THE PHYSICS OF TREE LEAF SIZE Nick Curran, Morgan Irons, Ben Wang October 8, 2013 “Physical Limits to Leaf Size in Tall Trees”. Kaare Jensen and Maciej Zwieniecki. Physical Review Letters.Vol 110. January 4, 2013

IntroductionIntroduction 1. Why do trees grow where they grow? 2. The need to effectively transport sugar-rich fluid throughout the tree leads to restricted tree height. Xylem Vessel Phloem Vessel

Fluid Flow Rate Throughout A Tree Fluid-Flow Theory

Leaf Size Versus Tree Height Leaf Size (cm) Tree Height (m Tree Height (m )

Hypothesis Statement: “The near-uniform leaf size of the tallest trees is set by the requirements of their vascular system.” Hypothesis Statement: “The near-uniform leaf size of the tallest trees is set by the requirements of their vascular system.”

MethodsMethods Flow Velocity Energy Max Leaf Length Min Leaf Length Botanical Data set  Mathematical model Botanical Data set  Mathematical model Assumed an Ohmic analogy to describe plant vasculature Assumed an Ohmic analogy to describe plant vasculature The flow velocity u, is inversely proportional to tree height h The flow velocity u, is inversely proportional to tree height h Energy E, is proportional to flow velocity Energy E, is proportional to flow velocity The maximum leaf length I max maximizes energy gained per leaf. The maximum leaf length I max maximizes energy gained per leaf. The minimum leaf length I min allows for a transport mechanism that is barely faster than diffusion alone The minimum leaf length I min allows for a transport mechanism that is barely faster than diffusion alone

RESULTSRESULTS  Data set of recorded tree height h, and range of leaf length l, of 1925 species from 327 genera and 93 families  Noticeable drop in leaf length variability for taller tree species  Is there a relationship between the sugar export rate and its distribution network that sets a minimum and maximum for leaf size?

RESULTSRESULTS

CONCLUSIONSCONCLUSIONS  Leaf size in trees are limited by the dimensions of their phloem transport vasculature  At a certain height, trunk resistance becomes sufficiently large that larger leaf size is no longer practical from a metabolic investment perspective.  If leaves are too small, the flow will be too slow to reach plant tissues at a reasonable rate  Patterns observed are not strictly phylogenetic but are caused by intrinsic physical effects of transport systems