THE PHYSICS OF TREE LEAF SIZENick Curran, Morgan Irons, Ben WangOctober 8, 2013

“Physical Limits to Leaf Size in Tall Trees”. Kaare Jensen and Maciej Zwieniecki. Physical Review Letters.Vol 110. January 4, 2013

Introduction1. 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)

Hypothesis Statement:“The near-uniform leaf size of the tallest trees is set

by the requirements of their vascular system.”

MethodsFlow Velocity

Energy

Max Leaf Length

Min Leaf Length

• Botanical Data set Mathematical model• Assumed an Ohmic analogy to describe plant

vasculature• The flow velocity u, is inversely proportional to tree

height h• Energy E, is proportional to flow velocity• The maximum leaf length Imax maximizes energy

gained per leaf. • The minimum leaf length Imin allows for a transport

mechanism that is barely faster than diffusion alone

RESULTS 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?

RESULTS

CONCLUSIONS 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