Formation of a Structure of Exponentially Forking Branches with a Steady-state Amount of Current-year Shoots in a Hardwood Tree Crown

Forking branches are a structural pattern characterizing a tree species. For a tree species, as a sessile organism, the forking structure is essential for gaining solar energy by spreading leaves in lighter spaces as quickly as possible. The structure is an outcome of a process in which a mother shoot of a branch produces multiple daughter shoots, and thus allows a tree to exponentially increase the amount of leaves available for photosynthetic production. On the other hand, in closed hardwood forests, tree crowns are so close to each other that there is very little space for “exponential” expansion of tree crowns [8]. How can the nature of branch forking, which appears to result in an exponential increase of leaf amount, be consistent with crown development in closed hardwood stands where crown expansion is limited due to a lack of available space? To answer such a question, analyses of demographic (birth and death) and morphological patterns of annual shoots (the portion of shoots elongated during a year) in tree crowns are useful, since they can clarify how the shoot population in a crown develops and is maintained [1, 2, 3, 5, 6, 7, 9, 10, 11, 12, 13]. Here, we begin by showing an example of the structural pattern of a branch as observed in the top canopy of a closed hardwood forest. We then show how the observed pattern can be formed by introducing a model simulating demographic and structural patterns of the annual shoots.