Explanation found for Leonardo Da Vinci's tree rule?


More than 500 years ago, Leonardo da Vinci observed a particular relationship between the size of a tree’s trunk and the size of its branches. Specifically, the combined cross-sectional areas of a tree’s daughter branches are equal to the cross-sectional area of the mother branch. However, da Vinci didn’t know why tree branching followed this rule, and few explanations have been proposed since then. But now in a new study, physicist Christophe Eloy from Aix-Marseille University in Aix-en-Provence, France, has shown that this tree structure may be optimal for enabling trees to resist wind-induced stresses.

According to the 'young investigator' Rizwan Aratsu -

I tested ten species of trees in the vicinity of Princeton, New Jersey, to see if they do indeed adhere to the rule of conservation as asserted by the Italian master and those who followed him. Based on my review of the literature, I expected to find that trees would either conserve area or not depending on the porosity of their wood to water. To my surprise, I found that all ten species conserve cross-sectional area in approximately the same way despite large differences in porosity. In particular, their twigs roughly doubled in cross-sectional area across each branching while their larger branches approximated area-preservation, as Leonardo had predicted. Rather than precisely preserving area, the trees actually tended to increase in area ever so slightly as I moved from trunk to twig tips.

From Da Vinci's notebook- 

In his notebook, Leonardo da Vinci made this sketch depicting the branching pattern of trees. He depicted that the total thickness of branches along each of the arcs would equal the thickness of the trunk. Source-  Rizwan Aratsu

Wind -the new explanation? 

(Left) A model of tree branching. (Middle) A tree skeleton with all branches having the same thickness. (Right) The same tree with branch diameters calculated from a model accounting for wind-induced stress, which closely follows Leonardo’s rule.  Source -Physics.org


Eloy has proposed that Leonardo’s rule is a consequence of trees adapting their growth to optimally resist wind-induced stresses. It’s well-known that plants can alter their growth patterns in response to mechanical sensation, such as wind. The phenomenon, called “thigmomorphogenesis,” means that wind can influence the trunk and branch diameters of a tree as its growing. The underlying cellular mechanisms of this phenomenon are largely unknown.

Interestingly the extent of applicability of the Da Vinci's tree rule so far only extends to 10 species-

“Actually, Leonardo’s rule has not been assessed for that many species,” Eloy said. “So far, it seems to be hold for about 10 species. The problem is that it takes a lot of time to measure a single tree, which has thousands of branches, and the data are usually very scattered. Besides, some species clearly do not satisfy Leonardo's rule, such as baobabs, koas, and most bushes.”

I wonder if Rizwan Aratsu's sample of 10/10 has any species in common with the 10 mentioned by Eloy above.