Table 1. Existing publications on single tree volume and stem shape models for teak.
Source Region Model Application Modelling Dataset
Pérez and Kanninen (2003) Costa Rica Total and merchantable stem volume 111 trees
Age 2–47 years
Diameter 2–59 cm
Malimbwi et al. (2005) Tanzania Total stem volume -
van Zyl (2005) Tanzania Stem volume, height and form 222 trees
Diameter 8–79 cm
Height 9–34 m
Figueiredo et al. (2006) Brazil Stem volume and profile 159 trees
Age 7–10 years
Pérez (2008) Costa Rica Total and merchantable stem volume 25 trees
Age 8–46
Diameter 9–55 cm
Reggiani (2009) Brazil Total stem volume -
Figueiredo et al. (2014) Brazil Stem volume and height
(a book with some 40 equations for teak volume and height) 		-
Ribeiro (2014) Brazil Stem heartwood volume 40 trees
Diameter 10–35 cm
Height 14–27 m
Fallas (2017) Costa Rica Total and merchantable stem volume of clonal teak trees 306 trees
Age 3–12 years
Diameter 9–32 cm
Table 2. Existing publications on stand-level growth and yield models for teak.
Source Region Model Application Modelling Dataset Comments
Nunifu (1997) Ghana Stand-level yield models for dominant height, diameter, basal area, volume and biomass. Weibull model for diameter distribution modelling. 100 sample plots
Age 3–40 years 		Modelling data includes only low yield sites
Bermejo (2004) Costa Rica Yield models/tables based on dominant height development 318 sample plots Modelling data covers only first half of full rotation.
Drescher (2004) Brazil Stand-level yield models for mean diameter, dominant height, form factor, stocking, basal area and volume 162 sample plots
Age 2–10 years
Diameter 8–21 cm
Height 10–18 m 		Modelling data covers only first half of full rotation.
Pérez and Kanninen (2005) Costa Rica Stand-level growth curves for mean diameter and dominant height as a function of age 150 sample plots
Age 1–47 years 		 
García el al. (2006) Brazil Diameter distribution models for early thinning simulations 239 sample plots
Age < 96 months 		 
Saraiva et al. (2006) Brazil Diameter distribution models for early thinning simulations 239 sample plots
Age < 96 months 		Same data as in García et al. (2006)
Batista (2007) Brazil Dominant height model for young teak plantations Age < 12 years  
Pérez (2008) Costa Rica Stand-level dominant height curve 25 sample trees  
Tewari et al. (2014) India Stand-level growth curves for dominant height, mortality, basal area and volume 22 sample plots with 3 consecutive measurements
Age 11–38 years 		 
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Fig. 1. Location of the teak growth and yield study area in Panama (Panama Este and Darien Provinces).

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Fig. 2. Climate in different locations in the study area. Mean annual temperature and its standard deviation (graph a); total annual rainfall and its standard deviation (graph b); monthly average temperature (graph c); monthly average rainfall (graph d).

Table 3. Soil characteristics in teak plantations in the study area and teak optimum requirements for soil parameters as reported in published literature.
Soil Parameter Unit Method N Mean St. Dev. Teak Optimum Source
Sand % Bouyoucos 305 20% 11% 55…65% (1)
Loam % Bouyoucos 305 15% 6% … …
Clay % Bouyoucos 305 65% 13% 35...45% (1)
Organic matter % Walkey-Black 305 1.0% 0.7% 2.5…4.0+% (1)
pH NA Water 1:2.5 305 6.1 0.6 5.5…6.2…7.2 (1)
P mg l–1 Mehlich-1 305 10.2 20.1 3…10 (1) (4)
K mg l–1 Mehlich-1 305 157 98 >40…120+ (1)
Ca meq 100 g–1 KCL 305 23.1 13.2 1.5…4.0+ (1)
Mg meq 100 g–1 KCL 305 7.4 8.3 1.0…4.0 (1)
Ca + Mg meq 100 g–1 KCL 305 30.5 16.4 2.5…6.0+ (1)
Al meq 100 g–1 KCL 305 0.6 1.3 <0.2 (1)
CEC meq 100 g–1 Cation calculation 305 31.7 16.2 4…10+ (1)
Acid saturation % (Al + H)/CEC 305 4% 10% <3…8% (2) (3) (4)
Base saturation % (K + Ca + Mg)/CEC 305 95% 11% n.a. n.a.
Calcium saturation % Ca/CEC 305 69% 11% >40...62…75% (2) (3) (4) (5)
Teak optimum values according to:
  (1) Jerez and Coutinho (2017) (Brazil)
  (2) Alvarado and Fallas (2004) (Costa Rica)
  (3) Vaidés (2004) (Guatemala)
  (4) Mollinedo et al. (2005) (Panama)
  (5) Fernández-Moya et al. (2015) (Central America)
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Fig. 3. Soil texture in teak plantations in the study area (n = 305). Clay, silt and sand separate were analysed on 0–20 cm and 20–40 cm sampling depths (graphs a and b respectively). View larger in new window/tab.

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Fig. 4. Sample tree data relationships (n = 433) in stem volume and taper curve modelling dataset (d = stem diameter at 1.3 m height, h = stem height).

Table 4. Number of sample plots in the yield model dataset.
Age SI20 < 25.5 SI20 > 25.5 Total n
<10 791 971 1762
>10 472 400 872
Total n 1263 1371 2634
Table 5. Stand parameter summary in the yield model dataset.
Parameter Age D Dmax Dmin H Hd N G V SI20
Min 1.5 3.7 4.7 0.5 3.2 3.5 20 0.2 1.2 9.5
Max 19.9 43.3 54.4 39.0 29.9 30.3 1260 28.0 312.2 42.6
Mean 8.9 20.3 24.1 15.6 17.4 18.0 441 11.2 98.8 25.5
Median 7.7 20.4 24.2 15.9 17.8 18.3 360 11.3 95.9 25.6
D = mean diameter (cm); Dmax, Dmin = maximum and minimum diameters (cm); H = mean height (m); Hd = Dominant height (m); N = stocking (trees ha–1); G = basal area (m2 ha–1); V = total stem volume (m3 ha–1); SI20 = Dominant height at base age of 20 years (m).
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Fig. 5. Conceptual description of the forest simulator and optimisation model.

Table 6. Selected single-entry and double-entry stem volume models.
Model Equation N R² RMSE Bias
D8 v = –0.23959 + 0.036738 × d 383 0.970 0.056 –0.001
D10 v = 8.2091 × exp(–70.331 / d) 383 0.970 0.079 +0.003
DH21 v = 0.000032589 × d2 × h 383 0.974 0.074 +0.011
DH22 v = 0.029387 + 0.000031543 × d2 × h 383 0.973 0.073 +0.000
DH29 v = 0.000078168 × d2 + 0.00020175 × (h – 1.3)2 + 0.000025461 × d2 × h – 0.0000000094597 × d × h2 383 0.978 0.068 –0.005
DH35 v = 0.0028011 × d + 0.0059896 × (h – 1.3) + 0.000030872 × d2 × h 383 0.978 0.066 –0.003
v = stem volume (m3); d = diameter at 1.3 m above the stump (cm); h = stem height (m).
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Fig. 6. Stem volume model validation with re-sampled data. Single-entry Models D8 and D10, and double-entry models DH21, DH22, DH29 and DH35 were the best performing models in this study. For details of the other published models, see Table 1 and Table 2. d = stem diameter at 1.3 m height and v = stem volume.

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Fig. 7. Taper equation model (graph a) and residuals (graph b) (dx = diameter at height x; d0.2h = diameter at 20% relative height).

Table 7. Summary of Yield Models A, B and C. View in new window/tab.
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Fig. 8. Yield Model A, B and C performance with different Site Index values (D = stand mean diameter at 1.3 m height; V = stand total volume; SI = Site Index or dominant height with base age 20 years; A, B, C = volume models).

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Fig. 9. Merchantable volume harvest output comparison with the study of Bermejo et al. (2004) with Site Index SI = 26.5 and SI = 21.3 (graphs a and b), and log assortments as estimated with Model B and Model C (graphs c and d).

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Fig. 10. Total volume harvest output comparison with the study of Perez and Kanninen (2005) with diameter maximization growth scenario (graph a) and total volume maximization growth scenario (graph b), and respective log assortments as estimated with Model B and Model C (graphs c and d).

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Fig. 11. Site Index curve comparison (graph a) and Model curve set for site indices 18–30 (graph b). Hd = dominant height.

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Fig. 12. Log size output comparisons (Model C predicted vs Actuals) in four final harvest operations in Panama.