  The prevailing theory for metabolic scaling is based on area-preserved,
space-filling fractal vascular networks. However, it's known both theoretically
and experimentally that animals' vascular systems obey Murray's cubic branching
law. Area-preserved branching conflicts with energy minimization and hence the
least-work principle. Additionally, while Kleiber's law is the dominant rule
for both animals and plants, small animals are observed to follow the 2/3-power
law, large animals have larger than 3/4 scaling exponents, and small plants
have near-linear scaling behaviors. No known theory explains all the
observations. Here, I show that animals' metabolism is determined by their
Murray's vascular systems. For plants, the scaling is determined by the trunks'
hydraulic conductance and the leaves' photosynthesis. Both analyses agree with
data of various body sizes. Animals' scaling has a concave curvature while
plants have a convex one. The empirical power laws are approximations within
selected mass ranges. Generally, the 3/4-power law applies to animals of ~15 g
to 10,000 kg and the 2/3-power law to those of ~1 g to 10 kg. For plants, the
scaling exponent is 1 for small plants and decreases to 3/4 for those greater
than ~10 kg.
