BRANCH GEOMETRY AND EFFECTIVE LEAF AREA: A STUDY OF TERMINALIA-BRANCHING PATTERN. 2. SURVEY OF REAL TREES

Branching angles, the angles between branch units of lateral branch complexes, were measured for 32 species of tropical trees with Terminalia-branching pattern, representing seven dicotyledonous families. Angles of many but not all species are similar to the theoretical optimal values determined by computer simulations based on Terminalia catappa. These theoretical values maximize the effective leaf area of the branch complex. Real branching angles tend to remain relatively constant within a lateral branch complex, although a difference between sapling and adult branches was noted in T. muelleri. The pattern of mirror image symmetry of complexes within one branch tier appears to be random. The coefficient of variation is greater for the separate branching angles of a bifurcation than for the bifurcation angle as a whole. We conclude that observed branching angles optimize effective area in many species (as predicted by the T. catappa model). Large differences between the real and theoretical values for some species may be due to their dissimilarity to the T. catappa simulation. TERMINALIA-BRANCHING (or Aubreville's model) is a distinctive pattern of branching that occurs in at least 19 families of tropical dicotyledonous trees and is one of the 23 basic architectural models of tropical trees described by Halle and Oldeman (1970) and by Halle, Oldeman, and Tomlinson (1978). The regular repeating units and clustering of leaves has facilitated computer simulations of branching pattern and tree geometry in Terminalia catappa L. (Fisher and Honda, 1977, 1979). Using this simulation, we found that the real branching angles of the species are very similar to the theoretical angles which produce the maximum effective leaf area, EA, for a tree with this pattern of branching (Honda and Fisher, 1978). This demonstration of the optimization of a structural parameter for an obviously important biophysical feature, interception of light, is significant for the study of adaptive tree geometry. We have presented a detailed theoretical study of Terminalia-branching which shows how changes in some of the parameters of branch geometry influence the efI Received for publication 28 August 1978; revision accepted 26 February 1979. The cooperation of Mr. Ray Baker (Lyon Arboretum); Dr. R. de la Cruz (University of the Philippines); Dr. John Dransfield (Royal Botanic Gardens, Kew); Mr. R. Ramkissoon and Mr. M. B. Kalloo (University of the West Indies, Trinidad); and of the staffs of the Forest Research Institute (Kepong, Malaysia), the Kebun Raya (Bogor, Indonesia), and the Lyon Arboretum (University of Hawaii) is gratefully acknowledged. The assistance of Miss Janice Wassmer and Mr. Scott Norton and the manuscript review by Dr. James E. Eckenwalder are greatly appreciated. Research supported, in part, by a travel grant from the National Geographic Society and grant DEB77-13953 from the National Science Foundation. fective leaf surface (Fisher and Honda, 1979). We now present further data on the observed branching angles in T. catappa and 31 other species of trees with the same form of architecture. These new data permit an evaluation of the biological significance of our theoretical studies. MATERIALS AND METHODS-Branching angles of small trees and lower branches of large trees were measured directly, using a protractor. Only angles in the horizontal plane were taken. Higher branches in tall trees were photographed vertically. Branching angles of horizontal branches were measured from a photographic print or a projection of the negative. Only branches in the central region of the negative were used in an effort to minimize error due to parallax. The exact effective area of a leaf cluster or branch complex was calculated by weighing cut-outs of paper tracings of photographs or of leaf shadows cast from vertical illumination. The orientation of leaves and branches with respect to gravity was measured directly with a protractor weighted with a plumb. The cultivated and wild trees listed in Table 3 were either measured directly in the field or photographed at the following locations: Miami, Florida; Trinidad; Honolulu, Hawaii; Los Baiios, Philippines; Kepong and elsewhere in W. Malaysia; Bogor, Indonesia; and Singapore. Only those species for which there are a minimum of nine measurements are listed. RESULTs-Terminalia catappa-The general branching pattern of this species and the terminology applied to it were presented in Fisher and