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.

Modelling self-pruning and branch attributes for young Quercus robur L. and Fagus sylvatica L. trees

“…are younger and (2) branch diameter is bigger. The latter is consistent with the sink-source theory (Henriksson, 2001;Sone et al, 2009) and the branch-autonomy theory (Sprugel et al, 1991). Branch growth and branch mortality are the net result of the produced photosynthates within the branch (mainly driven by light and therefore depending on the branch environment and its social position in the crown), the energy cost to maintain the branch functioning and the downstream translocation of photosynthates.…”

Patterns of photoassimilate translocation to reproductive shoots from adjacent shoots in Camellia sasanqua by manipulation of sink-source balance between the shoots

“…It has been reported that the shoots or reproductive organs use photoassimilates translocated from the adjacent shoots as well as from those in the same shoot (Sprugel 2002). Sone et al (2009) showed that any of shading, defoliation and removal of long shoots of a branch in Acer rufinerve suppressed growth and leaf production in the neighboring branch in the next year. Obeso (1998) showed that fruit production decreased with the extent of defoliation on girdled branches, but not on un-girdled branches of Ilex aquifolium.…”

Tree Branching: Leonardo da Vinci's Rule versus Biomechanical Models

“…Leonardo da Vinci proposed that the sum of the cross-sectional area of all tree branches above a branching point at any height is equal to the cross-sectional area of the trunk or the branch immediately below the branching point [1]. This relationship can also be expressed by stating that the branch cross-sectional area below a given branching node is equal to the sum of the cross-sectional areas of daughter branches above the node [2]–[6]. This is known as Leonardo da Vinci's rule, or the area-preserving rule [2].…”