A fractal pipestem model to predict leaf area from stem-diameter Case study in a rubber agroforestry system on Sumatra, Indonesia

A research project has been started by ICRAF, on the subject of rubber agroforestry systems on Sumatra and West Kalimantan, Indonesia. The transformation of forests into tree-based production systems such as the rubber agroforests in Indonesia, can serve as an example elsewhere. Rubber agroforests are biodiverse, diversified systems, that have accomodated increasing population densities, while preserving a forest-like environment. A major issue for research is whether more productive rubber germplasm can allow intensification without much loss of biodiversity. To increase knowledge about the interactions in an agroforestry system, a model is being developed, in which all relevant processes are integrated. Experimental methods need to indicate the effect of separate interaction terms, and by quantifying key processes that lay underneath these interaction terms, a process-based model can be developed. Leaf area is considered to play a key role in radiation interception. The aim in this report is to investigate whether the 'fractal branching model' can be used to describe above-ground branching patterns, and whether it is useful to determine leaf area. To do this, the branching patterns in tree-crowns were analysed, to see whether these can be used to explain and predict the relation between tree stem and the leaf area of a tree. Branching patterns were described, using the proportionality factor 'a' and the allocation parameter 'q'. The proportionality factor a can be defined as: the ratio between the cross sectional area (csa) before a branching event and the sum of csa's after that branching event; q is defined as: the ratio between the largest csa, and the sum of all csa's, both after a branching event. Field- measurements were done mainly on three tree-species in rubber agroforests near Muara Bungo on Sumatra: Hevea brasiliensis, Trema tomentosa and Mallotus philippinensis. Regression analyses learn that in many cases diameter has a significant effect on branching parameters (a and q): prerequisites to Fractal branching' are not met. Especially in the case of Trema, a significant effect of branching order on a and q was found. A large part of the variation in the observed values remains un-explained. There could be other factors that need to be included to explain variation. Values found for average branching parameters (a and q) are characteristic for trees of the same species and DBH-class. Each species/D BH -class has its own parameter values for a and q, in which it differs from other species/DBH -classes. The predictions for leaf area that were made, using the fractal branching model, do not contradict with direct observations of leaf area. However, confidence intervals for the prediction of a random tree diverge very rapidly with increasing stem-diameter. Regardless the precision of predictions, the use of the fractal branching model decreases when for all species/DBH -classes many measurements need to be made, to determine the precise regression-equations for a and q that are needed.