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Metabolic scaling in plants

Metabolic scaling in plants. Frances Taschuk February 25, 2008. Y = Y 0 M b. Enquist: Quarter-power scaling. “single most important theme underlying all biological diversity” Branching networks distribute materials to all parts of an organism

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Metabolic scaling in plants

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  1. Metabolic scaling in plants Frances Taschuk February 25, 2008

  2. Y = Y0Mb

  3. Enquist: Quarter-power scaling • “single most important theme underlying all biological diversity” • Branching networks distribute materials to all parts of an organism • Fractal structure - scaling properties do not depend on details

  4. Predictions from Enquist’s scaling • Number of terminal branches/leaves scales with 3/4 • Trunk length with 1/4 • Trunk radius with 3/8 • Height scales with 1/4 • Number of branches grows logarithmically with mass

  5. Vascular systems

  6. Assumptions • Final branch sizes independent of body size • Number of branchings scales logarithmically with size Nc M3/4 • Area-preserving branching • πr2k = nπr2k+1

  7. Area-preserving branching in plants Vessel bundles

  8. Energetic results of plant structure • Geometry of branching network determines number of leaves --> photosynthetic area --> metabolic rate • Xylem transport provides measure of nutrient/water use --> measure of photosynthesis --> measure of metabolism

  9. 3/4 Scaling • Can derive from fluid transport and stem diameter scaling data • Fluid transport (Q0) relates to stem diameter (D): Q0 D1.778 • Stem diameter vs. mass: D  M0.412 • So Q0 M0.732 -- about 3/4

  10. More 3/4 Scaling • Can also derive from twig/leaf or wood/bark production • Leaves: PL D1.653 • Bark: PB D1.807 • Diameter scaling: D  M0.438 • So PL M0.724 and PB M0.791 -- exponents about 3/4

  11. Effects on plant size and abundance • Plant growth limited by competition for limited resources • Resource use scales with M3/4 • Constant resources at equilibrium, so Nmax (average M)-3/4 • Size is result of vascular network architecture and metabolism, not geometry

  12. But is this too general? • Plants and animals have important differences • Plants less constrained by vascular networks since they can exchange oxygen and carbon dioxide by diffusion into leaves

  13. Does plant metabolism follow power law scaling? • Reich et al (including Swat’s Jose-Luis Machado) published in Nature reporting on respiration of 500 plants from 43 species and 6 orders of magnitude, ages 1 month to 25 years • Large and high-quality data set • Found isometric (linear) relationship between respiration and mass

  14. Log-log Slope= .74 Linear Depends on nitrogen

  15. Controversy • Does the “universal” 3/4 scaling rule not apply to plants? • Respiration appears to scale isometrically with nitrogen supply rather than depending on vascular network • Or was the study too “seedling-specific”? • WBE model predicts that small plants will differ from 3/4 scaling • Smaller plants not subject to biomechanical stresses that result in 3/4 power law

  16. Resources • Pictures • http://norwegianredwood.com/gallery/d/1230-2/Redwood_Giant_Sequoia_Seedling_2151.jpg • http://cache.jalopnik.com/cars/assets/resources/2006/10/Sequoia-Big.jpg • http://www.freefoto.com/images/15/19/15_19_1---Tree--Sunrise--Northumberland_web.jpg • http://www.emc.maricopa.edu/faculty/farabee/BIOBK/92462b.jpg • http://www.nature.com/nature/journal/v439/n7075/full/439399a.html • http://www.nature.com/nature/journal/v439/n7075/abs/nature04282.html • http://www.nature.com/nature/journal/v395/n6698/abs/395163a0.html • http://www.sciencemag.org/cgi/reprint/276/5309/122.pdf • http://www.nature.com/nature/journal/v400/n6745/abs/400664a0.html

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