Unifying criticality and the neutral theory of neural avalanches.
The distribution of collective firing of neurons, known as a neural avalanche, obeys a power law. Three proposed explanations of this emergent scale-free behavior are criticality, neutral theory, and self-organized criticality. We show that the neutral theory of neural avalanches can be unified with criticality, which requires fine tuning of control parameters, and rule out self-organized criticality. We study a model of the brain for which the dynamics are governed by neutral theory. We identify the tuning parameters, which are consistent with experiments, and show that scale-free neural avalanches occur only at the critical point. The scaling hypothesis provides a unified explanation of the power laws which characterize the critical point. The critical exponents characterizing the avalanche distributions and divergence of the response functions are shown to be consistent with the predictions of the scaling hypothesis. We use an universal scaling function for the avalanche profile to find that the firing rate for avalanches of different sizes shows data collapse after appropriate rescaling. Critical slowing-down and algebraic relaxation of avalanches demonstrate that the dynamics are also consistent with the system being at a critical point. We discuss how our results can motivate future empirical studies of criticality in the brain.