Volume equations for native tropical species in Nigeria

Shadrach O. Akindele, Ph.D.Associate Professor of Forest Measurements

Department of Forestry and Wood Technology, Federal University of Technology, Akure, Nigeria.

and currently

Visiting Associate ProfessorDepartment of Forest Resources Management, University of British

Columbia, Vancouver, Canada. V6T 1Z4.

Presented at the 2005 Western Forest Mensurationists Conference held at Naniloa Resort, Hilo, Hawaii, USA. July 4-7, 2005.

BackgroundThe tropical rain forest

• major source of timber supply in Nigeria

• high plant diversity: Over 4,600 plant species identified (Ranked 11th in Africa)

• over 560 tree species (with a range of 30 to 70 species per hectare for trees ≥ 5 cm dbh) and MAI of 3 – 5 m3/ha/yr

• growth and yield studies in the rain forest face the challenges of high species diversity and limited data

• available data pooled together and used to fit volume functions for the common timber species in Nigeria.

The DataSources:• Forest Resources Study

funded by the African Development Bank and the Federal Government of Nigeria.

• Sampling study funded by the African Academy of Sciences.

Variables:• Diameter at breast height

overbark (in cm);• Stump diameter overbark (in

cm);• Merchantable height (in m);• Merchantable volume (in

m3).

Summary of the data used

Total Number of Species 77

Total number of observations 2391

Dbh range (cm) 20.0 – 230.0

Merchantable height range (m) 1.8 – 42.8

Tree volume range (m3) 0.0330 – 55.44

Number of Species with n ≥ 100 2

Number of Species with n ≥ 50 13

Number of Species with n ≥ 30 33

The wide range in the data is a reflection of the great variability that is typical of tropical rain forest data

Fitting volume functions for tropical forest data – the three possibilities

– Using the data for each species separately to fit equations for individual species.

– Combining the data for all species and fitting a single set of equations for all species combined together.

– Classifying the species into groups and combining the data for all species within each group to fit equations for the group. The number of equations will depend on the number of groups into which the species are classified.

Species Grouping• The 33 species with n ≥ 30 were used

to form the basis for species grouping;

• A volume equation of the form V = aDbHc was fitted for each species;

• The regression parameters were standardised and used as basis for grouping the species;

• Cluster analysis (using PROC FASTCLUS module in SAS) was used to aggregate the 33 species into 5 groups;

• Discriminant analysis (using PROC DISCRIM module) was used to assign the remaining species to the 5 existing groups.

The volume equation

After series of model fitting trials, the generalised logarithmic model (Clutter, et al., 1983) was selected for the species groups.

Expressing volume (V) as a function of dbh (D) and height (H), the model in its original form is:

with the assumption that σ is proportional to weighted regression was used.

The regression model is:

where

The parameter estimates are:

ibi

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Results of the Cluster Analysis

Cluster Frequency Mean Absolute Deviation

Maximum Distance

from Cluster Seed

Nearest Cluster

Distance to the Nearest

Cluster

1 5 0.2703 1.0709 5 2.6114

2 4 0.3204 1.0964 5 1.7238

3 5 0.3167 2.1172 5 1.8002

4 6 0.2932 1.1950 5 1.7306

5 13 0.1935 1.2642 2 1.7238

All the test statistics (Wilk’s Lambda, Pillai’s Trace, Hotelling-Lawley Trace and Roy’s Greatest Root) gave significant results (p<0.0001).

1

4

2

5

3

Results of the Cluster Analysis contd.Grouping of the 33 species with n ≥ 30.

Cluster 11. Daniellia ogea2. Erythrophleum suaveolens3. Symphonia globulifera4. Trilepsium madagascariense5. Xylopia aethiopica

Cluster 21. Alstonia boonei2. Manilkara obovata3. Pterocarpus osun4. Terminalia superba

Cluster 31. Carapa procera2. Hylodendron gabunense3. Mitragyna ledermannii4. Ricinodendron heudelotii5. Triplochiton scleroxylon

Cluster 41. Ceiba pentandra2. Celtis zenkeri3. Coelocaryon preussii4. Cordia millenii5. Eribroma oblonga6. Funtumia elastica

Cluster 51. Afzelia africana2. Albizia zygia3. Antiaris toxicaria4. Detarium senegalense5. Guarea cedrata6. Mansonia altissima7. Pentadesma butyracea8. Piptadeniastrum africanum9. Pterygota macrocarpa10. Pycnanthus angolensis11. Sterculia rhinopetala12. Strombosia pustulata13. Terminalia ivorensis

Results of the Discriminant AnalysisAssigning the remaining species into Clusters

Cluster 1

1. Copaifera mildbraedii2. Guarea thompsonii3. Khaya ivorensis

Cluster 2

1. Amphimas pterocarpoides2. Brachystegia eurycoma3. Brachystegia kennedyi4. Canarium schweinfurthii5. Khaya grandifoliola6. Nesogordonia papaverifera7. Scottellia coriacea

Cluster 3

1. Blighia sapida2. Bombax buonopozense3. Cyclicodiscus gabunensis4. Irvingia gabonensis5. Lophira alata6. Lovoa trichilioides7. Pentaclethra macrophylla8. Poga oleosa9. Sterculia tragacantha10.Trichilia gilgiana11.Trichilia monadelpha

Results of the Discriminant Analysis contd.

Cluster 5

1. Albizia ferruginea2. Antrocaryon klaineanum3. Diospyros mespiliformis 4. Distemonanthus benthamianus5. Entandrophragma cylindricum6. Funtumia africana7. Gossweilerodendron balsamiferum8. Holoptelea grandis9. Milicia excelsa10.Petersianthus macrocarpus11.Staudtia stipitata12.Stemonocoleus micranthus13.Trichilia prieuriana

Cluster 4

1. Brachystegia nigerica2. Chrysobalanus icaco3. Dialium guineense4. Hannoa klaineana5. Lannea welweitschii6. Mitragyna stipulosa7. Nauclea diderrichii8. Pterocarpus santalinoides9. Tetrapleura tetraptera10.Trichilia retusa

Estimates of Parameters of the Volume Equation for each Cluster

ibi

bii HDbbV 32

10

CLUSTER n b0 b1 b2 b3 _SSE_

1 363 0.0002 1.4560 1.1461 0.0076 4.55E-08

2 292 0.0002 1.8020 0.8770 -0.04 3.4E-08

3 377 7E-05 1.9250 0.9610 0.0076 5.67E-08

4 456 4E-05 1.8590 1.2323 0.0325 7.31E-08

5 903 7E-05 1.9810 0.9160 -0.002 1.19E-07

Residual Plots for each cluster

Cluster 1

-0.00004

-0.00003

-0.00002

-0.00001

0

0.00001

0.00002

0.00003

0.00004

0 0.00001 0.00002 0.00003 0.00004 0.00005 0.00006 0.00007 0.00008

Predicted Value

Res

idua

l

Cluster 2

-0.00004

-0.00003

-0.00002

-0.00001

0

0.00001

0.00002

0.00003

0.00004

0 0.00001 0.00002 0.00003 0.00004 0.00005 0.00006 0.00007

Predicted Value

Res

idua

l

Cluster 3

-0.00004

-0.00003

-0.00002

-0.00001

0

0.00001

0.00002

0.00003

0.00004

0.00005

0.00006

0.00007

0 0.00001 0.00002 0.00003 0.00004 0.00005 0.00006 0.00007

Predicted Value

Res

idua

l

Cluster 4

-0.00004

-0.00002

0

0.00002

0.00004

0.00006

0.00008

0 0.00001 0.00002 0.00003 0.00004 0.00005 0.00006 0.00007

Predicted Value

Res

idua

l

Residual Plots for each cluster

Cluster 5

-0.00004

-0.00003

-0.00002

-0.00001

0

0.00001

0.00002

0.00003

0.00004

0 0.00001 0.00002 0.00003 0.00004 0.00005 0.00006 0.00007

Predicted Value

Res

idua

l

Concluding Remarks1. Cluster and discriminant analyses were found to be effective in

grouping the tropical timber species encountered in this study.2. Most species in the same genus fell into different clusters, suggesting

that taxonomy alone should not be used as basis for aggregation in volume estimation.

3. Although the clusters generated in this study are adequate in the context of the data available, further work is required to incorporate measures of tree form into the clustering process.

4. More data are required to re-calibrate the models for those species with very few observations.

5. For tropical timber species in Nigeria, the generalised logarithmic volume function performed better than other forms of volume equations. To stabilised the error variance, D2H was found to be the appropriate weighting factor.

6. The tree volume equations for the species groups appear to be more robust due to relatively large number of observations and should therefore be used instead of the species-specific equations for which sample size was small.

Acknowledgements

International Tropical Timber Organisation For funding the study

Federal Department of Forestry, Abuja, Nigeria and Dr. Victor Adekunle, NigeriaFor providing the data

Federal University of Technology, Akure, NigeriaFor approving my release to carry out the study

University of British Columbia, Vancouver, CanadaFor providing facilities to carry out the study and funds to attend the Conference

Dr. Valerie LeMay, UBCFor her contribution to the data analysis.

For more information, contact:

Email:

sakindel@interchange.ubc.ca

Website:

http://www.forestry.ubc.ca/biometrics/

THANK YOU