Braz. J. Biol., 2015, vol. 75, no. 1, p. 152-156152152
http://dx.doi.org/10.1590/1519-6984.09813 Original Article
Non-destructive linear model for leaf area estimation
in Vernonia ferruginea Less
Souza, MC.a,b* and Amaral, CL.c
aPrograma de Pós-graduação em Ciências Biológicas (Biologia Vegetal), Departamento de Botânica,
Instituto de Biociências, Universidade Estadual Paulista – UNESP, Avenida 24 A, 1515, Bairro Bela Vista,
CEP 13506-900, Rio Claro, SP, Brazil
bDepartamaneto de Ciências Farmacêuticas, Faculdade de Ciências Farmacêuticas de Ribeirão Preto, Universidade de
São Paulo – USP, Avenida do Café, s/n, Bairro Monte Alegre, CEP 14040-903, Ribeirão Preto, SP, Brazil
cPrograma de Pós-graduação em Agronomia (Produção Vegetal), Faculdade de Ciências Agrárias e Veterinárias,
Universidade Estadual Paulista – UNESP, Via de Acesso Prof. Paulo Donato Castellane, s/n,
CEP 14884-900, Jaboticabal, SP, Brazil
*e-mail: marcelo.claro.souza@gmail.com
Received: June 11, 2013 – Accepted: October 10, 2013
(With 4 figures)
Abstract
Leaf area estimation is an important biometrical trait for evaluating leaf development and plant growth in field and
pot experiments. We developed a non-destructive model to estimate the leaf area (LA) of Vernonia ferruginea using
the length (L) and width (W) leaf dimensions. Different combinations of linear equations were obtained from L, L2,
W, W2, LW and L2W2. The linear regressions using the product of LW dimensions were more efficient to estimate
the LA of V. ferruginea than models based on a single dimension (L, W, L2 or W2). Therefore, the linear regression
“LA=0.463+0.676WL” provided the most accurate estimate of V. ferruginea leaf area. Validation of the selected model
showed that the correlation between real measured leaf area and estimated leaf area was very high.
Keywords: Asteraceae, cerrado, savanna, statistical model, validation.
Modelo linear não-destrutivo para estimativa de área
foliar de Vernonia ferruginea Less
Resumo
A estimativa de área foliar é um importante traço biométrico para avaliação do desenvolvimento foliar e do crescimento
vegetal em experimentos de campo e casa-de-vegetação. Foi desenvolvido um modelo linear não destrutivo capaz
de estimar a área foliar (AF) de Vernonia ferruginea usando o comprimento (C) e a largura (L) foliar. Diferentes
combinações de equações lineares foram obtidas a partir de C, C2, L, L2, CL e C2L2. As regressões lineares usando o
produto de dimensões CL foram mais eficientes para estimar a AF de V. ferruginea do que os modelos baseados em
uma única dimensão (C, L, C2 ou L2). O modelo linear “AF = 0,463+0,676 CL” forneceu com maior precisão a AF de
V. ferruginea em relação aos demais modelos testados. A validação do modelo selecionado revelou elevada correlação
entre a área foliar real e a área foliar estimada pelo modelo.
Palavras-chave: Asteraceae, cerrado, modelos estatísticos, savana, validação.
1. Introduction
The leaf area measurement is one of the most common
parameters evaluated in green house and field ecophysiological
studies (Wang and Zhang, 2012) on Brazilian savanna
(locally know as “cerrado”) woody species, crops and
weeds. Therefore, the accurate measurements of leaf area
(LA) in field experiments may be time-consuming and
generally requires the use of expensive equipment (e.g.
portable leaf area meters). Such destructive methods require
the excision of the leaves, thus removing the possibility of
successive measurements of the same leaf. The excision of
a large number of leaves (causing the artificial reduction
of the leaf life span) can interfere with the photosynthesis
rate, reducing the plant growth and interfering with the
phenology of this species, due to the reduction of the
canopy (Chabot and Hicks, 1982). In conservation areas
(e.g. cerrado), many researchers are conducting different
research using the same communities at the same time. So,
Braz. J. Biol., 2015, vol. 75, no. 1, p. 152-156 153153
Leaf area estimation of Vernonia ferruginea
the excision of the leaves can interfere with the results of
other experiments that are sharing the same group of plants.
The use of non-destructive models to estimate the leaf
area has been used to understand the ecophysiology of
crops (e.g., Crocus sativus L. (Kumar, 2009), Juglans nigra
L. (Zellers et al., 2012), terrestrial weeds (e.g. Merremia
cissoides Lam. (Carvalho et al., 2011a) and aquatics (e.g.
Pistia stratiotes L. (Carvalho et al., 2011b)), and more
recently cerrado species (e.g. Styrax ferrugineus Nees &
Mart and Styrax pholii A. DC. (Souza and Habermann,
2014)). Linear models based on length and width leaf
measurements have been considered the most simple and
efficient models to estimate the leaf area of some species
(Demirsoy and Lang, 2010, Giuffrida et al., 2011, Wang
and Zhang, 2012). However, models to estimate the leaf
area of the cerrado species are almost absent. So, non-
destructive models to estimate LA are not only required
by agronomists, but also biologists and ecologists.
Vernonia ferruginea (Asteraceae) is a native species
from Brazilian’s cerrado with a good distribution by the
cerrado remains. This species is often found as an invasive
species of wastelands, pastures and shoulders of highways
in São Paulo state, Brazil. The aim of this study was to
develop and validate an efficient and non-destructive model
to estimate the leaf area of V. ferruginea using leaf length
and width dimensions.
2. Material and Methods
2.1. Studied site
This study was carried out in a field within Jaboticabal
municipality, São Paulo state, Brazil (21°14’19’’S,
48°16’09’’W). The climate in this region may be classified
as CWA with a wet season from October to March and
a dry season from April to September. The mean annual
temperature is approximately 23 °C and the total annual
rainfall is approximately 1411 mm.
2.2. Plant samples and leaf measurements
We sampled a total of 200 well-developed leaves of 10
adult V. ferruginea plants in the beginning of March 2013.
Immediately after cutting, leaves were carefully placed in
plastic bags and transported to the laboratory. They were
individually scanned at 300 dpi, using a HP Photosmart
C3100 series scanner coupled to a microcomputer. Leaf
area (LA), length (L) and width (W) of each leaf were
determined using the software ImageJ (Rasband, 2013),
where L is the maximum length along the midrib and
W is the maximum value perpendicular to the midrib
(Figure 1). The LA is expressed in cm2 while L and W
are expressed in cm.
2.3. Model building
We used the 200 leaf measurements described above,
testing the relation between LA and L and/or W (Table 1).
Leaf area (LA) was considered to be the dependent variable,
while the independent variables were L, L2, W, W2, the
product of LW and L2W2. We tested the internal validity
of the models using the coefficient of determination (R2),
mean square error (MSE), error sum of squares (SSE)
and predicted residual error sum of squares (PRESS)
as described in Ghoreishi et al. (2012). Residuals were
also analyzed to determine the presence of outliers and
non-constant error variance (Rouphael et al., 2010). The
best model was selected according to the combination
of the higher R2 and the lowest MSE, SSE and PRESS
(Table 1, Figure 2).
When L and W were involved in the same model, we
tested the co-linearity between them calculating the variance
inflation factor (VIF) (Marquardt, 1970) and the tolerance
value (T) (Gill, 1986). If the VIF value was higher than
Table 1. Fitted coefficient and constant values of the models used to determine the leaf area of Vernonia ferruginea.
Coefficient of determination (R2), error sum of squares (SSE), mean square errors (MSE) and predicted residual error sum
of squares (PRESS).
model n° model tested Fitted coefficient and constant SSE MSE PRESS R2*α (±SE) β (±SE)
1 LA = α + βL 0.330 1.340 2.149 0.185 902.831 4.560 920.618 0.404
2 LA = α + βL2 8.063 0.682 0.147 0.013 913.580 4.614 933.211 0.397
3 LA = α + βW -2.644 0.955 5.855 0.301 521.525 2.634 531.670 0.656
4 LA = α + βW2 6.186 0.486 0.955 0.047 492.872 2.489 502.010 0.675
5 LA = α + βLW 0.463 0.217 0.676 0.009 56.032 0.283 57.019 0.963
6 LA = α + βL2W2 8.212 0.130 0.014 0.000 74.347 0.375 76.118 0.951
Standard errors in parenthesis. L - length (cm), W - width (cm), LA - leaf area (cm2), * p<0.0001, n=200.
Figure 1. Vernonia ferruginea’s leaf showing the position of
leaf length (L) and width (W).
Braz. J. Biol., 2015, vol. 75, no. 1, p. 152-156154
Souza, MC. and Amaral, CL.
154
10 or if the T value was smaller than 0.10, the co-linearity
may interfere with the final result, making necessary the
exclusion of one of the variables from the model.
2.4. Model validation
To further validate the developed model, 185 extra leaves
of V. ferruginea were sampled from the same site on the same
year and season, but from different plants. The LA, L and
W were measured according to the procedures previously
described. The predicted leaf area (PLA) of each leaf was
determined according to the parameters obtained from the
selected model. We performed a linear regression using
the PLA and the observed leaf area (OLA = LA measured
with ImageJ) (Figure 3). The correlation between OLA and
PLA was tested using a Spearman-Rank test (Souza and
Habermann, 2014). The relative bias was estimated by the
mean of differences (d) and the standard deviation of the
differences (SD) (Figure 4). The distribution is considered
normal if at least 97% of the differences in a population lie
between the limits of agreement (Rouphael et al., 2010).
Linear regressions between LA, L and W were performed
using R 2.15.1 (R Core Team, 2012). The MSE and SSE
were determined using the R package systemfit while the
PRESS was determined using the R package asbio.
3. Results
The LA of V. ferruginea ranged from 6.73 to 22.97 cm2
(average = 14.43 cm2), the L ranged from 4.49 to 9.52 cm
(average = 6.93 cm) and the W ranged from 1.95 to 4.04 cm
(average = 2.99 cm). The VIF was smaller than 10 (1.01) and
T was higher than 0.1 (0.99), showing that the co-linearity
between W and L may be considered negligible, and both
variables may be included in the models n° 5 and 6.
All models were statistically significant (p<0.001).
The regression analysis suggested that LA was strongly
Figure 3. Validation of the model PLA = 0.463 + 0.676LW
for estimating the leaf area of Vernonia ferruginea
correlating observed leaf area (OLA) vs. predicted leaf area
(PLA).
Figure 4. Difference between observed leaf area (OLA)
and predicted leaf area (PLA) estimated by PLA = 0.463 +
0.676LW versus the OLA of Vernonia ferruginea (validation
experiment). The solid line is the mean of the differences;
the dotted lines are the limits of agreement, calculated as d
± 3SD. Where d is the mean of the differences and SD is the
standard deviation of the differences.
Figure 2. Plot of the selected model for estimating the leaf
area of Vernonia ferruginea.
correlated with LW and L2W2 but not so strongly correlated
with L, L2, W and W2 (Table 1). The model n°5 presented
the highest R2 and lowest SSE, MSE and PRESS in relation
to the other models (Table 1), being considered the most
efficient model to predict V. ferruginea’s leaf area (PLA
= 0.463 + 0.676LW) (Figure 2).
Braz. J. Biol., 2015, vol. 75, no. 1, p. 152-156 155155
Leaf area estimation of Vernonia ferruginea
To validate the selected model, we predicted the leaf
area of 185 leaves of V. ferruginea using the model n° 5.
The correlation between OLA and PLA was significant
(rs=0.999) by Spearman-Rank test. We also observed
significant correlation after applying a new linear
correlation between OLA and PLA (R2=0.95, p<0.001)
(Figure 3). Considering that sometimes the correlation is
an insufficient analysis to explain relationship between
OLA and PLA, we plotted the differences between PLA
and OLA against OLA (Figure 4). In the current study we
observed that the differences between PLA and OLA were
normally distributed and 98.4% of the plots lay between
d ± 3SD (Figure 4).
4. Discussion
Regression analysis suggested significant correlations
(p<0.001) between LA and L, L2, W, W2, LW and L2W2.
These correlations seem universal since they were previously
observed in many models to estimate LA of crops (for
references see Rouphael et al. 2010), bedding plants
(Giuffrida et al., 2011) and woody species (Ghoreishi et al.,
2012) among others). These significant relations were
most evident between LA vs. LW and LA vs. L2W2, and
in both cases, we observed coefficients of determination
(R2) higher than 0.95 (Table 1). The model based on the
relationship between LA vs. LW (model n° 5) was selected
not only based on the higher R2 but also because it presented
smaller SSE, MSE and PRESS than the model between
LA vs. L2W2. This criterion was used in accordance with
Rouphael et al. (2010) and Giuffrida et al. (2011).
In this study, we clearly observed that models with a
single measurement of L, L2, W and W2 were less acceptable
for estimating the LA of V. ferruginea, presenting R2 around
0.40 for the models using L and L2, and 0.66 for models
using W and W2. Souza and Habermann (2014) observed
a similar pattern when estimating the leaf area of Styrax
ferrugineus (savanna species) and S. pohlii (riparian forest
species). In fact, the differences observed for S. pohlii among
the models using a single measurement (L or W) were not
so discrepant as observed by V. ferruginea, producing the
lowest R2 (0.82) observed for the model correlating LA
and W2. However, as observed in this paper, the lowest R2
(0.58) found among the models used to estimate the LA of
S. ferrugineus was observed in the models that correlated
LA and L, and LA and L2.
As observed by Rouphael et al., (2010), the shape
coefficient of the selected model (model n°5, β = 0.68)
can be described by a shape between an ellipse (0.78)
and a triangle (0.50) of the same length and maximum
width. Our shape coefficient (0.68) showed similarity to
those calculated for native species and crops. Values of
0.68 have been reported by S. pohlii, 0.70 for S. ferrugineus
(Souza and Habermann, 2014), 0.72 for Rosa hybrida
L. (Rouphael et al., 2010), 0.68 for Helianthus annuus
L. (Rouphael et al., 2007), 0.69 for Diospyros kaki
L. (Cristofori et al., 2008) and 0.73 for Salvia sclarea
L. (Kumar and Sharma, 2010).
5. Conclusion
A simple and efficient model (LA=0.463+0.676LW) was
developed, and validated, to estimate the LA of Vernonia
ferruginea. Considering that leaf length and width can be
easily measured with a ruler, this model is an important tool
for ecophysiological studies of V. ferruginea in the field
or greenhouse experiments. The use of this model would
enable researches to do non-destructive measurements and
repeat measurements in the same leaf, excluding the use of
expensive electronic equipment such as leaf area meters.
Acknowledgements
The authors acknowledge the Fundação de Amparo à Pesquisa
no Estado de São Paulo (FAPESP) and Coordenação de
Aperfeiçoamento de Pessoal de Nível Superior (CAPES) for
the PhD scholarships of MCS (Proc. FAPESP #2010/07809-
1) and CLA. We are also grateful to Nara O. Vogado and
to Katharine Carroll for the English review.
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