	6.314	0.993
7) Linear	Length×Width	4.797^*	0.961^*	0.989^*	0.978	4.358	5.646	0.994
8) Quadratic	Length×Width	5.741^*	0.954^*	0.989^*	0.978	4.393	5.687	0.994
9) Power	Length×Width	3.378^*	0.973^*	0.989^*	0.978	4.336	5.613	0.994
LA = 6.7940 + 0.8259LW (Grecco et al. 2011GRECCO, E.D. et al. Estimation of leaf area index and determination of light extinction coefficient of pumpkin Cucurbita moschata var. japanese. Idesia, v.29, p.37-41, 2011. Available from: <Available from: http://dx.doi.org/10.4067/S0718-34292011000100006 >. Accessed: Nov. 12, 2018. doi: 10.4067/S0718-34292011000100006. http://dx.doi.org/10.4067/S0718-34292011... )	Length×Width	11.797^*	1.003^ns	0.989^*	0.978	12.309	13.468	0.970
LA = 4.77 + 0.61W² (Rouphael et al. 2006ROUPHAEL, Y. et al. Leaf area estimation from linear measurements in zucchini plants of different ages. Journal of Horticultural Science & Biotechnology, v.81, p.238-241, 2006. Available from: <Available from: http://dx.doi.org/10.1080/14620316.2006.11512056 >. Accessed: Nov. 12, 2018. doi: 10.1080/14620316.2006.11512056. http://dx.doi.org/10.1080/14620316.2006.... )	Width	8.075^*	1.058^*	0.988^*	0.977	15.250	16.569	0.957

^(1)*Linear coefficient differs from zero, according to the t test at P<0.05. ^nsnon-significant. ^(2)*Slope coefficient differs from one, according to the t test at p<0.05. ^nsnon-significant. ^(3)*Pearson correlation coefficient differs from zero, according to the t test at p<0.05. ^ns non-significant.

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[1] E-mail: m.toebe@gmail.com. ^*Corresponding author.