  The origin of allometric scaling of metabolic rate is a long-standing
question in biology. Several models have been proposed for explaining the
origin; however, they have advantages and disadvantages. In particular,
previous models only demonstrate either two important observations for the
allometric scaling: the variability of scaling exponents and predominance of
3/4-power law. Thus, these models have a dispute over their validity. In this
study, we propose a simple geometry model, and show that a hypothesis that
total surface area of cells determines metabolic rate can reproduce these two
observations by combining two concepts: the impact of cell sizes on metabolic
rate and fractal-like (hierarchical) organization. The proposed model both
theoretically and numerically demonstrates the approximately 3/4-power law
although several different biological strategies are considered. The model
validity is confirmed using empirical data. Furthermore, the model suggests the
importance of heterogeneity of cell size for the emergence of the allometric
scaling. The proposed model provides intuitive and unique insights into the
origin of allometric scaling laws in biology, despite several limitations of
the model.
