Theoretical Considerations of Vessel Diameter and Conductive Safety in Populations of Vessels

Abstract

Several characteristics of vessel populations were studied using two assumptions: that conductive capacity is proportional to the fourth power of the radius, r4, and that within a water‐stressed plant, wide vessels cavitate before narrow vessels. To compare the relative safety of vessel populations, we developed an index, the VC50, which indicates the percentage of vessels that remain water filled and functional when the plant has lost 50% of its conducting capacity from cavitations. If the population of vessels has a normal bell‐shaped distribution of diameters, VC50 will depend on the standard deviation (σ). With a large σ, VC50 is 86% or higher. Once the widest vessels—constituting 14% of all vessels and 50% of conducting capacity—have cavitated, the plant will still have 86% of its vessels water filled and functional. In contrast, with a small σ, the VC50 is 66% or lower; the VC50 of a population with a moderate σ is ca. 73%. If vessel diameter distribution is uniform, all vessel width classes have equal numbers of vessels, and VC50 is high, ca. 85%. Positively skewed populations, with increased numbers of narrow vessels, are safer ($$\mathrm{VC}\,_{50}=83\% $$) than negatively skewed populations (increased numbers of wide vessels; $$\mathrm{VC}\,_{50}=67\% $$).