Maintenance mechanisms of the pipe model relationship and Leonardo da Vinci’s rule in the branching architecture of Acer rufinerve trees

Abstract

The pipe model relationship (constancy of branch cross-sectional area/leaf area) and Leonardo da Vinci’s rule (equality of total cross-sectional area of the daughter branches and cross-sectional area of their mother branch) are empirical rules of tree branching. Effects of branch manipulation on the pipe model relationships were examined using five Acer rufinerve trees. Half the branches in each tree were untreated (control branches, CBs), and, for the others (manipulated branches, MBs), either light intensity or leaf area (both relating to photosynthetic source activity), or shoot elongation (source + sink activities), was reduced, and responses of the pipe model relationships were followed for 2 years. The pipe model relationship in MBs changed by suppression of source activity, but not by simultaneous suppression of source + sink activities. The manipulations also affected CBs in the year of manipulation and both branches in the next year. The branch diameter growth was most affected by light, followed by shoot elongation and leaf area, in that order. Because of the decussate phyllotaxis of A. rufinerve, one branching node can potentially have one main and two lateral branches. Analysis of 295 branching nodes from 13 untreated trees revealed that the da Vinci’s rule held in branching nodes having one shed branch but not in the nodes without branch shedding, indicating the necessity of natural shedding of branches for da Vinci’s rule to hold. These analyses highlight the importance of the source–sink balance and branch shedding in maintenance of these empirical rules.