Study Overturns Leonardo da Vinci’s Tree Rule, Revealing Greater Climate Vulnerability of Trees

Leonardo da Vinci’s notebooks record a simple rule: a branch’s thickness equals the sum of the thicknesses of the branches that split from it. For centuries artists and botanists used this principle to sketch trees and to model how wood transports water.

Stuart Sopp and Ruben Valbuena, plant scientists at the University of California, Davis, examined the xylem—the microscopic tubes that move water from roots to leaves—in over 300 branches from 12 temperate species. They measured the cross‑sectional area of each parent branch and compared it to the combined area of its daughter branches using confocal microscopy and 3D imaging.

On average, the daughter branches’ xylem area exceeded the parent’s by about 8 %, and the rule held true in only 38 % of the samples. The discrepancy grew larger in thicker, older limbs, which dominate the canopy of mature forests.

Because the internal transport network is less balanced than da Vinci’s formula predicts, large trees may struggle to move water efficiently during droughts, making them more prone to hydraulic failure. This implies that current climate‑vegetation models, which often assume the da Vinci rule, could overestimate forest resilience to warming.

Future work will test whether the observed xylem mismatch translates into higher mortality rates under experimental heat and drought conditions. Scientists will also watch for updates to global carbon‑cycle forecasts that incorporate the revised branching architecture.

What to watch next: upcoming field experiments that measure tree mortality under simulated climate stress, and revised ecosystem models that incorporate the new branching measurements.