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American Journal of  
Life Science and Innovation (AJLSI)

Tree Taper Model for Selected Tree Species within University of  Ibadan, Oyo State
Aderinola Adeola Deborah1*, Jackson Vincent Obukojopo2

Volume 1 Issue 2, Year 2022
ISSN: 2833-1397 (Online)

DOI: https://doi.org/10.54536/ajlsi.v1i2.777
https://journals.e-palli.com/home/index.php/ajlsi

Article Information ABSTRACT

Received: October 16, 2022

Accepted: October 21, 2022

Published: October 27, 2022

In this study, the performance of  different types of  taper model for predicting tree diame-
ters of  Terminalia radii (Tent tree) at Heritage Park and Tectonia grandis (Teak) at teak plan-
tation within University of  Ibadan was examined. Data from pure (monoculture) stands of  
T. radii (Heritage Park) and T. grandis (Teak Plantation) containing a total of  146 tent trees 
and 131 teak trees respectively. Five taper models developed by various researchers were 
adopted, fitted and evaluated. The comparison of  the model performances was basically on 
the analysis of  three goodness-of-fit statistics and residue analysis found model 5 to be most 
superior in predicting the stem diameter at any point for the two species in the two study 
areas. The Model 2 exhibited the worst performance in fitting statistics and residual analysis 
results. Therefore, the same taper model should be used for prediction of  diameter of  the 
two tree species within University of  Ibadan.

Keywords
Heritage Park, Model, Teak 
Plantation, Terminalia Radii, 
Tectonia Grandis

1 Department of  Social and Environmental Forestry, University of  Ibadan, Nigeria
2 Department of  Forest Production and Products, University of  Ibadan, Nigeria
* Corresponding author’s e-mail: adeyemiadeola90@gmail.com

INTRODUCTION
Tree Taper can be defined as the rate of  narrowing in 
diameter along the tree stem of  a given form (Gray 
1956). It can be expressed as a function of  height above 
ground level, total tree height, and diameter at breast 
height (Clutter et al., 1983). The term ‘taper’ function is 
often used interchangeably with tree form, where ‘form’ 
refers to the shape of  the tree (Max and Burkart,1976).  
In 1946, Mesavage and Girard asserted that the tree 
taper is the degree to which a tree stem or bole decreases 
in diameter as a function of  height above the ground, 
where tree with a high degree of  taper is called a poor 
taper tree and those with low taper are refer to as good 
taper tree.  Also explained that the form of  a tree can be 
represented by a certain form class called Girard which 
denoted as the ratio expressed as percentage of  butt-log 
scaling diameter to diameter as the breast height. The 
traditional geometric shape of  tree can be expressed as a 
mathematical function of  height above ground level, total 
tree height, and diameter at breast height (D) (Sloboda 
and Saboroske 1981). 
Taper equations are very useful as they can provide 
information about diameter at any height, and height 
at any diameter based only on commonly taken tree 
measurements (Byrne and Reed 1986). Furthermore, 
taper equations can be used to derive volume equations 
by integration when the equation is rotated around the 
longitudinal axis of  a tree (Bruce et al. 1968; Byrne and 
Reed, 1986). 
Many types of  taper modeling techniques have been 
proposed and applied over the years. These mathematical 
functions are generally described as taper functions tree 
(Max and Burkart,1976). Its function is essential and play 
a pivotal role in forest inventory and growth projection, as 
well as in forest management planning (Rupsy,2018). The 
function can provide a suitable and relevant information 
for decision making at an individual tree level, stand level 

and forest level (Gray,1956).
According to Wang et al. (1998), the vulnerability and 
susceptibility of  a tree to wind damage is majorly 
influenced or determined by the slenderness coefficient 
or taper of  the tree. Whereas, the heritage park and teak 
plantation are mainly for the recreational and research 
purpose respectively, their accommodative status are 
mostly high every time. With this the taper of  the selected 
tree species should be determined, in order to know their 
susceptibility to wind throw. 
Over some decades, tree taper functions have been widely 
studied all over the world like taper and stem volume 
equations for the mixed stands developed by Kaya (2016) 
only for the mixed stands of  black pine and scots pine 
in Devrek Region of  Zonguldak but there is little or no 
documentation on taper model with respect to University 
of  Ibadan. In this recent study, parameters have been 
estimated for the adopted models developed in other 
countries.

METHODOLOGY
Study Area
Data used in this study were collected from two (2) study 
area which are within the University of  Ibadan campus. 
University of  Ibadan is located along Oyo Road, Ibadan 
in Akinyele Local Government Area of  Oyo State, 
Nigeria.  It lies between latitude 7o26’35’’N to 7o27’33’’N 
and longitude 3o53’57’’E to 3o54’06’’E. The campus 
is characterized by dry and rainy season. The relative 
humidity is very high during the rainy season and low 
during dry season (Akinyele, 2010). The two locations are 
Heritage Park and the University Teak Plantation.

University Teak Plantation
University of  Ibadan (UI) Tectona grandis plantation lies 
between latitudes 7°456′ N to 7°45.834′ N and longitudes 
3°90.942′ E to 3°90.508′ E, within the tropical rainforest in 

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the South-western part of  Nigeria with mean altitude of  
227m above sea level and total land area of  approximately 
8 ha (Ezenwenyi et al., 2018). The Soils in the University 
of  Ibadan teak plantation is Ferric luvisol but mostly 
derived from sandstones (Falade, 2017). The average 
texture in the top 15 cm was 58.8 % sand, 18.4 % silt and 
22.8 % clay and thus, the soil textural class is loamy sand 
(Falade and Oyeleye, 2011). Located beside the University 
of  Ibadan international Conference Centre (UIICC) and 
extends through to the Distance Learning Centre along 
Ajibode Road Ibadan in Akinyele Local Government 
area of  Oyo State. The plantation is managed by 
Department of  Forestry Resource management. (Now; 
social and environmental Forestry & Forest products and 

production). It was established mainly for education and 
research purpose.

Heritage Park
This park was situated in the campus opposite Queen 
Elizabeth Hall after the university’s main gate (First gate). 
The park was comprised of  Terminalia radii (Tent tree). It 
serves as a recreation, relaxation and reading center for 
students and staffs, beautification purpose and habitat for 
birds the university. The plantation is a relative flat surface 
with loamy/clayey soil and a gradual slope surface. There 
are little outcrops of  rocks scattered within the plantation.  
The park is approximately 1.34ha in size.

Figure 1: Map showing Study Locations ( Heritage park and Teak plantation) in University of  Ibadan Sampling 
Procedure

Sample Techniques
Systematics technique was used to select 2(two) Trancept 
alternately in the 8ha UI teak plantation with distance 
of  70meters from one another, 5 plots were laid from 
each making 10plots in total with mechanical spacing 
of  10meters.  All living trees within each plot were 
enumerated and measured which makes 131trees in total. 
For Heritage Park, all the tree were also enumerated and 
measured (total enumeration) with the total number of  
146trees. UI teak plantation and heritage park mainly 
comprised of  exotic trees which are Tectonia grandis (Teak) 
and Terminalia radii (Tent tree) respectively.

Tree Taper models
The tree taper (d) usually expressed as a function of  
Diameter at breast height (D), total height (H) and 
upper(top) stem/bole height (h). The most common 
expression or illustration for functional form of  a taper 
equations is:
d = f  (D, H, h).
Taper equations can be represented in many forms: 
example in a; single simple quadratic form or complex 
form describing sections of  trees. 

According to James and Kozak (1984), the standing tree 
taper equations for several species produce more reliable 
estimates than the inside bark equations. In respect to 
this observation, the Diameter over bark was used in this 
study.
Kozak et al. (1969) asserted that the real advantage of  
complex taper models were little, therefore Single taper 
functions were adopted for the study

Adopted Tree Taper Models
Kozak et al. (1969) Model: This model was developed 
mainly on the basic relationship of  a single parabolic 
function. It was conditioned by  (h/H-1)  and (h2/H2 -1)  
as predictor variables, when h equals to H, estimated 
diameter gives exactly zero.

Sharma and Oderwald (2001) Model: this function implies 
a certain condition; when h = H, d= 0, and when h = BH 
(BH is breast height equal to 1.3 m), d = D

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better the model.
Statistical Test (indices):

where Yi and hi is observation, Yi and hi is prediction, n is 
number of  observations, P is the numbers of  estimated 
parameters, x2 is critical value obtained at α =0.05, H is 
average height, ϒ is standard normal deviate, RSS is sum 
of  square regression.
Graphs of  residuals were plotted against predicted values 
and independent variables, and these were examined for 
evidence of  bias. In addition, frequency distributions 
of  residuals were examined whether data deviate from 
normality or not.

Ranking of  Models
The traditional standard or ordinal ranks for model 
performance was used. It shows the order of  the models 
adopted. The models were compared using four fitting 
statistics, the method of  relative ranking was not used 
because the same model superior others in all the indices 
and the exact position of  each model was easy to allocate.

RESULTS AND DISCUSSION
Results
The descriptive statistic summary of  the raw data 
is presented in table 1. It shows the mean(average), 
standard error of  mean, standard deviation, minimum 
and maximum statistical value for the Terminalia radii and 
Tectonia grandis.

Ormerod (1973) Model: Sharma and Oderwald (2001) 
Model condition also applies to this Ormerod.  Another 
condition is that if  β =1, the resulting tree profile is conic 
and when β is one-half  the resulting tree form or shape 
is parabolic (Reed and Byrne 1985) and when β > 1 but 
less than one-half  i.e., three-fourths (3/4), the tree shape 
is between a cone and a parabola which usually called 
“paracone”.

Polynomial Series Model: This model represents the 
general and common form of  polynomial. Figueired-
Filho et al. (1996) noted that high degree polynomials 
have been used in some studies but the most common 
ones are around fifth degree polynomial

Byrne and Reed (1986): this is the transformation form 
of  Ormerod (1973) Model

Where: D=Diameter at Breast Height, H= Total height, 
d= diameter over bark at height h (m), BH = breast 
height equal to 1.3 m h= height of  ith point from ground 
(m), β1- βn= coefficient

Evaluation for the judgement of  model performance
All the fits and tests were carried out on R Program. 
The 4 (four) goodness of  fit were used to evaluate the 
adequacy of  the models. Fit statistics of  residual analyses 
were also employed alongside with the graphical methods 
of  residual plotting. Goodness of  Fit statistics used 
were among the most common ones. they included: 
RMSE (Root Mean Square Error), Ecrit (Critical Error), 
AIC (Akaike information criterion) and BIC (Bayesian 
information criterion). The smaller the statistics are, the 

Table 1: Descriptive statistics for the individual tree variables for the two (2) study sites
Study site Species Variable Mean Std Error Std D Min Max
HP Terminalia 

radii
d (cm) 15.602 0.456 5.506 3.930 12.630
Dbh (cm) 32.524 0.642 7.761 10.600 58.400
h(m) 6.949 0.171 2.069 2.000 13.000
H(m) 15.404 0.251 3.029 6.000 21.000
d/D 0.478 0.010 0.126 0.250 0.750
h/H 0.458 0.011 0.133 0.147 0.880
G(m2) 0.088 0.003 0.039 0.009 0.268
G/ha (m2/ha) 0.066 0.002 0.030 0.007 0.201
V(m3/) 1.981 1.101 13.306 0.089 161.565
V/ha(m3/ha) 1.486 0.826 9.980 0.067 121.174

TP Tectonia 
grandis

d(cm) 54.855 35.210 4.570 6.750 33.430
Dbh(cm) 38.835 0.797 9.125 13.500 65.800
H (m) 17.265 0.369 4.225 3.250 28.000
H(m) 30.395 0.592 6.777 12.500 50.000
d/D 0.463 0.007 0.082 0.285 0.714
h/H 0.570 0.008 0.088 0.260 0.880

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G(m2) 0.125 0.005 0.059 0.014 0.340
G/ha (m2/ha) 0.312 0.013 0.148 0.036 0.850
V (m3/) 1.587 0.079 0.899 0.094 4.836
V/ha (m3/ha) 3.967 0.196 2.247 0.230 12.090

Where Dbh=Diameter at Breast Height, THT= Total height, d= diameter over bark at height h (m); h= height of  ith point from 
ground (m), HP=Heritage Park, TP= Teak Plantation,G= Basal area, V= Volume

Table 2: Tree Taper Model Estimation for two Species 
Study site Species Model Parameters Estimate Standard 

Error
P-value

HP Terminalia radii 1 β1 -0.284 0.2168 0.192
β2 -0.104 0.154 0.5

2 β1 2.606 0.0313 <2e-16
3 β1 1.396 0.060 <2e-16
4 β0 -2.123 2.074 0.308

β1 11.353 26.485 0.669
β2 -52.409 124.703 0.675
β3 121.806 274.648 0.658
β4 -140.843 285.453 0.623
β5 63.068 112.744 0.577

5 β1 0.557 0.025 <2e-16
β2 0.275 0.077 0.000497

TP Tectonia grandis 1 β1 0.529 0.280 0.060779
β2 -0.643 0.180 0.000511

2 β1 2.305 0.014 <2e-16
3 β1 0.965 0.025 <2e-16
4 β0 -103.13 21.84 6.16E-06

β1 988.28 210.33 6.79E-06
β2 -3719.94 789.66 6.48E-06
β3 6808.25 1445.35 6.47E-06
β4 -6057.94 1289.99 6.86E-06
β5 2095.87 449.04 7.73E-06

5 β1 0.525 0.037 <2e-16
β2 0.179 0.085 0.0361

Where H P= Heritage park, TP= Teak plantation, β (1, 2, 3….) is coefficient

Residual Analysis
Graphical representation of  residuals was plotted for 
each tree taper model and they are presented in Figure 
2 and 3. Visualizations of  the residuals plotted against 
the predicted showed that only model 4 of  both study 
sites produced more homogeneous residual variance than 
other models. It was obviously that precisions in residual 
analysis predictions for both study sites were not similar. 
The ranges of  Errors in the predictions of  all models 
were not distributed uniformly, some distributed between 
+100 to -100 while some -10 to +10.
Also, some models were more biased than others. The 
model 5 of  Heritage Park is less biased in the distribution 
while model 5 of  Teak plantation is moderately biased 
and the alternative models from the both study sites. 
There were more differences in the trend residual 

distributions for the five models for two study sites. 
Also, the models are dependently distributed except the 
model 5 (Byrne and Reed 1986) of  both study site that 
are independently distributed. Further evaluation of  the 
models used in the study were shown in the results of  fit 
statistics.
The statistical analysis for the normality distribution of  
residual used to indicate whether the residual of  each 
model violated the assumption of  normality or not. 
The Shapiro-wilk test from table 3 reveal that model 3 and 
1 statistical values were greater than p-level for Terminalia 
radii and only model 3 statistic greater than p-value for 
Tectonia grandis. And the yardstick for shapiro -wilk is that 
statistic value greater than the level of  hypothesis (0.05) 
indicated the acceptance of  null hypothesis and this 
implies that the data are normally distributed while the 

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smaller statistical implies that the normality assumption 
are violated. Model 5 (Byrne and Reed 1986) of  the 
studies gave the lesser value and this inferred that their 

residual was not normally distributed but the Model 
3(Ormerod,1973) of  the both selected study sites were 
normally distributed.

Figure 2: Graphical representation of  Residual analysis for the Heritage Park (Terminalia radii)

Figure 3: Graphical representation of  Residual analysis for the Teak plantation (Tectonia grandis)

Evaluation statistics 
Table 3 showed Goodness of  fit used to examine the 
five tree taper models adopted for the two study sites. 
Those statistics were RMSE (Root Mean Square Error,) 
Ecrit (Critical Error), AIC (Akaike information criterion) 
and BIC (Bayesian information criterion). The smaller 
the statistics are, the better the model. The assessment 
showed that Model 5 gave the superior performance 

while Model 2 (Sharma and Oderwald, 2001) gave worst 
performance which inferred from the fact that Byrne and 
Reed 1986 model (Model 5) gave lowest value of  AIC, 
RMSE, Ecrit and BIC statistics (goodness of  fit)
Moreover, Ormerod,1973 model (model 3) follows Byrne 
and Reed 1986 (Model 5) in terms of  statistics evaluation, 
standard Error and significant level (0.05).

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Table 3: The Evaluation statistics for the two species
Study site Species Model RMSE AIC BIC Ecrit Shapiro
HP Terminalia 

radii
1 139.9 1860.966 1869.917 100.338 3.435^05
2 164.1 1906.754 1912.721 118.179 0.0014
3 5.659 923.418   929.385 2.000 13.000
4 9.223 1070.926 1096.81 6.524 0.107
5 3.917 816.97 825.92 2.810 0.012

TP Tectonia 
grandis

1 132.1 1655.285 1663.91 89.720 8.759^-05
2 143.9 1676.743 1682.493 98.123 0.008
3 4.233 752.803 758.554 2.886 0.799
4 8.305 934.229 954.355 5.551 0.015
5 3.281 687.005 695.631 2.228 3.55^-04

DISCUSSION
Five taper models were adopted for study. Most models 
are bias only model 5 are not biased. The remain models 
(taper functions) used in this study performed poorly. The 
screening test were carried out on all models examining 
residual plots because they were obvious biased. Only 
one model was relatively unbiased (Model 5), and it was 
chosen as the best. The model 2 point is only estimated 
parameter that is very sensitive it was the least among 
others function. According to Sharma and Oderwald, 
2001; it takes a purely parabolic form to depict a tree 
shape if  it is greater than 2, the function predicts the 
diameter at the butt much larger than diameter at breast 
height ‘D’; and if  it is smaller than 2, the function predicts 
the diameter at the butt smaller than diameter at breast 
height ‘D’. the both study site model 2 estimated values 
were greater than 2. So, this finding is accordance with 
Sharma and Oderwald, 2001.
Model 3 by Ormerod (1973) was biased. it may be the 
outcome of  estimated diameters (overestimate) of  all 
stem sizes.
The result of  study by Reed and Byrne (1985), in 
which the same taper function was applied to jack pine, 
contradicts the findings. In Reed and Byrne (1985) 
finding, it was observed that the values of  estimated 
parameter (β1) less than 0.5 while this study estimated it 
as 1.396 for Terminalia Radii (Heritage Park) and 0.965 for 
Teak Plantation.
According to the Reed and Byrne (1985) report when 
β1 estimated value less than 0.5 this implies tree stems 
are cylindrical and when β =1, the resulting tree profile 
is conic and when β is one-half  the resulting tree form 
or shape is parabolic and when β > 1 but less than one-
half; three-fourths (3/4), the tree shape is between a cone 
and a parabola which usually called “paracone”. With 
this observation, the two species could be categories to 
different form, this finding inferred the Terminalia radii 
and Tectonia grandis in the two study sites are “Paraconic” 
and “Conic” respectively.
The Model 5 (Byrne and Reed,1986) was best model 
due to the superior performance towards the goodness 
of  fit and residual analysis. This may be the result of  
transformation process occur from model 3 (Ormerod 

1973) to Model 5. Since both models’ findings closely 
with one another for the two species, two models can 
work interchangeably for predicting of  the tree diameters.

CONCLUSIONS
All taper functions adopted in this study are simple to use 
(single function) and provide a more accurate diameter 
prediction at a specified height.
The results of  the statistical analyses indicated that 
Model 5 (Byrne and Reed, 1986) gave the overall best 
performance in predicting tree diameter at a specified 
height.
Moreso, the study concluded that both Tectonia grandis in 
Teak Plantation and Terminalia radii in Heritage Park are 
not cylindrical in shape(form). So, the two species were 
not susceptible (prone) to windbreak, there should be 
no wind damage record for the two species in the two 
study sites. Ormerod (1973) model could be used for the 
estimation of  tree form (shape) for the two species.
The observed result for this study is significant for 
prediction of  stem diameter at any point (stem taper) 
for T. radii stand as well as T. grandis stand depending 
on various ecological factors, stand size and silvicultural 
management of  the certain forest. 

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