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Vessel length is an important functional trait for plant hydraulics, because it determines the ratio of flow resistances posed by lumen and pit membranes and hence controls xylem hydraulic efficiency. The most commonly applied methods to estimate vessel lengths are based on the injection of silicon or paint into cut-off stem segments. The number of stained vessels in a series of cross-sections in increasing distance from the injection point is then counted. The resulting infusion profiles are used to estimate the vessel length distribution using one of several statistical algorithms. However, the basis of these algorithms has not been systematically analysed using probability theory.

We derive a general mathematical expression for the expected shape of the infusion profile for a given vessel length distribution, provide analytic solutions for five candidate distributions (exponential, Erlang(2), gamma, Weibull, and log …