Can a time varying external drive give rise to apparent criticality in neural systems?

The finding of power law scaling in neural recordings lends support to the hypothesis of critical brain dynamics. However, power laws are not unique to critical systems and can arise from alternative mechanisms. Here, we investigate whether a common time-varying external drive to a set of Poisson units can give rise to neuronal avalanches and exhibit apparent criticality. To this end, we analytically derive the avalanche size and duration distributions, as well as additional measures, first for homogeneous Poisson activity, and then for slowly varying inhomogeneous Poisson activity. We show that homogeneous Poisson activity cannot give rise to power law distributions. Inhomogeneous activity can also not generate perfect power laws, but it can exhibit approximate power laws with cutoffs that are comparable to those typically observed in experiments. The mechanism of generating apparent criticality by time-varying external fields, forces or input may generalize to many other systems like dynamics of swarms, diseases or extinction cascades. Here, we illustrate the analytically derived effects for spike recordings in vivo and discuss approaches to distinguish true from apparent criticality. Ultimately, this requires causal interventions, which allow separating internal system properties from externally imposed ones.Author summary: The analysis of complex systems in nature introduces several challenges, because typically a number of parameters either remain unobserved or cannot be controlled. In particular, it can be challenging to disentangle the dynamics generated within the system from that imposed by the environment. With this difficulty in mind, we reinvestigate the popular hypothesis that neural dynamics is poised close to a critical point. Criticality is characterized by power-law scaling and has been linked to favorable computational properties of networks. Power-law distributions for “neural avalanches,” i.e., spatio-temporal clusters of neural activity, have been observed in various neural systems and support the criticality hypothesis. Here we show that approximate power laws do not necessarily reflect critical network dynamics but can be imposed externally on non-critical networks, i.e., by driving the network with input of specific statistics. We derive these results analytically and illustrate them both in simulations and using neural recordings. The findings indicate that more caution and additional tests are required for distinguishing between genuine and apparent criticality. Ultimately, this requires causal interventions, not only in neural systems, but in many other complex dynamical systems that are subject to time-varying external forces, such as the dynamics of swarms, diseases or extinction cascades.