Tree growth variables are important tree characteristic connected to forestry activities. This study focused on crown width as it reflects general tree health and provide habitat to diverse plants and animals. Therefore, this research work aimed to develop and validate a crown width prediction models for sustainable management of Gmelina arborea in Federal University of Technology, Akure, Nigeria. Three linear and nonlinear models were fitted for the prediction of crown-width using diameter at breast height (Dbh), total tree height and tree Slenderness coefficient as the predictive variables. Performance of the models was ranked according to best fit using the Akaike information criterion (AIC) and adjusted coefficient of determination (Radj2). The result showed that crown width was significant and shows strong correlation with other tree growth variables. The selected models showed high value of adjusted coefficient of determination. Although, it was revealed that multiple linear-binomial and polynomial model had the highest adjusted coefficient of determination (Radj2= 98%) but binomial model had the least Akaike information criterion (AIC= -637.46) which make it to be rank as the best model, while monomolecular non-linear model had the least adjusted coefficient of determination (Radj2 = 93%) and largest Akaike information criterion (AIC= -359.12).

1. Crown Width Models for Gmelina arborea Roxb. Stands at Obanla, Federal University of Technology, Akure, Nigeria
Crown Width Models for Gmelina arborea Roxb. Stands at
Obanla, Federal University of Technology, Akure, Nigeria
*1O.G. Olugbadieye, 2F.E Adesuyi, 3J.O. Daramola, 4T.S. Bola
1,2,3,4Department of Forestry and Wood Technology, Akure, Nigeria Federal University of Technology. P.M.B 704, Ondo
State, Akure, Nigeria
Tree growth variables are important tree characteristic connected to forestry activities. This study
focused on crown width as it reflects general tree health and provide habitat to diverse plants and
animals. Therefore, this research work aimed to develop and validate a crown width prediction
models for sustainable management of Gmelina arborea in Federal University of Technology,
Akure, Nigeria. Three linear and nonlinear models were fitted for the prediction of crown-width
using diameter at breast height (Dbh), total tree height and tree Slenderness coefficient as the
predictive variables. Performance of the models was ranked according to best fit using the Akaike
information criterion (AIC) and adjusted coefficient of determination (Radj
2
). The result showed
that crown width was significant and shows strong correlation with other tree growth variables.
The selected models showed high value of adjusted coefficient of determination. Although, it was
revealed that multiple linear-binomial and polynomial model had the highest adjusted coefficient
of determination (Radj
2
= 98%) but binomial model had the least Akaike information criterion (AIC=
-637.46) which make it to be rank as the best model, while monomolecular non-linear model had
the least adjusted coefficient of determination (Radj
2
= 93%) and largest Akaike information
criterion (AIC= -359.12).
Keywords: Model, Diameter at breast height, Tree height, Akaike information criterion.
INTRODUCTION
Crown, diameter at breast height (Dbh) and height are
important characteristic of tree variables,which many of
the forestry activities and processes are related with.Tree
crown is one complement of net primary production and its
dimensions reflect general tree health and provide habitat
to diverse plants and animals (Popoola and Adesoye,
2012; Chukwu et al., 2017a). It forms the tree growing
space, which is associated with the availability of all of the
required supplies for the tree growth. A tree's crown
therefore denotes the above-ground spatial requirements
needed for a tree to survive, grow, and reproduce (Brian
et al., 2005). The crown displays the leaves to allow the
capture of radiant energy for photosynthesis. Thus,
measurement of a tree crown is often needed to assist in
the quantification of tree growth (Kozlowski et al., 1991).
The size of a tree crown has a marked effect on and is
strongly correlated with the growth of the tree and its
various parts (Temesgen et al., 2005).
Crown width measurement is not frequently carried out in
forest inventories. This might be due to the difficulties in
measurement, yet this value has wide applicability in
forestry (Russell and Weiskittel, 2011). It is relevant in
studies of stand growth and tree density (Hemery et al.,
2005). Despite the importance of tree crown width to forest
inventory and measurement, little attention has been given
to it (Chukwu et al., 2017b). This cause may have resulted
to low market value or unavailability of market for tree
crown. However, crown size, being closely related to the
photosynthetic capacity of a tree, is an important
parameter in studies of the growth of individual trees
(Elmugheira and Elmamoun 2014). Estimates of crown
width can be used to calculate stand canopy closure,
*Corresponding author: O.G. Olugbadieye, Department
of Forestry and Wood Technology, Akure, Nigeria Federal
University of Technology. P.M.B 704, Ondo State, Akure,
Nigeria. Email: oloruntobigideon@gmail.com; Tel:
+2348065131748.
Co-Author 2
Email: adesuyifisola@gmail.com
3
Email: daramolajoseph53@gmail.com
4
Email: tomiyosishadrackbola@gmail.com
Research Article
Vol. 6(2), pp. 062-066, December, 2019. © www.premierpublishers.org. ISSN: 2167-0465
International Journal of Forestry and Wood Science

2. Crown Width Models for Gmelina arborea Roxb. Stands at Obanla, Federal University of Technology, Akure, Nigeria
Olugbadieye et al. 063
which is important for assessing wildlife habitat suitability,
fire risk, and understory light conditions for regeneration
(Crookston and Stage, 1999). Therefore, Crown models
are needed for interpreting forest inventories of growing
stock and for determining the cultural treatment to be
employed (Chuwku et al., 2017b).
Models for crown width prediction using other growth
variables such as Dbh, total height and tree slenderness
coefficient (TSC) are tools that can be recommended by
forest managers to provide precise and suitable
information on recent growing stock since crown width
models can be used as input variable forest growth and
yield. Though, preferences have been given to diameter at
breast height over other predictors, due to its ease and
accuracy of measurement on the field. Also, since the
crown dimensions depends on the status of the neighbour
trees, then a covariate of tree height variation or TSC can
be used to explain most of the variance in the model. Any
attempt that can improve the accuracy of measuring,
predicting and analysing these variables should be taken
into consideration (Vange et al., 2018). The choice of
Gmelina arborea for this study is justified by its unique
importance in the pulp and paper mills as well as the
indispensability roles it plays in forest soil conservation
and ecosystem management. Therefore, the study aimed
to develop and validate a crown width prediction models
for sustainable management of Gmelina arborea within the
Federal University of Technology, Akure, Nigeria.
MATERIALS AND METHOD
Tree Species Description
Gmelina arborea is described by Orwa et al. (2009) as an
unarmed, moderately sized to large deciduous tree with a
straight stem. It is wide spreading with numerous branches
forming a large shady crown, attains a height of 30 m or
more and a Dbh of up to 4.5 m. It has bark smooth, pale
ashy-grey or grey to yellow with black patches and
conspicuous corky circular lenticels. Gmelina arborea is
one of the world’s most valuable trees for the productions
of pulp and paper. According to Ogunkunle (2010) and
Adesuyi et al. (2019) Gmelina arborea has longer than
average fibre length, Runkel ratio of less than 1, low basic
wood density and low chemical extractives; these unique
properties makes it’s a good quality for paper production.
A high interest is therefore needed to be place on the
growth of this species.
Study Area
The research was carried out at Gmelina plantation,
Forestry Nursery Unit, Teaching and Research Farm,
Federal University of Technology, Akure (FUTA). FUTA
lies in the South-western Nigeria in the rainforest
vegetation zone. It is geographically geo-referenced on
coordinate lines of 734393E, 808614N on the western
flank and 737291E, 806714N on the Eastern flank of
meridians (Oyinloye and Sunday, 2014). The site was
allocated to the Department of Forestry and Wood
Technology, with the aim to aid teaching and research in
the Department. The total land area of the plantation is
0.2014 ha.
Sampling Procedure and Data Collection
Complete enumeration of the plantation was made for this
study. Data were collected for all the living trees
encountered in the stand whose Dbh is ≥ 5cm. Total height
(THT) and Dbh were collected for all the trees for further
analysis. Total height, which is the height from the ground
through the tree stem to the tip of the tree, was measured
using the wide scale Spiegel Relaskop. Diameter at the
breast height was measured at 1.3 m above the ground
level using the diameter tape and the crown width using
meter tape. The tree crown width measurements were
based on the assumption that the vertical projection of a
tree crown is circular. Four radii were measured and, in the
direction, forming equal angles (Zuhaidi, 2009; Chukwu et
al., 2017b). CW was calculated using the following
formulae:
𝑪𝑾 = ∑
𝒓 𝒊
𝟐
Equation (1)
Where;
CW= crown width (m), and
𝑟𝑖 = projected crown radii measured on four axes
Tree slenderness coefficient (TSC) was derived using the
following formulae:
𝐓𝐒𝐂 =
𝑻𝑯𝑻
𝑫𝒃𝒉
Equation (2)
Where,
TSC=Tree slenderness coefficient,
THT=Tree total height (m), and
DBH=Diameter at breast height (m)
Fitting of crown width models
Three linear and nonlinear models were fitted for the
prediction of crown-width using Dbh, total height and TSC
(also known as the Height-Diameter Ratio) as the
predictive variables. Performance of the models was
ranked according to best fit using the Akaike information
criterion (AIC) and adjusted coefficient of determination
(Radj
2).
𝐶𝑊 = 𝑏0 + 𝑏1 𝐷𝑏ℎ
Simple Linear Model Equation (3)
𝐶𝑊 = 𝑏0 + 𝑏1 𝐷𝑏ℎ + 𝑏2 𝑇𝐻𝑇
Multiple Linear-Binomial Model Equation (4)
𝐶𝑊 = 𝑏0 + 𝑏1 𝐷𝑏ℎ + 𝑏2 𝑇𝐻𝑇 + 𝑏3 𝑇𝑆𝐶
Multiple Linear-Polynomial Model Equation (5)
𝐶𝑊 = 𝑏0 × 𝐸𝑥𝑝(𝑏1 𝐷𝑏ℎ)
Exponential Model Equation (6)

3. Crown Width Models for Gmelina arborea Roxb. Stands at Obanla, Federal University of Technology, Akure, Nigeria
Int. J. For. Wood Sci. 064
𝐶𝑊 = 𝑏0 × 𝐷𝑏ℎ 𝑏1
Power Model Equation (7)
𝐶𝑊 = 𝑏0 × (1 − 𝐸𝑥𝑝(−𝑏1 𝐷𝑏ℎ))
Monomolecular Model Equation (8)
Where: Dbh is diameter at breast height (cm), THT is the
total height (m), TSC and b0, b1, b2 and b3 are regression
parameters.
RESULT AND DISCUSSION
The result presented in figure 1 showed the present status
of the tree species in the study area. Gmelina arborea had
diameter at breast height that ranged from 5.5 to 35 cm.
The result showed that trees are more concentrated in the
diameter class of 10 to 20 cm, followed by 46 trees with
diameter size of 20 to 30 cm and 32 trees were recorded
under the Dbh class of 5 to 10 cm and lastly, 2 tree stands
had a Dbh size 35 m and above. Gmelina arborea had
crown width distribution between 3.00 to 10 m. Most of the
trees (96) encountered had crown width sizes between 5
to 7 m, followed by 57 trees which had 3 to 5 m crown width
sizes while 35 and 3 tree stands had crown width
distribution of 7 to 9m and 9m and above, respectively.
Figure 1: Diameter at breast height and Crown Width
Distributions of Gmelina arborea Tree.
The descriptive statistics for individual trees of Gmelina
arborea was revealed in Table 1. The result showed the
mean and standard error value for the tree growth
variables which are diameter at breast height (16.1± 0.45
cm), total height (10.3± 0.13 m), tree slenderness
coefficient (also known as Height-Diameter ratio) which is
also the (0.70± 0.01) and crown width (6.0± 0.11 m). The
minimum and maximum of tree growth characteristics
ranged from 0.40 to 6.30 and 1.20 to 35.00, respectively.
The result of the Pearson’s correlation matrix was
presented in Table 2. The result showed both the direction
and strength of the linear association between the growth
variables. Crown width was significant and shows strong
correlation with other tree growth variables. Both positive
and negative correlation was observed between the
growth variables. Correlation was recorded between Dbh
and THT with correlation coefficient of 0.96, while
correlation coefficient for Dbh and CW, THT and CW, TSC
and CW, are 0.98, 0.93 and -0.96 respectively. The highest
correlation coefficient of 0.98 was found between Dbh and
CW, while the lowest correlation coefficient of 0.93 was
between total height and crown width (Table 2)
Table 1: Summary of tree growth variables of the study
area
Variables Mean ± SE Min. Max. No of stem
Dbh (cm) 16.1± 0.45 5.5 35.0 191
THT(m) 10.3± 0.13 6.3 13.5
TSC 0.7± 0.01 0.40 1.20
Crown width (m) 6.0±0.11 3.4 10.2
Where: THT is Total Tree Height, TSC is Tree Slenderness
Coefficient, SE=Standard Error
Table 2: Pearson’s correlation between growth variables
Variables Dbh THT TSC CW
Dbh 1.00
THT 0.96 1.00
TSC -0.96 -0.97 1.00
CW 0.98 0.93 -0.96 1.00
Where: Dbh =Diameter at breast, THT=Total tree height,
TSC=Tree slenderness, CW= Crown Width
Crown width Models
The models selected for the estimation of crown width with
their assessment criteria were presented in Table 3. The
selected models showed high value of adjusted coefficient
of determination. Although, it was revealed that multiple
linear-binomial and polynomial model had the highest
adjusted coefficient of determination (Radj
2= 98%) but
binomial model had the least Akaike information criterion
(AIC= -637.46) which make it to be rank as the best model,
while monomolecular non-linear model had the least
adjusted coefficient of determination (Radj
2 = 93%) and
largest Akaike information criterion (AIC= -359.12).

4. Crown Width Models for Gmelina arborea Roxb. Stands at Obanla, Federal University of Technology, Akure, Nigeria
Olugbadieye et al. 065
Table 3: Models with Assessment criteria
Models Radj
2 AIC F-ratio
CW = 2.50+0.21Dbh 96 -526.03 5181.52
CW = 6.94+0.32Dbh-0.58THT 98 -637.46 4743.38
CW = 7.05+0.31Dbh-0.58THT-
0.09TSC 98 -636.04 3155.12
CW = 3.38×Exp(0.03Dbh) 0.95 -431.34 37699.61
CW = 1.25×DBH0.57 0.96 -480.77 43918.33
CW = 9.77×(1-Exp(-0.06DBH) 0.92 -359.12 23240.98
The result of the best model (binomial) using Student’s t-
test showed that there is no significant difference between
the observed and predicted crown width as shown in Table
4 (p = 0.43). The result revealed the t-stat value, 0.78 is
less than the t-critical values, 1.96. This confirmed the
goodness of fit of the models.
Table 4: Validation result with Student’s t-test
Observed
crown width
Predicted
crown width
Mean 5.89 5.99
t Stat -0.78
P(T<=t) one-tail 0.21
t Critical one-tail 1.64
P(T<=t) two-tail 0.43
t Critical two-tail 1.96
DISCUSSION
Tree crown distribution is an effective method for
describing a forest stand because tree productivity,
gaseous exchange and health depends largely on the
crown dimensions (Adesoye and Ezenwenyi, 2014;
Chukwu et al., 2018). The result of the present study
showed the current status of tree species in the study area.
A total of 191 trees whose Dbh was≥5cm was used for this
study. The descriptive statistics of tree growth variable of
the study area showed that the mean Dbh value was 16.10
cm. This indicates that most of the trees encountered in
this study area were below the minimum merchantable
size of 48cm stipulated by logging policy of south western
Nigeria (Adekunle, 2007). The distribution of number of
trees into Dbh size classes for the study area is a nearly
bell shape expected of a plantation. This indicated healthy
recruitment potentials; the lower class diameter tree
stands could develop into mature trees and replace the old
ones in the future if proper conservation efforts are
sustained (Ogana and Gorgoso, 2015).The result of the
correlation between tree growth variables and crown width
of G. arborea species in the study area showed inverse
associations with TSC. This implies that crown width
decreases with increase in HSC. Comparable result was
reported by Temesgen et al. (2005) and Chukwu et al.
(2018) as in the case of crown ratio and TSC.
Model fitting and evaluation are important parts of model
building (Popoola and Adesoye, 2012). A number of
different models were examined for predicting crown width
using simple linear, binomial, polynomial, power and
monomolecular functions. The model generated for this
study were assessed and validated with several statistical
indices that were recommended by Vanclay (1988). One
distinctive independent variable that has been widely used
by several authors (Elmugheira and Elmamoun, 2014;
Chuwku et al., 2018) is diameter at breast height. This is
because of the high relationship between the two variables
and high impact the Dbh has on crown width. Total height
is also used as predictive variable because the crown of
target trees also depends on the height of neighbouring
trees, including the relation between heights to the
diameter of the target tree and that its neighbours will
improve the model accuracy. The TSC (also known as
height diameter ratio) is another variable used due to its
ability to quantify the development of stages of the
plantation and also show structural variation in trees. The
larger the TSC value, the more unstable the stand
structure. Generally, all the models consistently gave good
fit to the Gmelina arborea data in the study area with
binomial model found fit for the prediction of crown width
of the forest stand with incorporation of Dbh, total height
as the predictive variables. This was due to the very high
values found for the adjusted coefficients of determination
and the least values of AIC shows the form is well adapted
and biologically realistic. Although the binomial model
made use of Dbh and THT as predictors but Dbh is
regarded as the main predictive variable while THT is
included to improve the model accuracy. This make this
study to be similar to the findings of Adesoye and
Ezenwenyi (2015) who reported that Dbh is a good
predictor of Crown diameter but the study is in total
disagreement to the findings of Avsar and Avvildiz (2005)
who observed that crown diameter-Dbh relationship can
be described by power model.
The result of the paired t-test showed that there is no
significant difference between the observed and predicted
crown width. This shows that the binomial model is valid
for estimation of G. arborea stands in the study area.
Hence could be used for growth predictions in the
plantation studied with confidence.
CONCLUSION
The study identified binomial model as best for the
prediction of crown width of Gmelina arborea Roxb.
Stands at Obanla, Federal University of Technology,
Akure, Nigeria which can be applied for effective and
sustainable management of the plantation. It has also
provided significant information on the growth of the
species in the study area. Further studies need to be done
to test applicability of these model across similar
ecosystem and to relate the growth rates/patterns in both
Dbh, THT and crown width of open grown tree species to
the fitted models.

5. Crown Width Models for Gmelina arborea Roxb. Stands at Obanla, Federal University of Technology, Akure, Nigeria
Int. J. For. Wood Sci. 066
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Accepted 14 December 2019
Citation: Olugbadieye OG, Adesuyi FE, Daramola JO,
Bola TS (2019). Crown Width Models for Gmelina arborea
Roxb. Stands at Obanla, Federal University of
Technology, Akure, Nigeria. International Journal of
Forestry and Wood Science, 6(2): 062-066.
Copyright: © 2019 Olugbadieye et al. This is an open-
access article distributed under the terms of the Creative
Commons Attribution License, which permits unrestricted
use, distribution, and reproduction in any medium,
provided the original author and source are cited.