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Determination of site quality is a basic tool for proper selection of locations and species, in management of forest plantations. Throughout the Caribbean studies of site quality are few and are hampered by statistical limitations, inappropriate growth models, and limited data. We fitted growth curves for dominant height to evaluate and classify 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 Caribbean region. This model proved a useful tool, not only for site quality evaluation, but also for improved teak plantation planning and management.
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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 322 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 treesha-1), thinned to 760 treesha-1, and
thinned to 395 treesha-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 treesha-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 m2ha-1, 17
m2ha-1, 19 m2ha-1, 21 m2ha-1, and 25 m2ha-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 seedlingsha-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
ha-1 by two thinnings between years 79 and 1213.
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 1127 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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... Height growth modeling of teak in tropical America has predominantly used traditional methods such as guide curve or algebraic difference approach, least squares or nonlinear mixed-effects estimation methods, and Schumacher-, Korf-, Hossfeld-or Bertalanffy-Richards-type equations (Keogh 1982;Bermejo et al 2004;Torres et al 2012). For a provisional teak site classification, least squares methods were used to estimate a Schumacher-type height model with 144 observations of top height, dominant height and dominant-codominant height from 13 Latin American and Caribbean countries (Keogh 1982). ...
... The Hossfeld-type equation was considered the best and used to draw height curves for three site indices (23, 21, and 19 m at a base age of 10 years) representing best, average, and worst site qualities, respectively (Bermejo et al 2004). Torres et al (2012) used Bertalanffy-Richards-and Korf-type equations to model teak height growth with repeated measurements from 44 PSPs in the Atlantic Coastal Plain region of Colombia. Nonlinear mixed-effects models specified with a single random effect and alternative variance structures (constant, power and exponential function of the mean) were fitted, and site quality classes were identified based on deviations from the average site. ...
... The Korf-type equation was the best model based on statistical performance. Five site index classes, using a base age of 12 years, were depicted, with site index of about 23 m for the highest quality site (Torres et al 2012). ...
Article
Teak (Tectona grandis L.f.) plantations are increasingly being established in tropical regions to meet a rising demand for its highly valued timber. Teak plantations have been established in the Atlantic Coastal Plain region of Colombia, a region climatically suitable for teak growth by having a monsoon climate with a unimodal precipitation pattern. Tree diameter at breast height (DBH, 1.3 m above ground) and mean top height, periodically measured over a 17-year period in 44 permanent sampling plots of size 0.06 and 0.10 ha, were used in this study. A stochastic differential equation (SDE), along with a Bertalanffy–Richards-type height growth model, was used to model and estimate top height growth of teak plantations in Colombia. Environmental noise and height measurement errors were explicitly considered as the main uncertainty sources of mean top height growth. The best model for estimating mean top height, based on statistical performance and biological rationale, had the asymptote defined as a local parameter and the growth rate and shape specified as global parameters. This model outperformed its counterpart that had the growth rate specified as a local parameter and asymptote and shape as global parameters. The selected model also outperformed alternative approaches such as the mixed-effects model, generalized algebraic difference approach, and the dummy variable method. Estimated trajectories for the mean top height of teak in Colombia are biologically sound based on the measured height series and previous studies in Latin America. Results suggest that most of the uncertainty associated with the mean top height growth of teak plantations in Colombia was largely explained by environmental noise. The best estimated model using the SDE approach can be useful for predicting height growth and evaluating site productivity of teak plantations in Colombia and in neighbouring countries with biophysical characteristics similar to those where teak has been planted in Colombia.
... with α, β, y > 0. In [23] the Korf growth function is used for the assessment of current and mean annual increments of Douglas-fir compared to other tree species (see also [37]). Moreover, in [27] it is used for the construction of domestic yield tables, whereas Torres et al. [33] used Korf and von Bertalanffy models to fit curves as non-linear effects models, showing that Korf model was superior. On the ground of the above mentioned investigations, in this paper we aim to propose a new growth model which cannot be obtained as a special case of the models (3), (6) and (7). ...
... Furthermore, by virtue of (28), the mean E y (t) is identical to the curve N (t) given in (13). Hence, due to (36), from (37) one hasλ −μ = α/β, withλ andμ defined in (33). From the results shown in Table 4, E y (t) is strictly increasing, and clearly it tends to the carrying capacity, i.e. lim t→∞ E y (t) = ye α/β ≡ C. ...
Article
We propose a new deterministic growth model which captures certain features of both the Gompertz and Korf laws. We investigate its main properties, with special attention to the correction factor, the relative growth rate, the inflection point, the maximum specific growth rate, the lag time and the threshold crossing problem. Some data analytic examples and their performance are also considered. Furthermore, we study a stochastic counterpart of the proposed model, that is a linear time-inhomogeneous birth-death process whose mean behaves as the deterministic one. We obtain the transition probabilities, the moments and the population ultimate extinction probability for this process. We finally treat the special case of a simple birth process, which better mimics the proposed growth model.
... : h 100 = altura dominante; exp = exponencial; e t = idade.Como o índice de sítio, determinado por meio da altura dominante (h 100 ) em função da idade (t) em uma determinada idade de referência, é uma ferramenta básica para a seleção de locais e de espécies no manejo de plantios florestais(TORRES et al., 2012),Conceição et al. (2012) concluíram que a expressão (4) foi apropriada para plantios de Tectona grandis no estado do Pará.Sajjaduzzaman et al. (2005) estabeleceram que a equação (5) foi satisfatória para a espécie em Bangladesh, eTorres et al. (2012) verificaram que o ajuste da equação (6) foi efetivo para a cultura de Tectona grandis na Colômbia. ...
... : h 100 = altura dominante; exp = exponencial; e t = idade.Como o índice de sítio, determinado por meio da altura dominante (h 100 ) em função da idade (t) em uma determinada idade de referência, é uma ferramenta básica para a seleção de locais e de espécies no manejo de plantios florestais(TORRES et al., 2012),Conceição et al. (2012) concluíram que a expressão (4) foi apropriada para plantios de Tectona grandis no estado do Pará.Sajjaduzzaman et al. (2005) estabeleceram que a equação (5) foi satisfatória para a espécie em Bangladesh, eTorres et al. (2012) verificaram que o ajuste da equação (6) foi efetivo para a cultura de Tectona grandis na Colômbia. ...
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RESUMO: Considerando a crescente necessidade por informações detalhadas que visem orientar o manejo dos povoamentos homogêneos de Tectona grandis, o presente trabalho teve como objetivo determinar e avaliar a capacidade produtiva do sítio florestal em povoamentos jovens de da espécie de duas regiões do estado de Mato Grosso, Brasil. Dessa forma, foram utilizados dados de povoamentos homogêneos com até 11 anos de idade localizados nos municípios de Santo Antônio do Leverger e Brasnorte. Assim, a equação gerada pelo modelo monomolecular descreveu de forma adequada e eficiente o comportamento da variável altura dominante para a determinação da capacidade produtiva do sítio, cujo desenvolvimento da Tectona grandis foi maior no estado de Mato Grosso, quando é comparada com regiões da África e da Ásia, além de ser semelhante às localidades das Américas Central e do Sul. Isso demonstrou a importância da cultura para o fornecimento de matéria-prima nobre no setor florestal brasileiro e para o atendimento das demandas internacionais, bem como para a redução da pressão antrópica sobre as formações florestais naturais.  PALAVRAS-CHAVE: Teca; índice de sítio; altura dominante; modelo monomolecular.
... Results demonstrated comparatively lower productivity (timber volume, biomass, and carbon) in impoverished sites. Numerous studies on the significance of site quality in growth of hardwood species such as clonal teak have concurred that the determination of site quality based on tree performance has proved to be more reliable than the biophysical attributes, such as soil fertility, altitude and slope (Torres et al. 2012;Manson et al. 2013;Sadono 2017). Moreover, the responses of trees on specific site condition will vary depending on its adaptability (King et al. 2013;Binkley et al. 2017). ...
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Clonal teak plantation has been extensively developed in Java and providing a purposeful contribution to improve the productivity of the state forests. It also plays a crucial role in climate change mitigation and serves as a primary source of renewable energy. However, information about its stand dynamics has been rarely documented. This study investigated the growth, biomass, carbon stock, and energy storage along an age series of clonal teak plantation. The study site was located in the Kendal Forest Management Unit. Data were collected from 14 different compartments as the priority sites of clonal teak establishment. Every compartment had similar site quality but different in age stand. Results demonstrated that the incremental rate of diameter and height was higher during the initial period between 1 and 3 years. The mean volume increased along with age and reached its maximum value at 14 years (164.54 m3 ha�1 ). Biomass distribution in each tree component varied from 8.75 to 66.72%. More than 80% biomass production was accumulated above ground. Total carbon stock improved from 2.68 Mg ha�1 at 1 year to 54.01 Mg ha�1 at 14 years. Our study noted that the total energy storage in clonal teak plantation increased progressively from 22.71 106 MJ ha�1 at 1 year to 377.74 106 MJ ha�1 at 14 years. Overall, this study concluded the growth, biomass, carbon, and energy in clonal teak increased progressively with age. Further investigations are still required to understand the stand dynamics of clonal teak at different sites.
... Even though T. grandis has been shown to grow well outside of Panama (Upadhyay et al. 2005) and parts of Panama where soil fertility is high (Kraenzel et al. 2003;Bermejo et al. 2004), our work shows that T. grandis underperforms in low fertility sites on clay soils (also see Lugo 1997), which are representative of much of Central Panama. When compared to site index curves, the T. grandis in this study fits into Class IV (of five classes) based on work from Puerto Rico, Venezuela, and Colombia (Keogh 1982;Friday 1987;Torres et al. 2012). By tree and stand volume estimates, T. grandis in this study also underperforms compared to T. grandis from another study conducted in the Panama Canal Watershed (Stefanski et al. 2015). ...
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Finding suitable tree species that not only grow well on nutrient poor soils but are also safe financial investments is one of the major obstacles to successful reforestation efforts in the tropics. Our study compared the financial viability and growth of valuable timber species in monocultures and mixtures on infertile soils. Our work shows the extraordinary growth in volume and value of Dalbergia retusa and Terminalia amazonia while underscoring the poor financial viability of Tectona grandis and Pachira quinata , all commonly planted timber species in Panama and much of Central and South America. Using Bayesian statistics, our predictions show that T. amazonia monocultures could reach nearly 200 m ³ ha ⁻¹ of merchantable volume after 30 years compared to the ~ 40 m ³ ha ⁻¹ that T. grandis could accumulate in the same time frame. While D. retusa monocultures did not have the highest predicted merchantable volumes of all the species, it did have the highest predicted net present value (NPV), with a predicted mean NPV of > US$97,000 ha ⁻¹ , quadrupling the species with the next highest monoculture’s NPV, T. amazonia monocultures (~ US$20,000 ha ⁻¹ ). Our work emphasizes that reforestation can be financially viable on low nutrient soils, even in the absence of fertilization or other silvicultural manipulations, if species selection and site are carefully considered and matched.
... Autores como Corona et al. (1999), Torres Del Valle et al. (2012, Akindele 1991y Minoche et al., (2017 apuntan que mediante el índice de sitio es posible clasificar la productividad, lo que permite una estimación más precisa del volumen esperable, y con ello optimizar la planificación y la prescripción de actividades para un deseado manejo silvicultural de la masa. ...
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(Introducción): Es necesario cuantificar y predecir con confiabilidad el volumen de madera para facilitar la gestión de la producción forestal. (Objetivo): Elaborar tablas de volumen comercial a partir de la selección de modelos matemáticos en distintas calidades de sitio, para plantaciones clonales de Tectona grandis L.f. (Metodología): Se evaluaron 3 calidades de sitio, según el índice de sitio (IS) 27, 24 y 21, respectivamente. A 263 árboles en pie (119 árboles para el IS27, 119 para el IS24 y 28 para el IS21) se les midió el diámetro al tocón y a 1.3 m sobre el nivel del suelo. Posteriormente, cada 1.5 m, hasta completar la altura total. El volumen del árbol se obtuvo mediante la sumatoria de cada sección cubicada con la fórmula de Smalian. Para cada índice de sitio, se ajustaron modelos por el método de mínimos cuadrados ordinarios con el paquete estadístico Statgraphics Centurion XVI. Se verificó el cumplimiento de los supuestos de autocorrelación de los residuos mediante la prueba de Durbin-Watson. La selección del modelo se hizo a partir de la sumatoria basada en la normalización de los parámetros estadísticos evaluados. (Resultados) Los modelos seleccionados tuvieron buenos ajustes (R²≥ 94 %), bajos errores de estimación (≤ 3 %), muy prácticos por usar solo el diámetro normal (DAP) como variable predictora. (Conclusiones): Junto con la tabla de volumen comercial construida, los modelos son una herramienta útil para cuantificar, de forma rápida y precisa, el volumen comercial con corteza de teca clonal hasta 15 cm de diámetro mínimo.
... De maneira geral, os valores médios de altura dominante foram superiores aos obtidos em povoamentos de Teca na Índia (UPADHYAY et al., 2005) e na Colômbia (TORRES et al., 2012), para os piores sítios. Aos 25 anos os sítios mais pobres apresentaram altura de 11,0 m em ambos os estudos, em relação aos 19,8 m obtido no presente estudo. ...
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The knowledge of the site is necessary to understand the production and forest management. The objective of this study was to determine the productive capacity of Teak in southwestern Mato Grosso State, through the analysis of site index curves, to forest harvesting. The data were collected in permanent plots and the stem analysis of 32 dominant trees of two stands, 33 and 34 years old. Eight site index models were adjusted and the selection criteria followed the lowest standard deviation, the highest adjusted coefficient of determination, F test value and the absence of trends in the graphical analysis of the residuals. The site index curves were prepared by the method of the guide curve. Soil samples were collected for physical analysis and macronutrients. The model presented by Hoerl had the best fit and it was found that the database follows an anamorphic pattern, thus, the growing trend is the same between the curves. Four site index curves were generated in an age-index of 30 years and three productivity classes of Teak were established. The soil characteristics of the region are favorable to the cultivation of Teak and the curves illustrate the productive potential for the species.
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(Introducción): Se presenta un nuevo sistema de clasificación de sitios para Tectona grandis L.F. basado en información recolectada durante más de 30 años de investigación, con el fin de contribuir al manejo silvicultural de una de las especies más importantes en Costa Rica. (Objetivo): Construir curvas actualizadas de índice de sitio para plantaciones de teca. (Metodología): Los datos provienen del análisis fustal de 55 de árboles dominantes con edades entre 6 y 40 años, a la edad de corte, seleccionados en diferentes localidades de la Vertiente del Pacífico. Estos fueron combinados con mediciones de altura dominante provenientes de 38 parcelas permanentes medidas entre los 10 y 32 años que eran parte de 6 ensayos formales de crecimiento y rendimiento. Se definieron modelos de crecimiento, ajustados por regresión no lineal de efectos mixtos, considerando que se trata de mediciones repetidas anualmente. Se trabajó con seis modelos matemáticos: Richards, Gompertz, Logístico, Korf, Mitscherlich y Weibull. Previo al ajuste, los modelos fueron reparametrizados en función de la altura dominante observada (S), a la edad base de 16 años, asociándola a un efecto aleatorio. El mejor modelo se escogió de acuerdo con criterios de información y estadísticos de bondad de ajuste. (Resultados): Los criterios de información de Akaike y Bayesiano indican que el modelo de Korf fue superior a los demás, tanto en su variante anamórfica como polimórfica; los estadísticos bondad de ajuste confirmaron esta apreciación. El análisis de los residuos mostró un mejor ajuste para este modelo al proyectar el crecimiento en altura dominante con la edad. Aunque el modelo polimórfico fue superior, la tendencia observada parece descartar la existencia de una asíntota común para las plantaciones de teca creciendo en las diferentes calidades de sitio. (Conclusiones): Los resultados mostraron que los datos de análisis fustal y de parcelas permanentes presentan patrones similares, los cuales son representados adecuadamente por el modelo de Korf.
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Teak is an important forest plantation species in Lao PDR (Laos), that has been planted extensively by smallholders, supplying domestic industries and international markets. There have been significant advances in the intensive silvicultural management of teak focused on the production of high-quality timber. Laos is not an exception. With support from the Australian Centre for International Agricultural Research, there have been advances in the understanding and knowledge of appropriate management practices for smallholder teak, as well as development of supporting technologies (i.e. ex situ conservation, genetic improvement, growth models, thinning and pruning prescriptions, and agroforestry systems). This paper summarises published information on the silviculture and management of teak, including improvement of genetic resources, stocking rate, thinning and agroforestry systems used in Asia, Africa, Latin America and Oceania, and relates this to the current situation in northern Laos. The challenge is to now transfer this knowledge to the teak smallholders, professionals, educators and policy decision makers of Laos.
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Although Mato Grosso has the largest planted planted with Tectona grandis in Brazil, there is still a lack of studies involving local effects on growth and production, as well as techniques for monitoring and analyzing these effects. Thus, research aimed at the productive potential of the species in different regions of Mato Grosso are basic information that contribute to the forest management of the species. The objective of this work was to evaluate the growth of teak in different locations in the state of Mato Grosso; verify the accuracy of data from trunk analysis (ANATRO) to estimate tree height; evaluate the thickness and content of tree bark; and to test artificial intelligence modeling for volumetric prediction of teak. Six stands were evaluated in different municipalities, and the database was from ANATRO. For the estimation of growth at dominant height, nonlinear regression models were used; the accuracy of height estimation by ANATRO was performed comparing its heights, with data observed in the field at the level of individual trees in one of the stands under study; the thickness of the bark was estimated using different adjustment strategies applying a polynomial and a simple linear model, both with fixed and random effects and for the volumetric prediction of teak trees, the Schumacher-Hall regression model and artificial neural networks were used. The quality of estimates and predictions was assessed through statistics and graphical analyzes. It was observed that teak presents different growing trends in dominant height at each site. The ANATRO technique overestimates tree heights at ages below four years. The polynomial model can be used to estimate the thickness of the bark of teak trees. The bark thickness is influenced by age and should be inserted into the modeling process. Teak bark content may represent 15% of the total volume in trees with smaller diameters (<10 cm). Artificial neural networks are efficient for the estimation and volumetric prediction of Tectona grandis trees.
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Site index curves serve to classify lands in function of their productive capacity for a forest species. In this study, linear and non-linear models were used to develop site index curves for teak (Tectona grandis L. F.) in the western plains of Venezuela using data from permanent and temporary plots that cover more than 30 years of measurement. The Schumacher model, in its linear and non-linear forms, was fit using variants of fixed and mixed effects. The analysis of the results showed better fit of the non-linear mixed models than of the other models in terms of bias and precision, suggesting the convenience of using models that consider repeated measurements in the same plot. The site index curves generated show the dominant height growth variability of this species in Venezuela in the areas that are appropriate for its establishment under traditional management.
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Site index curves serve to classify lands in function of their productive capacity for a forest species. In this study, linear and non–linear models were used to develop site index curves for teak (Tectona grandis L. F.) in the western plains of Venezuela using data from permanent and temporary plots that cover more than 30 years of measurement. The Schumacher model, in its linear and non–linear forms, was fit using variants of fixed and mixed effects. The analysis of the results showed better fit of the non–linear mixed models than of the other models in terms of bias and precision, suggesting the convenience of using models that consider repeated measurements in the same plot. The site index curves generated show the dominant height growth variability of this species in Venezuela in the areas that are appropriate for its establishment under traditional management.
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Teak (Tectona grandis Linn F.) is a popular exotic species in Ghana, widely grown in industrial plantations and small scale community woodlots. In spite of its importance, local information on the growth and yield of this species is lacking. Presented here are the results of a preliminary investigation into the growth and yield of teak in northern Ghana. Data were collected from 100 temporary sample plots from plantations ranging in age from 3 to 40 years. A standard volume equation, site index curves and provisional empirical yield tables were developed and presented. Site index curves were used to classify plantations into site classes of I, II and III, in order of decreasing productivity. Yield functions indicate that teak can be grown on biologically optimum rotations of 31, 38 and 48 years on site classes I, II and III, respectively. At extended rotations with the adoptions of suitable thinning schedules, trees of sawlog sizes could be obtained on site class I.
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We present a comparative yield study from permanent plots in 18.7 year-old teak plantations with different stocking levels (spacing + thinning regime treatments) at the Caparo Forest Experimental Station (Barinas, Venezuela). The goal was to obtain preliminary comparative information about the effects of late thinning in teak plantations. The plots represent a series of stocking levels including from narrow spacing (2500 trees/ha: 2 X 2 m) to wide spacing (4 X 4 m), and with zero, one, or two thinnings. The results show the effects of stocking levels on yield of products with diameter specification greater than 25 cm. Plots with intensive thinning (plots 31 and 32) and wide spacing and moderate thinning (plot 8 with 4 X 4 m, and thinning at age 13.8 years) showed the greatest proportion of timber products with diameter specifications of 25, 30, and 35 cm. In reference to late thinning, the results suggest that there is not danger of damaging the plantation by prescribing heavy thinnings (up to 60% of the actual density). If the goal is to produce saw timber, the best stocking regime for these plantations appears to be a wide initial spacing (4 X 4 m) and a relatively heavy commercial thinning at ages between 10 and 14 years.
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This new, biologically based, nonlinear regression model produces polymorphic site index and height curves as a function of prediction age and a height at any age. The curves are constrained to pass through the origin and appropriate heights at any index age. The model was parametrized on 970 stem-analyzed trees and tested on tree measurements from 147 permanent sample plots. Compared with other lodgepole pine (Pinuscontorta var. latifolia Engelm.) height models in Alberta, this model had fewer parameters, yet showed better accuracy and precision than the other models. Above all, the new model provides compatible site index and height estimates, and it can predict height without prior knowledge of site index.
Book
Se analizan las características de los modelos de crecimiento y sus principales utilidades en el ámbito forestal, y posteriormente se describen y analizan 74 funciones, incluyendo las más frecuentemente utilizadas y aquellas que han parecido más interesantes, convenientemente sistematizadas y clasificadas, con la finalidad de simplificar su elección y ajuste a cualquier conjunto de datos. Se completa la obra con un ejemplo de ajuste de los modelos a una serie de árboles de dos importantes especies forestales españolas, el pino gallego (Pinus pinaster) y el abedul (Betula celtiberica). The principal characteristics of growth models and their utilities are analyzed. Then 74 functions, including the most frequently used, are classified and described with detail in order to simplify the election and fit processes of any forestry data set. An example of the utility of these models is presented when 24 different functions are fitted to age-dominant height data of maritime pine (Pinus pinaster) and birch (Betula celtiberica).
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This paper deals with the height—growth classification of teak in a region that includes the Caribbean, Central America (Belize and Panama), Venezuela and Colombia. Top height, dominant height and dominant-codominant height data from 13 countries have been used as the basis for compiling a provisional regional site classification chart. The latter, although only tentatively valid, should be practically applicable throughout; as more data become available it shall be possible to revise and adjust it. Selected curves from the chart are compared to Asian, Indonesian and Nigerian curves. Recommendations about the application of the chart are given.