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

Abstract

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 (D_fract), 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 (f _q) was 0.8 for all species. Mean fractal dimension (D_fract) values (1.5–1.7) for all species showed that branching patterns had an increasing magnitude of intricacy. Since D_fract values were ≥1.5, branching patterns within species were self similar. Basal diameter (D₁₀), proximal diameter and D_fract 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.

Keywords

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

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