Metabolic scaling in plantsMetabolic scaling in plants

Frances Taschuk

February 25, 2008

Frances Taschuk

February 25, 2008

Y = Y0Mb

Enquist: Quarter-power scalingEnquist: 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

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 systemsVascular systems

AssumptionsAssumptions 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

Nc M3/4

Area-preserving branching πr2

k = nπr2k+1

Area-preserving branching πr2

k = nπr2k+1

Area-preserving branching in plants

Area-preserving branching in plants

Vessel bundlesVessel bundles

Energetic results of plant structure

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 Scaling3/4 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

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

More 3/4 ScalingMore 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

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

Effects on plant size and abundance

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

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

But is this too general?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?

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

ControversyControversy

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

ResourcesResources 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

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