Universal trade-off between vessel size and number and its implications for plant hydraulic function

The functional traits of angiosperm vessels influence water transport and, therefore, metabolism and performance. Among these traits is a trade-off between vessel diameter and number, known as the "packing rule", which has been abundantly confirmed. But how packing rule is connected to major dimensions of variation in hydraulic function remains unclear across and within diverse species. Using data from the primary literature spanning 3992 species for intraspecific data and 54 species for interspecific data, and newly acquired data from the branches of 80 tree species, we examine the ways that key xylem traits plus leaf mass covary with the packing rule for stems across and within species. We analyzed vessel diameter, individual vessel lumen area, vessel density (number of vessels per unit area), lumen fraction (the product of individual vessel lumen area and vessel density), non-vessel lumen fraction (total area minus total lumen area), specific stem conductivity, and wood density. Mean vessel lumen area scaled approximately as the - 1.0 power of vessel density across the pooled data. Little variation in the lumen fraction was attributable to total vessel lumen area, whereas the lumen fraction was positively correlated with vessel density in stems and branches across all species. Wood density was weakly negatively correlated with mean vessel lumen area, but was not correlated with either lumen or non-vessel lumen fractions in branches or stems across species. Vessel area scaled positive with leaf mass. Specific stem conductivity was correlated with mean vessel lumen area and wood density. These results validate and extend the implications of the packing rule, and identify and define the limits of hydraulic efficiency and safety strategies within and across angiosperm species.