Evaluation of mathematical equations for estimating leaf area in rapeseed

Dalmago, Genei Antonio; Bianchi, Cleusa Adriane Menegassi; Kovaleski, Samuel; Fochesatto, Elizandro

doi:10.5935/1806-6690.20190050

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Crop Science • Rev. Ciênc. Agron. 50 (3) • Jul-Sep 2019 • https://doi.org/10.5935/1806-6690.20190050 copy

Evaluation of mathematical equations for estimating leaf area in rapeseed¹ 1 Pesquisa financiada pela Embrapa, com apoio da FAPERGS, CNPQ e CAPES

Avaliação de equações matemáticas para estimar a área foliar de canola

Authorship SCIMAGO INSTITUTIONS RANKINGS

ABSTRACT

The aim of this study was to evaluate estimations of leaf area in rapeseed (Brassica napus L.) and the potential for application to different genotypes, environmental conditions and types of crop management. In experiments conducted during 2013, 2014, 2016 and 2017, three genotypes of rapeseed, five doses of nitrogen and three sowing dates were used. Leaves were randomly collected from different plants and positions on the plants. The leaf area (LA), and maximum width (W) and length (L) were determined for each leaf, and the product of L and W (LxW) was calculated. Fifty-six equations for estimating LA in rapeseed, where the independent variables were W, L or LxW, were compiled from the bibliography and evaluated in this work. The evaluation was made using the following statistics: significance of the linear (a) and angular (b) coefficients of the regression around the 1:1 line, concordance index (d), bias index (BIAS), mean absolute error (MAE), mean relative error (MRE), random mean squared error (MSE_r) and systematic mean squared error (MSE_s). Only 11 equations showed the a and b coefficients as not being different from 0 and 1 respectively. However, only 10 were suitable, as they displayed the lowest values for d, BIAS, MAE and RME, and the MSE_s was smaller than the MSE_r. The MAE ranged from 5.4 cm² to 16.2 cm², well within the error range for generating the equations. LA in rapeseed can be estimated by general biometric equations without considering the specificity of the genotype or the morphological type of the leaf.

Key words:
Brassica napus; Colza; Modelling; Leaf area index

Data set	Statistic
Data set	n	Mn	M	MD	Mx	SD	CV(%)	K	A	KS(p)
L - Length of the leaf blade (cm)
TD	546	3.6	18.2	17.5	46.5	7.7	42.2	-0.41^ns ns Kurtosis or asymmetry differ from zero by t-test at 5% probability of error	0.40^ns ns Kurtosis or asymmetry differ from zero by t-test at 5% probability of error	0.028
TD_MN	408	3.6	17.0	15.9	46.5	7.7	45.4	0.05^ns ns Kurtosis or asymmetry differ from zero by t-test at 5% probability of error	0.65^ns ns Kurtosis or asymmetry differ from zero by t-test at 5% probability of error	0.006
H61	336	3.6	20.3	20.2	37.0	7.1	35.1	-0.76^ns ns Kurtosis or asymmetry differ from zero by t-test at 5% probability of error	0.10^ns ns Kurtosis or asymmetry differ from zero by t-test at 5% probability of error	0.273
H61_MN	198	3.6	19.1	18.5	37.0	7.4	38.9	-0.67^ns ns Kurtosis or asymmetry differ from zero by t-test at 5% probability of error	0.27^ns ns Kurtosis or asymmetry differ from zero by t-test at 5% probability of error	0.329
Diam	105	4.0	14.9	14.0	29.0	5.7	37.8	-0.53^ns ns Kurtosis or asymmetry differ from zero by t-test at 5% probability of error	0.41^ns ns Kurtosis or asymmetry differ from zero by t-test at 5% probability of error	0.422
M6	105	4.3	15.0	12.5	46.5	8.9	59.6	1.36^ns ns Kurtosis or asymmetry differ from zero by t-test at 5% probability of error	1.28^ns ns Kurtosis or asymmetry differ from zero by t-test at 5% probability of error	0.040
W - Width of the leaf blade (cm)
TD	546	2.0	8.4	7.7	20.5	3.6	42.3	-0.11^ns ns Kurtosis or asymmetry differ from zero by t-test at 5% probability of error	0.58	<0.001
TD_MN	408	2.0	7.7	7.0	20.5	3.3	43.5	0.71^* * Kurtosis or asymmetry differ from zero by t-test at 5% probability of error. nsKurtosis or asymmetry differ from zero by t-test at 5% probability of error	0.82^* * Kurtosis or asymmetry differ from zero by t-test at 5% probability of error. nsKurtosis or asymmetry differ from zero by t-test at 5% probability of error	0.007
H61	336	2.0	9.5	9.2	20.5	3.6	37.8	-0.28^ns ns Kurtosis or asymmetry differ from zero by t-test at 5% probability of error	0.43^* * Kurtosis or asymmetry differ from zero by t-test at 5% probability of error. nsKurtosis or asymmetry differ from zero by t-test at 5% probability of error	0.024
H61_MN	198	2.0	8.6	8.2	20.5	3.5	41.0	0.54^* * Kurtosis or asymmetry differ from zero by t-test at 5% probability of error. nsKurtosis or asymmetry differ from zero by t-test at 5% probability of error	0.73^* * Kurtosis or asymmetry differ from zero by t-test at 5% probability of error. nsKurtosis or asymmetry differ from zero by t-test at 5% probability of error	0.010
Diam	105	2.1	6.9	6.8	14.5	2.5	35.5	0.18^ns ns Kurtosis or asymmetry differ from zero by t-test at 5% probability of error	0.57^* * Kurtosis or asymmetry differ from zero by t-test at 5% probability of error. nsKurtosis or asymmetry differ from zero by t-test at 5% probability of error	0.669
M6	105	2.1	6.6	6.0	15.3	3.2	48.3	-0.02^ns ns Kurtosis or asymmetry differ from zero by t-test at 5% probability of error	0.83^* * Kurtosis or asymmetry differ from zero by t-test at 5% probability of error. nsKurtosis or asymmetry differ from zero by t-test at 5% probability of error	0.118
LxW - Product of the length and width of the leaf blade (cm²)
TD	546	7.2	178.0	136.2	672.4	137.5	77.3	0.57^ns ns Kurtosis or asymmetry differ from zero by t-test at 5% probability of error	1.06^ns ns Kurtosis or asymmetry differ from zero by t-test at 5% probability of error	<0.001
TD_MN	408	7.2	153.0	114.2	672.4	129.2	84.4	0.73^ns ns Kurtosis or asymmetry differ from zero by t-test at 5% probability of error	1.08^ns ns Kurtosis or asymmetry differ from zero by t-test at 5% probability of error	<0.001
H61	336	7.2	214.0	185.0	672.4	140.1	65.5	-0.11^ns ns Kurtosis or asymmetry differ from zero by t-test at 5% probability of error ^ns	0.76^ns ns Kurtosis or asymmetry differ from zero by t-test at 5% probability of error	0.003
H61_MN	198	7.2	187.8	148.0	672.4	137.8	73.4	0.73^ns ns Kurtosis or asymmetry differ from zero by t-test at 5% probability of error	1.08^ns ns Kurtosis or asymmetry differ from zero by t-test at 5% probability of error	0.007
Diam	105	8.4	116.2	93.8	420.5	81.2	69.9	1.23^ns ns Kurtosis or asymmetry differ from zero by t-test at 5% probability of error	1.15^ns ns Kurtosis or asymmetry differ from zero by t-test at 5% probability of error	0.010
M6	105	11.4	124.3	71.4	660.3	135.1	108.7	3.58^ns ns Kurtosis or asymmetry differ from zero by t-test at 5% probability of error	1.91^ns ns Kurtosis or asymmetry differ from zero by t-test at 5% probability of error	<0.001
LA - Leaf area (cm²)
TD	546	3.7	90.6	66.8	461.1	75.0	82.8	2.05^ns ns Kurtosis or asymmetry differ from zero by t-test at 5% probability of error	1.35^ns ns Kurtosis or asymmetry differ from zero by t-test at 5% probability of error	<0.001
TD_MN	408	3.7	76.1	54.6	461.1	69.2	91.0	3.75^ns ns Kurtosis or asymmetry differ from zero by t-test at 5% probability of error	1.67^ns ns Kurtosis or asymmetry differ from zero by t-test at 5% probability of error	<0.001
H61	336	4.2	214.0	185.0	461.1	140.1	65.5	-0.11^ns ns Kurtosis or asymmetry differ from zero by t-test at 5% probability of error	0.76^ns ns Kurtosis or asymmetry differ from zero by t-test at 5% probability of error	0.001
H61_MN	198	4.2	95.9	75.5	461.1	79.8	83.2	3.75^ns ns Kurtosis or asymmetry differ from zero by t-test at 5% probability of error	1.67^ns ns Kurtosis or asymmetry differ from zero by t-test at 5% probability of error	0.003
Diam	105	3.7	58.1	45.3	214.6	42.4	73.0	1.49^ns ns Kurtosis or asymmetry differ from zero by t-test at 5% probability of error	1.21^ns ns Kurtosis or asymmetry differ from zero by t-test at 5% probability of error	0.066
M6	105	4.9	56.8	35.1	260.5	58.7	103.4	2.64^ns ns Kurtosis or asymmetry differ from zero by t-test at 5% probability of error	1.73^ns ns Kurtosis or asymmetry differ from zero by t-test at 5% probability of error	<0.001

N^o.	Equation	r²	Bibliographic reference
01	AF = -1.1711 + 0.7324W + 1.0704W²	0.93	*Cargnelutti Filho et al. (2015)*CARGNELUTTI FILHO, A. et al. Estimação da área foliar de canola por dimensões foliares. Bragantia, v. 74, n. 2, p. 139-148, 2015.
02	AF = 1.3000W^1.9336	0.95	*Cargnelutti Filho et al. (2015)*CARGNELUTTI FILHO, A. et al. Estimação da área foliar de canola por dimensões foliares. Bragantia, v. 74, n. 2, p. 139-148, 2015.
03	AF = 0.6189LxW^0.9401	0.96	*Cargnelutti Filho et al. (2015)*CARGNELUTTI FILHO, A. et al. Estimação da área foliar de canola por dimensões foliares. Bragantia, v. 74, n. 2, p. 139-148, 2015.
04	AF = 1.6467 + 0.4525LxW	0.94	*Cargnelutti Filho et al. (2015)*CARGNELUTTI FILHO, A. et al. Estimação da área foliar de canola por dimensões foliares. Bragantia, v. 74, n. 2, p. 139-148, 2015.
05	AF = -2.0169 + 1.4464L + 0.1517L²	0.93	*Cargnelutti Filho et al. (2015)*CARGNELUTTI FILHO, A. et al. Estimação da área foliar de canola por dimensões foliares. Bragantia, v. 74, n. 2, p. 139-148, 2015.
06	AF = 1.0579W^2.0383	0.97	*Cargnelutti Filho et al. (2015)*CARGNELUTTI FILHO, A. et al. Estimação da área foliar de canola por dimensões foliares. Bragantia, v. 74, n. 2, p. 139-148, 2015.
07	AF = -48.6371 + 7.3031L	0.89	*Cargnelutti Filho et al. (2015)*CARGNELUTTI FILHO, A. et al. Estimação da área foliar de canola por dimensões foliares. Bragantia, v. 74, n. 2, p. 139-148, 2015.
08	AF = -75.6346 + 20.1473W	0.92	*Cargnelutti Filho et al. (2015)*CARGNELUTTI FILHO, A. et al. Estimação da área foliar de canola por dimensões foliares. Bragantia, v. 74, n. 2, p. 139-148, 2015.
09	AF = 1.4154W^1.9096	0.96	*Cargnelutti Filho et al. (2015)*CARGNELUTTI FILHO, A. et al. Estimação da área foliar de canola por dimensões foliares. Bragantia, v. 74, n. 2, p. 139-148, 2015.
10	AF = 0.7425CxW^0.9167	0.97	*Cargnelutti Filho et al. (2015)*CARGNELUTTI FILHO, A. et al. Estimação da área foliar de canola por dimensões foliares. Bragantia, v. 74, n. 2, p. 139-148, 2015.
11	AF = 9.34484W	0.76	*Tartaglia et al. (2016)*TARTAGLIA, F. de L. et al. Modelos não destrutivos para determinação da área foliar em canola. Revista Brasileira de Engenharia Agrícola e Ambiental, v. 20, n. 6, p. 551-556, 2016.

Equation Number	Data set
Equation Number	TD	TD_MN	H61	H61_MN	Diam	M6
Linear coefficient - a
01	-0.19^ns ns Linear coefficient does not differ from 0 by t-test at 5% probability of error	-1.92^ns ns Linear coefficient does not differ from 0 by t-test at 5% probability of error	2.03^ns ns Linear coefficient does not differ from 0 by t-test at 5% probability of error	-0.16^ns ns Linear coefficient does not differ from 0 by t-test at 5% probability of error	-1.55^ns ns Linear coefficient does not differ from 0 by t-test at 5% probability of error	-4.45^* * Angular coefficient does not differ from 1 by t-test at 5% probability of error
02	-1.37^ns ns Linear coefficient does not differ from 0 by t-test at 5% probability of error	-3.03^* * Angular coefficient does not differ from 1 by t-test at 5% probability of error	0.59^ns ns Linear coefficient does not differ from 0 by t-test at 5% probability of error	-1.57^ns ns Linear coefficient does not differ from 0 by t-test at 5% probability of error	-2.25^ns ns Linear coefficient does not differ from 0 by t-test at 5% probability of error	-5.17^* * Angular coefficient does not differ from 1 by t-test at 5% probability of error
03	-8.41^* * Angular coefficient does not differ from 1 by t-test at 5% probability of error	-7.79^* * Angular coefficient does not differ from 1 by t-test at 5% probability of error	-12.45^* * Angular coefficient does not differ from 1 by t-test at 5% probability of error	-14.48^* * Angular coefficient does not differ from 1 by t-test at 5% probability of error	-5.59^* * Angular coefficient does not differ from 1 by t-test at 5% probability of error	0.07^ns ns Linear coefficient does not differ from 0 by t-test at 5% probability of error
04	-5.16^* * Angular coefficient does not differ from 1 by t-test at 5% probability of error	-5.01^* * Angular coefficient does not differ from 1 by t-test at 5% probability of error	-8.14^* * Angular coefficient does not differ from 1 by t-test at 5% probability of error	-10.73^* * Angular coefficient does not differ from 1 by t-test at 5% probability of error	-3.96^* * Angular coefficient does not differ from 1 by t-test at 5% probability of error	1.96^ns ns Linear coefficient does not differ from 0 by t-test at 5% probability of error
05	-3.56^ns ns Linear coefficient does not differ from 0 by t-test at 5% probability of error	-2.92^ns ns Linear coefficient does not differ from 0 by t-test at 5% probability of error	-8.22^ns ns Linear coefficient does not differ from 0 by t-test at 5% probability of error	-11.54^* * Angular coefficient does not differ from 1 by t-test at 5% probability of error	-7.31^* * Angular coefficient does not differ from 1 by t-test at 5% probability of error	4.^ns ns Linear coefficient does not differ from 0 by t-test at 5% probability of error
06	3.37^* * Angular coefficient does not differ from 1 by t-test at 5% probability of error	1.46^ns ns Linear coefficient does not differ from 0 by t-test at 5% probability of error	6.19^* * Angular coefficient does not differ from 1 by t-test at 5% probability of error	3.87^* * Angular coefficient does not differ from 1 by t-test at 5% probability of error	1.01^ns ns Linear coefficient does not differ from 0 by t-test at 5% probability of error	-2.07^ns ns Linear coefficient does not differ from 0 by t-test at 5% probability of error
07	-8.01^* * Angular coefficient does not differ from 1 by t-test at 5% probability of error	-5.03^ns ns Linear coefficient does not differ from 0 by t-test at 5% probability of error	-18.48^* * Angular coefficient does not differ from 1 by t-test at 5% probability of error	-16.92^* * Angular coefficient does not differ from 1 by t-test at 5% probability of error	-0.48^ns ns Linear coefficient does not differ from 0 by t-test at 5% probability of error	4.28^ns ns Linear coefficient does not differ from 0 by t-test at 5% probability of error
08	-3.98^* * Angular coefficient does not differ from 1 by t-test at 5% probability of error	-1.45^ns ns Linear coefficient does not differ from 0 by t-test at 5% probability of error	-12.06^* * Angular coefficient does not differ from 1 by t-test at 5% probability of error	-9.58^* * Angular coefficient does not differ from 1 by t-test at 5% probability of error	5.41^* * Angular coefficient does not differ from 1 by t-test at 5% probability of error	7.40^* * Angular coefficient does not differ from 1 by t-test at 5% probability of error
09	-2.52^* * Angular coefficient does not differ from 1 by t-test at 5% probability of error	-4.12^* * Angular coefficient does not differ from 1 by t-test at 5% probability of error	-0.77^ns ns Linear coefficient does not differ from 0 by t-test at 5% probability of error	-2.89^ns ns Linear coefficient does not differ from 0 by t-test at 5% probability of error	-3.05^ns ns Linear coefficient does not differ from 0 by t-test at 5% probability of error	-5.93^* * Angular coefficient does not differ from 1 by t-test at 5% probability of error
10	-10.64^* * Angular coefficient does not differ from 1 by t-test at 5% probability of error	-9.81^* * Angular coefficient does not differ from 1 by t-test at 5% probability of error	-15.17^* * Angular coefficient does not differ from 1 by t-test at 5% probability of error	-16.97^* * Angular coefficient does not differ from 1 by t-test at 5% probability of error	-7.12^* * Angular coefficient does not differ from 1 by t-test at 5% probability of error	-1.44^ns ns Linear coefficient does not differ from 0 by t-test at 5% probability of error
11	7.04^ns ns Linear coefficient does not differ from 0 by t-test at 5% probability of error	-2.71^ns ns Linear coefficient does not differ from 0 by t-test at 5% probability of error	31.62^* * Angular coefficient does not differ from 1 by t-test at 5% probability of error	7.02^ns ns Linear coefficient does not differ from 0 by t-test at 5% probability of error	20.53^ns ns Linear coefficient does not differ from 0 by t-test at 5% probability of error	-7.60^ns ns Linear coefficient does not differ from 0 by t-test at 5% probability of error
Angular coefficient - b
01	0.96^ns ns Linear coefficient does not differ from 0 by t-test at 5% probability of error	0.99^* * Angular coefficient does not differ from 1 by t-test at 5% probability of error	0.95^ns ns Linear coefficient does not differ from 0 by t-test at 5% probability of error	0.98^* * Angular coefficient does not differ from 1 by t-test at 5% probability of error	0.97^* * Angular coefficient does not differ from 1 by t-test at 5% probability of error	1.02^* * Angular coefficient does not differ from 1 by t-test at 5% probability of error
02	0.99^* * Angular coefficient does not differ from 1 by t-test at 5% probability of error	1.02^* * Angular coefficient does not differ from 1 by t-test at 5% probability of error	0.98^* * Angular coefficient does not differ from 1 by t-test at 5% probability of error	1.01^* * Angular coefficient does not differ from 1 by t-test at 5% probability of error	0.99^* * Angular coefficient does not differ from 1 by t-test at 5% probability of error	1.04^ns ns Linear coefficient does not differ from 0 by t-test at 5% probability of error
03	1.25^ns ns Linear coefficient does not differ from 0 by t-test at 5% probability of error	1.22^ns ns Linear coefficient does not differ from 0 by t-test at 5% probability of error	1.30^ns ns Linear coefficient does not differ from 0 by t-test at 5% probability of error	1.32^ns ns Linear coefficient does not differ from 0 by t-test at 5% probability of error	1.19^ns ns Linear coefficient does not differ from 0 by t-test at 5% probability of error	1.01^* * Angular coefficient does not differ from 1 by t-test at 5% probability of error
04	1.24^ns ns Linear coefficient does not differ from 0 by t-test at 5% probability of error	1.22^ns ns Linear coefficient does not differ from 0 by t-test at 5% probability of error	1.29^ns ns Linear coefficient does not differ from 0 by t-test at 5% probability of error	1.31^ns ns Linear coefficient does not differ from 0 by t-test at 5% probability of error	1.22^ns ns Linear coefficient does not differ from 0 by t-test at 5% probability of error	1.01^* * Angular coefficient does not differ from 1 by t-test at 5% probability of error
05	1.12^ns ns Linear coefficient does not differ from 0 by t-test at 5% probability of error	1.05^* * Angular coefficient does not differ from 1 by t-test at 5% probability of error	1.22^ns ns Linear coefficient does not differ from 0 by t-test at 5% probability of error	1.21^ns ns Linear coefficient does not differ from 0 by t-test at 5% probability of error	1.12^ns ns Linear coefficient does not differ from 0 by t-test at 5% probability of error	0.80^ns ns Linear coefficient does not differ from 0 by t-test at 5% probability of error
06	0.90^ns ns Linear coefficient does not differ from 0 by t-test at 5% probability of error	0.93^ns ns Linear coefficient does not differ from 0 by t-test at 5% probability of error	0.89^ns ns Linear coefficient does not differ from 0 by t-test at 5% probability of error	0.91^ns ns Linear coefficient does not differ from 0 by t-test at 5% probability of error	0.92^ns ns Linear coefficient does not differ from 0 by t-test at 5% probability of error	0.97^* * Angular coefficient does not differ from 1 by t-test at 5% probability of error
07	1.17^ns ns Linear coefficient does not differ from 0 by t-test at 5% probability of error	1.08^ns ns Linear coefficient does not differ from 0 by t-test at 5% probability of error	1.30^ns ns Linear coefficient does not differ from 0 by t-test at 5% probability of error	1.24^ns ns Linear coefficient does not differ from 0 by t-test at 5% probability of error	0.97^* * Angular coefficient does not differ from 1 by t-test at 5% probability of error	0.87^ns ns Linear coefficient does not differ from 0 by t-test at 5% probability of error
08	1.01^* * Angular coefficient does not differ from 1 by t-test at 5% probability of error	0.99^* * Angular coefficient does not differ from 1 by t-test at 5% probability of error	1.08^ns ns Linear coefficient does not differ from 0 by t-test at 5% probability of error	1.07^ns ns Linear coefficient does not differ from 0 by t-test at 5% probability of error	0.83^ns ns Linear coefficient does not differ from 0 by t-test at 5% probability of error	0.88^ns ns Linear coefficient does not differ from 0 by t-test at 5% probability of error
09	0.98^ns ns Linear coefficient does not differ from 0 by t-test at 5% probability of error	1.00^* * Angular coefficient does not differ from 1 by t-test at 5% probability of error	0.97^ns ns Linear coefficient does not differ from 0 by t-test at 5% probability of error	0.99^* * Angular coefficient does not differ from 1 by t-test at 5% probability of error	0.97^* * Angular coefficient does not differ from 1 by t-test at 5% probability of error	1.02^* * Angular coefficient does not differ from 1 by t-test at 5% probability of error
10	1.21^ns ns Linear coefficient does not differ from 0 by t-test at 5% probability of error	1.18^ns ns Linear coefficient does not differ from 0 by t-test at 5% probability of error	1.27^ns ns Linear coefficient does not differ from 0 by t-test at 5% probability of error	1.28^ns ns Linear coefficient does not differ from 0 by t-test at 5% probability of error	1.14^ns ns Linear coefficient does not differ from 0 by t-test at 5% probability of error	0.98^* * Angular coefficient does not differ from 1 by t-test at 5% probability of error
11	1.07^* * Angular coefficient does not differ from 1 by t-test at 5% probability of error	1.08^* * Angular coefficient does not differ from 1 by t-test at 5% probability of error	0.90^* * Angular coefficient does not differ from 1 by t-test at 5% probability of error	1.07^* * Angular coefficient does not differ from 1 by t-test at 5% probability of error	0.58^ns ns Linear coefficient does not differ from 0 by t-test at 5% probability of error	1.05^* * Angular coefficient does not differ from 1 by t-test at 5% probability of error

Statistic	Equation number
Statistic	1	2	3	4	5	6	7	8	9	10	11
Total data (TD)
BIAS index	0.04	0.02	-0.12	-0.15	-0.07	0.06	-0.07	0.03	0.05	-0.07	-0.13
d	0.99	0.99	0.96	0.96	0.92	0.99	0.91	0.98	0.99	0.97	0.58
MAE	10.1	9.7	14.0	15.0	20.2	11.1	22.1	15.0	10.6	12.6	46.7
MRE	15.4	15.2	13.2	13.9	23.7	14.9	35.0	43.2	17.5	14.3	86.0
MSE_r	208	194	232	231	804	245	744	355	199	250	854
MSE_s	13	9	482	522	620	58	700	44	23	337	3666
TD minus the extreme nitrogen treatment (TD_MN)
BIAS index	0.04	0.02	-0.10	-0.12	-0.01	0.06	-0.01	0.03	0.05	-0.04	-0.20
d	0.99	0.99	0.96	0.96	0.93	0.99	0.92	0.98	0.99	0.97	0.50
MAE	9.2	9.0	10.7	11.5	16.2	9.6	18.3	15.1	9.8	10.1	46.8
MRE	17.3	17.2	12.7	13.1	24.6	16.2	38.6	52.9	19.8	14.9	101.4
MSE_r	176	164	211	207	761	205	728	384	169	229	1170
MSE_s	11	16	323	351	342	25	394	32	24	225	3811
Data for the Hyola 61 genotype (H61)
BIAS index	0.03	0.01	-0.15	-0.17	-0.12	0.06	-0.10	0.03	0.04	-0.10	-0.21
d	0.99	0.99	0.94	0.94	0.88	0.99	0.87	0.98	0.99	0.95	0.52
MAE	11.8	11.3	18.8	20.0	26.2	13.4	28.4	15.5	12.1	16.7	55.2
MRE	13.1	12.7	14.1	15.0	23.5	13.4	30.0	28.6	14.4	14.2	66.3
MSE_r	272	253	274	275	843	323	759	337	258	294	964
MSE_s	14	5	822	869	1236	93	1412	121	21	605	5066
H61 minus the extreme nitrogen treatment (H61_MN)
BIAS index	0.02	0.01	-0.13	-0.15	-0.07	0.05	-0.05	0.02	0.04	-0.08	-0.39
d	0.99	0.99	0.95	0.95	0.89	0.99	0.88	0.98	0.99	0.96	0.48
MAE	11.1	10.9	15.5	16.3	22.3	12.0	25.0	16.0	11.6	14.3	61.3
MRE	15.3	15.1	13.7	14.0	25.1	15.0	33.9	38.4	17.1	15.2	84.3
MSE_r	255	237	267	260	853	302	837	401	242	290	1764
MSE_s	8	15	725	756	1018	40	1177	133	19	554	6262
Diamond genotype (Diam)
BIAS index	0.06	0.05	-0.08	-0.12	0.00	0.06	0.04	0.10	0.09	-0.02	0.10
d	0.99	0.99	0.98	0.98	0.97	0.98	0.97	0.97	0.98	0.99	0.52
MAE	6.9	6.6	6.9	8.1	8.5	7.0	10.6	12.5	7.6	5.9	32.2
MRE	16.8	16.7	12.4	13.5	19.8	15.6	32.5	46.5	19.8	13.6	110.2
MSE_r	92	87	27	25	110	104	188	177	90	30	537
MSE_s	13	11	79	117	61	15	18	60	26	38	1255
ALHTM6 genotype (M6)
BIAS index	0.06	0.05	-0.01	-0.04	0.15	0.07	0.07	-0.01	0.08	0.05	0.06
d	0.98	0.98	0.99	0.98	0.95	0.98	0.96	0.95	0.98	0.99	0.52
MAE	7.9	7.9	5.4	5.7	12.5	7.5	13.5	15.9	8.7	6.2	35.2
MRE	21.4	21.5	10.9	10.9	28.3	19.0	53.6	86.6	25.1	15.5	122.2
MSE_r	107	103	92	101	444	115	326	368	109	96	675
MSE_s	20	26	6	10	141	15	28	4	31	8	1828

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E-mail: ccarev@ufc.br

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Brasil

Brasil

Evaluation of mathematical equations for estimating leaf area in rapeseed1 1 Pesquisa financiada pela Embrapa, com apoio da FAPERGS, CNPQ e CAPES

Avaliação de equações matemáticas para estimar a área foliar de canola

ABSTRACT

Evaluation of mathematical equations for estimating leaf area in rapeseed¹ 1 Pesquisa financiada pela Embrapa, com apoio da FAPERGS, CNPQ e CAPES