Journal of Forestry Research

, Volume 23, Issue 1, pp 1–12 | Cite as

Fractal analysis of canopy architectures of Acacia angustissima, Gliricidia sepium, and Leucaena collinsii for estimation of aboveground biomass in a short rotation forest in eastern Zambia

Original Paper


A study was conducted at Msekera Regional Agricultural Research Station in eastern Zambia to (1) describe canopy branching properties of Acacia angustissima, Gliricidia sepium and Leucaena collinsii in short rotation forests, (2) test the existence of self similarity from repeated iteration of a structural unit in tree canopies, (3) examined intra-specific relationships between functional branching characteristics, and (4) determine whether allometric equations for relating aboveground tree biomass to fractal properties could accurately predict aboveground biomass. Measurements of basal diameter (D10) at 10cm aboveground and total height (H), and aboveground biomass of 27 trees were taken, but only nine trees representative of variability of the stand and the three species were processed for functional branching analyses (FBA) of the shoot systems. For each species, fractal properties of three trees, including fractal dimension (Dfract), bifurcation ratios (p) and proportionality ratios (q) of branching points were assessed. The slope of the linear regression of p on proximal diameter was not significantly different (P < 0.01) from zero and hence the assumption that p is independent of scale, a pre-requisite for use of fractal branching rules to describe a fractal tree canopy, was fulfilled at branching orders with link diameters >1.5 cm. The proportionality ration q for branching patterns of all tree species was constant at all scales. The proportion of q values >0.9 (fq) was 0.8 for all species. Mean fractal dimension (Dfract) values (1.5–1.7) for all species showed that branching patterns had an increasing magnitude of intricacy. Since Dfract values were ≥1.5, branching patterns within species were self similar. Basal diameter (D10), proximal diameter and Dfract described most of variations in aboveground biomass, suggesting that allometric equations for relating aboveground tree biomass to fractal properties could accurately predict aboveground biomass. Thus, assessed Acacia, Gliricidia and Leucaena trees were fractals and their branching properties could be used to describe variability in size and aboveground biomass.


aboveground biomass allometric equations bifurcation ratio fractal dimension fractal properties functional branching characteristics relative equity self similarity 


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  1. Allen AP, Pockman WT, Restrepo C, Milne BT. 2008. Allometry, growth and population regulation of the desert shrub Larrea tridentata. Functional Ecology, 22: 197–204.CrossRefGoogle Scholar
  2. Betram JEA. 1989. Size-dependent differential scaling in branches: the mechanical design of trees revisited. Trees, 4: 241–253.Google Scholar
  3. Berntson GM. 1996. Fractal geometry scaling and description of plant root. In: A. Eshel and U. Kafkafi (eds), The hidden half. New York: Marcel Dekker, pp. 259–272.Google Scholar
  4. Brown S. 1997. Estimating biomass and biomass change of tropical forests: a primer. FAO Forestry Paper, 134, Rome Italy.Google Scholar
  5. Brown IF, Martineri LA, Thomas WW, Moreira MZ, Ferreira CAC, Victoria RA. 1995. Uncertainty in biomass of Amazonian forests: an example from Rondonia, Brazil. Forest Ecology and Management, 75: 175–189.CrossRefGoogle Scholar
  6. Brown JH, Gillooly JH, Allen AP, Savage VM, West GB. 2004. Toward a metabolic theory of ecology. Ecology, 85: 1771–1789.CrossRefGoogle Scholar
  7. Brown TB, Witschey WRT, Liebovitch LS. 2005. The broken past: Fractals in archaeology. Journal of Archeological Method and Theory, 12(1): 37–78CrossRefGoogle Scholar
  8. Camarero JJ, Siso S, Gil-Pelgrin E. 2003. Fractal dimension does not adequately describe the complexity of leaf margins of Quercus species. Real Jardin Botanico de Madrid, 60(1): 63–71Google Scholar
  9. Cannel MGR. 1983. Plant management in agroforestry: manipulation of trees, population densities and mixtures of trees and herbaceous crops. In: P.A. Huxley (ed), Plant Research and Agroforestry. Nairobi, Kenya: ICRAF,, pp. 455–488.Google Scholar
  10. Claesson S, Sahlen K, Lundmark T. 2001. Functions for biomass estimation of young Pinus sylvestris, Picea abies and Betula spp. from stands in Northern Sweden with high stand densities. Scandinavian Journal of forestry, 16: 138–146.CrossRefGoogle Scholar
  11. Delitti, WBC, Pausas JG. 2006. Biomass and mineralmass estimates in a “cerrado” ecosystem. Revista Brasileira Botânica, 29(4): 531–40.CrossRefGoogle Scholar
  12. Dzerzon H, Sievänen R, Kurth W, Pertunen J, Sloboda B. 2003. Enhanced possibilities for analyzing tree strctures as provided by interface between different modeling systems. Silva Fennica, 37(1): 31–44.Google Scholar
  13. Enquist BJ. 2002. Universal scaling in tree and vascular plant allometry: toward a general quantitative theory linking plant form and functions from cells to ecosystems. Tree Physiology, 22: 1045–1064.PubMedCrossRefGoogle Scholar
  14. Enquist BJ, Brown JH. West GB. 1998. Allometric scaling of plant energetic and population density. Nature, 395: 163–165.CrossRefGoogle Scholar
  15. Fitter AH, Stickland TR. 1992. Fractal characterization of root system architecture. Functional Ecology, 6: 632–635.CrossRefGoogle Scholar
  16. Gisiger T. 2001. Scale invariance in biology: coincidence or footprint of a universal mechanism. Biological Review 76: 161–209.CrossRefGoogle Scholar
  17. Halley JM, Hartley S, Kallimanis AS, Kunin WE, Lennon JJ, Sgardelis SP. 2004. Uses and abuses of fractal methodology in ecology. Ecology Letters, 7(3): 254–271.CrossRefGoogle Scholar
  18. Harrington G. 1979. Estimating aboveground biomass of trees and shrubs in a Eucalyptus populnea F. Mull. Woodland by regression of mass on tree trunk diameter and plant height. Australian Journal of Botany, 27: 135–143.CrossRefGoogle Scholar
  19. IPCC. 2006. Guidelines for national greenhouse gas inventories. IGES, ISBN 4-88788-032-4.Google Scholar
  20. IPCC. 2007. Climate Change 2007: The Physical Science Basis. Basic Summary for Policy Makers. Available at
  21. Jackson NA, Griffiths H, Zeron M. 1995 Aboveground biomass of seedling and semi-mature Sesbania sesban, a multipurpose tree species, estimated using allometric regressions. Agroforestry Systems, 29: 103–112.CrossRefGoogle Scholar
  22. Kale M, Sing S, Roy PS, Desothali V, Ghole VS. 2004. Biomass equations of dominant species of dry deciduous forests in Shivupuri district, Madya Pradesh. Current Science, 87(5): 683–687.Google Scholar
  23. Kaonga ML, Coleman L. 2008. Modelling soil organic turnover in improved fallows in eastern Zambia using the RothC model. Forest Ecology and Management, 256(5): 1160–1166.CrossRefGoogle Scholar
  24. Kaonga ML, Bayliss-Smith TP. 2009. Carbon pools in tree biomass and the soil in improved fallows in eastern Zambia. Agroforestry Systems, 76: 37–51.CrossRefGoogle Scholar
  25. Kaonga ML, Bayliss-Smith TP. 2010. Allometric models for estimation of aboveground carbon stocks in improved fallows in eastern Zambia. Agroforestry Systems, 78: 217–232.CrossRefGoogle Scholar
  26. Ketterings QM, Coe R, van Noordiwijk M, Ambagau Y, Palm CA. 2001. Reducing uncertainty in the use of allometric equations for predicting aboveground biomass in mixed secondary forests. Forest Ecology Management, 146: 199–209.CrossRefGoogle Scholar
  27. Koziowski J, Konarzewski M. 2004. Is West Brown and Enquist’s model of allometric scaling mathematically correct and biologically relevant. Functional Ecology, 18: 283–289.CrossRefGoogle Scholar
  28. Kumar VSK, Tewari VP. 1999. Aboveground biomass tables for Azadrachta indica a. Juss. International Forest Review, 1(2): 109–111.Google Scholar
  29. Litton CM, Kauffman JB. 2008. Allometric models for predicting aboveground biomass in two widespread plants in Hawaii. Biotropica, 40(3): 313–320.CrossRefGoogle Scholar
  30. Lott JE, Howard SB, Black CR, Ong CK. (2000) Allometric estimation of above-ground biomass and leaf area in managed Grevillea robusta agroforestry systems. Agroforestry Systems, 49: 1–15.CrossRefGoogle Scholar
  31. Makela A, Valentine H. 2006. Crown ratio influences allometric scaling in trees. Ecology, 87(12): 2967–2972.PubMedCrossRefGoogle Scholar
  32. Masi CEA, Maranville JW. 1998. Evaluation of sorghum root branching using fractals. Journal of Agricultural Sciences, 131: 259–265.CrossRefGoogle Scholar
  33. McMahon TA, Kronauer RE. 1976: Tree structures: deducing the principles of mechanical design. Journal of Theoretical Biology, 50: 443–446.CrossRefGoogle Scholar
  34. Niklas KJ. 1995. Size-dependent allometry of tree height and trunk diameter. Journal of Botany, 75: 217–227.Google Scholar
  35. Nygren P, Berninger F, Ozier-Lafontaine H, Lecompte F, Ramirez C, Salas E. 1998. Modelling of tree systems in agroforestry. Paper presented at the National Root Seminar, University of Joensuu, 1–2 December 1998.Google Scholar
  36. Ong JE, Gong, WK, Wong CH. 2004. Allometry and partitioning of the mangrove, Rhizophora apiculata. Forest Ecology and Management, 188(1–3): 395–408.CrossRefGoogle Scholar
  37. Otieno K, Onim JFM, Bryant MJ, Dzowela BH. 1991. The relation between biomass yield and linear measures of growth in Sesbania sesban in western Kenya. Agroforestry Systems, 13: 131–141.CrossRefGoogle Scholar
  38. Ozier-Lafontaine H, Lecompte F, Sillon JN. 1999. Fractal analysis of root architecture of Gliricidia for spatial prediction of root branching, size and mass: model development and evaluation in agroforestry. Plant Soil, 209: 167–180.CrossRefGoogle Scholar
  39. Price CA, Enquist B. 2007. Scaling mass and morphology in leaves:an extension of the WBE model. Ecology, 88(5): 1132–1141.PubMedCrossRefGoogle Scholar
  40. Richardson AD, zu Dohna H. 2003. Predicting root biomass from branching patternsof Douglas-fir rooting systems. Oikos, 100: 96–104.CrossRefGoogle Scholar
  41. Saatchi SS, Houghton A, Dos Santos Alvala RC, Soare JV, Yu Y. 2007. Distribution of aboveground biomass in the Amazon. Global Change Biology, 13: 816–837.CrossRefGoogle Scholar
  42. Sağlan B, Kűcűki O, Bilgili E, Durmaz D, Basal I. 2008. Estimating fuel biomass of some shrub species (Maquis) in Turkey. Turkish Journal of Agriculture, 32: 349–356.Google Scholar
  43. Saint-André L, M’bou Mabiala A, Mouvondy W, Jourdan C, Roupsard A, Deleporte P, Hamel O, Nouvellon Y. 2005. Age-related equations for above- and below-aground biomass of Eucalyptus hybrid in Congo. Forest Ecology and Management, 205: 199–214.CrossRefGoogle Scholar
  44. Smith DM. 2001 Estimation of tree root lengths using fractal branching rules: a comparison with soil coring for Grevillea robusta. Plant Soil, 229: 295–301.CrossRefGoogle Scholar
  45. Snowdon P. 1991 A ratio estimator for bias correction in logarithmic regressions. Canadian Journal of Forest Research, 21: 720–724.CrossRefGoogle Scholar
  46. Spek LY, Van Noordwijk M. 1994 Proximal root diameter as a predictor of total root size for fractal models. II. Numerical model. Plant soil, 164: 119–127.CrossRefGoogle Scholar
  47. Sugihala G, May RM. 1990 Applications of fractals in ecology. Tree, 5(3):79–86.Google Scholar
  48. Tucote DL, Pelletier JD, Newman WI. 1998. Networks with side branching in biology. Journal of Theoretical Biology, 193: 577–592.CrossRefGoogle Scholar
  49. Van TK, Rayachhetry MB, Centre D. 2000. Estimating aboveground biomass of Melaleuca quinquenenervia in Florida, USA. Journal of Aquatic Plant Management, 38, 62–67.Google Scholar
  50. Van Noordwijk M, Mulia R. 2002. Functional branch analysis as a tool for fractal scaling above- and belowground trees for their additive and nonadditive properties. Ecological Modelling, 149: 41–51.CrossRefGoogle Scholar
  51. Van Noordwijk M, Spek LY, De Willigen P. 1994. Proximal root diameters as predictors of total root size for fractal branching models. I. Theory. Plant Soil, 164: 107–118.CrossRefGoogle Scholar
  52. West GB, Brown JH, Enquist BJ. 1999: A general model for the structure and allometry plant vascular systems. Nature, 400: 664–667.CrossRefGoogle Scholar
  53. William N. 1997. Fractal geometry gets measure of life scales. Science 276: 34.CrossRefGoogle Scholar

Copyright information

© Northeast Forestry University and Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.A Rocha International, Sheraton HouseCastle Park, CambridgeUK

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