Metabolic scaling in plants Frances Taschuk February 25, 2008 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  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

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

Vascular systems

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

Area-preserving branching in plants Vessel bundles

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

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  Stem diameter vs. mass: D  M  So Q 0  M 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  Stem diameter vs. mass: D  M  So Q 0  M about 3/4

More 3/4 Scaling  Can also derive from twig/leaf or wood/bark production  Leaves: P L  D  Bark: P B  D  Diameter scaling: D  M  So P L  M and P B  M exponents about 3/4  Can also derive from twig/leaf or wood/bark production  Leaves: P L  D  Bark: P B  D  Diameter scaling: D  M  So P L  M and P B  M exponents about 3/4

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

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

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

Log-log Slope=.74 Linear Depends on nitrogen

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

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