Testing the packing rule across the twig–petiole interface of temperate woody species

Abstract

Theories that incorporate the area-preserving rule of Leonardo da Vinci predict that the sum of the crosssectional lumen area of xylem conduits (vessels or tracheids) is constant across different levels of branching. If true, this rule obtains the packing rule, according to which (1) vessel cross-sectional lumen area (A) will negatively and isometrically scale to vessel number per unit area (N) and (2) the distal to proximal vessel diameter ratio (DR = D n?1 /D n ) should scale as the -1/2 power of the distal to proximal vessel number ratio (NR = N n?1 /N n ), i.e., DR = NR -1/2 . Using data collected from the terminal twigs and the petioles of 60 temperate (27 evergreen and 33 deciduous) woody species from southwestern China, we determined the scaling relationships for A versus N and for DR versus NR. Analyses of the data revealed contrasting scaling exponents and normalization constants for A versus N and for DR versus NR and no consistent trend across the two species groupings or between the two organ types (as predicted by the area-preserving and packing rules). These results caution against applying these rules ubiquitously to all species or to different organ types (even on the same plant).

Sent to the Corner: xylem vessel anatomy not surface area determines megaphyll hydraulics inCecropia obtusaTrécul (Urticaceae)

“…However, despite the increasing return on hydraulic performance enabled by the variation in Dmh, there must be a trade-off between Dmh and fvessel. This statement is in agreement with the theoretical model of the packing rule (Sperry et al 2008, Chen et al 2012), which predicts that fvessel should isometrically scale with conduit size and thus allows for the area-preserving branching of vessels across different branching levels.…”

The pipe model theory half a century on: a review

“…As in the case of tapering rules, the area-preserving rule has been tested with regard to cross-sectional areas of ring increments, SW and whole axes excluding bark (Nikinmaa, 1992;Yamamoto and Kobayashi, 1993;Hatsch, 1997;Sone et al, 2005Sone et al, , 2009. Furthermore, it should be noted that Leonardo da Vinci's rule was also tested at a microanatomical scale by considering xylem conduit dimensions and comparing it with the Murray law to investigate how branching systems optimize hydraulic flux to woody and leafy organs (McCulloh et al, 2003;Chen et al, 2012;Price et al, 2014;Carvalho et al, 2017a, b).…”

Scaling relationships and vessel packing in petioles

“…This finding also suggests that because Sperry's packing rule optimizes the balance between conduit number and size after mechanical requirements have been met, xylem in petioles is likely to be functioning mechanically to some extent, but xylem alone is unable to meet the mechanical requirements of the petiole. Shrubs and trees appear to be mixed in their adherence to the packing rule in larger studies at the stem-leaf junction (Chen et al, 2012). We propose that this wide variation in adherence results from the combination of different proportions of tissues for petiole support in conjunction with anatomical variation in bundle number, as well as remarkable plasticity in petiole construction.…”

“…Values range from -1.44 in oaks to -2.73 in maples (Savage et al, 2010;Savage et al, 2015). A previous study found limited evidence for adherence to the packing rule across the twig-petiole interface (Chen et al, 2012), but vessel packing in petioles has not been further investigated. Vessel packing in petioles could differ from that in woody stems because xylem in petioles is commonly primary xylem.…”