Unifying criticality and the neutral theory of neural avalanches

The interest in the question of criticality in the brain has been prompted by experiments which show that the collective firing of neurons (neural avalanches) follow power-law distributions. Three proposed explanations of this emergent scale-free behavior are criticality, neutral theory, and self-organized criticality. We study a model of the brain for which the dynamics are governed by neutral theory and find that the scale-free behavior is controlled by the proximity to a critical point. Our results unify the neutral theory of neural avalanches with criticality, which requires fine tuning of control parameters, and rule out self-organized criticality. We use tools from percolation theory to characterize the critical properties of the neural avalanches and identify the tuning parameters, which are consistent with experiments. The scaling hypothesis provides a unified explanation of the power laws which characterize the neural avalanches. We discuss how our results can motivate future empirical studies of criticality in the brain.