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THE PHYSICS OF TREE LEAF SIZE

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. Introduction. Why do trees grow where they grow?.

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THE PHYSICS OF TREE LEAF SIZE

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  1. 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 MaciejZwieniecki. Physical Review Letters.Vol 110. January 4, 2013

  2. Introduction • 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

  3. Fluid Flow Rate Throughout A Tree Fluid-Flow Theory

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

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

  6. Methods Flow Velocity • 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 Imaxmaximizes energy gained per leaf. • The minimum leaf length Imin allows for a transport mechanism that is barely faster than diffusion alone Energy Max Leaf Length Min Leaf Length

  7. 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?

  8. Results

  9. 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

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