WBE West, Brown, Enquist

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WBE (West, Brown, Enquist) Universal allometric
scaling
Y Y0Mb
Y functional trait or process such as
respiration, water transport,
photosynthesis Y0 proportionality constant M
body mass b 0.75 or multiple of 0.25
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Identical scaling with different intercepts
Plotting data on log-log scale may yield
acceptable r2, but lead to choice of
biologically inappropriate function
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Scaling of water transport with plant size
Enquist et al. Nature 1998
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Where does the 3/4 power scaling with mass come
from?
Q ? D1.778
Data compiled by Enquist et al. Mean computed
from two references Product of exponents
D ? M0.412
Q ? M0.732
How was Q D1.778 obtained?
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Is an exponent gt1 for scaling with diameter
biologically reasonable?
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Scaling of water use with tree size in 17
angiosperm species

• Sigmoid functions provided best fits
• Conifers showed substantially lower water use at
  a given size
• Relationships for conifers also appeared to be
  sigmoid

Meinzer, F.C., Bond, B.J., Warren, J.M.
Woodruff, D.R. (2005) Does water use scale
universally with tree size? Functional Ecology
19 558-565
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4-parameter sigmoid function
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Scaling exponents WBE predicted
2.33 Tropical angiosperms SA
1.9r1.76 Pseudotsuga menziesii Thuja
plicata Quercus garryana SA 0.37r1.42
Meinzer et al. Funct. Ecol 2005
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