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Journal of Forestry Research (2012) 23(3): 405–411
DOI 10.1007/s11676-012-0277-x
Site index for teak in Colombia
Danny A. Torres • Jorge I. del Valle • Guillermo Restrepo
Received: 2011-04-18; Accepted: 2011-08-29
© Northeast Forestry University and Springer-Verlag Berlin Heidelberg 2012
Abstract: Determination of site quality is a basic tool for proper selec-
tion of locations and species, in management of forest plantations.
Throughout the Caribbean studies of site quality are few and are ham-
pered by statistical limitations, inappropriate growth models, and limited
data. We fitted growth curves for dominant height to evaluate and clas-
sify site quality of teak (Tectona grandis) plantations by using data from
44 permanent sample plots established since 1990 in 3−22 years old teak
plantations in the Colombian Caribbean region. We used Korf ’s and von
Bertalanffy’s models to fit curves as non-linear effects models. Both
models, with a single random parameter, were considered as adequate for
dominant height growth modelling, but Korf’s model was superior. The
resulting curves were anamorphic and closely reflected high variability in
site quality. Five site classes were clarified: at a base age of 12 years old,
teak reached a mean dominant height of 24.8 m on the best sites, 9.8 m in
the worst sites, and in the averages sites, 15.8-18.8 m. Using this model,
we identified the best and the worst sites for teak plantations in the Car-
ibbean region. This model proved a useful tool, not only for site quality
evaluation, but also for improved teak plantation planning and manage-
ment.
Keywords: Tectona grandis; site index; growth modelling; permanent
sample plots; Colombia
Introduction
Forest site quality refers to the sum of factors that affect the
productive capacity of forests. Factors can be classified into three
The online version is available at http://www.springerlink.com
Danny A. Torres
Office National de Forêts International. 2, av. de Saint-Mandé, 75 570
Paris Cedex 12, France. E-mail: danny.torres@onf.fr
Jorge I. del Valle ( )
Universidad Nacional de Colombia sede Medellín, Apartado Aéreo 568,
Medellín, Colombia. E-mail: jidvalle@unal.edu.co
Guillermo Restrepo
Independent consultant, E-mail: grestrepo@une.net.co
Responsible editor: Yu Lei
groups: climatic, biotic, and edaphic (Carmean 1979). Site quality
is defined as the potential production of timber in a particular site
for a particular species or a specified forest type (Clutter et al.
1983). The most commonly used method is direct sampling of the
mean height of dominant trees in a stand, because in even-aged
stands it is little affected by stand density or thinning (Clutter et al.
1983). Site quality correlates closely with timber production in
terms of volume or biomass (Clutter et al. 1983). According to this
method, site index (SI) is defined as a measure of site quality,
based on the mean height of dominant and co-dominant trees of
arbitrarily sampled age classes (Carmean 1979). The curves of SI
that result from classifying and categorizing height growth curves
can be fitted in several ways, but always through height-age
coordinate pairs.
Previous studies used the SI method for determining site qual-
ity in teak (Tectona grandis L.f.) plantations, but most used data
from temporary plots (Nunifu and Murchinson 1999; Henao
1982; Keogh 1981 and 1982; Bermejo et al. 2004). Quite often,
when Permanent Sampling Plots (PSPs) were used, the possible
existence of polymorphism was not corroborated (Vaides et al.
2004; Upadhyay et al. 2005; Jerez-Rico et al. 2011). Most re-
searchers used the guide curve method (or proportional curves
method), which generates anamorphic curves and uses the
non-versatile Schumacher’s model (Nunifu and Murchinson
1999; Henao 1982; Keogh 1982; Bermejo et al. 2004; Vaides et
al. 2004; Jerez-Rico et al. 2011). Although this method has re-
ceived little attention, it is important because the presence of
polymorphic patterns can indicate two things. First, the height
growth of a species is sensitive to silvicultural treatments. Sec-
ond, silvicultural treatments are often continued after trees have
reached heights where the treatments no longer have an impact.
Therefore, one species may show both patterns of growth.
Upadhyay et al. (2005) used both the guide curve and the differ-
ence equation method with PSPs to develop site index curves in
teak plantations in India using the Hossfeld IV growth model.
They found the polymorphic difference equation method to be
superior. From research on teak management regimes, it can be
inferred that growth in height is independent of stand density. A
15 year stand of teak in Nigeria received three treatments: un-
thinned (2,200 trees⋅ha-1), thinned to 760 trees⋅ha-1, and
thinned to 395 trees⋅ha-1 (Lowe 1976). When the stand was 20
ORIGINAL PAPER
Journal of Forestry Research (2012) 23(3): 405–411
406
years old, the fastest tree growth was unrelated to the treatments.
Vincent et al. (2000) carried out a thinning experiment in Barinas,
Venezuela. In a 13-year-old teak plantation, they established
several spacing regimes from 2 m × 2 m to 4 m × 4 m. At 18.7
years, there was no relationship between dominant tree height
and thinning regime. Jerez-Rico et al. (2011), working in the
western plains of Venezuela, examined data from permanent and
temporary plots of teak that included more than 30 years of
measurements. Initial spacing varied from 2 m × 2 m to 4 m × 4
m, and density at sampling ranged from 200 to 2,400 trees⋅ha-1.
They found that dominant height was little affected by tree den-
sity. On the Peninsula of Nicoya, Costa Rica, Chaves et al.
(2003) established a thinning experiment in a seven year old teak
plantation with the following treatments: 15 m2⋅ha-1, 17
m2⋅ha-1, 19 m2⋅ha-1, 21 m2⋅ha-1, and 25 m2⋅ha-1. The experi-
ment continued until trees reached 20 years in age. Growth in the
dominant tree height was not affected by treatments. Jerez-Rico
et al. (2011) used mixed models to study the growth of teak.
The first approaches in Colombia for studying the growth of
teak were from Echeverri (1968) and Rodríguez (1968), but they
did not attempt to develop site index curves. Henao (1982), in a
plantation of the Department of Córdoba and on the basis of
average tree height from temporary sample plots, found no sig-
nificant quality differences between sites. A recent and continu-
ing study of SI is the site classification chart for the Caribbean,
Central America, Venezuela, and Colombia (Keogh 1982). In our
study, the data for Colombia were taken from the Venegas report
in 1977 “Reply to teak questionnaire”, performed by the FAO
COL/74/005 Project. In recent decades, various timber compa-
nies planted teak not only in Colombia but also in other Carib-
bean countries. However, the foresters from the Caribbean use
few teak site index studies to properly manage this species. In
Colombia, we used the result of Keogh (1982) that was based on
limited data and used outdated methods. Our study aims to use
modern statistical techniques and widely accepted growth mod-
els to develop a family of site index curves for teak from the
Colombian Caribbean. Our results are applicable to all Caribbean
teak plantations.
Materials and methods
Study area
In Colombia, and particularly in the Córdoba Department, Co-
lombian Caribbean region, teak has been planted for over 70
years (Rodríguez 1968; Echeverri 1968; Keogh 1981). According
to the Holdridge (1982) classification scheme, the area falls un-
der the lowlands monsoonal association of the humid tropical
forest life zone. The rainfall regime is unimodal and at the most
representative weather station (IGAC 1978) averages 2,479
mm/yr. Approximately, 30% of rain falls between August and
September and less than 60 mm per month falls during January
and February. The annual mean temperature is 27°C, with daily
amplitude of 10°C. Relative humidity varies from 75% to 84%.
All teak plantations are on colluvial-alluvial soils with flu-
vial-lacustrine deposits used for livestock grazing before the
plantations were established (IGAC 1989).
Data source
In 1990, 20 Permanent Sampling Plots (PSPs) were established in
the teak plantations of the Córdoba Department, and the number
of PSPs was increased in subsequent years (Fig. 1). The age of the
PSPs ranged from 3 to 22 years. In 2011, there were 44 PSPs. The
PSPs had two plot sizes. The plot size of 23 PSPs was 600 m2 (i.e.:
30 m × 20 m) and the plot size of the remaining 21 PSPs was
1,000 m2 (i.e.: 40 m × 25 m). Diameters at breast height (1.3 m
above ground) and dominant height (mean tree height of the 100
tallest trees per hectare) were measured annually. Dominant
height was used as an indicator variable for site quality.
Fig. 1 Study area. The dots show the location of the permanent plots.
All the PSPs were subjected to the same management regime.
The plantation stocking density was 1,600 seedlings⋅ha-1 (i.e., a
spacing of 2.5 m × 2.5 m), manual weeding was carried out three
times during the first two years and once each year in subsequent
Journal of Forestry Research (2012) 23(3): 405–411
407
years until the end of the rotation. Pruning was carried out in
years five and nine. Basal area was maintained close to 26
m²⋅ha-1 by two thinnings between years 7−9 and 12−13.
Modelling
In order to fit mean dominant height growth functions, two mod-
els used in silviculture were evaluated: von Bertalanffy (or
Chapman-Richards’s, Eq. 1), and Korf (Eq. 2) (Kiviste et al.
2002).
()
[]
2
1
exp1
β
β
tAHd −−= (1)
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛−= 2
1
exp
β
β
t
AHd (2)
where, Hd is the dominant height (m), A is the asymptote (m) or
maximum value reached by Hd, β1 and β2 are the unknown pa-
rameters, t is the age (year) corresponding to each Hd, and exp() is
the exponential operator (Euler’s constant).
As all data were collected in PSPs, this is a typical case of re-
peated measures over time (or longitudinal data) without inde-
pendence among intra-plot measurements. Therefore, there can be
serious problems in autocorrelation of errors, when the parameters
are estimated by conventional least squares methods (linear or
non-linear). Besides the problem of autocorrelation, growth and
yield data from permanent plots usually exhibit heteroscedasticity
(Gregoire 1987).
A non-linear mixed-effect model was used to derive reliable
estimators of the growth model parameters. It enabled modelling
of the intra-individual covariance structure, assuming that (usu-
ally one or two) individual-independent, small-dimension latent
random-effects vectors existed in the model (SAS 1999). To apply
this method, a re-parameterization of models (Eq. 1 and Eq. 2)
was made (Fang and Bailey 2001), by changing the value of the
asymptote A by an unknown parameter β1. The value of β1 cor-
responds to the expected value of Hd when t = t0. Then Eq. 1 and
Eq. 2 can be represented in the following way:
()
()
3
02
2
1exp1
exp1
β
β
β
β
⎥
⎦
⎤
⎢
⎣
⎡
−−
−−
=t
t
dH (3)
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛−= 33
0
21
11
exp
ββ
ββ
t
t
dH (4)
Where, β1 = φ + b, unknown parameter corresponding to the SI
value for a base age of t0 = 12 years. A mixed parameter is con-
sidered fixed for both models (i.e., it has a fixed (φ) and a random
(b) part), and β2 and β3 are unknown parameters.
Using this model, polymorphic and anamorphic growth curves
can be obtained. Several authors (Cieszewski and Bella 1989;
Cieszewski and Bailey 2000; Fang and Bailey 2001) examined
the properties of these models. Eq. 3 and Eq. 4 are fitted follow-
ing a single random effect in the β1 parameter, and each model is
evaluated considering three variance structures: constant vari-
ance, variance as a potential function of the mean, and variance
as an exponential function of the mean, for a total of six models.
Each model is evaluated in terms of the statistical significance of
the parameters, and is compared through both the Akaike infor-
mation criterion (AIC) and the Bayes information criterion (BIC).
The selected model undergoes a diagnostic of residuals, as pro-
posed by Fang and Bailey (2001). This modelling phase was
performed using the NLM Procedure in SAS System for Win-
dows V. 8 (SAS 1999).
Site classes
After selecting the best model, we estimated the SI for the average
site (random parameter = 0). We then identified sites above or
below the average by considering the variation of the random
parameter. We then ranked sites according to the intervals of four
standard deviations (± 2 standard deviations around the average
site).
To place each plot in its corresponding site class, the SI for
each plot measurement was estimated (by isolating the β1 pa-
rameter of the selected model) and the value was placed in the
corresponding category. This procedure is also useful to evaluate
the goodness of fit, because all of the measurements from the
same plot should be placed in the same site class. Another way in
which site classes can be assigned is by plotting on a coordinate
diagram the curves that outline each site class, and then plotting
the estimations of Hd for each plot.
Results
Exploratory analysis of the database
Scatter plots of the dominant height for some of the PSPs are
depicted in Fig. 2. Not all 44 PSPs are shown in Fig. 2, because
many PSPs overlapped, and it was difficult to correctly interpret
the scattering. However, the scatter plots show high variability in
the growth of teak in the study area, reaching dominant heights at
16 years ranging from 11−27 m. It is important to highlight the
heteroscedastic nature of the scattered plots in Fig. 2 because
variability increased with age. In most but not all cases, domi-
nant trees sampled in successive sampling periods were the same.
Therefore, there was temporal autocorrelation in the series of
dominant height, another problem for the regression analysis.
Modelling
The parameters of Eq. 3 and 4, evaluated on each one of the
variance structures, were statistically significant with a confi-
dence level of 95% (Table 1). The values of the two selection
criteria for each model are shown in Table 1 under the three
Journal of Forestry Research (2012) 23(3): 405–411
408
variance structures.
0
5
10
15
20
25
30
0 3 6 9 12 15 18 21
Age (a)
Dominant mean height (m)
Fig. 2 Mean dominant height versus age for 14 out of 20 PSPs
measured nine or more times. Points with equal shape belong to the
same plot
Though all of the models were statistically acceptable, the
models with variance as an exponential function of the mean were
better (3.3 and 4.3). Of two values, Korf’s model (4.3) was the
most appropriate, because its Bayesian’s criterion was slightly
lower than for von Bertalanffy’s model (Table 1) with the vari-
ance of Hd as an exponential function of its mean, and a base age
of 12 years (Eq. 5). There were no evident autocorrelation (Fig. 3),
heteroscedasticity, or lack of fitness problems in relation to ob-
servation order (observation number or the predicted values). The
lack of outliers in Fig. 3 suggests a normal error distribution. The
statistical results show that the non-linear mixed-effect model
corrected the residual problems inherent in longitudinal data. It
should be noted that von Bertalanffy’s model also shows similar
characteristics of residuals (Fig. 3)
⎥
⎦
⎤
⎢
⎣
⎡⎟
⎠
⎞
⎜
⎝
⎛−−= 65,065,0 12
11
96.1exp28.17 t
dH (5)
-3
-2
-1
0
1
2
3
0 50 100 150 200 25
0
Residuals
-3
-2
-1
0
1
2
3
5 101520253
0
Berrtalanfy model 3.3
-3
-2
-1
0
1
2
3
0 50 100 150 200 25
0
Observation oder
-3
-2
-1
0
1
2
3
5 101520253
0
Hd est.
Fig. 3 Residuals of the dominant height (Hd) as a function of both, observation order and estimated value (Hd est.)
Table 1. Results of the information criteria: Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC)a.
3 (von Bertalanffy) 4 (Korf)
Model 3.1 3.2 3.3 4.1 4.2 4.3
Variance structure Constant Potential Exponential Constant Potential Exponential
AIC* 586.5 583.4 579.1 578.5 575.2 570.7
BIC* 591.2 588.1 583.8 583.3 579.9 475.4
a The lower the value, the better the model. von Bertalanffy’s and Korf’s growth models were similar and statistically acceptable. Korf’s model (4.3) was
the most appropriate because it achieved the minimum Bayesian criteria.
Eq. 4 can be also written with site SI as a dependent variable of
age (t) and Hd. This is accomplished by isolating the parameter β1,
which, as mentioned above, corresponds to SI at base age of 12
years, and by replacing the values of the other parameters pre-
sented on Eq. 5. In this way, Eq. 6 can be obtained.
Journal of Forestry Research (2012) 23(3): 405–411
409
⎥
⎦
⎤
⎢
⎣
⎡⎟
⎠
⎞
⎜
⎝
⎛−−
=
65.065.0 12
11
96.1exp t
Hd
SI (6)
Site index classes
When intervals of ±2 standard deviations are considered around
the average site, five intervals are needed to cover the complete
range of Hd. SI limits for each category are shown in Table 2 and
the corresponding SI curves are shown in Fig. 4. There was great
variability in the site indexes. For trees twelve years old, the site
index curves covered plantations from approximately 9.8 m up to
24.7 m of dominant height.
Table 2． Limiting values for site index classes for teak in Colombia
separated by intervals of ±2 standard deviations around the average
site
SI
Site index
classes Lower limit (m) Upper limit (m) Number of PSPs
I 21.7677 24.7617 4
II 18.7737 21.7677 12
III 15.7797 18.7737 17
IV 12.7857 15.7797 8
V 9.7917 12.7857 3
Fig. 4 Site index curves for teak (12 years base age). Dotted lines are
the SI curves and continuous lines are limits of each SI classes (I to V)
Discussion
Estimated values of SI were similar for different ages of the same
PSP. Fig. 2 and Fig. 4 show high variability of SIs. Dominant
height followed an anamorphic curve, and this was confirmed by
the satisfactory fit of this kind of model. As discussed in the
introduction, there is abundant evidence that height increase in
teak is poorly related with stand density. This result differed from
the findings of Fang and Bailey (2001), who researched slash pine,
and considered all parameters as mixed due to the high variability
of silvicultural treatments. They found height increments that fit
polymorphic curves. In our study, only a random parameter was
necessary due to the anamorphic nature of the curves.
Height growth of the dominant teak trees was well represented
by Korf’s model as modified (Fang and Bailey 2001). Moreover,
this model eliminated the incompatibility problem between tree
height growth and SI described by Curtis et al. (1973). Another
advantage of the model is that it does not vary with changes in
base age (Bailey and Clutter 1974). This means that the SI pre-
dicted by the model is independent of the reference age (Fang and
Bailey 2001).
In our plantations, 39% of the PSPs were categorized as the
average site class III. The proportion of PSPs with SI classes
above the average (Classes I and II) was 35%, while 26% of PSPs
were below the average site class (Classes IV and V). The shape
of SI curves resembled those of Henao (1982) (Fig. 5a). In the
value range, they resemble more those of Keogh (1982) (Fig. 5b).
This last result is interesting, because in the Colombian Caribbean
all of the SI classes reported by Keogh (1982) for Central America,
the Caribbean, Venezuela, and Colombia were represented. The
site ranges, presented by Miller (1969) for Trinidad, by Bermejo
et al. (2004) and Pérez and Kanninen (2005) for Costa Rica, by
Jerez-Rico et al. (2011) for Venezuela and by Vaides et al. (2004)
for Guatemala, also fell within the SI curves developed in this
study. However, top height in Ghana at 12 years varied between 8
m on the poorest sites and 15 m on the best sites (Nunifu and
Murchinson 1999), figures substantially lower than in the Carib-
bean.
Both Henao (1982) and Keogh (1982) in Colombia used
Schumacher’s model (Schumacher 1939), which is a simplifica-
tion of Korf’s model (Eq. 2) because the β2 exponent of t is equal
to one. This simplification reduces the versatility of Korf’s model,
compelling the function to reach a change in concavity (Point of
inflexion in t = β1/2, and Hd = 0.135A) at exactly 13.5% of the
asymptotic value without relation with the recognized explosive
initial height growth of teak. This is why the work of Henao and
Keogh underestimated the initial growth and the SI of teak (Fig.
5a and 5b).
Upadhyay et al. (2005) used the Hosfeldt IV model (Kiviste et
al. 2002) for top height SI curves at 25 years base age for teak in
India according to 150 PSPs established in all teak plantations in
the country, representing the top height from 4 to 93 years. Similar
sites were estimated by these curves at their base age, an approach
different to that used in this study. At 25 years the poorest sites
were the same as in our study (Hd = 11 m) and the best sites were
similar (29 m in our study versus 28 m in the Indian study).
However, the slope of SI curves in our study began higher and
then declined, while the SI curves of the Indian study maintain a
more stable slope. Both mean SI curves intersected at t ≈32
years. Therefore, after this year the Indian SI curves predicted
higher top height than dominant height as found in our study. The
opposite occurred before 32 years of age (Fig. 6). In spite of the
large database in the Indian study, they did not measure, but rather
estimated the top height of the trees by using an allometric rela-
tionship between the quadratic mean diameter of ten trees with
larger diameter per plot versus the average height of these trees
(Upadhyay et al. 2005). Because trees with the largest diameter
0
5
10
15
20
25
30
0 5 10 15 20 25
Age (a)
Hd (m)
Journal of Forestry Research (2012) 23(3): 405–411
410
are not necessarily the tallest, this procedure tends to overestimate
the top height of the older trees with larger diameters. This is due
to the fact that old trees continue growing in diameter but do not
necessarily grow more in height. The same pattern results when SI
curves of Upadhyay et al. (2005) are compared with many of the
published teak SI curves (Miller 1969; Henao 1982; Keogh 1982;
Malende and Temu 1990; Nunifu and Murchison 1999; Bermejo
et al. 2004; Mora and Meza 2004; Pérez and Kanninen 2005;
Jerez-Rico et al. 2011).
(a)
0
5
10
15
20
25
30
35
0 5 10 15 20 25
Age (a)
Dominant mean height (m)
(b)
0
5
10
15
20
25
30
35
0 5 10 15 20 25
Age (a)
Dominant mean height (m)
Fig. 5 Comparison of SI curves in the study (solid lines) with (a)
Henao (1982) and (b) Keogh (1980) SI curves (dotted lines)
0
5
10
15
20
25
0 5 10 15 20 25 30 35 4 0 45 50
Age (a)
Dominant & top Height (m)
Ind ia ( Top Heig ht)
Colombia (Dominant Height)
Fig. 6 Comparison between the mean SI curve in t the study (thick
dark line) and Upadhyay et al. (2005) mean SI curve (thin clear line)
Growth of dominant tree height for teak in Colombia reflects
site quality. The array of sites yields an anamorphic system of
curves, allowing site classification for this species. In the Co-
lombian Caribbean region, most previously reported ranges of SI
for teak throughout the tropics are represented.
Potential users of this study for the site index classes of a teak
plantation must use the same criterion for dominant height as
used in this research for modelling SI curves. In this way, with
the knowledge of the dominant height (i.e. the mean height of
100 tallest trees per hectare (Hd) or its estimation through per-
manent or temporary sample plots) and the corresponding age,
the coordinate pair (Hd, age) can be plotted as in Fig. 4. Thus,
the site class to which the measures correspond can be identified.
In order to calculate the SI, that is, the exact value of Hd ex-
pected at 12 years, Eq. 6 must be used. This value can be catego-
rized afterwards, when confronted with the limit values of each
SI class presented in Table 2.
Acknowledgement
We thank the following institutions: Reforestadora del Caribe
S.A and the DIME (Research Direction of the National Univer-
sity of Colombia, Medellin Branch) for providing the funds for
this project. We are also grateful to two anonymous referees
whose comments have improved our paper.
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