Transcript Metabolic scaling and plant vasculature

Metabolic scaling in plants
Frances Taschuk
February 25, 2008
Y=
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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
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
Vascular systems
Assumptions
 Final branch sizes independent of body size
 Number of branchings scales logarithmically
with size
Nc 
 Area-preserving branching
 πr2k = nπr2k+1
3/4
M
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
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
More 3/4 Scaling
 Can also derive from twig/leaf or
wood/bark production
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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
 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?
 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
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
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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
Resources
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Pictures
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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