  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.
