1. Marcelo Carvalho de Rezende¹, Helio Garcia Leite², Leonardo Pereira Fardin³.
GROWTH AND YIELD MODELS OF Tectona
grandis L. f. (TEAK) PLANTATIONS
The patterns of tree growth and yield were, mostly, proposed by
Schumacher (1939), Buckman (1962) and clutter (1963). These
can be classified, as their flexibility in empirical models,
semiempirical and biological, the latter being the one that best
describe growth trends (Pienaar, 1965). All of them include effects
such as age, site index, basal area and frequency. The choice of
model depends on the type of information, the level of detail
required, the stand characteristics and the type of data available
(Leite, 2009). In the case of stands subjected to thinning, we
indicate models of varying density, such as Clutter (1963) and
Buckman (1962), individual tree models or distribution of
diameters.
The data used in this study came from 89 permanent plots of
continuous forest inventory stands measured between 1998 and
2009, in stands of Tectona grandis located in Jangada - MT.
To adjust the guide curve and subsequent classification of yield
capacity, we used an index age of 72 months and the logistic
model:
𝐻𝑑 = α 1 + 𝛽𝑒−𝛾𝐼 −1
+ 𝜀
Hd = dominant height in m; I = age in months; α, β, and γ = parameters, and ε = random
error, ε ~ NID (0,σ²)
The growth and yield was predicted using the Clutter model (1963),
in the usual way:
𝐿𝑛𝐵2 = 𝐿𝑛𝐵1 𝐼1 𝐼2
−1
+ 𝛼0 1 − 𝐼1 𝐼2
−1
+ 𝛼1 1 − 𝐼1 𝐼2
−1
𝑆1 + 𝜀
𝐿𝑛𝑉2 = 𝛽0 + 𝛽1 𝐼2
−1
+ 𝛽2 𝑆 + 𝛽3 𝐿𝑛𝐵2 + 𝜀
𝑉2= volume at age projection 𝐼2, in m³.ha-¹; 𝐼2 = projection age in months; 𝐼1= current age in
months; 𝑆1= site index in the present age, in m; 𝐵1= basal area at current age 𝐼1, in m².ha-¹;
𝐵2= basal area at current age 𝐼2, in m².ha-¹; 𝛼𝑖 𝑎𝑛𝑑 𝛽𝑖= parameters; 𝐿𝑛 = natural logarithm,
and ε = random error, ε ~ NID (0, σ² ).
The model adjustment was made by the method of least squares in
two stages, using the software Eviews 6.0. To assure the quality of
the adjustment, the analysis was combined with the residue value
of the correlation coefficient between the observed and estimated
values ​​of basal area and volume.
[1] Buckman, R.E. Growth and yield of red pine in Minnesota. Washington, D.C.: USDA, 1962. 50 p. (Tech Bull, 1272).
[2] Campos, J.C.C. e Leite, H.G. Mensuração florestal: perguntas e respostas. 3. ed. Viçosa, MG: Editora UFV, 2009. 548 p.
[3] Clutter, J.L. Compatible growth and yield models for loblolly pine. Forest Science, v. 9, n. 3, p. 354-371, 1963.
[4] Nogueira, G.S.; Leite, H.G.; Campos, J.C.C.; Takizawa, F.H.; Couto, L. Avaliação de um modelo de distribuição diamétrica ajustado
para povoamentos de Tectona grandis submetidos a desbaste. Revista Árvore, Viçosa, MG, v. 30, p. 377-388, 2006.
[5] Pienaar, L.V. Quantitative theory of forest growth. 1965. 191 f. Thesis (Ph. D.) – University of Washington, Seattle, Washington,
1965.
[6] Schumacher, F.X. A new grouth curve and its application to timber – yield. Journal Forestry, v. 37, p. 817-820, 1939.
Based on the concept of site index it was obtained the guide curve:
Hd = S1 1
+ 3,0262801e−0,018245818(6)
(13,0262801e−0,018245818.I
)−1
The logistic sigmoid model represented the dominant height data
efficiently and can be used to classify the productive capacity of teak
stands.
The Clutter model in its usual form is efficient for modeling the growth
and yield of the stand.
¹ Arauco do Brasil, Rua Roberto Hauer 160, 81610-180 – Curitiba – PR – Brasil. marceloarvore@gmail.com ² Universidade Federal de Viçosa, Av. Peter
Henry Rolfs, s/n Campus Universitário 36570-000 – Viçosa – MG – Brasil. hgleite@gmail.com ³ Floresteca Av. Gov. João Ponce de Arruda, 1054 78110-375 -
Várzea Grande – MT – Brasil. leonardo.fardin@floresteca.com.br
0
5
10
15
20
25
30
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Dominant
Height (m)
Age (years)
Guide-Curve of a thinned Teak stand
17
15
13
11
9
7
0
5
10
15
20
25
0 5 10 15 20 25
Estimated
basal
areal
(m².ha-1)
Observed basal area (m².ha-1)
-100
-60
-20
20
60
100
0 5 10 15 20 25
Observed basal area (m².ha-1)
Error (%)
0
50
100
150
200
250
0 50 100 150 200 250
Estimated
volume
(m³.ha-1)
Oberved volume (m³.ha-1)
-100
-60
-20
20
60
100
0 50 100 150 200 250
Observed volume (m³.ha-1)
Error (%)
Figure 2. Relations between the observed and predicted values ​​of
the variables basal area and volume, using the Clutter model and the
distribution of the error.
Figure 1. Site index curves obtained by the method of the guide
curve using a sigmoidal model for a stand of Tectona grandis in the
State of Mato Grosso, index-age 72 years.
Introduction
Material & Methods
Results & Discussion
Acknowledgement
References