Volume equations for native tropical species in Nigeria

1. 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 Professor Department 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.

2. Background The 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.

5. The Data Sources: 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).

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

7. 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.

8. 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.

9. 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:

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

11. 1 2 3 4 5

12. Results of the Cluster Analysis contd. Grouping of the 33 species with n ≥ 30. • Cluster 4 • Ceiba pentandra • Celtis zenkeri • Coelocaryon preussii • Cordia millenii • Eribroma oblonga • Funtumia elastica • Cluster 1 • Daniellia ogea • Erythrophleum suaveolens • Symphonia globulifera • Trilepsium madagascariense • Xylopia aethiopica • Cluster 5 • Afzelia africana • Albizia zygia • Antiaris toxicaria • Detarium senegalense • Guarea cedrata • Mansonia altissima • Pentadesma butyracea • Piptadeniastrum africanum • Pterygota macrocarpa • Pycnanthus angolensis • Sterculia rhinopetala • Strombosia pustulata • Terminalia ivorensis • Cluster 2 • Alstonia boonei • Manilkara obovata • Pterocarpus osun • Terminalia superba • Cluster 3 • Carapa procera • Hylodendron gabunense • Mitragyna ledermannii • Ricinodendron heudelotii • Triplochiton scleroxylon

13. Results of the Discriminant Analysis Assigning the remaining species into Clusters • Cluster 3 • Blighia sapida • Bombax buonopozense • Cyclicodiscus gabunensis • Irvingia gabonensis • Lophira alata • Lovoa trichilioides • Pentaclethra macrophylla • Poga oleosa • Sterculia tragacantha • Trichilia gilgiana • Trichilia monadelpha • Cluster 1 • Copaifera mildbraedii • Guarea thompsonii • Khaya ivorensis • Cluster 2 • Amphimas pterocarpoides • Brachystegia eurycoma • Brachystegia kennedyi • Canarium schweinfurthii • Khaya grandifoliola • Nesogordonia papaverifera • Scottellia coriacea

14. Results of the Discriminant Analysis contd. • Cluster 4 • Brachystegia nigerica • Chrysobalanus icaco • Dialium guineense • Hannoa klaineana • Lannea welweitschii • Mitragyna stipulosa • Nauclea diderrichii • Pterocarpus santalinoides • Tetrapleura tetraptera • Trichilia retusa • Cluster 5 • Albizia ferruginea • Antrocaryon klaineanum • Diospyros mespiliformis • Distemonanthus benthamianus • Entandrophragma cylindricum • Funtumia africana • Gossweilerodendron balsamiferum • Holoptelea grandis • Milicia excelsa • Petersianthus macrocarpus • Staudtia stipitata • Stemonocoleus micranthus • Trichilia prieuriana

15. Estimates of Parameters of the Volume Equation for each Cluster

16. Residual Plots for each cluster

17. Residual Plots for each cluster

18. ConcludingRemarks • Cluster and discriminant analyses were found to be effective in grouping the tropical timber species encountered in this study. • 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. • 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. • More data are required to re-calibrate the models for those species with very few observations. • 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. • 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.

19. Acknowledgements International Tropical Timber Organisation For funding the study Federal Department of Forestry, Abuja, Nigeria and Dr. Victor Adekunle, Nigeria For providing the data Federal University of Technology, Akure, Nigeria For approving my release to carry out the study University of British Columbia, Vancouver, Canada For providing facilities to carry out the study and funds to attend the Conference Dr. Valerie LeMay, UBC For her contribution to the data analysis.

20. For more information, contact: Email: sakindel@interchange.ubc.ca Website: http://www.forestry.ubc.ca/biometrics/ THANK YOU