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Metabolic scaling is governed by Murray's network in animals and by hydraulic conductance and photosynthesis in plants

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.