Allometric scaling of brain activity explained by avalanche criticality

Allometric scaling laws, such as Kleiber's law for metabolic rate, highlight how efficiency emerges with size across living systems. The brain, with its characteristic sublinear scaling of activity, has long posed a puzzle: why do larger brains operate with disproportionately lower firing rates? Here we show that this economy of scale is a universal outcome of avalanche dynamics. We derive analytical scaling laws directly from avalanche statistics, establishing that any system governed by critical avalanches must exhibit sublinear activity-size relations. This theoretical prediction is then verified in integrate-and-fire (IF) neuronal networks at criticality and in classical self-organized criticality (SOC) models, demonstrating that the effect is not model-specific but generic. The predicted exponents align with experimental observations across mammal species, bridging dynamical criticality with the allometry of brain metabolism. Our results reveal avalanche criticality as a fundamental mechanism underlying Kleiber-like scaling in the brain.