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

2. Y = Y 0 M b

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  “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  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  Final branch sizes independent of body size  Number of branchings scales logarithmically with size N c  M 3/4  Area-preserving branching  πr 2 k = nπr 2 k+1  Area-preserving branching  πr 2 k = nπr 2 k+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  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 (Q 0 ) relates to stem diameter (D): Q 0  D 1.778  Stem diameter vs. mass: D  M 0.412  So Q 0  M 0.732 -- about 3/4  Can derive from fluid transport and stem diameter scaling data  Fluid transport (Q 0 ) relates to stem diameter (D): Q 0  D 1.778  Stem diameter vs. mass: D  M 0.412  So Q 0  M 0.732 -- about 3/4

10. More 3/4 Scaling  Can also derive from twig/leaf or wood/bark production  Leaves: P L  D 1.653  Bark: P B  D 1.807  Diameter scaling: D  M 0.438  So P L  M 0.724 and P B  M 0.791 -- exponents about 3/4  Can also derive from twig/leaf or wood/bark production  Leaves: P L  D 1.653  Bark: P B  D 1.807  Diameter scaling: D  M 0.438  So P L  M 0.724 and P B  M 0.791 -- exponents about 3/4

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

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

16. 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  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

17. Resources  Pictures Pictures  http://norwegianredwood.com/gallery/d/1230-2/Redwood_Giant_Sequoia_Seedling_2151.jpg 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://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.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/full/439399a.html  http://www.nature.com/nature/journal/v439/n7075/abs/nature04282.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.nature.com/nature/journal/v395/n6698/abs/395163a0.html  http://www.sciencemag.org/cgi/reprint/276/5309/122.pdf http://www.sciencemag.org/cgi/reprint/276/5309/122.pdf  http://www.nature.com/nature/journal/v400/n6745/abs/400664a0.html http://www.nature.com/nature/journal/v400/n6745/abs/400664a0.html  Pictures Pictures  http://norwegianredwood.com/gallery/d/1230-2/Redwood_Giant_Sequoia_Seedling_2151.jpg 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://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.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/full/439399a.html  http://www.nature.com/nature/journal/v439/n7075/abs/nature04282.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.nature.com/nature/journal/v395/n6698/abs/395163a0.html  http://www.sciencemag.org/cgi/reprint/276/5309/122.pdf http://www.sciencemag.org/cgi/reprint/276/5309/122.pdf  http://www.nature.com/nature/journal/v400/n6745/abs/400664a0.html http://www.nature.com/nature/journal/v400/n6745/abs/400664a0.html