# Neutral theory and scale-free neural dynamics

## TL;DR

This paper proposes that scale-free neural avalanches can arise from neutral drift dynamics, rather than criticality, challenging the common assumption that such behavior indicates the brain operates at a phase transition point.

## Contribution

It introduces a model showing scale-invariant neural avalanches emerge from neutral dynamics, not criticality, emphasizing the role of causal information in analyzing neural activity.

## Key findings

- Neural avalanches can be scale-free without criticality.
- Neutral drift explains power-law distributed avalanches.
- Causal information is crucial for accurate avalanche analysis.

## Abstract

Avalanches of electrochemical activity in brain networks have been empirically reported to obey scale-invariant behavior --characterized by power-law distributions up to some upper cut-off-- both in vitro and in vivo. Elucidating whether such scaling laws stem from the underlying neural dynamics operating at the edge of a phase transition is a fascinating possibility, as systems poised at criticality have been argued to exhibit a number of important functional advantages. Here we employ a well-known model for neural dynamics with synaptic plasticity, to elucidate an alternative scenario in which neuronal avalanches can coexist, overlapping in time, but still remaining scale-free. Remarkably their scale-invariance does not stem from underlying criticality nor self-organization at the edge of a continuous phase transition. Instead, it emerges from the fact that perturbations to the system exhibit a neutral drift --guided by demographic fluctuations-- with respect to endogenous spontaneous activity. Such a neutral dynamics --similar to the one in neutral theories of population genetics-- implies marginal propagation of activity, characterized by power-law distributed causal avalanches. Importantly, our results underline the importance of considering causal information --on which neuron triggers the firing of which-- to properly estimate the statistics of avalanches of neural activity. We discuss the implications of these findings both in modeling and to elucidate experimental observations, as well as its possible consequences for actual neural dynamics and information processing in actual neural networks.