Plant hydraulics models

The hydraulics tool fits two kinds of curve: xylem vulnerability to embolism, and leaf pressure–volume curves.

Water potentials are negative MPa throughout. PhytKit converts the common alternatives and says so in warnings:

• Potentials reported as positive tension are made negative.
• Columns named in bar are converted to MPa.
• Percentages are converted to fractions.

Vulnerability curves

--model vulnerability. The sigmoidal model of Pammenter & Van der Willigen (1998), fitted in conductance space so the maximum conductance is a free parameter:

\[ K(\Psi) = \frac{K_{max}}{1 + \exp\!\left[-\frac{S}{25}(\Psi - P_{50})\right]} \]

Parameter	Meaning
Kmax	Conductance at full hydration
P50	Water potential at 50% loss of conductivity (MPa)
S	Slope at P50 (% MPa⁻¹)

The equivalent percent loss of conductivity is \(PLC = 100\,(1 - K/K_{max})\), the "sigmoidal" model of the fitplc package.

Your file can give either:

• PLC, which is converted to relative conductance \(1 - PLC/100\), so Kmax is near 1. Fractions (0–1) are recognized as well as percentages.
• A conductance column (K, Kleaf, Kstem and similar), used as is. Kmax then starts at the largest measured value.

Pressure–volume curves

--model pvcurve. Leaf water potential as a function of relative water content \(w\) (Sack, John & Buckley 2018; Tyree & Hammel 1972):

\[ \Psi(w) = \pi_o\left[\max\!\left(0,\ \frac{w - w_{tlp}}{1 - w_{tlp}}\right)\right]^{\varepsilon} - \frac{\pi_o}{w} \]

The first term is turgor pressure, which falls to zero at the turgor loss point \(w_{tlp}\). The second is the osmotic potential. At full hydration (\(w = 1\)) they cancel, and \(\Psi = 0\).

Parameter	Meaning
πo	Osmotic pressure at full turgor (MPa, positive)
wtlp	Relative water content at turgor loss
ε	How turgor relaxes as the leaf dries above the turgor loss point (a proxy for bulk wall elasticity)

The result also reports a derived value: the water potential at turgor loss, \(\Psi_{tlp} = -\pi_o / w_{tlp}\), as psi_tlp.

Relative water content may be a fraction or a percentage.

See Fit pressure–volume curves and Fit a vulnerability curve.