Incoprea hypothesis tests · volume II

Trees Stop at a Hydraulic Limit

Forestry & Fire Ecology · notebook volume 16 · Model n = 200

The claim

Maximum tree height is set by the ratio of water potential gradient to path length, so taller trees need disproportionately safer xylem.

What was tested

Maximum height should be set by the cavitation threshold divided by the potential gradient, and the xylem safety a tree needs should rise faster than linearly with height.

Falsified by: Height limited by mechanical support alone would remove the hydraulic term.

Method

Cohesion-tension model: leaf potential = soil potential (-0.1 MPa) minus gravitational head (0.0098 MPa/m) minus path resistance (1.2e-4 MPa/m2 times height squared). Maximum height solves leaf potential = P50. Xylem safety required at a given height is the negative of the leaf potential. Compared with the tallest measured living tree, a coast redwood at 115.9 m.

Result

2026-10-30T13:19:48.914086 image/svg+xml Matplotlib v3.11.2, https://matplotlib.org/ 1 2 3 4 xylem cavitation threshold |P50| (MPa) 60 80 100 120 140 160 maximum height (m) record 116 m Height from the hydraulic budget 20 40 60 80 100 120 140 height (m) 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 water potential (MPa) Safety demand grows faster than height required |P50| gravity only
Figure generated by code/tests/tree-height-hydraulic.py from the recorded run.
Predicted ceiling at P50 = -3 MPa (m)120
Record height (m)115.9
Required P50 at 116 m (MPa)2.85
Share from path resistance57%
supported

With a cavitation threshold of -3.0 MPa the model's ceiling is 120 m, close to the 116 m record. At that height the tree must hold xylem at 2.9 MPa, of which 57% is path resistance rather than gravity. The safety requirement is convex in height: doubling height more than doubles the potential a tree must survive.

Limits

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