Allometric models for estimating <i>Moringa oleifera</i> leaflets area

Macário, Ana Paula Silva; Ferraz, Rener Luciano de Souza; Costa, Patrícia da Silva; Brito Neto, José Félix de; Melo, Alberto Soares de; Dantas Neto, José

doi:10.1590/1413-7054202044005220

ABSTRACT

Moringa oleifera is a species of great economic, social and environmental importance, being employed for multiple purposes. Thus, the objective of this study was to fit regression models for estimating leaflets area as non-destructive method from linear measurements of leaflets of M. oleifera seedlings. The study was carried out at the Center for Agrarian and Environmental Sciences of the Paraíba State University. Three hundred leaflets of M. oleifera were collected and measured to determine length “L” and width “W” and, subsequently, leaflets area was quantified through ImageJ^® software. Using 200 leaflets, the univariate regression models were fitted, adopting length, width or the product of these dimensions “LW” and a bivariate model based on length and width as predictor variables of the observed leaflets area as dependent variable. The remaining 100 leaflets were used to evaluate the relationship between the observed leaflet area “OLA” and the estimated leaflets area “ELA”, based on Pearson’s correlation “r”; Willmott’s index of agreement “d” and index of confidence “c”; and root mean square error “RMSE”. It was found that allometric models can be used with high accuracy and performance to estimate the leaflets area of M. oleifera as non-destructive method, and recommended model is ELA = 0.035 + 0.720*LW. Future research is suggested for fittings of multivariate models to estimate the leaf area of M. oleifera from varying leaflet sizes, complete leaves, leaf fresh and dry weights, history of life and age of plants.

Index terms:
Linear measurements; empirical modeling; model validation

[1] ^*Corresponding author: ferragroestat@gmail.com

Parameters	Linear dimensions and area of leaflets used to fit models
Parameters	Length (cm)	Width (cm)	Leaflet area (cm²)
Sample arithmetic mean	1.595	1.142	1.445
Sample standard deviation	0.474	0.329	0.800
Maximum	2.831	1.950	3.602
Minimum	0.695	0.443	0.253
Coefficient of variation (%)	29.717	28.840	55.365
Estimate of classes	Intervals of classes
Class of small leaflets	≤ 1.407	≤ 0.945	≤ 1.369
Class of medium leaflets	> 1.407 ≤ 2.119	> 0.945 ≤ 1.448	> 1.369 ≤ 2.486
Class of large leaflets	> 2.119	> 1.448	> 2.486
	Linear dimensions and area of leaflets used to validate models
Sample arithmetic mean	1.895	1.342	1.943
Sample standard deviation	0.436	0.305	0.789
Maximum	2.831	1.950	3.602
Minimum	0.944	0.597	0.456
Coefficient of variation (%)	23.008	22.706	40.607

Models	Coefficients and statistics of the models
Models	β₀	β₁	β₂	F_Calculated	R² _Adjusted
$E L A = β_{0} + β_{1} * L$	-1.104±0.064	1.598±0.039^**	-	1712.93	0.896
$E L A = β_{0} + β_{1} * W$	-1.227±0.055	2.340±0.047^**	-	2531.21	0.927
$E L A = β_{0} + β_{1} * L W$	0.035±0.015	0.720±0.007^**	-	12136.55	0.984
$E L A = β_{0} + β_{1} * L + β_{2} * W$	-1.331±0.037	0.737±0.045^**	1.402±0.065^**	3094.80	0.969

Models	Performance indices
Models	r	d	c	RMSE
$E L A = β_{0} + β_{1} * L$	0.912	0.950	0.866	0.324
$E L A = β_{0} + β_{1} * W$	0.946	0.969	0.917	0.258
$E L A = β_{0} + β_{1} * L W$	0.985	0.993	0.978	0.134
$E L A = β_{0} + β_{1} * L + β_{2} * W$	0.982	0.988	0.970	0.162

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Allometric models for estimating Moringa oleifera leaflets area

Modelos alométricos para estimativa de área de foliólulos de Moringa oleifera

ABSTRACT